JP5762247B2 - AC electric quantity measuring device and AC electric quantity measuring method - Google Patents

Description

  The present invention relates to an AC electricity quantity measuring device and an AC electricity quantity measuring method.

  In recent years, as the power flow in the power system has become more complex, it has become necessary to supply power with high reliability and quality, and in particular, the amount of AC electricity that measures the amount of electricity in the power system (AC electricity amount). The need for improved performance of measuring devices is increasing.

  Conventionally, as this type of alternating current electric quantity measuring device, for example, there are those shown in Patent Documents 1 and 2 below. In Patent Document 1 (protection control measurement system) and Patent Document 2 (wide area protection control measurement system), the frequency of the actual system is obtained with the change component (differential component) of the phase angle as the change from the rated frequency (50 Hz or 60 Hz). The method is disclosed.

  In these documents, the following formulas are disclosed as formulas for obtaining the frequency of the actual system, but these formulas are also formulas presented by Non-Patent Document 1 below.

2πΔf = dφ / dt
f (Hz) = 60 + Δf

  The following patent documents 3 and 4 are prior patent inventions by the inventors of the present application, and the contents of these inventions will be described later as appropriate.

JP 2009-65766 A JP 2009-71637 A Japanese Patent No. 4038484 Japanese Patent No. 4480647

“IEEE Standard for Synchrophasors for Power Systems” page 30, IEEE Std C37.118-2005.

  As described above, the methods disclosed in Patent Documents 1 and 2 and Non-Patent Document 1 are methods for obtaining a phase angle change component by differential calculation. However, the change of the instantaneous frequency value of the actual system is frequent and complicated, and the differential calculation is very unstable. For this reason, for example, there has been a problem that sufficient calculation accuracy cannot be obtained for frequency measurement.

  In addition, since the above method calculates the rated frequency (50 Hz or 60 Hz) as an initial value, a measurement error occurs when the measurement target is operating outside the system rated frequency at the start of the calculation. Thus, when the degree of deviation from the system rated frequency is large, there is a problem that the measurement error becomes very large.

  The present invention has been made in view of the above, and even when the measurement object is operating outside the system rated frequency, the AC electricity quantity measurement that enables highly accurate measurement of the AC electricity quantity is possible. It is an object of the present invention to provide an apparatus and an AC electric quantity measurement method.

  In order to solve the above-described problems and achieve the object, the present invention provides at least four continuous voltage instantaneous value data obtained by sampling an alternating voltage to be measured at a sampling frequency that is twice or more the frequency of the alternating voltage. The average value of the sum of the differential voltage instantaneous values other than the intermediate time is the differential voltage instantaneous value at the intermediate time among the three differential voltage instantaneous value data representing the distance between the tips of the two adjacent voltage instantaneous value data in FIG. A frequency coefficient calculation unit that calculates a normalized value as a frequency coefficient is provided.

  According to the present invention, there is an effect that it is possible to measure a high-accuracy AC electric quantity even when the measurement target is operating outside the system rated frequency.

FIG. 1 is a diagram showing a gauge differential voltage group (with DC offset) on a complex plane. FIG. 2 is a diagram illustrating a gauge voltage group (with DC offset) on a complex plane. FIG. 3 is a diagram showing a gauge voltage group (no DC offset) on the complex plane. FIG. 4 is a diagram illustrating a gauge power group on a complex plane. FIG. 5 is a diagram illustrating a gauge differential power group on a complex plane. FIG. 6 is a diagram illustrating a cage dual voltage group on a complex plane. FIG. 7 is a diagram illustrating a cage dual differential voltage group on a complex plane. FIG. 8 is a diagram illustrating a synchronized phasor group on a complex plane. FIG. 9 is a diagram illustrating a differentially synchronized phasor group on a complex plane. FIG. 10 is a diagram illustrating a functional configuration of the power measurement device according to the first embodiment. FIG. 11 is a flowchart illustrating a process flow in the power measurement apparatus according to the first embodiment. FIG. 12 is a diagram illustrating a functional configuration of the distance protection device according to the second embodiment. FIG. 13 is a flowchart showing a flow of processing in the distance protection device of the second embodiment. FIG. 14 is a diagram illustrating a functional configuration of the step-out protection device according to the third embodiment. FIG. 15 is a flowchart illustrating a process flow in the step-out protection device according to the third embodiment. FIG. 16 is a diagram illustrating a functional configuration of the time-synchronized phasor measuring device according to the fourth embodiment. FIG. 17 is a flowchart showing a flow of processing in the time-synchronized phasor measuring device according to the fourth embodiment. FIG. 18 is a diagram illustrating a functional configuration of the spatially synchronized phasor measuring device according to the fifth embodiment. FIG. 19 is a flowchart showing the flow of processing in the spatially synchronized phasor measuring device according to the fifth embodiment. FIG. 20 is a diagram illustrating a functional configuration of a transmission line parameter measurement system according to the sixth embodiment. FIG. 21 is a flowchart showing a flow of processing in the transmission line parameter measurement system of the sixth embodiment. FIG. 22 is a diagram illustrating a functional configuration of the synchronization input apparatus according to the seventh embodiment. FIG. 23 is a flowchart showing the flow of processing in the synchronous input device of the seventh embodiment. FIG. 24 is a diagram illustrating frequency coefficients calculated using the parameters of case 1. In FIG. FIG. 25 is a diagram illustrating a rotational phase angle calculated using the parameters of case 1. In FIG. FIG. 26 is a gain diagram of frequency measurement calculated using the parameters of case 1. FIG. 27 is a diagram illustrating frequency coefficients calculated using the parameters of case 2. In FIG. FIG. 28 is a diagram showing the instantaneous voltage, DC offset, gauge voltage, and voltage amplitude calculated with the parameters of case 2. FIG. 29 is a diagram showing the rotational phase angle and the actually measured frequency calculated with the parameters of case 2. FIG. 30 is a diagram illustrating a gauge effective synchronization phasor and a gauge invalid synchronization phasor calculated using the parameters of case 2. FIG. 31 is a diagram showing the synchronous phasor of the present application calculated using the parameters of case 2 in comparison with a conventional instantaneous value synchronous phasor. FIG. 32 is a diagram illustrating a time-synchronized phasor calculated using the parameters of case 2. FIG. 33 is a diagram illustrating frequency coefficients calculated using the parameters of case 3. FIG. 34 is a diagram illustrating measurement results of instantaneous voltage, gauge differential voltage, and voltage amplitude calculated using the parameters of case 3. FIG. 35 is a diagram illustrating a cosine function method synchronized phasor, a tangent function method synchronized phasor, and a symmetry breaking discrimination flag calculated using the parameters of case 3. FIG. 36 is a diagram illustrating a synchronized phasor calculated using the parameters of case 3. FIG. 37 is a diagram illustrating a voltage amplitude measurement result calculated using the parameters of case 3. FIG. 38 is a diagram illustrating a time-synchronized phasor calculated using the parameters of case 3. FIG. 39 is a diagram illustrating frequency coefficients calculated using the parameters of case 4. FIG. 40 is a diagram illustrating the instantaneous voltage, the gauge differential voltage, and the voltage amplitude calculated using the parameters of case 4. FIG. 41 is a diagram illustrating a cosine function method synchronization phasor, a tangent function method synchronization phasor, and a symmetry breaking discrimination flag calculated using the parameters of case 4. FIG. FIG. 42 is a diagram illustrating a synchronized phasor calculated using the parameters of case 4. FIG. FIG. 43 is a diagram showing a time-synchronized phasor calculated with the parameters of case 4. FIG. FIG. 44 is a diagram illustrating frequency coefficients calculated using the parameters of case 5. In FIG. FIG. 45 is a diagram showing the instantaneous voltage, gauge differential voltage, and voltage amplitude calculated with the parameters of case 5. FIG. 46 is a diagram illustrating a cosine function method synchronization phasor, a tangent function method synchronization phasor, and a symmetry breaking discrimination flag calculated using the parameters of case 5. FIG. FIG. 47 is a diagram illustrating a synchronized phasor calculated using the parameters of case 5. In FIG. FIG. 48 is a diagram showing the rotational phase angle calculated with the parameters of case 5. In FIG. FIG. 49 is a diagram illustrating actual frequencies calculated using the parameters of case 5. FIG. 50 is a diagram illustrating a time-synchronized phasor calculated using the parameters of case 5. FIG. 51 is a diagram showing the operation of the synchronization input device during simulation execution using the parameters of case 6. FIG. 52 is a diagram illustrating a gauge voltage group and a gauge differential voltage group on a complex plane. FIG. 53 is a diagram for explaining the relationship between the symmetric group sampling period T and the data collection sampling period T ₁ in more detail. FIG. 54 is a diagram illustrating a functional configuration of the frequency measurement device according to the fifteenth embodiment. FIG. 55 is a flowchart showing the flow of processing in the frequency measuring apparatus shown in FIG. FIG. 56 is a diagram showing a voltage instantaneous value waveform of case 7. FIG. 57 is a diagram illustrating frequency coefficients calculated using the parameters of case 7. In FIG. FIG. 58 is a diagram showing a rotational phase angle calculated using the parameters of case 7. In FIG. FIG. 59 is a diagram illustrating a determination result of symmetry breaking calculated with the parameters of case 7. In FIG. FIG. 60 is a diagram illustrating a frequency (actual frequency) calculated using the parameters of case 7. In FIG. FIG. 61 is a diagram showing a frequency change rate calculated using the parameters of case 7. In FIG. FIG. 62 is a diagram showing a voltage instantaneous value waveform of case 8. FIG. FIG. 63 is a diagram illustrating frequency coefficients calculated using the parameters of case 8. In FIG. FIG. 64 is a diagram showing the rotational phase angle calculated with the parameters of case 8. In FIG. FIG. 65 is a diagram showing a determination result of symmetry breaking calculated with the parameters of case 8. In FIG. FIG. 66 is a diagram illustrating the frequency (actual frequency) calculated using the parameters of case 8. In FIG. FIG. 67 is a diagram showing the frequency change rate calculated with the parameters of case 8. In FIG. FIG. 68 is a diagram showing a voltage instantaneous value waveform of case 9. FIG. FIG. 69 is a diagram illustrating frequency coefficients calculated using the parameters of case 9. In FIG. FIG. 70 is a diagram illustrating a rotational phase angle calculated using the parameters of case 9. In FIG. FIG. 71 is a diagram showing a determination result of symmetry breaking calculated with the parameters of case 9. In FIG. FIG. 72 is a diagram showing the frequency (actual frequency) calculated with the parameters of case 9. In FIG. FIG. 73 is a diagram showing a frequency change rate calculated with the parameters of case 9. In FIG.

  An AC electricity quantity measuring device and an AC electricity quantity measuring method according to embodiments of the present invention will be described below with reference to the accompanying drawings. In addition, this invention is not limited by embodiment shown below.

(Summary of the present invention)
The present invention relates to an AC electrical quantity measuring device that is a basic technology of a smart grid (smart power network), and the greatest feature is that the structure of AC voltage current is modeled by a symmetry group. In the conventional theory, the analysis was performed separately in the frequency domain and the time domain, but in the present invention, the frequency dependence (rotation phase angle, amplitude, phase angle between voltage and current, Phase angle difference) and time-dependent quantities (voltage current instantaneous value, synchronous phasor) are analyzed simultaneously. The inventor of the present application has already proposed an algorithm for calculating a synchronized phasor based on an instantaneous value synchronized phasor measurement method, and patents have been registered in Japan and the United States (Patent Document 3). However, in the method according to Patent Document 3 (instantaneous value synchronized phasor measurement method), there is an inversion region (the phase angle changes between 0 and π, counterclockwise or clockwise) in its own absolute phase angle. In the inversion region, the phase angle difference (time synchronization phasor, space synchronization phasor) cannot be determined, and the phase angle difference measured in the previous step needs to be latched.

  On the other hand, the present inventor has discovered the symmetry of AC voltage / current after filing the above-mentioned Patent Document 3, and has introduced the group theory of symmetry theory into the AC system (there are a plurality of unpublished prior applications). The present invention introduces such group theory of symmetry theory to synchronous phasor measurements. Thus, in the synchronous phasor measurement method according to the present invention, the rotational phase angle always changes counterclockwise between −π and π, so there is no need to latch the phase angle difference in the inversion region. Therefore, an accurate phase angle difference can be determined, which is effective for increasing the speed of the protection control process.

  The method of the present invention can be applied to various AC electric quantity calculations such as frequency coefficient measurement, rotational phase angle measurement, frequency measurement, amplitude measurement, DC offset measurement, synchronized phasor measurement, time synchronized phasor, and spatially synchronized phasor. I think.

(Meaning of terms)
In describing the AC electricity quantity measuring device and the AC electricity quantity measuring method according to the present embodiment, first, terms used in this specification will be explained.

Complex number: a number expressed in the form of a + jb using real numbers a and b and an imaginary unit j. In electrical engineering, since i is a current sign, the imaginary unit is represented by j = √ (−1). In the present application, a rotation vector is expressed using complex numbers.
Complex plane: a plane that represents a complex number in rectangular coordinates with a complex number as a point on a two-dimensional plane, a real part (Re) on the horizontal axis, and an imaginary part (Im) on the vertical axis.
Rotation vector: A vector that rotates counterclockwise on a complex plane related to the amount of electricity (voltage or current) of the power system. The real part of the rotation vector is an instantaneous value.
Differential rotation vector: A differential vector of two rotation vectors before and after one cycle of the sampling frequency. The real part of the differential rotation vector is the difference between the instantaneous values at two points around the sampling frequency of one cycle.
Sampling frequency: According to the sampling theorem, there is a restriction that the sampling frequency is more than twice the actual frequency. In Japan, 30-degree sampling is often used for power system monitoring and protection devices. In this case, the sampling frequency is 600 Hz in the 50 Hz system and 720 Hz in the 60 Hz system. In the smart meter applied to the smart grid, a great merit can be obtained by using the sampling frequency and the related measurement formula proposed for the protection control device of the power system.
Symmetric group sampling frequency (sampling frequency in Embodiment 1-14): This is the reciprocal of the extracted data period when various symmetric groups are calculated. In the present application, it is recommended to adopt a value that is four times the rated frequency (200 Hz for a 50 Hz system and 240 Hz for a 60 Hz system). This is because the influence of harmonic noise can be reduced by using a low symmetric group sampling frequency (abrupt changes such as voltage flicker can be dealt with by a symmetry breaking index).
-Data collection sampling frequency: It is the reciprocal of the measurement period of grid electricity. A higher data frequency sampling frequency is recommended. High-speed moving averaging processing can further reduce the influence of harmonic noise. Therefore, in the present application, it is possible to obtain a stable and highly accurate AC electric quantity by two processes of a symmetric process and a moving average process using a low symmetric group sampling frequency and a high data collection sampling.
System frequency: Basically, it means the rated frequency in the power system, and there are two types, 50 Hz and 60 Hz.
Real frequency: The actual frequency in the power system. This actual frequency slightly fluctuates in the vicinity of the rated frequency even when the power system is stable. The present application corresponds to all frequencies that are ½ of the sampling frequency. For example, when the generator of the power system is started, the frequency of the generator rises from 0 Hz to the rated frequency, and the frequency of the generator can be followed with high speed and high accuracy in the measurement method of the present application.
Rotation phase angle: A phase angle obtained by rotating a voltage rotation vector (hereinafter simply referred to as “voltage vector”) or a current rotation vector (hereinafter simply referred to as “current vector”) on a complex plane during one sampling frequency cycle. The rotational phase angle is a frequency dependent amount, and therefore, there is no significant change between several sampling points. If there is a large change between several sampling points, it is determined that there is a sudden change (symmetry breaking). A symmetry index is used for this determination.
Symmetry breaking: When the input waveform is a pure sine wave, the input waveform has symmetry. However, the symmetry of the input waveform is broken due to a sudden amplitude change, phase sudden change, or frequency sudden change of the input waveform. In order to detect this breaking of symmetry, the present application proposes several symmetry measures. Note that by providing a settling value for the symmetry index, symmetry breaking is not determined for small measurement errors and additive Gaussian noise. If the symmetry is broken, it is no longer a pure AC waveform, and the measurement is considered impossible, and the already measured value is latched. In order to reduce small measurement errors and additive Gaussian noise effects when symmetry exists, it is preferable to increase the number of symmetry groups used in the calculation and increase the measurement accuracy of the calculation results by moving average processing.
Gauge voltage group: A symmetric group composed of three voltage vectors continuous in time series. The same symmetrical group concept can be defined for currents other than voltage and power (active power and reactive power).
Gauge voltage: A voltage invariant calculated by the gauge voltage group.
Gauge differential voltage group: A symmetric group composed of three differential voltage vectors that are continuous in time series.
Gauge differential voltage: a differential voltage invariant calculated by a gauge differential voltage group.
-Frequency coefficient: This is a frequency measurement formula proposed for the first time in this application. It is a parameter calculated using three members of the gauge differential voltage group, and its value is a cosine function value of the rotational phase angle. Since the differential voltage is used, the measurement result is not affected by the DC offset of the input waveform.
DC offset: DC component of the input waveform.
Gauge bi-voltage group: a symmetric group composed of three consecutive voltage vectors at terminal 1 and two consecutive voltage vectors at terminal 2. A similar symmetry group concept can be defined for current.
Gauge bi-effective voltage group: A symmetric group composed of two voltage vectors in front of the terminal 1 and two consecutive voltage vectors of the terminal 2 of the gauge bi-voltage group.
Gauge bi-reactive voltage group: A symmetric group composed of two voltage vectors after the terminal 1 of the gauge bi-voltage group and two consecutive voltage vectors of the terminal 2.
Gauge bi-effective voltage: An invariable calculated by the gauge bi-effective voltage group.
Gauge bi-reactive voltage: An invariable calculated by the gauge bi-reactive voltage group.
Gauge dual differential voltage group: a symmetrical group composed of three consecutive differential voltage vectors at terminal 1 and two consecutive differential voltage vectors at terminal 2.
Gauge dual differential effective voltage group: a symmetric group composed of two differential voltage vectors before the terminal 1 and two consecutive differential voltage vectors of the terminal 2 of the gauge dual differential voltage group.
Gauge dual differential reactive voltage group: a symmetric group composed of two differential voltage vectors after terminal 1 of the gauge dual differential voltage group and two consecutive differential voltage vectors of terminal 2.
Gauge dual differential effective voltage: An invariable calculated by the gauge dual differential effective voltage group.
Gauge dual differential reactive voltage: An invariable calculated by the gauge dual differential reactive voltage group.
Gauge power group: A symmetric group composed of three consecutive voltage vectors and two consecutive current vectors.
Gauge active power group: A symmetric group composed of two voltage vectors in front of the gauge power group and two current vectors in succession.
Gauge reactive power group: A symmetrical group composed of two voltage vectors and two current vectors after the gauge power group.
Gauge active power: An invariable calculated by the gauge active power group.
Gauge reactive power: An invariable calculated by the gauge reactive power group.
Gauge differential power group: A symmetric group composed of three consecutive differential voltage vectors and two consecutive differential current vectors.
Gauge differential active power group: a symmetric group composed of two differential current vectors that are continuous with the two differential voltage vectors before the gauge differential power group.
Gauge differential reactive power group: A symmetric group composed of two differential voltage vectors followed by two differential voltage vectors after the gauge differential power group.
Gauge differential active power: An invariable calculated by the gauge differential active power group.
Gauge differential reactive power: An invariable calculated by the gauge differential reactive power group.
Synchronous phasor: An absolute phase angle of a voltage vector or current vector that rotates counterclockwise on a complex plane in a range of −180 degrees to +180 degrees at a rotational speed corresponding to an actual frequency is defined as a synchronized phasor. In the case of a phasor, it often refers to a display method that expresses a sine signal (cosine signal) as a complex number, but in this specification, it is used to mean a rotating absolute phase angle. The synchronous phasor has two characteristics. The first feature is that the size of the synchronized phasor is in the range of −180 degrees to +180 degrees. The second feature is that the direction is increased in one direction from −180 degrees to +180 degrees (counterclockwise). The synchronous phasor includes a voltage synchronous phasor and a current synchronous phasor. The synchronized phasor is a time-dependent amount, and the synchronized phasor changes at each sampling point.
Voltage absolute phase angle: In the present application, it means a voltage-synchronized phasor.
Current absolute phase angle: In the present application, it means a current synchronous phasor.
Gauge-synchronized phasor group: A symmetric group composed of three voltage vectors and two fixed unit vectors on the complex plane.
Gauge effective synchronized phasor: A calculation result of a formula using members of the gauge synchronized phasor group defined in the present application.
Gauge invalid synchronized phasor: A calculation result of a calculation formula using another member of the gauge synchronized phasor group defined in the present application.
Gauge differential synchronized phasor group: a symmetric group composed of three differential voltage vectors and two fixed differential unit vectors.
Gauge difference effective synchronized phasor: a calculation result of a calculation formula using members of the gauge difference synchronized phasor group defined in the present application.
Gauge difference invalid synchronized phasor: a calculation result of a calculation formula using another member of the gauge difference synchronized phasor group defined in the present application.
Time-synchronized phasor: This is the difference between the current synchronized phasor and the synchronized phasor at a specified time (for example, a point before one cycle of the power system rated frequency). Similar to the synchronized phasor, the variation range is between -180 degrees and +180. A time-synchronized phasor is a frequency dependent quantity. When the actual frequency does not change, the time-synchronized phasor does not change at a constant value. Similar to the synchronized phasor, the time synchronized phasor includes a voltage time synchronized phasor and a current time synchronized phasor.
Spatial synchronized phasor: The difference between the synchronized phasor at its own end and the synchronized phasor at the other end at the same time. The variation range is between -180 degrees and +180. A time-synchronized phasor is a frequency dependent quantity. If the real frequencies at both ends are the same and do not vary at the same time, the spatially synchronized phasor does not vary at a constant value. Similar to the synchronized phasor, the spatially synchronized phasor includes a voltage space synchronized phasor and a current space synchronized phasor.
Fixed unit vector group: a plurality of unit vectors (amplitude is 1) on the complex plane set for calculating a synchronized phasor.
Voltage-current phase angle: The phase angle between the voltage vector and the current vector. There is frequency dependence.
Voltage THD index: an index representing power quality using total harmonic distortion (THD) of voltage.
Current THD index: An index representing power quality using total harmonic distortion (THD) of current.
Synchronizing device: A device that operates to link separated systems under certain conditions (frequency difference, voltage amplitude difference, and phase difference are below a certain value). In a seventh embodiment to be described later, a new synchronous input device is proposed.
・ Independent operation detection device: A system in which distributed power sources are connected, and when the circuit breaker is opened due to an accident, etc., the disconnected system is in a state where power is supplied to customers with only the distributed power source. Say driving. It is necessary to detect the isolated operation promptly and reliably disconnect the distributed power source. This will be presented in Embodiment 8 to be described later.
・ Distance protection device: Measures the impedance of the transmission line, converts the distance to the failure point, and realizes fault protection for the transmission line.
-Step-out protection device: A device that detects step-out of the power system.
Instantaneous value synchronized phasor measurement method: This is a synchronized phasor calculation method presented in Patent Document 3 above. An instantaneous cosine function value calculated using the current voltage instantaneous value estimated value estimated by the least square method as a numerator and the current voltage amplitude estimated by a least square method as a denominator is defined as a synchronized phasor. Since the value of the anti-cosine function is always positive, the change range of the synchronized phasor changes between 0 and π, and there are two types of change directions, counterclockwise or clockwise.
Group synchrophasor measurement method: This is a synchrophasor calculation method presented in this application.

Next, an AC electricity quantity measuring device and an AC electricity quantity measuring method according to the present embodiment will be described. In this description, first, the concept (algorithm) of the AC electricity quantity measurement technique forming the gist of the present embodiment will be described, and then the configuration and operation of the AC electricity quantity measuring device according to the present embodiment will be described. In the following description, among lowercase letters in the alphabet, those with parentheses (for example, “v (t)”) represent vectors, and those without parentheses (for example, “v ₂ ”) represent instantaneous values. Shall. In addition, the capital letter notation (for example, “V _g ”) represents an effective value or an amplitude value.

(Gauge differential voltage group)
FIG. 1 is a diagram illustrating a group of gauge differential voltages on a complex plane. In FIG. 1, consider three differential voltage vectors v ₂ (t), v ₂ (tT), and v ₂ (t−2T) rotating counterclockwise at a real frequency on a complex plane. d is a DC offset. Since the instantaneous voltage value includes a DC offset, the imaginary axis Im of the complex plane is moved from O ′ to O. The three differential voltage vectors can be expressed as:

  Here, V is the amplitude of the alternating current component of the instantaneous voltage. Further, ω is a rotational angular velocity and is expressed by the following equation.

  Here, f is a real frequency. Further, T in the equation (1) is a sampling one cycle time, and is represented by the following equation.

Here, f _s is a sampling frequency. Further, α in the equation (1) is a phase angle obtained by rotating the voltage vector on the complex plane at time T.

  In FIG. 1, it can be seen that the three differential voltage vectors are symmetrical with respect to the intermediate differential voltage vector. These three differential voltage vectors form a gauge differential voltage group. Since time t can take any value, the symmetry of equation (1) is always maintained. Next, an expression for obtaining a frequency coefficient using these gauge differential voltage groups is disclosed.

(Frequency coefficient)
In FIG. 1, the first member v ₂ (t) and the last member v ₂ (t−2T) of the gauge differential voltage group are symmetrical with respect to the intermediate member v ₂ (tT). Therefore, the following calculation formula is proposed, and the calculation result is defined as a frequency coefficient.

Here, v ₂₁ , v ₂₂ , and v ₂₃ are the real part or imaginary part of the members of the gauge differential voltage group, respectively. The above formula is expanded below.

  The real part instantaneous value of each member of the gauge differential voltage group is as follows.

  Here, Re indicates the real part of the complex number. Substituting the real part of the differential voltage vector into the numerator of equation (4), the following equation is calculated.

  Further, when the real part of the differential voltage vector is substituted into the denominator of the equation (4), the following equation is calculated.

  From the above equations (6) and (7), the frequency coefficient is obtained as follows.

  That is, the frequency coefficient is a cosine function value of the rotation phase angle.

  The frequency coefficient is also obtained from the imaginary part of the differential voltage vector. The imaginary part instantaneous value of each member of the gauge differential voltage group is as follows.

  Here, Im indicates an imaginary part of a complex number. Substituting the imaginary part of the differential voltage vector into the numerator of equation (4), the following equation is calculated.

  Further, when the imaginary part of the differential voltage vector is substituted into the denominator of the equation (4), the following equation is calculated.

  From the above equations (10) and (11), the frequency coefficient is obtained as follows.

  Similar to the calculation result of the real part, the frequency coefficient is a cosine function value of the rotation phase angle. The above result is none other than that the gauge differential voltage group has symmetry and the frequency coefficient is a rotation invariant of the gauge differential voltage group. The above calculation method is referred to as a frequency coefficient method. The frequency coefficient is a very important parameter and is the basis of the subsequent calculation in the present invention.

(Rotation phase angle)
From the above equation (8) or (12), the rotational phase angle can be calculated as follows.

The frequency coefficient f _c satisfies the condition of the following expression.

  If the above conditional expression is not satisfied, it is determined that the input waveform is not an AC waveform.

(Frequency calculation based on rotation phase angle)
First, the definition of the rotational phase angle α is as follows.

Here, f is an actual frequency and f _s is a sampling frequency. From the above equations (13) and (15), the frequency is calculated as follows.

  Up to this point, the calculation formula for calculating the frequency was presented using only the gauge differential voltage group. Prior to the filing of the present invention, the inventor of the present application disclosed a calculation formula for calculating a frequency using two symmetrical groups of a gauge voltage group and a gauge differential voltage group (not disclosed at the time of filing of the present invention). ). Here, the gauge voltage that is a member of the gauge voltage group includes an offset component, but the gauge differential voltage that is a member of the gauge differential voltage group does not include an offset component. For this reason, the method according to the present invention can calculate the frequency regardless of the DC offset of the input waveform. Thus, by calculating the frequency coefficient, the frequency can be measured at high speed and online. For this reason, it is suitable for use in a frequency tracking type protection control device.

The accuracy and characteristics of this frequency coefficient measurement method will be clarified in the simulation section of Case 1 described later. In Table 1 below, several values are displayed for the relationship between the actual frequency, the frequency coefficient, and the rotational phase angle. F _s in the table is a sampling frequency.

(Sine function value of rotation phase angle and sine function value and cosine function value of rotation phase angle half angle)
For the subsequent amplitude calculation, the calculation formulas of the sine function value of the rotation phase angle and the sine function value and cosine function value of the rotation phase angle half angle are presented.

  From the above equation, the sine function value of the rotational phase angle is obtained using the following equation.

  Similarly, the sine function value and cosine function value of the rotational phase angle half angle are obtained using the following equations and the following equations.

(Gauge differential voltage calculation formula)
Next, the calculation formula of the gauge differential voltage is presented. The gauge differential voltage V _gd is obtained using the following equation.

  Substituting the above equation (5) into the equation in the square root of the above equation (20), the following equation is obtained.

(Voltage amplitude)
Using the above equations (17), (18), and (21), the voltage amplitude V is obtained as follows.

  The above equation (22) can be calculated directly using the time-series instantaneous value data, and furthermore, since the gauge differential voltage is calculated from the differential value of the instantaneous voltage value, the influence on the DC offset in the voltage waveform. High-speed and high-accuracy measurement is possible. When the sampling frequency is set to four times the system frequency (rated frequency) and the actual frequency is the rated frequency, the frequency coefficient is zero (see Table 1 above), and the following amplitude calculation formula is established.

(Calculation formulas for frequency coefficient and gauge differential voltage using multiple sampling data)
The calculation formulas of the frequency coefficient and the gauge differential voltage when having a plurality of sample data are as follows.

Here, v _2k is a differential voltage instantaneous value. By using three or more sampling data, there is an effect of reducing the influence of noise data superimposed on the input waveform.

  The above formulas (20) to (25) are calculation formulas when voltage data is used. However, calculation formulas when current data is used can be calculated in the same manner as for voltages.

(Calculation formula of frequency coefficient and gauge differential voltage from multiple current sampling data)
Formulas for calculating the frequency coefficient and the gauge differential current using a plurality of current sampling data are as follows:

Here, i _2k is a differential current instantaneous value.

(Current amplitude)
Using the above equations (17), (18) and (27), the current amplitude I is obtained as follows.

  The above equation (28) can be calculated directly using the time-series instantaneous value data, and furthermore, since the gauge differential current is calculated from the differential value of the instantaneous current value, the influence on the direct current offset in the current waveform. High-speed and high-accuracy measurement is possible.

(DC offset calculation method 1)
Next, a first method (DC offset calculation method 1) for calculating a DC offset using a gauge voltage group on a complex plane will be described. FIG. 2 is a diagram illustrating a group of gauge voltages on the complex plane when there is a DC offset.

In FIG. 2, three voltage vectors v ₁ (t), v ₁ (tT), and v ₁ (t−2T) that rotate counterclockwise at a real frequency on a complex plane constitute a gauge voltage group. d is a DC offset. Since the DC voltage offset is included in the voltage instantaneous value, the voltage instantaneous value is expressed by the following equation.

Frequency coefficients f _c of the AC portion of the voltage instantaneous value is determined by the gauge differential voltage (see equation (4)). Here, the three voltage vectors v ₁ (t), v ₁ (tT), and v ₁ (t−2T) that are members of the gauge voltage group are also symmetrical with respect to the center vector v ₁ (tT). This property is the same as the gauge differential voltage group. Therefore, from the analogy with the gauge differential voltage group, the following equation is established based on the above equation (4).

  From the above equation (30), the DC offset d is obtained as follows.

  In addition, the calculation formula of the DC offset by a plurality of gauge voltage groups is expanded as follows.

  When the sampling frequency is set to four times the power system rated frequency, assuming that the actual frequency is the rated frequency, the frequency coefficient is zero, and the following DC offset calculation formula is established.

  FIG. 3 is a diagram illustrating a group of gauge voltages on the complex plane when there is no DC offset. When the DC offset of each member of the gauge voltage group is canceled using the DC offset obtained above, a gauge voltage group as shown in FIG. 3 can be assumed. At this time, the three voltage vectors that are members of the gauge voltage group can be expressed by the following equations.

  When there is a DC offset, the real part instantaneous value of each member of the gauge voltage group can be expressed as the following equation.

Here, v ₁₁ , v ₁₂ , and v ₁₃ are current voltage instantaneous values one step before and two steps before, respectively, and d is a DC offset value.

(Gauge voltage calculation formula with DC offset)
Next, the calculation formula of the gauge voltage when there is a DC offset is presented. The first and last members of the gauge voltage group have symmetry with respect to the middle member. For this reason, the same relationship as the above equation (20) is established for the voltage component in which the DC offset is canceled. Therefore, the gauge voltage V _g when there is a DC offset is obtained using the following equation.

  Substituting the above equation (35) into the equation in the square root of equation (36), the following equation is obtained.

The gauge voltage V _g is an AC voltage rotation invariant and is an AC electric quantity not related to the DC offset.

(Voltage amplitude by gauge voltage)
Using the above equations (17) and (37), the voltage amplitude V can be obtained as follows.

(Gauge voltage calculation formula using multiple sampling data)
Similar to the gauge differential voltage, the gauge voltage calculation formula using a plurality of sampling data can be expressed as the following formula.

Here, V _1k is an instantaneous voltage value. If more sampling points are used, the number of gauge voltage groups can be increased and averaging processing can be performed, so that the influence of noise on the input waveform can be reduced. In the case of setting the sampling frequency to 4 times the power system nominal frequency, assuming the rated frequency actual frequency, frequency coefficients f _c becomes zero, the above equation (38), the following amplitude equation derived .

(DC offset calculation method 2)
Next, the second method (DC offset calculation method 2) for calculating the DC offset using the gauge voltage group on the complex plane will be described.

  First, the gauge voltage calculation formula (36) is developed as follows.

  Further, when the above expression (41) is developed, the DC offset d is obtained as follows.

  Further, the following equation is established by the above equations (17) and (22).

  If this equation (43) is substituted into the above equation (42), the DC offset calculation formula is expressed as follows.

  Further, if the equation (44) is expanded to a plurality of gauge voltage groups, the calculation formula of the direct current offset can be expressed as the following equation.

In the case of setting the sampling frequency to 4 times the power system nominal frequency, assuming the rated frequency actual frequency, frequency coefficients f _c becomes zero, the above equation (45), the following DC offset calculation formula guide It is burned.

(Gauge current calculation formula using multiple sampling data)
Similar to the gauge differential current, the gauge current calculation formula using a plurality of sampling data can be expressed as the following formula.

Here, i _1k is an instantaneous current value. If more sampling points are used, the number of gauge current groups can be increased and averaging can be performed, so that the influence of noise on the input waveform can be reduced.

(Current amplitude due to gauge current)
The current amplitude due to the gauge current is obtained by the following equation, as in the case of the gauge voltage.

(Rotational phase angle symmetry index 1)
Next, the first index (rotation phase angle symmetry index 1) of the methods using the rotation phase angle as an index for evaluating the symmetry of the input waveform will be described. The rotational phase angle symmetry index 1 is defined as follows:

Here, α _cos is the rotational phase angle calculated by the frequency coefficient method, and α _sin is the rotational phase angle calculated by the gauge voltage group or the gauge differential voltage group. These are expressed as follows:

  Here, the second equation of the above equation (50) is obtained from the relationship between the above equations (21) and (37).

  If the input waveform is a pure sine wave, the rotational phase angle symmetry index 1 shown in the equation (49) is zero.

On the other hand, when the rotational phase angle symmetry index 1 is larger than a predetermined threshold value, that is, when the relation of the following equation is satisfied with respect to the threshold value α _BRK , it is determined that the input waveform is not symmetrical and is not a pure sine wave. . In this case, the rotational phase angle, which is a measured value, is latched as necessary.

(Calculation of symmetry breaking time)
First, the symmetry breaking time is defined as follows:

Here, t _BRK0 is an integrated value of continuous symmetry breaking times up to the previous step, and t _BRK1 is a value of symmetry breaking time in the current step. T is a step size. If the symmetry is not broken, the symmetry breaking time t _{BRK0 is set} to zero.

  The longer the symmetry breaking time, the worse the power quality. By using this symmetry breaking time, it is possible to quantitatively monitor the power quality in the AC system, and to detect disturbances in the AC system.

(Rotational phase angle symmetry index 2)
Since the rotational phase angle symmetry index 1 always involves calculation of an inverse trigonometric function (see equations (49) and (50)), a required calculation time is required. Therefore, the second evaluation index (rotation phase angle symmetry index 2) that does not require calculation of the trigonometric function will be described. The rotational phase angle symmetry index 2 is defined as follows:

Here, the first term (sin (α / 2) _cos ) in the absolute value symbol can be obtained by the frequency coefficient method, and is the second term in the absolute value symbol (sin (α / 2) _sin ) can be obtained from a gauge voltage group or a gauge differential voltage group. These calculation formulas are shown in the above formulas (18) and (50), and will be described again here.

  If the input waveform is a pure sine wave, the rotational phase angle symmetry index 2 shown in the equation (54) is zero.

On the other hand, when the rotational phase angle symmetry index 2 is larger than the predetermined threshold value, that is, when the relation of the following equation is satisfied with respect to the threshold value sα _BRK , the input waveform is determined not to be a pure sine wave because the symmetry is broken. . In this case, the rotational phase angle, which is a measured value, is latched as necessary.

(Processing when symmetry is broken)
When the symmetry of the input waveform is broken, it may be necessary to latch the value before breaking the symmetry in the application as the protection control device. In such a case, for example, each of the rotation phase angle, frequency, and voltage amplitude is latched as follows.

Here, α _t , f _t , and V _t are the current rotational phase angle, frequency, and voltage amplitude, respectively, and α _tT , f _tT , and V _tT are the rotational phase angle, frequency, and voltage amplitude one step before, respectively. It is.

(Voltage amplitude symmetry index 1)
Next, a first index (voltage amplitude characteristic index 1) among methods using voltage amplitude as an index for evaluating the symmetry of the input waveform will be described. The voltage amplitude symmetry index 1 is defined as follows:

Here, V _gA and V _gdA are voltage amplitudes calculated by the gauge voltage group and the gauge differential voltage group, respectively, as follows.

  If the input waveform is a pure sine wave, the voltage amplitude symmetry index 1 shown in the equation (58) is zero.

On the other hand, when the voltage amplitude symmetry index 1 is larger than the predetermined threshold value, that is, when the relationship is expressed by the following equation with respect to the threshold value V _BRK , it is determined that the input waveform is broken in symmetry and is not a pure sine wave. In this case, the rotational phase angle, frequency, voltage amplitude, etc., which are measured values, are latched as necessary.

  The idea of the voltage amplitude symmetry index 1 can be similarly applied to the current amplitude. The expression expansion is omitted.

(Gauge power group)
FIG. 4 is a diagram illustrating a gauge power group on a complex plane. FIG. 4 shows three voltage vectors v (t), v (tT), and v (t−2T) that rotate counterclockwise at the real frequency on the complex plane, and counterclockwise at the real frequency on the complex plane. Two current vectors i (tT) and i (t−2T) rotating are shown in FIG. These three voltage vectors v (t), v (tT), v (t-2T) and the two current vectors i (tT), i (t-2T) are expressed as the following equations and the following equations, respectively. be able to.

(Gauge power group, Gauge active power group and Gauge reactive power group)
Here, the three voltage vectors v (t), v (tT), and v (t−2T) and the two current vectors i (tT) and i (t−2T) are defined as “gauge power group”. Of the rotation vectors forming the gauge power group, two voltage vectors v (t) and v (tT) and two current vectors i (tT) and i (t-2T) are referred to as a “gauge active power group”. Two voltage vectors v (tT) and v (t-2T) and two current vectors i (tT) and i (t-2T) are defined as a “gauge reactive power group”.

(Gauge active power)
The gauge active power is defined as follows using the above-mentioned gauge active power group.

Here, the instantaneous voltage values v ₁ and v ₂ are the real parts of the voltage vectors v (t) and v (tT), respectively, and are calculated as follows:

Similarly, the instantaneous current values i ₂ and i ₃ are the real parts of the current vectors i (tT) and i (t−2T), respectively, and are calculated as follows:

  If the above formulas (64) and (65) are substituted into the above formula (63), the calculation formula representing the gauge active power is converted as the following formula.

  That is, the calculation formula of the gauge active power can be expressed as the following formula.

(Gauge reactive power)
The gauge reactive power is defined as follows using the gauge reactive power group.

Here, the instantaneous voltage values v ₂ and v ₃ are the real parts of the voltage vectors v (tT) and v (t−2T), respectively, and are calculated as follows:

The instantaneous current values i ₂ and i ₃ are defined as shown in the equation (65). If the equations (65) and (69) are substituted into the equation (68), the gauge reactive power is calculated as follows. The calculating formula is converted as follows.

  In other words, the gauge reactive power calculation formula can be expressed as the following formula.

  From the above equations (67) and (71), the cosine function value and the sine function value of the voltage-current phase angle φ can be calculated using the following equations.

  Therefore, the active power and the reactive power are obtained by the following formulas according to a general power definition.

  Similarly, the apparent power is obtained by the following equation according to the general definition of power.

  Similarly, the power factor is obtained as follows.

(Gauge power symmetry index)
Next, a method using gauge power as an index for evaluating the symmetry of the input waveform will be described. The gauge power symmetry index is defined as follows:

Here, (cosφ) _VI and (cosφ) _PF are cosine function values of the voltage-current phase angle φ calculated as follows.

  In the above equation (76), if the input waveform is a pure sine wave, the gauge power symmetry index is zero.

On the other hand, when the gauge power symmetry index is larger than a predetermined threshold value, that is, when the gauge power symmetry index is in the relationship of the following equation with respect to the threshold value S _BRK1 , the input waveform is determined to be broken and not a pure sine wave. In this case, the measured value (calculated value) is latched as necessary.

(Distance protection formula)
Next, a calculation formula for distance protection is presented. First, the following calculation formula is obtained by the definition of impedance.

  From the real part and the imaginary part of the above equation, the resistance and inductance can be calculated as follows:

In the above equation, _Ig is a gauge current and f is an actually measured frequency.

(Step-out protection calculation formula)
Next, a calculation formula for step-out protection is presented. Note that details of the calculation formula for step-out protection are disclosed in Patent Document 4, so refer to that document. According to this patent document 4, step-out discrimination of the power system is performed using the following equation.

Here, V _C is the step-out center voltage in front of the monitoring transmission line from the substation where the protective device is disposed, V is the self-end voltage amplitude, φ _vi is the phase angle between the transmission line voltage and current, and ΔV _STEP is the set value. (For example, 0.3 PU). Here, when there is a power system fault in the vicinity where the out-of-step protection device is installed, the calculated V _C rapidly decreases, whereas the change in V _C in the case of out-of-step is at a constant speed. Change. By utilizing this property, it is possible to prevent malfunction of the step-out protection device.

The formula for calculating the step-out center voltage V _C is as follows.

  In order to reduce the influence of noise, a plurality of sampling data may be used. The formula for calculating the gauge active power in a plurality of gauge active power symmetry groups is as follows.

  Moreover, the calculation formula of the gauge reactive power in the plurality of gauge reactive power symmetry groups is as follows.

  The time series data of each voltage instantaneous value and current instantaneous value is obtained using the following equation.

  Here, the time series data of the voltage vector and the current vector is obtained using the following equations.

  When the present invention is applied to the step-out protection device disclosed in Patent Document 4, the frequency fluctuation is automatically corrected when the step-out center voltage is calculated, so that a high-speed and high-precision step-out protection device can be realized. A more detailed description of the step-out protection device will be described in Embodiment 3 to be described later.

(Gauge differential power group)
FIG. 5 is a diagram illustrating a gauge differential power group on a complex plane. FIG. 5 shows three differential voltage vectors v ₂ (t), v ₂ (tT), and v ₂ (t−2T) rotating counterclockwise at the real frequency on the complex plane, and the real frequency on the complex plane. , Two differential current vectors i ₂ (tT) and i ₂ (t−2T) rotating counterclockwise are shown. These three voltage vectors v ₂ (t), v ₂ (tT), and v ₂ (t-2T) and the two current vectors i ₂ (tT) and i ₂ (t-2T) are respectively expressed by It can be expressed as:

(Gauge differential power group, Gauge differential active power group and Gauge differential reactive power group)
Here, three differential voltage vectors v ₂ (t), v ₂ (tT), v ₂ (t-2T) and two differential current vectors i ₂ (tT), i ₂ (t-2T) are expressed as “gauges”. It is defined as “differential power group”. Further, among the rotation vectors constituting the gauge power group, two differential voltage vectors v ₂ (t) and v ₂ (tT) and two differential current vectors i ₂ (tT) and i ₂ (t−2T) are expressed as “ “Gauge differential active power group”, and two differential voltage vectors v ₂ (tT) and v ₂ (t−2T) and two differential current vectors i ₂ (tT) and i ₂ (t−2T) are expressed as “ It is defined as “gauge differential reactive power group”.

(Cage differential active power)
The gauge differential active power is defined as follows using the gauge differential active power group.

Here, the differential voltage instantaneous values v ₂₁ and v ₂₂ are real parts of the differential voltage vectors v ₂ (t) and v ₂ (tT), respectively, and are calculated as follows:

Similarly, the instantaneous current values i ₂₂ and i ₂₃ are the real parts of the differential current vectors i ₂ (tT) and i ₂ (t−2T), respectively, and are calculated as follows:

  If the above (90) and (91) are substituted into the above equation (89), the calculation formula representing the gauge differential effective power is converted as the following equation.

  That is, the calculation formula of the gauge differential active power can be expressed as the following formula.

(Gauge differential reactive power)
The gauge differential reactive power is defined as follows using the gauge differential reactive power group.

Here, the differential voltage instantaneous values v ₂₂ and v ₂₃ are the real parts of the differential voltage vectors v ₂ (tT) and v ₂ (t−2T), respectively, and are calculated as follows:

The instantaneous current values i ₂ and i ₃ are defined as in the equation (91). If the equations (91) and (95) are substituted into the equation (94), the gauge differential reactive power The calculation formula representing is converted as follows.

  That is, the calculation formula of the gauge differential reactive power can be expressed as the following formula.

  From the above equations (93) and (97), the cosine function value and sine function value of the voltage-current phase angle φ can be calculated using the following equations.

  Therefore, the active power and the reactive power are obtained by the following formulas according to a general power definition.

  Similarly, the apparent power is obtained by the following equation according to the general definition of power.

  Similarly, the power factor is obtained as follows.

(Gauge differential power symmetry index)
Next, a method using gauge differential power as an index for evaluating the symmetry of the input waveform will be described. The gauge differential power symmetry index is defined as follows:

Here, (cos φ) _VI2 and (cos φ) _PF2 are cosine function values of the voltage-current phase angle φ calculated as follows.

  In the above equation (102), if the input waveform is a pure sine wave, the gauge differential power symmetry index is zero.

On the other hand, when the gauge differential power symmetry index is larger than the predetermined threshold value, that is, when the relationship of the following equation with respect to the threshold value S _BRK2 is satisfied, it is determined that the input waveform is not symmetrical and is not a pure sine wave. In this case, the measured value (calculated value) is latched as necessary.

(Distance protection formula)
Next, a calculation formula for distance protection is presented. First, the following calculation formula is obtained by the definition of impedance.

  From the real part and the imaginary part of the above equation, the resistance and inductance can be calculated as follows:

In the above equation, I _gd is a gauge differential current, and f is an actually measured frequency. In the distance protection using the gauge power group, the measurement (calculation) can be performed with higher accuracy because it is not affected by the DC offset due to the CT saturation as compared with the case where the gauge power group is used.

  The coefficient distance k is calculated using the following equation.

Here, L ₀ is the inductance of the entire transmission line, and L is the inductance calculated by the above equation (106). For example, if k = 50%, it means that a failure has occurred at the midpoint of the transmission line.

(Distance protection symmetry index)
Next, a method of using the result of the distance protection calculation as an index for evaluating the symmetry of the input waveform will be described. The distance protection symmetry index is defined as follows:

Here, L _g and L _gd are inductances calculated as follows.

  In the above equation (109), if the input waveform is a pure sine wave, the distance protection symmetry index is zero.

On the other hand, when the distance protection symmetry index is larger than the predetermined threshold value, that is, when the relationship is _expressed by the following expression with respect to the threshold value S _DZBRK , it is determined that the input waveform is broken in symmetry and is not a pure sine wave. In this case, the measured values (resistance and inductance) are latched as necessary.

(Step-out protection calculation formula)
In the above equation (82), the calculation formula for the step-out center voltage using the gauge current and the gauge power is shown. On the other hand, the calculation formula of the step-out center voltage using the gauge differential current and the gauge differential power is as follows.

  In the distance protection using the gauge power group, the measurement (calculation) can be performed with higher accuracy because it is not affected by the DC offset due to the CT saturation as compared with the case of using the gauge power group.

(Step-out protection symmetry index)
Next, a method of using the calculation result of the step-out center voltage as an index for evaluating the symmetry of the input waveform will be described. The step-out protection symmetry index is defined as follows:

Here, V _Cg and V _Cg are step-out center voltages calculated as follows.

  In the above equation (113), if the input waveform is a pure sine wave, the step-out protection symmetry index is zero.

On the other hand, when the step-out protection symmetry index is larger than the predetermined threshold value, that is, when the relationship of the following equation is _{satisfied with} respect to the threshold value S _VCBRK , it is determined that the input waveform is broken in symmetry and is not a pure sine wave. In this case, the measured value (step-out center voltage) is latched as necessary.

  In order to reduce the influence of noise, a plurality of sampling data may be used. The calculation formula of the gauge differential active power in a plurality of gauge differential active power symmetry groups is as follows.

  Moreover, the calculation formula of the gauge differential reactive power in a plurality of gauge differential reactive power symmetry groups is as follows.

  The time series data of each voltage instantaneous value and current instantaneous value is obtained using the following equation.

  Here, the time series data of the voltage vector and the current vector is obtained using the following equations.

(Phase difference between buses)
Next, in one terminal (hereinafter referred to as “terminal 1”) on a certain bus (or power transmission line) and the other terminal (hereinafter referred to as “terminal 2”) on the same bus, A phase difference between the rotation vectors (terminal phase difference between the buses) between the terminals 1 and 2 when both rotation vectors have the same frequency will be described. In the following, a case where the rotation vector is a voltage vector will be described as an example. In addition, when the frequencies of the rotation vectors at the terminals 1 and 2 are different, a spatial synchronization phasor described later may be used.

(Calculation of voltage phase difference between buses)
FIG. 6 is a diagram illustrating a cage dual voltage group on a complex plane. FIG. 6 shows three voltage vectors v ₁ (t), v ₁ (tT), and v ₁ (t−2T) of the voltage instantaneous value V ₁ that rotates counterclockwise at the real frequency on the complex plane at the terminal 1. ) And two voltage vectors v ₂ (tT) and v ₂ (t−2T) of the voltage instantaneous value V ₂ rotating counterclockwise at the real frequency on the complex plane. These three voltage vectors v ₁ (t), v ₁ (tT), v ₁ (t-2T) and the two voltage vectors v ₂ (tT), v ₂ (t-2T) are respectively expressed by It can be expressed as:

(Gauge bi-voltage group, Gauge bi-effective voltage group and Gauge bi-reactive voltage group)
Here, three voltage vectors v ₁ (t), v ₁ (tT), v ₁ (t-2T) at the terminal ₁ and two voltage vectors v ₂ (tT), v ₂ (t-2T) at the terminal 2 are used. ) Is defined as “gauge dual voltage group”. In addition, two voltage vectors v ₁ (t) and v ₁ (tT) and two voltage vectors v ₂ (tT) and v ₂ (t−2T) among the rotation vectors forming the gauge dual voltage group are expressed as “gauge”. "Bi-effective voltage group" and two voltage vectors v ₁ (tT), v ₁ (t-2T) and two voltage vectors v ₂ (tT), v ₂ (t-2T) It is defined as “voltage group”. The terms “active” and “invalid” in “gauge dual effective voltage group” and “gauge dual reactive voltage group” are structurally similar to “gauge active power group” and “gauge reactive power group”. It is.

(Gauge dual effective voltage)
Using the above-mentioned gauge bi-effective voltage group, the gauge bi-effective voltage is defined as follows.

Here, the instantaneous voltage values v ₁₁ and v ₁₂ at the terminal 1 are the real parts of the voltage vectors v ₁ (t) and v ₁ (tT), respectively, and are calculated as follows:

Similarly, the instantaneous voltage values v ₂₂ and v ₂₃ at the terminal 2 are the real parts of the voltage vectors v ₂ (tT) and v ₂ (t−2T), respectively, and are calculated as follows:

  If the above formulas (122) and (123) are substituted into the above formula (121), the calculation formula representing the gauge effective voltage is converted as the following formula.

  That is, the calculation formula of the gauge dual effective voltage can be expressed as follows.

(Gauge dual reactive voltage)
The gauge bi-reactive voltage is defined as follows using the above-mentioned gauge bi-reactive voltage group.

Here, the instantaneous voltage values v ₁₂ and v ₁₃ at the terminal 1 are the real parts of the voltage vectors v ₁ (tT) and v ₁ (t−2T), respectively, and are calculated as follows:

The instantaneous voltage values v ₂₂ and v _{23 at} the terminal 2 are defined as shown in the equation (123). If the equations (123) and (127) are substituted into the equation (126), the gauge The calculation formula representing the bi-reactive voltage is converted as follows.

  That is, the calculation formula of the gauge dual reactive voltage can be expressed as the following formula.

  From the above formulas (125) and (129), the cosine function value and the sine function value of the voltage phase angle difference φ (hereinafter simply referred to as “voltage phase angle difference φ”) between the terminals 1 and 2 are as follows. Can be calculated.

  Therefore, the voltage phase angle difference φ is obtained by the following equation using the above equation.

  In addition, there exists a relationship of following Formula between each gauge voltage and each voltage amplitude in terminal 1,2.

As shown in the following equation, it is also possible to directly calculate the cosine function of the voltage phase angle difference φ using V _pg , V _qg , and f _C.

(Gauge bivoltage symmetry index)
Next, a method using a gauge dual voltage as an index for evaluating the symmetry of the input waveform will be described. The gauge dual voltage symmetry index is defined as follows:

Here, (cosφ) _V11 and (cosφ) _V12 are cosine function values of the voltage phase angle difference φ calculated as follows.

  In the above equation (134), if the input waveform is a pure sine wave, the gauge dual voltage symmetry index is zero.

On the other hand, when the gauge _bivoltage symmetry index is larger than a predetermined threshold value, that is, when the relationship is _expressed by the following equation with respect to the threshold value _V2BRK1 , it is determined that the input waveform is broken in symmetry and is not a pure sine wave. In this case, the measured value (voltage phase angle difference) is latched as necessary.

  In order to reduce the influence of noise, a plurality of sampling data may be used. The calculation formula of the gauge dual effective voltage in the plurality of gauge dual effective voltage groups is as follows.

  Moreover, the calculation formula of the gauge bi-reactive voltage in a plurality of gauge bi-reactive voltage groups is as follows.

  The time series data of the instantaneous voltage value at each terminal is obtained using the following equation.

  Here, the time-series data of the voltage vector at each terminal is obtained using the following equation.

(Gauge dual differential voltage group, Gauge dual differential effective voltage group and Gauge dual differential reactive voltage group)
FIG. 7 is a diagram illustrating a cage dual differential voltage group on a complex plane. FIG. 7 shows three differential voltage vectors v ₁₂ (t), v ₁₂ (tT), and v ₁₂ (t−) of the voltage instantaneous value V ₁ that rotates counterclockwise at the real frequency on the complex plane at the terminal 1. 2T) and two differential voltage vectors v ₂₂ (tT) and v ₂₂ (t-2T) of the voltage instantaneous value V ₂ rotating counterclockwise at the real frequency on the complex plane at the terminal 2 are shown. Yes. These three voltage vectors v ₁₂ (t), v ₁₂ (tT), v ₁₂ (t-2T) and the two voltage vectors v ₂₂ (tT), v ₂₂ (t-2T) It can be expressed as:

Here, the three differential voltage vectors v ₁₂ (t), v ₁₂ (tT), v ₁₂ (t−2T) at the terminal 1 and the two differential voltage vectors v ₂₂ (tT), v ₂₂ (t -2T) is defined as “gauge dual difference voltage group”. Of the rotation vectors forming the gauge dual differential voltage group, two differential voltage vectors v ₁₂ (t) and v ₁₂ (tT) and two differential voltage vectors v ₂₂ (tT) and v ₂₂ (t−2T) Is defined as a “gauge dual differential effective voltage group”, and two differential voltage vectors v ₁₂ (tT) and v ₁₂ (t−2T) and two differential voltage vectors v ₂₂ (tT) and v ₂₂ (t−2T) ) Is defined as “gauge dual differential reactive voltage group”.

(Cage dual differential effective voltage)
The gauge dual differential effective voltage is defined as follows using the above-mentioned gauge dual differential effective voltage group.

Here, the instantaneous voltage values v ₁₂₁ and v ₁₂₂ of the terminal 1 are the real parts of the differential voltage vectors v ₁₂ (t) and v ₁₂ (tT), respectively, and are calculated as follows:

Similarly, the instantaneous voltage values v ₂₂₂ and v ₂₂₃ at the terminal 2 are the real parts of the differential voltage vectors v ₂₂ (tT) and v ₂₂ (t−2T), respectively, and are calculated as follows:

  By substituting the above equations (144) and (145) into the above equation (143), the calculation equation representing the gauge dual difference effective voltage is converted as the following equation.

  That is, the calculation formula of the gauge dual difference effective voltage can be expressed as the following formula.

(Cage dual differential reactive voltage)
Using the cage dual differential reactive voltage group, the gauge dual differential reactive voltage is defined as follows.

Here, the differential voltage instantaneous values v ₁₂₂ and v ₁₂₃ at the terminal 1 are the real parts of the differential voltage vectors v ₁₂ (tT) and v ₁₂ (t−2T), respectively, and are calculated as follows:

Note that the differential voltage instantaneous values v ₂₂₂ and v _{223 at} the terminal 2 are defined as in the equation (145). If the equations (145) and (149) are substituted into the equation (148), The calculation formula representing the gauge dual differential reactive voltage is converted as follows.

  That is, the calculation formula of the gauge dual difference reactive voltage can be expressed as the following formula.

  From the above equations (147) and (151), the cosine function value and sine function value of the voltage phase angle difference φ between the terminals 1 and 2 can be calculated using the following equations. As described above, the cosine function value and the sine function value of the voltage phase angle difference can be calculated using the following equations.

  Therefore, the voltage phase angle difference φ is obtained by the following equation using the above equation.

  In addition, there exists a relationship of following Formula between each gauge differential voltage and each differential voltage amplitude in terminal 1,2.

As shown in the following equation, the voltage phase angle difference φ can also be directly calculated using V _pgd , V _qgd , and f _C.

(Gauge dual difference voltage symmetry index)
Next, a method using a gauge dual difference voltage as an index for evaluating the symmetry of the input waveform will be described. The gauge dual difference voltage symmetry index is defined as follows.

Here, (cosφ) _V21 and (cosφ) _V22 are cosine function values of the voltage phase angle difference φ calculated as follows.

  In the above equation (156), if the input waveform is a pure sine wave, the gauge dual difference voltage symmetry index is zero.

On the other hand, when the gauge dual difference voltage symmetry index is larger than the predetermined threshold value, that is, when the relationship is _expressed by the following equation with respect to the threshold value V _2BRK2 , it is determined that the input waveform has broken symmetry and is not a pure sine wave. . In this case, the measured value (voltage phase angle difference) is latched as necessary.

  In order to reduce the influence of noise, a plurality of sampling data may be used. The calculation formula of the gauge dual differential effective voltage in a plurality of gauge dual differential effective voltage groups is as follows.

  Moreover, the calculation formula of the gauge dual differential reactive voltage in a plurality of gauge dual differential reactive voltage groups is as follows.

  The time series data of the instantaneous voltage value at each terminal is obtained using the following equation.

  Here, the time-series data of the voltage vector at each terminal is obtained using the following equation.

  The above description can be applied to the cage dual current group and the cage dual differential current group. The expression expansion is omitted.

  When obtaining the voltage phase angle difference as described above, it is assumed that the actual frequencies at the terminals 1 and 2 are the same. However, when the frequencies at the terminals 1 and 2 are different, the spatially synchronized phasor described below is used. It is preferable.

(Synchronized phaser)
FIG. 8 is a diagram illustrating a synchronized phasor group on a complex plane. On the complex plane of FIG. 8, three voltage vectors v ₁ (t), v ₁ (tT), and v ₁ (t−2T) that rotate counterclockwise at the real frequency and two fixed unit vectors v ₁₀ (0), v ₁₀ (1) are shown. Here, the three voltage vectors v ₁ (t), v ₁ (tT), and v ₁ (t−2T) can be expressed by the following equations.

  As shown in the above “meaning of term”, the synchronous phasor is an absolute phase angle of a voltage vector or a current vector that rotates counterclockwise on a complex plane. Because of the absolute phase angle, the synchronized phasor is a time-dependent amount that changes from moment to moment. Therefore, if the synchronized phasor is expressed as it is, a component that changes depending on the rotational phase angle and a component that changes depending on time are included. Therefore, the above equation (163) shows the absolute phase angle component at a certain time point when the time is stopped. If the DC voltage is included in the voltage vector, the following processing may be applied after calculating the DC offset component using the above calculation method, subtracting the calculated DC offset component, and canceling.

Two fixed unit vectors v ₁₀ (0) and v ₁₀ (1) can be expressed by the following equations.

  Here, α is the rotational phase angle determined online.

(Gauge synchronized phasor group, Gauge enabled synchronized phasor group and Gauge disabled synchronized phasor group)
The three voltage vectors v ₁ (t), v ₁ (tT), v ₁ (t-2T) and two fixed unit vectors v ₁₀ (0), v ₁₀ (1) shown in FIG. It is defined as “phasor group”. In addition, two voltage vectors v ₁ (tT), v ₁ (t-2T) and two fixed unit vectors v ₁₀ (0), v ₁₀ (1) among the vectors constituting the gauge synchronous phasor group are expressed as “gauge”. "Effective synchronous phasor group" and two voltage vectors v ₁ (t), v ₁ (tT) and two fixed unit vectors v ₁₀ (0), v ₁₀ (1) It is defined as

The terms “valid” and “invalid” in the “gauge active synchronous phasor group” and “gauge invalid synchronous phasor group” are the rotation invariants of the “gauge active power group” and “gauge reactive power group” that are symmetric groups. This is given because it is similar to the “gauge active power” and “gauge reactive power” which are the calculation results of. The same applies to the gauge difference synchronized phasor group, the gauge difference effective synchronized phasor group, and the gauge difference invalid synchronized phasor group described below. However, the gauge synchronous phasor group includes a rotating vector (v ₁ (t), v ₁ (tT), v ₁ (t-2T)) and a stationary vector (v ₁₀ (0), v ₁₀ (1)), the gauge power group is a vector (v (t), v (tT), v (t-2T), i (tT), i ( There is a structural difference in that it consists of t-2T)).

(Gauge enabled sync phasor and gauge disabled sync phasor)
The gauge effective synchronization phasor is defined as follows using the gauge effective synchronization phasor group.

  Further, the gauge invalid synchronization phasor is defined as follows using the gauge invalid synchronization phasor group.

The instantaneous voltage values v ₁₁ , v ₁₂ , and v ₁₃ in the above equations (165) and (166) are the real parts of the voltage vectors v ₁ (t), v ₁ (tT), and v ₁ (t−2T), respectively. Is calculated as:

Similarly, the instantaneous values v ₁₀₀ and v ₁₀₁ of the two fixed unit vectors are real parts of the fixed unit vectors v ₁₀ (0) and v ₁₀ (1), respectively, and are calculated as follows:

By substituting v ₁₁ and v ₁₂ in the above equation (167) and v ₁₀₀ and v ₁₀₁ in the above equation (168) into the above equation (165), the calculation formula representing the gauge effective synchronous phasor is converted as follows: Is done.

  That is, the calculation formula of the gauge effective synchronous phasor can be expressed as the following formula.

Further, if v ₁₂ and v ₁₃ in the above expression (167) and v ₁₀₀ and v ₁₀₁ in the above expression (168) are substituted into the above expression (166), the calculation expression representing the gauge invalid synchronization phasor is as follows: Is converted to

  That is, the calculation formula of the gauge invalid synchronized phasor can be expressed as the following formula.

  In the above equations (170) and (172), the frequency dependency amounts V and α and the time dependency amount φ are expressed in one calculation expression.

(Calculation at the imaginary part of the voltage vector)
In the above description, the calculation is performed using the real part of the voltage vector, but the imaginary part of the voltage vector may be used. The calculation formula using the imaginary part of the voltage vector is presented below.

First, assuming that the voltage instantaneous values v ₁₁ , v ₁₂ , and v ₁₃ are the imaginary part instantaneous values of the voltage vectors v ₁ (t), v ₁ (tT), and v ₁ (t-2T), they are calculated as follows: The

Similarly, assuming that the instantaneous values v ₁₀₀ and v _{101 of the} fixed unit vectors are the imaginary part instantaneous values of the fixed unit vectors v ₁₀ (0) and v ₁₀ (1), they are calculated as follows:

Substituting v ₁₁ and v ₁₂ in the above equation (173) and v ₁₀₀ and v ₁₀₁ in the above equation (174) into the above equation (165), the calculation formula representing the gauge effective synchronous phasor is converted as follows: Is done.

Further, if v ₁₂ and v ₁₃ in the above equation (173) and v ₁₀₀ and v ₁₀₁ in the above equation (174) are substituted into the above equation (166), the calculation equation representing the gauge invalid synchronized phasor is as follows: Is converted to

  The above expression (169) and expression (175) coincide. In addition, the above formula (171) and the formula (176) coincide. Thus, the results are the same regardless of whether the real part or the imaginary part of the voltage vector is used. This means that the synchronized phasor of the AC sine wave has symmetry.

(Synchronous phasor cosine function method)
From the above equations (170) and (172), the following relationship is obtained.

  From the above equation, the cosine function of the synchronized phasor is expressed by the following equation.

  Therefore, the synchronized phasor is obtained using the following equation.

  Thus, it can be seen that the synchronized phasor changes from −180 degrees to +180 degrees and is a time-dependent amount.

(Synchronous phasor tangent function method)
When the above equation (177) is used, the relationship of the following equation is obtained.

  From the above equation, the tangent function of the synchronized phasor is expressed by the following equation.

  Therefore, the synchronized phasor is obtained using the following equation.

  There is no voltage amplitude variable V in the equation (182). Therefore, if the input waveform is symmetric, the results of equations (179) and (182) should be equal from the requirement for symmetry. Therefore, when the calculation results of the equations (179) and (182) are different, the symmetry of the input waveform is broken, and it is possible to determine that the input waveform is not a pure sine wave. A synchronized phasor symmetry index using the properties of these equations will be described later.

(Calculation formula of gauge effective synchronized phasor with multiple sampling data)
The calculation formula of the gauge effective synchronous phasor in the case of having a plurality of sample data (sampling point number n) is given by the following formula.

In the above equation, v _1k is time series data of voltage instantaneous values. Further, v _10k is a member of a fixed unit vector group represented by the following formula and the following formula.

(Calculation formula for gauge invalid synchronized phasor with multiple sampling data)
The calculation formula of the gauge invalid synchronization phasor in the case of having a plurality of sample data (sampling point number n) is given by the following formula.

(Complex number representation of voltage vector)
First, the real part and the imaginary part of the voltage vector can be expressed as follows:

Here, v _re and v _im are the real part and imaginary part of the voltage vector, respectively, and are calculated as follows using equations (172) and (178).

  This equation (188) is a very important equation, which means that the real part of the voltage vector is the instantaneous voltage fundamental wave value. Using this equation (188), the real part and imaginary part of the voltage vector can be calculated directly from the time series data.

When the above expression (188) is converted into an expression using the frequency coefficient f _C , the real part and the imaginary part of the voltage vector are expressed by the following expressions.

  From the above equation (189), the voltage amplitude V can be calculated as follows.

Further, as shown in the following equation, the cosine function of the synchronized phasor φ can be directly calculated using SA _P , SA _Q , and f _C.

(Synchronous phasor cosine function symmetry index)
Next, a method using the cosine function of the synchronized phasor as an index for evaluating the symmetry of the input waveform will be described. The synchronous phasor cosine function symmetry index is defined as follows:

Here, (cosφ) _SP11 and (cosφ) _SP12 are cosine function values of the synchronized phasor φ calculated as follows.

  In the above equation (193), if the input waveform is a pure sine wave, the synchronous phasor cosine function symmetry index is zero.

On the other hand, when the synchronized phasor cosine function symmetry index is larger than a predetermined threshold value, that is, when the relationship is expressed by the following expression with respect to the threshold value SPS _sym1 , the input waveform is determined not to be a pure sine wave due to broken symmetry. . In this case, the measured value is latched as necessary.

  The above description can also be applied to the current vector and its current amplitude. The expression expansion is omitted.

  The description so far regarding the synchronized phasor has been based on the assumption that the actual frequency is unknown, that is, the actual frequency is not necessarily the rated frequency. On the other hand, in the following explanation regarding the synchronized phasor, it is assumed that the actual frequency is known, that is, the actual frequency is the rated frequency, or is changing in the vicinity of the rated frequency (50 Hz or 60 Hz) but can be regarded as the rated frequency. I will explain. This assumption makes it possible to perform high-speed measurement with various monitoring control devices, and for example, it is possible to apply to smart meters.

(When α = 90 °)
The case where the rotational phase angle α is 90 ° means, for example, a sampling frequency of 200 Hz for a 50 Hz system, and a sampling frequency of 240 Hz for a 60 Hz system. At this time, the real value of each member constituting the fixed unit vector group is as shown in the following equation.

  Here, k = n−2, n is the number of sampling points.

  The gauge effective synchronized phasor can be calculated using the following equation.

Here, v _1K is time series data of instantaneous voltage values.

  The gauge invalid synchronized phasor can be calculated using the following equation.

Here, v _{1 (K-1)} is time series data of voltage instantaneous values.

(Complex expression of voltage vector when α = 90 °)
When α = 90 °, from the equation (188), the real part and the imaginary part v _re and v _im of the voltage vector can be simplified as the following expressions, respectively.

  Therefore, the voltage amplitude V can be calculated as follows.

  If the equation (179), which is a calculation formula based on the synchronous phasor cosine function method described above, is used, the synchronous phasor can be calculated using the following equation.

  In general protection control devices in Japan, 30 ° sampling (α = 30 °) is widely used. Also in the case of α = 30 °, calculation formulas such as a voltage amplitude, a synchronized phasor, a gauge effective synchronized phasor, and a gauge invalid synchronized phasor can be derived as described above. Note that the specific expression expansion is the same as described above, and a description thereof will be omitted here.

(Voltage amplitude symmetry index 2)
Next, a second index (voltage amplitude characteristic index 2) among the methods using the voltage amplitude as an index for evaluating the symmetry of the input waveform will be described. The voltage amplitude symmetry index 2 is defined as follows:

Here, V _SA and V _gdA are voltage amplitudes calculated by the gauge synchronous phasor group and the gauge differential voltage group, respectively, as follows.

  If the input waveform is a pure sine wave, the voltage amplitude symmetry index 2 shown in the equation (201) is zero.

On the other hand, when the voltage amplitude symmetry index 2 is larger than the predetermined threshold value, that is, when the relationship is expressed by the following equation with respect to the threshold value V _BRK , it is determined that the input waveform is not symmetrical and is not a pure sine wave. In this case, the rotational phase angle, frequency, voltage amplitude, etc., which are measured values, are latched as necessary.

  The idea of the voltage amplitude symmetry index 2 can be similarly applied to the current amplitude. The expression expansion is omitted.

(Synchronous phasor symmetry index)
Next, a method using a synchronized phasor as an index for evaluating the symmetry of the input waveform will be described. The synchronous phasor symmetry index is defined as follows:

Here, φ _cosA and φ _tanA are synchronized phasors calculated by the synchronized phasor cosine function method and the synchronized phasor tangent function method, respectively, as follows.

  If the input waveform is a pure sine wave, the synchronous phasor symmetry index shown in equation (204) is zero.

On the other hand, when the synchronous phasor symmetry index is larger than a predetermined threshold value, that is, when the relation of the following equation is satisfied with respect to the threshold value φ _BRK , it is determined that the input waveform is broken in symmetry and is not a pure sine wave. At this time, the synchronized phasor is estimated as follows.

Here, φ _t and φ _tT are the current synchronized phasor and the synchronized phasor one step before, respectively. F is the actual frequency and T is the sampling frequency 1 cycle. Note that the estimated value of the synchronized phasor presented here has various uses. In an embodiment 13 to be described later, an instantaneous value estimation method is introduced.

(Differential Synchrophasor)
FIG. 9 is a diagram illustrating a differentially synchronized phasor group on a complex plane. On the complex plane of FIG. 9, there are three differential voltage vectors v ₂ (t), v ₂ (tT), and v ₂ (t−2T) that rotate counterclockwise at the real frequency, and two fixed difference unit vectors. v ₂₀ (0) and v ₂₀ (1) are shown. Here, the three differential voltage vectors v ₂ (t), v ₂ (tT), v ₂ (t-2T) and the two fixed differential unit vectors v ₂₀ (0), v ₂₀ (1) are It can be expressed by the following formula.

(Gauge differential synchronized phasor group, Gauge differential effective synchronized phasor group and Gauge differential invalid synchronized phasor group)
The three differential voltage vectors v ₂ (t), v ₂ (tT), and v ₂ (t−2T) shown in FIG. 9 and the two fixed differential unit vectors v ₂₀ (0) and v ₂₀ (1) are expressed as “ It is defined as a “gauge differential synchronized phasor group”. In addition, two differential voltage vectors v ₂ (tT) and v ₂ (t−2T) and two fixed differential unit vectors v ₂₀ (0) and v ₂₀ (1) among the vectors forming the gauge differential synchronous phasor group. Is defined as a “gauge difference effective synchronous phasor group”, and two voltage vectors v ₂ (tT) and v ₂ (t−2T) and two fixed unit vectors v ₂₀ (0) and v ₂₀ (1) are defined as “ It is defined as “Gauge difference invalid synchronized phasor group”.

(Gauge differential valid synchronous phasor and Gauge differential invalid synchronous phasor)
The gauge difference effective synchronization phasor is defined as follows using the gauge difference effective synchronization phasor group.

  Further, the gauge difference invalid synchronization phasor is defined as follows using the gauge difference invalid synchronization phasor group.

The instantaneous voltage values v ₁₁ , v ₁₂ and v ₁₃ in the above equations (209) and (210) are the real parts of the differential voltage vectors v ₂ (t), v ₂ (tT) and v ₂ (t−2T), respectively. Yes, it is calculated as:

Similarly, the instantaneous values v ₂₀₀ and v ₂₀₁ of the two fixed unit vectors are the real parts of the fixed difference unit vectors v ₂₀ (0) and v ₂₀ (1), respectively, and are calculated as follows:

By substituting v ₂₁ and v ₂₂ in the above equation (211) and v ₂₀₀ and v ₂₀₁ in the above equation (212) into the above equation (209), the calculation formula representing the gauge difference effective synchronous phasor is as follows: Converted.

  That is, the calculation formula of the gauge difference effective synchronous phasor can be expressed as the following formula.

Further, if v ₂₀ and v ₂₁ in the above equation (211) and v ₂₀₀ and v ₂₀₁ in the above equation (212) are substituted into the above equation (210), the calculation equation representing the gauge difference invalid synchronization phasor is as follows: Is converted as follows.

  That is, the equation for calculating the gauge difference invalid synchronization phasor can be expressed as the following equation.

(Calculation at the imaginary part of the differential voltage vector)
In the above description, the calculation is performed using the real part of the differential voltage vector, but the imaginary part of the differential voltage vector may be used. Below, the calculation formula using the imaginary part of the differential voltage vector is presented.

First, assuming that the voltage instantaneous values v ₂₁ , v ₂₂ , and v ₂₃ are the imaginary part instantaneous values of the voltage vectors v ₂ (t), v ₂ (tT), and v ₂ (t-2T), they are calculated as follows: The

Similarly, if the instantaneous values v ₂₀₀ and v _{201 of the} fixed unit vectors are also the imaginary part instantaneous values of the fixed unit vectors v ₂₀ (0) and v ₂₀ (1), they are calculated as follows:

By substituting v ₂₁ and v ₂₂ in the above equation (217) and v ₂₀₀ and v ₂₀₁ in the above equation (218) into the above equation (209), the calculation formula representing the gauge difference effective synchronous phasor is as follows: Converted.

Also, if v ₂₀ and v ₂₁ in the above equation (217) and v ₂₀₀ and v ₂₀₁ in the above equation (218) are substituted into the above (209) equation, the calculation formula representing the gauge difference invalid synchronous phasor is as follows: Is converted as follows.

  The above equation (214) and equation (219) coincide. Also, the above equation (216) and the equation (220) coincide. Thus, the results are the same whether using the real part or the imaginary part of the differential voltage vector. This means that an AC sine wave differentially synchronized phasor has symmetry.

(Differential synchronous phasor cosine function method)
From the above equation (214) and equation (216), the following relationship is obtained.

  From the above equation, the cosine function of the differentially synchronized phasor is expressed by the following equation.

  Therefore, the differential synchronization phasor is obtained using the following equation.

  Since the differential synchronization phasor obtained by the above equation is calculated using the differential voltage vector, there is an advantage that the influence of the DC offset in the voltage waveform is small.

(Differential synchronous phasor tangent function method)
When the above equation (221) is used, the relationship of the following equation is obtained.

  From the above equation, the tangent function of the differential synchronization phasor is expressed by the following equation.

  Therefore, the differential synchronization phasor is obtained using the following equation.

  Since the differential synchronization phasor obtained by the above equation is calculated using the differential voltage vector, there is an advantage that the influence of the DC offset in the voltage waveform is small.

(Calculation formula of gauge difference effective synchronous phasor with multiple sampling data)
The calculation formula of the gauge difference effective synchronous phasor in the case of having a plurality of sample data (sampling point number n) is given by the following formula.

In the above equation, v _2k is time-series data of differential voltage instantaneous values. Further, v _20k is a member of a fixed difference unit vector group expressed by the following formula and the following formula.

(Calculation formula of gauge difference invalid synchronized phasor with multiple sampling data)
The calculation formula of the gauge difference invalid synchronization phasor in the case of having a plurality of sample data (sampling point number n) is given by the following formula.

(Complex number representation of voltage vector)
First, the real part v _re and the imaginary part v _im of the voltage vector can be expressed by the following equations using equations (216) and (222).

  This equation (231) is a very important equation, and the real part and imaginary part of the voltage vector can be calculated directly from the time series data.

When the above equation (231) is converted into an equation using the frequency coefficient f _C , the real part and the imaginary part of the voltage vector are expressed by the following equations.

  From the above equation (232), the voltage amplitude V can be calculated as the following equation.

Further, as shown in the following equation, the cosine function of the synchronized phasor φ can be directly calculated using SD _P , SD _Q , and f _C.

(Differential synchronous phasor cosine function symmetry index)
Next, a method of using the cosine function of the differential synchronization phasor as an index for evaluating the symmetry of the input waveform will be described. The differential synchronization phasor cosine function symmetry index is defined as follows.

Here, (cosφ) _SP21 and (cosφ) _SP22 are cosine function values of the synchronized phasor φ calculated as follows.

  In the above equation (236), if the input waveform is a pure sine wave, the synchronous phasor cosine function symmetry index is zero.

On the other hand, when the differential synchronization phasor cosine function symmetry index is larger than a predetermined threshold value, that is, when the relationship is expressed by the following equation with respect to the threshold value SPS _sym2 , it is determined that the input waveform is not symmetrical and is not a pure sine wave. To do. In this case, the measured value is latched as necessary.

  The above description can also be applied to the current vector and its current amplitude. The expression expansion is omitted.

  The description so far regarding the differentially synchronized phasor has been based on the assumption that the actual frequency is unknown, that is, the actual frequency is not necessarily the rated frequency. On the other hand, in the following explanation regarding the differential synchronous phasor, the actual frequency is known, i.e., the actual frequency is the rated frequency, or is fluctuating in the vicinity of the rated frequency (50 Hz or 60 Hz), but can be regarded as the rated frequency. I will explain. This assumption makes it possible to perform high-speed measurement with various monitoring control devices, and for example, it is possible to apply to smart meters.

(When α = 90 °)
The case where the rotational phase angle α is 90 ° means, for example, a sampling frequency of 200 Hz for a 50 Hz system, and a sampling frequency of 240 Hz for a 60 Hz system. At this time, the real value of each member constituting the fixed unit vector group is as shown in the following equation.

  Here, k = n−2, n is the number of sampling points.

  Here, the following equation is established from the above equations (170), (172), (214), and (216).

  Therefore, the following judgment formula is proposed as a judgment formula for judging the symmetry breaking of the input AC voltage.

  Here, ε is a settling value. When the above equation is satisfied, it is determined that the symmetry of the input AC waveform is broken. In this case, for example, it is preferable to perform the process of latching the value of the previous step without adopting the calculation result of the synchronous phasor described below.

(Complex expression of voltage vector when α = 90 °)
When α = 90 °, the real part and the imaginary part v _re and v _im of the voltage vector can be simplified from the equation (231) as shown in the following equations.

  Therefore, the voltage amplitude V can be calculated as follows.

  If the equation (223), which is a calculation formula based on the above-described synchronous phasor cosine function method, is used, the synchronous phasor can be calculated using the following equation.

  In general protection control devices in Japan, 30 ° sampling (α = 30 °) is widely used. When α = 30 °, calculation formulas such as a voltage amplitude, a synchronized phasor, a gauge difference effective synchronized phasor, and a gauge difference invalid synchronized phasor can be derived as described above. Since specific expression expansion is the same as described above, description thereof is omitted here.

  Further, as described above, the voltage amplitude and the synchronized phasor can be calculated using either the gauge synchronized phasor group or the gauge differential synchronized phasor group. However, when both of these methods can be used, it is preferable to apply a calculation method using a differentially synchronized phasor group that is not affected by the DC offset of the input waveform.

  The above description can be applied to the calculation process of the synchronous phasor based on the current vector. The expression expansion is omitted.

(Voltage amplitude symmetry index 3)
Next, a third index (voltage amplitude characteristic index 3) among methods using voltage amplitude as an index for evaluating the symmetry of the input waveform will be described. The voltage amplitude symmetry index 3 is defined as follows:

Here, V _SD and V _gdA are voltage amplitudes calculated by the gauge difference synchronized phasor group and the gauge difference voltage group, respectively, as follows.

  If the input waveform is a pure sine wave, the voltage amplitude symmetry index 3 shown in the equation (244) is zero.

On the other hand, when the voltage amplitude symmetry index 3 is larger than the predetermined threshold value, that is, when the relationship is expressed by the following equation with respect to the threshold value V _BRK , it is determined that the input waveform is broken and is not a pure sine wave. In this case, the rotational phase angle, frequency, voltage amplitude, etc., which are measured values, are latched as necessary.

  The idea of the voltage amplitude symmetry index 3 can be similarly applied to the current amplitude. The expression expansion is omitted.

(Voltage amplitude symmetry index 4)
Next, a fourth index (voltage amplitude characteristic index 4) among the methods using the voltage amplitude as an index for evaluating the symmetry of the input waveform will be described. The voltage amplitude symmetry index 4 is defined as follows:

Here, V _SA and V _SD are voltage amplitudes calculated by the gauge synchronous phasor group and the gauge differential synchronous phasor group, respectively, as follows.

  If the input waveform is a pure sine wave, the voltage amplitude symmetry index 4 shown in the equation (247) is zero.

On the other hand, when the voltage amplitude symmetry index 4 is larger than the predetermined threshold value, that is, when the voltage amplitude symmetry index 4 has the following relationship with respect to the threshold value V _BRK , it is determined that the input waveform is broken and is not a pure sine wave. In this case, the rotational phase angle, frequency, voltage amplitude, etc., which are measured values, are latched as necessary.

  The idea of the voltage amplitude symmetry index 4 can be similarly applied to the current amplitude. The expression expansion is omitted.

(Synchronous phasor symmetry index)
Next, a method using a differentially synchronized phasor as an index for evaluating the symmetry of the input waveform will be described. The differential synchronization phasor symmetry index is defined as follows:

Here, φ _cosD and φ _tanD are synchronized phasors calculated by the differential synchronized phasor cosine function method and the differential synchronized phasor tangent function method, respectively.

  If the input waveform is a pure sine wave, the differentially synchronized phasor symmetry index shown in equation (250) is zero.

On the other hand, when the differential synchronization phasor symmetry index is larger than a predetermined threshold value, that is, when the relationship is expressed by the following equation with respect to the threshold value φ _BRK , it is determined that the input waveform has broken symmetry and is not a pure sine wave. At this time, the synchronized phasor is estimated using the above-described equation (206).

(Gauge valid / invalid synchronous phasor symmetry index)
Next, a method using a gauge effective / invalid synchronization phasor as an index for evaluating the symmetry of the input waveform will be described.

  First, as shown in the equation (239), the following equation is established from the equations (170), (172), (214), and (216).

Here, SA _P and SD _P are a gauge effective synchronization phasor and a gauge difference effective synchronization phasor, respectively, and SA _Q and SD _Q are a gauge invalid synchronization phasor and a gauge difference invalid synchronization phasor, respectively.

Here, when the absolute value of the difference between the first term and the second term in the expression (252) is defined as a gauge effective / invalid synchronization phasor symmetry index, the difference synchronization phasor symmetry index SAD _sym If it is smaller than the predetermined threshold φ _BRK , it is determined that the input waveform is a sine wave.

On the other hand, when the differential synchronization phasor symmetry index SAD _sym is larger than the predetermined threshold φ _BRK , it is determined that the input waveform is not symmetrical and is not a pure sine wave.

(Estimation of instantaneous voltage fundamental wave value)
The voltage fundamental wave instantaneous value is a real part of the voltage vector and is expressed by the following equation as shown in the above equation (189).

Here, V is the voltage amplitude, phi _V synchronization phasor, SA _P voltage gauge effective synchronization phasor, the SA _Q gauge disable synchronization phasor, f _C is the frequency coefficients.

  If the above calculation methods are combined appropriately, the calculated voltage amplitude and the synchronized phasor itself eliminate the influence of DC offset, non-sinusoidal waveform, correlated Gaussian noise, etc. A value is obtained.

  Similarly, the current fundamental wave instantaneous value is the real part of the voltage vector and is expressed by the following equation similar to the above equation (189).

Here, I is the voltage amplitude, phi _I synchronous phasor current, SA _P gauge valid synchronization phasor, SA _Q gauge disable synchronization phasor, is f _C is the frequency coefficients.

Incidentally, (254) and SA _P, SA _Q in formula, the SA _P, SA _Q in (255) below, but the symbols are the same, the contents of the symbols (values) are different. SA _P and SA _{Q in} equation (254) have values calculated from voltage data, and f _C is also calculated using voltage data. On the other hand, SA _P and SA _{Q in} equation (255) have values calculated from the current data, and f _C is also calculated using the current data. In an embodiment 14 to be described later, an application example to an active filter will be described.

(THD indicator)
For monitoring the power quality, the following two THD indicators are proposed. Note that the smaller the value of the THD index, the higher the power quality. On the contrary, when the value of the THD index is large, it means that the power quality is lowered. Specifically, it indicates that harmonic noise, voltage flicker, etc. exist in the voltage waveform / current waveform.

(Voltage THD index)
A voltage THD index, which is one index for evaluating power quality, is defined as the following equation.

Here, v _LK is the actual voltage instantaneous value, v _rek is the voltage fundamental wave instantaneous value calculated above, and d _V is the voltage DC offset. N is the number of samplings in one cycle of the rated frequency in the power system, and is calculated using the following equation.

Here, f _S is a sampling frequency, and f ₀ is a rated frequency. “Int” is a function that extracts an integer part.

  Similarly, a current THD index, which is another index for evaluating power quality, is defined as the following equation.

Here, i _LK is the actual current instantaneous value, i _rek is the current fundamental wave instantaneous value calculated by the above equation (255), and d _I is the current DC offset. N, f _S and f ₀ are as described above.

  The various calculation formulas presented above can be applied to various AC electric quantity measuring devices. In the following, 14 embodiments are presented as application examples of the AC electric quantity measuring device. Needless to say, the present invention is not limited to these embodiments.

(Embodiment 1)
FIG. 10 is a diagram illustrating a functional configuration of the power measurement device according to the first embodiment, and FIG. 11 is a flowchart illustrating a process flow in the power measurement device.

  As shown in FIG. 10, the power measurement apparatus 101 according to the first embodiment includes an AC voltage / current instantaneous value data input unit 102, a frequency coefficient calculation unit 103, a gauge active power calculation unit 104, a gauge reactive power calculation unit 105, an active voltage The power and reactive power calculation unit 106, the apparent power calculation unit 107, the power factor calculation unit 108, the symmetry breaking determination unit 109, the interface 110, and the storage unit 111 are configured. Here, the interface 110 performs a process of outputting a calculation result or the like to a display device or an external device, and the storage unit 111 performs a process of storing measurement data, a calculation result, or the like.

  In the above configuration, the AC voltage / current instantaneous value data input unit 102 performs a process of reading the voltage instantaneous value and the current instantaneous value from the instrument transformer (PT) and the current transformer (CT) provided in the power system. (Step S101). In addition, each data of the read voltage instantaneous value and current instantaneous value is stored in the storage unit 111.

  The frequency coefficient calculation unit 103 calculates a frequency coefficient based on the calculation process described above (step S102). This frequency coefficient calculation process can be explained as follows when it is explained in a comprehensive manner including the concept of the calculation process described above. That is, in order to satisfy the sampling theorem, the frequency coefficient calculation unit 103 has two adjacent voltage instantaneous value data in the continuous voltage instantaneous value data sampled at a sampling frequency that is twice or more the frequency of the AC voltage to be measured. The value obtained by normalizing the average value of the sum of the differential voltage instantaneous values other than the intermediate time with the differential voltage instantaneous value at the intermediate time among the three differential voltage instantaneous value data representing the distance between the tip voltage instantaneous value data Is calculated as a frequency coefficient.

  The gauge active power calculation unit 104 calculates the gauge active power based on the calculation process described above (step S103). The processing of the gauge active power calculation unit 104 can also be described generally as follows. That is, the gauge active power calculation unit 104 is sampled at two sampling voltage instant value data of the three predetermined voltage points sampled at the sampling frequency and two sampling voltage instant values at an earlier measurement time, and the sampling frequency. The value obtained by a predetermined product difference calculation using the differential current instantaneous value data of two points later in the measurement time out of the three instantaneous current value data sampled at the same time as the predetermined three voltage instantaneous values. Processing to calculate as active power is performed.

  The gauge reactive power calculation unit 105 calculates gauge reactive power based on the above-described calculation process (step S104). More specifically and in general terms, the gauge reactive power calculation unit 105 includes voltage instantaneous value data at two points whose measurement time is late among the three predetermined voltage instantaneous value data consecutively sampled at the sampling frequency, Predetermined product difference based on differential current instantaneous value data of two points later in measurement time out of three instantaneous current value data sampled at the sampling time and sampled at the same time as the predetermined three voltage instantaneous values A process of calculating a value obtained by calculation as a gauge reactive power is performed.

  The active power and reactive power calculator 106 calculates the frequency coefficient calculated by the frequency coefficient calculator 103, the gauge active power calculated by the gauge active power calculator 104, and the gauge reactive power calculator 105. The active power is calculated using the gauge reactive power (step S105). Further, the active power and reactive power calculation unit 106 calculates reactive power using the frequency coefficient calculated by the frequency coefficient calculation unit 103 and the gauge reactive power calculated by the gauge reactive power calculation unit 105 (step) S105).

  The apparent power calculation unit 107 includes a frequency coefficient calculated by the frequency coefficient calculation unit 103, a gauge active power calculated by the gauge active power calculation unit 104, and a gauge reactive power calculated by the gauge reactive power calculation unit 105. Is used to calculate the apparent power (step S106).

  The power factor calculation unit 108 includes the frequency coefficient calculated by the frequency coefficient calculation unit 103, the gauge active power calculated by the gauge active power calculation unit 104, and the gauge reactive power calculated by the gauge reactive power calculation unit 105. Is used to calculate the power factor (step S107).

  The symmetry breaking determination unit 109 determines symmetry breaking using, for example, a gauge power symmetry index (step S108). When the symmetry breaking is not determined (step S108, No), the process proceeds to step S110. On the other hand, when it is determined that the symmetry is broken (step S108, Yes), the measured value (calculated value) is latched (step S109), and then the process proceeds to step S110. In addition, you may use things other than a gauge electric power symmetry parameter | index as a determination parameter | index which determines the breaking of symmetry.

  In the last step S110, the process for determining whether or not to end the above-described overall flow is performed. If it is not the end (step S110, No), the processes from steps S101 to S109 are repeated.

  In the above description, the frequency coefficient, active power, reactive power, apparent power, and power factor are calculated based on the differential voltage instantaneous value data and the differential current instantaneous value data. However, as shown in the above calculation process as well. You may make it calculate based on voltage instantaneous value data and electric current instantaneous value data.

  The contents of the overall processing related to the frequency coefficient calculation unit 103, the gauge active power calculation unit 104, and the gauge reactive power calculation unit 105 when calculating based on the instantaneous voltage value data and the instantaneous current value data are as follows. It is.

  The gauge active power calculation unit 104 samples the voltage instantaneous value data at two points earlier in the measurement time out of the three consecutive voltage instantaneous value data sampled at the sampling frequency and the sampling frequency, Gauge active power is the value obtained by a predetermined product difference calculation using the three instantaneous voltage values and the three instantaneous current data sampled at the same time, and the differential current instantaneous data at the two later measuring times. The process which calculates as follows is performed.

  The gauge reactive power calculation unit 105 samples the voltage instantaneous value data at two points whose measurement time is late among the three consecutive voltage instantaneous value data sampled at the sampling frequency and the sampling frequency. Gauge difference is invalid for the value obtained by the predetermined product difference calculation using the differential current instantaneous value data of two points of late measurement time among the three instantaneous voltage values sampled at the same time as the three instantaneous voltage values. Processing to calculate power is performed.

  The power calculation using the measurement result of the synchronized phasor is as follows. First, the phase angle between voltage and current is obtained using the following equation.

Here, φ _V and φ _i are a voltage synchronous phasor and a current synchronous phasor, respectively. The complex power W is expressed by the following equation using the active power P and the reactive power Q,

The active power P and the reactive power Q are expressed by the following equations using the voltage amplitude V, the current amplitude I, and the synchronous phasor φ _Vi , respectively.

  The active power P can be calculated from the first equation (261), and the reactive power Q can be calculated from the second equation. The power factor can be calculated using the following equation.

(Embodiment 2)
FIG. 12 is a diagram showing a functional configuration of the distance protection device according to the second embodiment, and FIG. 13 is a flowchart showing a flow of processing in the distance protection device.

  As shown in FIG. 12, the distance protection device 201 according to the second embodiment includes an AC voltage / current instantaneous value data input unit 202, a frequency coefficient calculation unit 203, a frequency calculation unit 204, a gauge current calculation unit 205, and a gauge active power calculation. Unit 206, gauge reactive power calculation unit 207, resistance and inductance calculation unit 208, gauge difference current calculation unit 209, gauge difference active power calculation unit 210, gauge difference reactive power calculation unit 211, resistance and inductance calculation unit 212, symmetry breaking A determination unit 213, a distance calculation unit 214, a circuit breaker trip unit 215, an interface 216, and a storage unit 217 are configured. The resistance and inductance calculation unit 208 is a calculation unit based on the gauge power group, and the resistance and inductance calculation unit 212 is a calculation unit based on the gauge differential power group. The interface 216 performs a process of outputting a calculation result or the like to a display device or an external device, and the storage unit 217 performs a process of storing measurement data, a calculation result, or the like. Note that a gauge voltage calculation unit may be provided instead of the gauge current calculation unit 205. Moreover, it may replace with the gauge difference electric current calculation part 209, and the structure provided with a gauge difference voltage calculation part may be sufficient.

  In the above configuration, the AC voltage current instantaneous value data input unit 202 performs a process of reading the voltage instantaneous value and the current instantaneous value from the instrument transformer (PT) and the current transformer (CT) provided in the power system. (Step S201). Note that the read data of the instantaneous voltage value and the instantaneous current value are stored in the storage unit 217.

  The frequency coefficient calculation unit 203 calculates a frequency coefficient based on the calculation process described above (step S202). This frequency coefficient calculation process is the same as or equivalent to the first embodiment. The frequency calculation unit 204 calculates a frequency (actual frequency) based on the frequency coefficient and the sampling frequency (step S203).

  The gauge current calculation unit 205 calculates a gauge current based on the calculation process described above (step S204). The calculation process of the gauge current can be explained as follows when it is explained in a general manner including the concept of the calculation process described above. That is, in order to satisfy the sampling theorem, the gauge current calculation unit 205, for example, square integration of current instantaneous value data of at least three consecutive points sampled at a sampling frequency that is twice or more the frequency of the alternating current to be measured. The current amplitude obtained by the calculation is normalized with the amplitude value of the alternating current, and is calculated as a gauge current. In the above-described calculation formula, as a square integral calculation, among three voltage instantaneous value data, an equation that averages the difference between the square value of the voltage instantaneous value at the intermediate time and the voltage instantaneous value product at other times than the intermediate time. Is illustrated.

  The gauge active power calculation unit 206 calculates the gauge active power based on the calculation process described above (step S205). Further, the gauge reactive power calculation unit 207 calculates the gauge reactive power based on the calculation process described above (step S206). Note that the gauge active power and gauge reactive power calculation processes are the same as or equivalent to those in the first embodiment.

  The resistance and inductance calculator 208 includes a frequency coefficient calculated by the frequency coefficient calculator 203, a gauge current calculated by the gauge current calculator 205, a gauge active power calculated by the gauge active power calculator 206, and The resistance is calculated using the gauge reactive power calculated by the gauge reactive power calculation unit 207 (step S207). In addition, the resistance and inductance calculation unit 208 includes a frequency coefficient calculated by the frequency coefficient calculation unit 203, a gauge current calculated by the gauge current calculation unit 205, and a gauge invalidity calculated by the gauge reactive power calculation unit 207. Inductance is calculated using electric power (step S207).

  Further, the gauge difference current calculation unit 209 calculates a gauge difference current based on the above-described calculation process (step S208). The gauge differential current calculation unit 209 can also be described generally as follows. That is, the gauge differential current calculation unit 209 is sampled at the sampling frequency, and the adjacent 2 in the current instantaneous value data of at least four consecutive points including the current instantaneous value data of the three points used when calculating the gauge current. For example, a value obtained by, for example, square integration calculation of the differential current instantaneous value data of the three points representing the distance between the tips of the current instantaneous value data of the points is normalized with the amplitude value of the alternating current and is calculated as a gauge differential current. In the above formula, as the square integral calculation, the difference between the square value of the differential current instantaneous value at the intermediate time and the differential current instantaneous value product other than the intermediate time among the three differential current instantaneous value data is calculated. An example of an averaging formula is shown.

  The gauge difference active power calculation unit 210 calculates the gauge difference active power based on the calculation process described above (step S209). The processing of the gauge difference active power calculation unit 210 can be described generally as follows. That is, the gauge difference active power calculation unit 210 calculates the three-point differential voltage that represents the distance between the tips of two adjacent voltage instantaneous value data in the predetermined four consecutive voltage instantaneous value data sampled at the sampling frequency. Among the instantaneous value data, the difference voltage instantaneous value data of two points whose measurement time is early and the current instantaneous value data of four points sampled at the same time as the voltage instantaneous value of the predetermined four points sampled at the sampling frequency. A value obtained by a predetermined product difference calculation based on the differential current instantaneous value data of two points whose measurement time is late among the three differential current instantaneous value data representing the tip-to-tip distance between the adjacent two instantaneous current value data. Is calculated as gauge differential active power.

  Further, the gauge difference reactive power calculation unit 211 calculates the gauge difference reactive power based on the above-described calculation process (step S210). The processing of the gauge difference reactive power calculation unit 211 can also be described generally as follows. The gauge differential reactive power calculation unit 211 is a three-point differential voltage instantaneous value that represents the distance between the tips of two adjacent voltage instantaneous value data in the predetermined four consecutive voltage instantaneous value data sampled at the sampling frequency. Among the data, the differential voltage instantaneous value data of two points whose measurement time is late and the current instantaneous value data of four points sampled at the same time as the voltage instantaneous value of the predetermined four points sampled at the sampling frequency are adjacent. A gauge is used to calculate the value obtained by the predetermined product difference calculation using the differential current instantaneous value data of the two points with the later measurement time out of the three differential current instantaneous value data representing the tip-to-tip distance between the two instantaneous current value data. A process for calculating the differential reactive power is performed.

  The resistance and inductance calculation unit 212 includes a frequency coefficient calculated by the frequency coefficient calculation unit 203, a gauge difference current calculated by the gauge difference current calculation unit 209, and a gauge difference calculated by the gauge difference active power calculation unit 210. The resistance is calculated using the active power and the gauge differential reactive power calculated by the gauge differential reactive power calculation unit 211 (step S211). In addition, the resistance and inductance calculation unit 212 is calculated by the frequency coefficient calculated by the frequency coefficient calculation unit 203, the gauge difference current calculated by the gauge difference current calculation unit 209, and the gauge difference reactive power calculation unit 211. The inductance is calculated using the gauge difference reactive power (step S211).

  The symmetry breaking determination unit 213 determines symmetry breaking using, for example, a gauge power symmetry index (step S212). When the symmetry breaking is not determined (No at Step S212), the distance (distance coefficient) to the failure point is calculated (Step S214), and it is further determined whether or not the protection device is activated (Step S215). Here, when it is determined that the protection device is activated (for example, the distance is within the settling range) (step S215, Yes), the circuit breaker is tripped (step S216), and the process proceeds to step S217 to activate the protection device. When it determines with not (step S215, No), it transfers to step S217, without tripping a circuit breaker. If it is determined that the symmetry is broken (step S212, Yes), the measured value (calculated value) is latched (step S213), and then the process proceeds to step S217. In addition, you may use things other than a gauge electric power symmetry parameter | index as a determination parameter | index which determines the breaking of symmetry.

  In the last step S217, it is determined whether or not to end the above-described overall flow. If not (No in step S217), the processes from step S201 to S216 are repeated.

  The frequency obtained in step S203 is an actual frequency. For this reason, unlike the conventional distance protection device, the distance protection device of the second embodiment can automatically correct the system actual frequency. Therefore, even when the system frequency is fluctuated due to an accident, highly accurate distance measurement is possible. Moreover, since the distance protection apparatus of this Embodiment provides the specific distance measurement value, it is applicable also to an accident point location apparatus.

  Note that the distance protection calculation using the measurement result of the synchronized phasor is as follows.

First, when the voltage-current phase angle is φ _vi and the voltage amplitude and the current amplitude are V and I, respectively, the impedance Z is expressed by the following equation:

  Since the resistance that forms the real part of the impedance and the inductance that forms the imaginary part are expressed by the following equations,

  When this device is applied to a distance protection device for a transmission line, the resistance of the transmission line from the place where the distance protection device is arranged to the ground fault point or the short-circuit point can be calculated from the first equation of (264) above. The inductance of the transmission line up to the ground fault point or the short circuit point can be calculated from the second equation of (264).

(Embodiment 3)
FIG. 14 is a diagram illustrating a functional configuration of the step-out protection device according to the third embodiment, and FIG. 15 is a flowchart illustrating a process flow in the step-out protection device.

  As shown in FIG. 14, the step-out protection device 301 according to the second embodiment includes an alternating voltage current instantaneous value data input unit 302, a frequency coefficient calculation unit 303, a gauge current calculation unit 304, a gauge active power calculation unit 305, a gauge Reactive power calculation unit 306, step-out center voltage calculation unit 307, gauge difference current calculation unit 308, gauge difference active power calculation unit 309, gauge difference reactive power calculation unit 310, step-out center voltage calculation unit 311, symmetry breaking determination unit 312, a circuit breaker trip unit 313, an interface 314, and a storage unit 315. The step-out center voltage calculation unit 307 is a calculation unit based on the gauge power group, and the step-out center voltage calculation unit 311 is a calculation unit based on the gauge difference power group. The interface 314 performs a process of outputting a calculation result or the like to a display device or an external device, and the storage unit 315 performs a process of storing measurement data, a calculation result, or the like.

  In the above configuration, the AC voltage / current instantaneous value data input unit 302 performs a process of reading the voltage instantaneous value and the current instantaneous value from the instrument transformer (PT) and the current transformer (CT) provided in the power system. (Step S301). Note that the read voltage instantaneous value and current instantaneous value data are stored in the storage unit 315.

  The frequency coefficient calculation unit 303 calculates a frequency coefficient based on the calculation process described above (step S302). This frequency coefficient calculation process is the same as or equivalent to the first and second embodiments. The gauge current calculation unit 304 calculates a gauge current based on the above-described calculation process (step S303). The gauge active power calculation unit 305 calculates the gauge active power based on the calculation process described above (step S304). The gauge reactive power calculation unit 306 calculates gauge reactive power based on the calculation process described above (step S305). The gauge current, gauge active power, and gauge reactive power calculation processes are the same as or equivalent to those in the second embodiment.

  The step-out center voltage calculation unit 307 includes a frequency coefficient calculated by the frequency coefficient calculation unit 303, a gauge current calculated by the gauge current calculation unit 304, a gauge active power calculated by the gauge active power calculation unit 305, and Then, the step-out center voltage is calculated using the gauge reactive power calculated by the gauge reactive power calculation unit 306 (step S306).

  The gauge difference current calculation unit 308 calculates a gauge difference current based on the above-described calculation process (step S307). The gauge difference active power calculation unit 309 calculates the gauge difference active power based on the above-described calculation process (step S308). The gauge difference reactive power calculation unit 310 calculates gauge difference reactive power based on the above-described calculation process (step S309). Note that the gauge difference current, gauge difference active power, and gauge difference reactive power calculation processes are the same as or equivalent to those of the second embodiment.

  The step-out center voltage calculation unit 311 includes a frequency coefficient calculated by the frequency coefficient calculation unit 303, a gauge current calculated by the gauge current calculation unit 304, a gauge active power calculated by the gauge active power calculation unit 305, and Then, the step-out center voltage is calculated using the gauge reactive power calculated by the gauge reactive power calculation unit 306 (step S310).

  The symmetry breaking determination unit 312 determines the breaking of symmetry using, for example, a gauge power symmetry index or a gauge differential power symmetry index (step S311). Here, when the symmetry breaking is not determined (step S311, No), it is further determined whether to activate the step-out protection device (step S313). Here, when it is determined that the step-out protection device is activated (for example, when the step-out center voltage is smaller than the set value (for example, 0.3 PU)) (step S313, Yes), the circuit breaker is tripped (step S314), When it transfers to step S315 and it determines with not starting a step-out protection apparatus (step S313, No), it transfers to step S315, without tripping a circuit breaker. If it is determined that the symmetry is broken (step S311, Yes), the measured value (calculated value) is latched (step S312), and then the process proceeds to step S315. In addition, you may use things other than a gauge power symmetry index, or a thing other than a gauge difference power symmetry index as a determination index for determining the breaking of symmetry.

  In the last step S315, it is determined whether or not the above-described overall flow is to be ended. If it is not ended (step S315, No), the processing from steps S301 to S314 is repeated.

  In the second embodiment, the embodiment in which the phasor measurement result is applied to the distance protection device has been described. However, also in the third embodiment, the phasor measurement result can be applied to the step-out protection device. .

(Embodiment 4)
FIG. 16 is a diagram illustrating a functional configuration of the time-synchronized phasor measuring device according to the fourth embodiment, and FIG. 17 is a flowchart illustrating a processing flow in the time-synchronized phasor measuring device.

  As shown in FIG. 16, the time-synchronized phasor measuring device 401 according to the fourth embodiment includes an AC voltage instantaneous value data input unit 402, a frequency coefficient calculation unit 403, a gauge differential voltage calculation unit 404, a voltage amplitude calculation unit 405, a rotation. Phase angle calculator 406, frequency calculator 407, DC offset calculator 408, gauge effective synchrophasor calculator 409, gauge invalid synchrophasor calculator 410, synchrophasor calculator (cosine function method) 411, synchrophasor calculator (tangent) Function method) 412, symmetry breaking discriminating unit 413, synchronized phasor estimating unit 414, rotational phase angle latching unit 415, frequency latching unit 416, voltage amplitude latching unit 417, time synchronizing phasor calculating unit 418, interface 419, and storage unit 420. It is configured with. The interface 419 performs a process of outputting a calculation result or the like to a display device or an external device, and the storage unit 420 performs a process of storing measurement data, a calculation result, or the like. In addition, it may replace with the gauge effective synchronous phasor calculation part 409, and the structure provided with a gauge difference effective synchronous phasor calculation part may be sufficient. Moreover, it may replace with the gauge invalid synchronous phasor calculation part 410, and the structure provided with a gauge difference invalid synchronous phasor calculation part.

  In the above configuration, the AC voltage instantaneous value data input unit 402 performs a process of reading the voltage instantaneous value from the instrument transformer (PT) provided in the power system (step S401). Note that the read voltage instantaneous value data is stored in the storage unit 420.

  The frequency coefficient calculation unit 403 calculates a frequency coefficient based on the calculation process described above (step S402). This frequency coefficient calculation process is the same as or equivalent to that of Embodiment 1-3.

  The gauge difference voltage calculation unit 404 calculates a gauge difference voltage based on the above-described calculation process (step S403). More specifically and in general terms, the gauge differential voltage calculation unit 404 is sampled at the sampling frequency, and is at least four consecutive voltages sampled at a sampling frequency that is twice or more the frequency of the AC voltage to be measured. Gauge differential voltage obtained by normalizing the value obtained by, for example, square integral calculation of the differential voltage instantaneous value data of three points representing the distance between the two adjacent voltage instantaneous value data in the instantaneous value data with the amplitude value of the AC voltage. The process which calculates as follows is performed. In the above-described calculation formula, the difference between the square value of the differential voltage instantaneous value at the intermediate time and the differential voltage instantaneous value product other than the intermediate time among the three differential voltage instantaneous value data is calculated as the square integral calculation. An example of an averaging formula is shown.

  The voltage amplitude calculation unit 405 calculates the voltage amplitude using the frequency coefficient calculated by the frequency coefficient calculation unit 403 and the gauge difference voltage calculated by the gauge difference voltage calculation unit 404 (step S404). The rotation phase angle calculation unit 406 calculates the rotation phase angle using the frequency coefficient calculated by the frequency coefficient calculation unit 403 (step S405). The frequency calculation unit 407 calculates a frequency using the frequency coefficient calculated by the frequency coefficient calculation unit 403 (step S406).

  The DC offset calculation unit 408 includes 3 of the 3 points of differential voltage instantaneous value data used when calculating the gauge differential voltage or 4 points of voltage instantaneous value data that is the basis of the 3 points of differential voltage instantaneous value data. The DC offset is calculated using the voltage instantaneous value data of the point and the frequency coefficient calculated by the frequency coefficient calculation unit 403 (step S407).

  The gauge effective synchronization phasor calculation unit 409 calculates a gauge effective synchronization phasor based on the above-described calculation process (step S408). More specifically and in general terms, the gauge effective synchronous phasor calculation unit 409 includes two voltage instantaneous value data with a later measurement time among three consecutive voltage instantaneous value data sampled at the sampling frequency, A first fixed unit vector on the same complex plane as the AC voltage (AC current) to be measured, and a delay by the rotational phase angle calculated by the rotational phase angle calculation unit 406 with respect to the first fixed unit vector Then, a process of calculating a value obtained by a predetermined product difference operation with the second fixed unit vector as a gauge effective synchronous phasor is performed.

  The gauge invalid synchronization phasor calculation unit 410 calculates a gauge invalid synchronization phasor based on the above-described calculation process (step S409). More specifically and in general terms, the gauge invalid synchronization phasor calculation unit 410 includes two instantaneous voltage values at the earlier measurement time of the three instantaneous voltage data used to calculate the effective gauge synchronization phasor. A process of calculating a value obtained by a predetermined product difference calculation using the data and the first and second fixed unit vectors used when calculating the gauge effective synchronization phasor as a gauge invalid synchronization phasor is performed.

  The synchronized phasor calculation unit (cosine function method) 411 applies the calculation process by the above-described cosine function method, and the gauge effective synchronization phasor and gauge invalid synchronization phasor calculation unit 410 calculated by the gauge effective synchronization phasor calculation unit 409. A synchronous phasor is calculated using the calculated gauge invalid synchronous phasor, the rotational phase angle calculated by the rotational phase angle calculation unit 406, and the voltage amplitude calculated by the voltage amplitude calculation unit 405 (step S410).

  Further, the synchronous phasor calculation unit (tangent function method) 412 applies the calculation process based on the tangent function method described above, and the gauge effective synchronization phasor and gauge invalid synchronization phasor calculation unit 410 calculated by the gauge effective synchronization phasor calculation unit 409. The synchronous phasor is calculated using the gauge invalid synchronous phasor calculated in step S1 and the rotational phase angle calculated by the rotational phase angle calculation unit 406 (step S411).

  The symmetry breaking determination unit 413 determines symmetry breaking using, for example, a synchronized phasor symmetry index (step S412). If it is determined that the symmetry is broken (step S412, Yes), the synchronized phasor estimation unit 414 estimates the synchronized phasor (step S413), and the rotational phase angle latch unit 415 latches the rotational phase angle ( In step S414, the frequency is latched by the frequency latch unit 416 (step S415), the voltage amplitude is latched by the voltage amplitude latch unit 417 (step S416), and then the process proceeds to step S418. On the other hand, when it is not determined that the symmetry is broken (step S412, Yes), the time synchronization phasor calculation unit 418 calculates a time synchronization phasor (step S417), and then the process proceeds to step S418. The time synchronization phasor is a difference value between the current synchronization phasor and the synchronization phasor one or several cycles before, and is calculated as follows.

Here, φ _t is the current synchronized phasor, and φ _t-T0 is the synchronized phasor at the specified time (time T0 before the current time).

  In the last step S418, it is determined whether or not to end the above-described overall flow. If it is not completed (No in step S418), the processes from step S401 to S417 are repeated.

(Embodiment 5)
FIG. 18 is a diagram illustrating a functional configuration of the spatially synchronized phasor measuring device according to the fifth embodiment, and FIG. 19 is a flowchart illustrating a processing flow in the spatially synchronized phasor measuring device.

  As shown in FIG. 18, a spatially synchronized phasor measuring device 502 according to Embodiment 5 includes a synchronized phasor / time stamp receiving unit 503, a spatially synchronized phasor calculating unit 504, a control signal transmitting unit 505, an interface 506, and a storage unit 507. It is configured with. This space-synchronized phasor measuring device 502 is arranged at a power control station or the like. Also, in FIG. 18, there are provided synchronized phasor measurement units (PMUs) 501 (PMU 1 and PMU 2) arranged in a substation or the like, and information from these synchronized phasor measurement units 501 is a communication line. 508 is configured to be input through 508. The interface 506 performs a process of outputting a calculation result or the like to a display device or an external device, and the storage unit 507 performs a process of storing measurement data, a calculation result, or the like.

In the above configuration, the synchronized phasor / time stamp receiving unit 503 receives the synchronized phasor measured by the synchronized phasor measuring device 501 arranged elsewhere and the time stamp attached to the synchronized phasor (step S501). The space synchronization phasor calculation unit 504 calculates a space synchronization phasor that is a difference value between the synchronization phasor at the own end and the synchronization phasor at the other end (step S502). The spatial synchronization phasor phi _SP is calculated as follows.

Here, φ ₁ is a synchronized phasor of terminal 1 at a specified time. Φ ₂ is a synchronized phasor of the terminal 2 at the same time, and is calculated as follows.

  Here, t1 is the time tag of the synchronized phasor at terminal 1, and t2 is the time tag of the synchronized phasor at terminal 2. These time tag values preferably use coordinated universal time called UTC (universal time coordinated) using GPS or the like.

  The control signal transmission unit 505 determines the stability / instability of the system using the spatial synchronization phasor calculated by the spatial synchronization phasor calculation unit 504, and outputs a control signal when the system becomes unstable due to step-out. Transmit (step S503).

  In the last step S504, the process for determining whether or not to end the above-described overall flow is performed. If it is not the end (step S504, No), the processes from step S501 to S503 are repeated.

(Embodiment 6)
FIG. 20 is a diagram showing a functional configuration of the transmission line parameter measurement system according to Embodiment 6, and FIG. 21 is a flowchart showing a processing flow in this transmission line parameter measurement system.

  As shown in FIG. 20, the transmission line parameter measurement system according to Embodiment 6 is configured to include two synchronized phasor measuring devices 601 (PMU1) and synchronized phasor measuring devices 602 (PMU2). The synchronized phasor measuring devices 601 and 602 include an instantaneous voltage value from an instrument transformer (PT) provided on a transmission line, an instantaneous current value from a current transformer (CT), a GPS time signal from a GPS device, and the like. Entered. The synchronized phasor measuring device 602 on the terminal 2 side measures its own voltage amplitude and synchronized phasor, and notifies the synchronized phasor measuring device 601 on the terminal 1 side through the communication line 603. The synchronized phasor measuring device 601 calculates its own voltage amplitude and synchronized phasor (step S601), receives the measurement result of the synchronized phasor measuring device 602 (step S602), and uses both measurement results to determine the transmission line parameters. Is calculated (step S603). According to the proposed technique of the present invention, the voltage / current amplitude and the synchronized phasor at both ends can be measured.

  In the last step S604, it is determined whether or not to end the above-described overall flow. If not (No in step S604), the processes from step S601 to S603 are repeated.

  Note that, as shown in the lower part of FIG. 20, the procedure for calculating the transmission line parameters when the transmission line is regarded as a π-type equivalent circuit is as follows.

  First, the measurement result by the instrument transformer (PT) and the current transformer (CT) is expressed by the following equation.

Here, V ₁ , V ₂ , φ _V1 , and φ _V2 are voltage amplitudes and voltage synchronization phasors at each end, respectively, and I ₁ , I ₂ , φ _I1 , and φ _I2 are current amplitudes and currents at each end, respectively. Synchronous phasor. Moreover, the admittance which is a track | line parameter of a power transmission line is represented as follows.

Here, R ₁ and R ₂ are resistors, L is an inductance, and C is a capacitance. Also, according to Kirchhoff's law, the circuit equation is as follows.

  From the equation (270), the following solution is obtained.

  Therefore, the transmission line parameters can be obtained from the equations (269) and (271) as follows.

  In the above equation, “Re” and “Im” mean to take the real part and imaginary part of the complex number, respectively. F is an actual frequency.

(Embodiment 7)
FIG. 22 is a diagram illustrating a functional configuration of the synchronization input device according to the seventh embodiment, and FIG. 23 is a flowchart illustrating a process flow in the synchronization input device.

  As illustrated in FIG. 22, the synchronization input device 701 according to the seventh embodiment includes a voltage measurement unit 702, a frequency calculation unit 703, a voltage amplitude calculation unit 704, a voltage synchronization phasor calculation unit 705, a frequency comparison unit 706, and a voltage amplitude comparison. Unit 707, space synchronization phasor calculation unit 708, synchronization input operation delay time calculation unit 709, synchronization input operation execution unit 710, interface 711, and storage unit 712. The interface 711 performs a process of outputting a calculation result or the like to a display device or an external device, and the storage unit 712 performs a process of storing measurement data, a calculation result, or the like.

  Next, the flow of processing of the synchronization input device 701 will be described with reference to FIGS. The individual functions of each part are based on the above-described calculation formula and overlap with the description in the devices of the first to sixth embodiments. Is omitted.

  The voltage measuring unit 702 receives an instantaneous voltage value from a voltage transformer (PT) provided at one end and the other end of the power system, and measures each voltage (voltage at both ends) (step S701). The frequency calculation unit 703 calculates each frequency (both ends frequency) at the terminals 1 and 2 (step S702). The voltage amplitude calculation unit 704 calculates the voltage amplitudes (terminal voltage amplitudes) at the terminals 1 and 2 (step S703). When the power system is a separated system, the expression representing the voltage measured at each end is as follows.

Here, V ₁ and φ ₁ are the current voltage amplitude and voltage-synchronized phasor at terminal 1, respectively, and V ₂ and φ ₂ are the current voltage amplitude and voltage-synchronized phasor at terminal 2, respectively.

  The voltage synchronization phasor calculation unit 705 calculates each voltage synchronization phasor (both ends voltage synchronization phasor) at the terminals 1 and 2 (step S704), and the frequency comparison unit 706 compares the frequencies at both ends (step S705). In this comparison process, a determination process of the following equation is performed.

Here, f ₁ is the calculated frequency (actual frequency) of the terminal 1, and f ₂ is the calculated frequency (actual frequency) of the terminal 2. Δf _SET is a specified value for determination.

  The voltage amplitude comparison unit 707 compares the voltage amplitudes at both ends (step S706). In this comparison process, a determination process of the following equation is performed.

Here, V ₁ is the calculated voltage amplitude of the terminal 1, and V ₂ is the calculated summer amplitude of the terminal 2. ΔV _SET is a specified value for determination.

  When the conditions of the above equations (274) and (275) are satisfied, the space synchronization phasor calculation unit 708 calculates the space synchronization phasor using the voltage synchronization phasor of the terminals 1 and 2 calculated by the voltage synchronization phasor calculation unit 705. (Step S707).

The synchronization input operation delay time calculation unit 709 calculates a synchronization input operation delay time (synchronization device operation delay time: T _ASY ) (step S708). In addition, the process of this step S708 is performed in the following procedures (substeps).

First, the synchronization input operation delay time calculation unit 709 calculates the synchronization input prediction time T _est using the following equation.

Here, f ₁ and φ ₁ are the current real frequency and voltage-synchronized phasor at the terminal 1, respectively, and f ₂ and φ ₂ are the current real wave number and voltage-synchronized phasor at the terminal 2, respectively. Therefore, the synchronization input prediction time T _est shown in the equation (276) means a time difference corresponding to the spatial synchronization phasor between the terminals 1 and 2.

Note that when a command is transmitted to the synchronous input device, it is necessary to consider the calculation time (logic calculation time) of the device and the transmission time of the control signal. Assuming that the logic calculation time is T _CAL and the control signal transmission time is T _COM , the synchronization input device operation delay time T _ASY and the synchronization input prediction time T _est , and these logic calculation time T _CAL and control signal transmission time T _COM There is a relationship shown in the following equation.

Therefore, the synchronization input device operation delay time _TASY can be calculated based on the following equation.

Returning to this flow, the synchronization input operation execution unit 710 performs the synchronization input operation based on the synchronization input device operation delay time _TASY shown in the equation (279) (step S709).

  In the last step S710, the process for determining whether or not to end the above-described overall flow is performed. If not (No in step S710), the processes from step S701 to S709 are repeated.

(Embodiment 8)
In the eighth embodiment, a frequency measurement device and a frequency change rate measurement device will be described. In addition, the following description demonstrates as an example the case where the frequency measurement method mentioned above is applied to the starting logic at the time of starting the independent operation detection apparatus which is one of the monitoring control apparatuses.

  First, a typical frequency change rate determination formula in the isolated operation detection device is shown. This determination formula is as follows.

Here, f _t , f _t-T0 , and df _SET are a specified time T 0 (for example, three cycle times of the rated frequency) and a starting settling value for detecting an independent operation, respectively.

  According to the frequency coefficient measurement method of the present invention described above, the symmetry breaking of the voltage waveform can be determined by various symmetry indices such as a rotational phase angle symmetry index. In addition, by latching already measured data, it is possible to avoid the influence on the measurement result such as voltage flicker. For this reason, it is possible to provide a highly accurate frequency measuring device and frequency change rate measuring device.

  Since the frequency coefficient measuring method of the present invention is superior to the conventional method in detecting the phase jump, it is possible to avoid erroneous start due to the phase jump. In addition, in the conventional apparatus, various measures are taken in order to avoid erroneous start of phase jump, so that the detection time becomes long. For this reason, by using the method of the present application, it is possible to provide a high-speed and highly reliable isolated operation detection device that suppresses erroneous starting. For the phase jump detection, a detailed simulation result is presented in case 4 described later.

(Embodiment 9)
In the ninth embodiment, an overvoltage protection device and a low voltage protection device will be described. In addition, since most of the protection control devices in Japan employ 30 ° sampling (α = 30 °), the following description is an example of the case of 30 ° sampling. First, the frequency coefficient in the case of 30 ° sampling is obtained as follows from the above equation (12).

By substituting the frequency coefficient f _C into the equation (22), a calculation formula for overvoltage protection is proposed as shown in

Here, V is an actual voltage amplitude, V _gd is a gauge differential voltage, and V _high is a settling value.

  Similarly, in the case of 30 ° sampling, a calculation formula for low voltage protection shown in the following formula is proposed.

Here, V is an actual voltage amplitude, V _gd is a gauge differential voltage, and V _low is a settling value.

  The above two formulas use only the differential voltage. For this reason, the overvoltage protection device and the low voltage protection device having these calculation formulas have a very small influence of the DC offset. Therefore, it is possible to reduce the influence of CT saturation and greatly contribute to high-speed operation of overvoltage or undervoltage protection.

(Embodiment 10)
In the ninth embodiment, the 30 ° sampling overvoltage protection device has been described. In the tenth embodiment, a 30 ° sampling overcurrent protection device will be described.

  First, the frequency coefficient obtained by the above equation (280) is substituted into the equation (28), and a calculation formula for overcurrent protection shown in the following equation is proposed.

Here, I is an actual current amplitude, I _gd is a gauge differential current, and I _SET is a settling value.

  The above formula uses only the differential current. For this reason, in the overcurrent protection device having these calculation formulas, the influence of the DC offset becomes very small. Therefore, the influence of CT saturation can be reduced, which can greatly contribute to the high-speed operation of overcurrent protection.

(Embodiment 11)
In the eleventh embodiment, a current differential protection device will be described. Here, two examples of the current phase difference measurement method and the synchronized phasor measurement method will be described as examples.

(Current phase difference measurement method)
First, the current measured at each end of the transmission line (terminals 1 and 2) or at each end of the electrical equipment (transformer, generator, etc.) located across the transmission line can be expressed as: it can.

Here, I _{1 and} I ₂ are current amplitudes at the terminals 1 and ₂ , respectively. Φ ₁₂ is the phase difference of the current vector between the terminals 1 and 2. As the current vector, it is preferable to use a differential current that is less affected by CT saturation.

  The instantaneous value comparison calculation formula as the current differential protection device is as follows.

When the above equation is satisfied, it is possible to determine that the failure is within the ward. When the communication time is taken into consideration, the current vector phase difference φ ₁₂ is corrected as follows.

Here, f is an actually measured frequency and T _transfer is a communication time. Calculation may be performed by substituting the result of equation (286) into equation (285).

(Synchronous phasor measurement method)
In this method, the current amplitude and the current-synchronized phasor in each end of the transmission line (terminals 1 and 2) or electrical equipment (transformer, generator, etc.) at each end located across the transmission line are measured. These current amplitudes and currents when using a current-synchronized phasor can be expressed by

Here, I ₁ and φ _I1 are the current amplitude and current-synchronized phasor at the current time at the terminal 1, respectively. Similarly, I ₂ and φ _I2 are the current amplitude and current-synchronized phasor at terminal 2, respectively. As a current vector to be used, it is preferable to use a differential current that is less affected by CT saturation.

  The instantaneous value comparison calculation formula as the current differential protection device is as follows.

  When the above equation is satisfied, it is possible to determine that the failure is within the ward.

  Moreover, you may use the instantaneous value comparison calculation formula shown to following Formula as a current differential protective device.

  When the above equation is satisfied, it is possible to determine that the failure is within the ward.

  In these current differential protection devices, it is needless to say that time synchronization between the terminals 1 and 2 is necessary, and comparison must be made using instantaneous values or phase angles at the same time. It goes without saying that the information transmission time between the terminals 1 and 2 must be taken into account when synchronizing.

(Embodiment 12)
In the twelfth embodiment, several symmetrical voltage dividing devices, symmetrical current measuring devices, symmetrical power measuring devices, and symmetrical impedance measuring devices will be described.

(Symmetric voltage divider 1)
The three-phase voltage of the power system is measured as follows.

Here, V _A , V _B , and V _C are the voltage amplitudes of the A phase, the B phase, and the C phase, respectively. Φ _VBA and φ _VCA are the phase difference between the B phase voltage and the A phase voltage and the phase difference between the C phase voltage and the A phase voltage, respectively. Note that these voltage amplitude and phase difference are measured by the proposed method of the present application (phase angle difference calculation method between both buses having the same frequency at both ends).

(Symmetric voltage divider 2)
The three-phase voltage of the power system is measured as follows.

Here, V _A , V _B , V _C , φ _VA , φ _VB , and φ _VC are the voltage amplitudes and synchronous phasors of A phase, B phase, and C phase, respectively. These voltage amplitudes and phase differences are measured by the proposed method of the present application.

  Next, using the symmetric coordinate method, zero-phase, positive-phase, and negative-phase voltages are calculated as in the following equation.

Here, the coefficients α and α ² of the symmetric transformation matrix are expressed by the following equations.

α = e ^{j2π / 3} , α ² = e ^{-j2π / 3}

  Conventionally, devices that measure zero-phase, positive-phase, and reverse-phase voltages measure the symmetrical voltage by the symmetric coordinate method, but it is assumed that the actual frequency is the rated frequency. On the other hand, if the actual frequency is not the rated frequency, a measurement error occurs. In contrast, the present invention calculates the phase angle difference between the phases (B phase and A phase, C phase and A phase) using the actual frequency calculation (measurement) result, or calculates the direct synchronized phasor. doing. For this reason, for example, even when the actual frequency deviates from the rated frequency with reference to the A phase, automatic frequency correction is performed, and high-precision measurement is possible.

(Symmetric current measuring device 1)
The three-phase current of the power system is measured as follows.

Here, I _A , I _B , and I _C are voltage amplitudes of the A phase, the B phase, and the C phase, respectively. Φ _IBA and φ _ICA are the phase difference between the B phase current and the A phase current and the phase difference between the C phase current and the A phase current, respectively. These current amplitude and phase difference are measured by the proposed method of the present application.

(Symmetric current measuring device 2)
The three-phase current of the power system is measured as follows.

Here, I _A , I _B , I _C , φ _IA , φ _IB , and φ _IC are current amplitudes and synchronous phasors of A phase, B phase, and C phase, respectively. These current amplitude and phase difference are measured by the proposed method of the present application.

  Next, using the symmetric coordinate method, zero-phase, positive-phase, and reverse-phase currents are calculated as in the following equation.

  The symmetrical current measuring device has the same high-accuracy characteristics as the symmetrical voltage measuring device.

(Symmetric power measurement device)
By using the symmetrical voltage and current measured by the above-described symmetrical voltage measuring method and the symmetrical current measuring method, the symmetrical power shown by the following equation can be obtained.

Here, P ₁ , P ₂ , and P ₃ are active powers of zero phase, positive phase, and negative phase, respectively, and Q ₁ , Q ₂ , and Q ₃ are zero phase, positive phase, and negative phase, respectively. Reactive power.

(Symmetric impedance measuring device)
Using the symmetrical voltage and current measured by the above-described symmetrical voltage measurement method and symmetrical current measurement method, the symmetrical impedance shown in the following equation can be obtained.

Here, Z ₀ , Z ₁ , Z ₂ are impedances of zero phase, positive phase, and negative phase, respectively, and R ₀ , R ₁ , R ₂ are resistances of zero phase, positive phase, and negative phase, respectively. L ₀ , L ₁ , and L ₂ are in-components of zero phase, normal phase, and reverse phase, respectively.

  The above calculation formula can be applied to all calculations of symmetrical components related to the power system protection control device.

(Embodiment 13)
In the thirteenth embodiment, a high-speed instantaneous value estimation method suitable for a differential protection control device will be described.

  When differential protection is implemented, time-series data of the other end is received and a communication normal stamp is attached to each point. Further, when performing the differential protection operation, several time series data (for example, 12 points) stored in the AI table (AI: analog input data) are used. However, if an instantaneous failure or the like of the communication line occurs, the current data cannot be received. Therefore, all the 11-point data stored in the already received AI table are also invalidated, and all the next AI table By the time the data is normal, the differential protection operation is locked. In such a differential protection operation logic, high-speed performance as a protection device is impaired. The technique of this embodiment improves this point.

  First, according to the frequency coefficient measurement method using a gauge voltage group, the frequency coefficient can be calculated using the following equation.

Here, v _t , v _tT , and v _t−2T are current voltage instantaneous values one step before and two steps before, respectively. It is assumed that the frequency coefficient does not change suddenly, and a value calculated from already received data is used. Therefore, the instantaneous value estimated value at the present time can be estimated using the voltage instantaneous value one step before and two steps before as shown in the following equation.

  When an instantaneous failure occurs in the communication line, the current instantaneous value data is estimated using the above and stored in the AI table. This method ensures the high speed of the protection device.

(Embodiment 14)
In the fourteenth embodiment, a harmonic current compensator will be described. In the following description, the harmonic current compensator will be described as an example when applied as an active filter of a power system.

  First, the active filter output current in the single-phase circuit is obtained as follows.

Here, i _AF is an active filter output current, i _L is an actual alternating current instantaneous value, i _re is a fundamental wave instantaneous value, I is a fundamental wave current amplitude, and φ _I is a current synchronous phasor. Further, when the expression (255) is substituted into the above expression, the following expression is obtained.

Here, SA _P is a gauge effective synchronization phasor, SA _Q is a gauge invalid synchronization phasor, and f _C is a frequency coefficient. If the above equation is used, the active filter output current can be calculated directly from the time-series input data.

  Next, the usefulness and effects of the present invention will be described using numerical examples from cases 1 to 6. First, parameters of case 1 are as shown in Table 2 below.

  First, when using the parameters of case 1, the input waveform is displayed as a cosine function as in the following equation.

  FIG. 24 is a diagram illustrating frequency coefficients calculated using the parameters of case 1. In FIG. As can be seen from FIG. 24 and the following equation (representing equation (8)), the frequency coefficient is a cosine function.

As shown in FIG. 24, the frequency coefficient decreases as the frequency increases, and varies between 1 and -1. When the frequency coefficient is 1, the frequency is zero and is so-called direct current. When the frequency coefficient is −1, the frequency is f _S / 2, which is half the sampling frequency.

  Here, the equation (13) representing the rotational phase angle is shown again below.

  According to the above expression (304), the rotational phase angle can take a positive or negative value, but in reality, as shown in FIG. 25, the rotational phase angle is always positive and is between 0 and 180 degrees. When the actual frequency is less than half of the sampling frequency, the magnitude of the rotational phase angle is directly proportional to the magnitude of the actual frequency. When the actual frequency is 1/4 of the sampling frequency, the rotation phase angle is 90 degrees and the frequency coefficient is zero.

  The optimum sampling frequency for the power system protection control device is four times the rated frequency. The term “optimum” here means to reduce the calculation load. Therefore, a sampling frequency of 200 Hz is recommended for a 50 Hz system, and a 240 Hz sampling frequency is recommended for a 60 Hz system.

  FIG. 26 is a gain diagram of frequency measurement calculated using the parameters of case 1. The following formula is used to calculate this gain.

Here, f ₁ is a frequency measurement value and f ₀ is an input theoretical frequency. Thus, if the frequency to be measured is less than half the sampling frequency of 600 Hz (300 Hz or less), frequency measurement without a theoretical error is possible. Note that this result is consistent with the sampling theorem.

  Next, measurement results (calculation results) using the parameters of case 2 will be described with reference to the drawings in FIGS. 27 to 32 are measurement results calculated with the parameters of case 2, respectively. FIG. 27 shows frequency coefficients, FIG. 28 shows instantaneous voltage, DC offset, gauge voltage and voltage amplitude, and FIG. 30 shows the rotational phase angle and the actually measured frequency, FIG. 30 shows the gauge effective synchronization phasor and the gauge invalid synchronization phasor, FIG. 31 shows the present application phasor and the conventional instantaneous value synchronization phasor, and FIG. 32 shows the time synchronization phasor. The parameters for case 2 are as shown in Table 3 below.

  According to Table 3, the real number instantaneous value function of the input waveform is expressed as follows.

  Further, the frequency coefficient when the input waveform shown in the above equation (306) is an instantaneous voltage value is obtained as follows.

  If the actual frequency is greater than 1/4 of the sampling frequency, the sign of the frequency coefficient is negative. As shown in FIG. 27, it can be seen that the measurement result and the theoretical value coincide with each other and the measurement is performed correctly.

  Further, the direct current offset when the input waveform shown in the above equation (306) is used as the instantaneous voltage value is obtained as follows.

  As shown in FIG. 28, the calculated value of the DC offset coincides with the input value and is measured correctly.

  Since the gauge voltage is a rotation invariant of the AC voltage, the gauge voltage after subtracting the DC offset from the instantaneous voltage value is obtained as follows.

  From the result of the above equation, the voltage amplitude is obtained as follows.

  The result of the above formula is in agreement with the input data in FIG. For ease of understanding, a DC offset component is added to the voltage amplitude in FIG.

  Further, from the result of the equation (307), the rotational phase angle is obtained as follows.

  When the frequency coefficient is negative, the rotational phase angle is greater than 90 degrees. As shown in FIG. 29, it can be seen that the measurement results agree with the theoretical values and are measured correctly.

  From the above equation (311), the actual frequency is obtained as follows.

  As shown in FIG. 29, it can be seen that the actually measured frequency matches the above-mentioned equation (312) and the input data in Table 2.

  Further, as shown in FIG. 30, it can be seen that the gauge effective synchronization phasor is equal to the gauge invalid synchronization phasor one step before.

  FIG. 31 is a diagram showing the present synchronized phasor calculated with the parameters of case 2 in comparison with a conventional instantaneous value synchronized phasor. In FIG. 31, the synchronous phasor of the present application is indicated by a black triangular mark, and the instantaneous value synchronous phasor disclosed in Patent Document 3 is indicated by a black circular mark.

  In FIG. 31, the synchronous phasor of the present application is a time-dependent amount and fluctuates in the range of −π to + π. Here, when the present synchronized phasor becomes positive, it coincides with the instantaneous value synchronized phasor. When the synchronized phasor of the present application is negative, the instantaneous value synchronized phasor does not become negative, but the absolute value is the same (sign reciprocal).

  The calculation formula of the instantaneous value synchronous phasor shown in Patent Document 3 (hereinafter referred to as “conventional invention” in this section) is as follows.

  Thus, the instantaneous value synchronization phasor according to the conventional invention is always positive. Therefore, in the conventional invention, there is an inversion region of the absolute end phase angle (the phase angle changes between 0 and π counterclockwise or clockwise), and the absolute phase angle rotates counterclockwise in the inversion region. It is not possible to accurately determine whether it is rotating or rotating clockwise. Further, in the conventional invention, when calculating a time-synchronized phasor or a space-synchronized phasor that is a difference between both absolute phase angles, an accurate value cannot be obtained in the phase angle inversion region. For this reason, in the conventional invention, the value of the previous step is latched.

  On the other hand, since the present invention is a method using a symmetric group, the absolute phase angle in the group synchronous phasor measurement method always changes in one direction counterclockwise between −π and π. There is no need to latch the difference. Therefore, an accurate time-synchronized phasor or space-synchronized phasor can be determined, which is very effective in high-speed protection control. The concept of noise processing is different between the present invention and the conventional invention. The conventional invention uses the least squares method, whereas the present invention reduces noise by increasing the number of symmetric groups.

  Further, the time synchronization phasor, which is the difference value between the current synchronization phasor and the synchronization phasor one cycle before, is obtained as follows when the rated frequency is 60 Hz.

  As shown in FIG. 32, the measurement result of the time synchronization phasor agrees with the theoretical value.

  Next, parameters of case 3-5 will be described. Case 3-5 is a Benchmark test case published in pp 47-51 of Non-Patent Document 1. For simplicity, the DC offset in the input waveform of case 3-5 is zero.

  Next, the measurement results using the parameters of case 3 will be described with reference to the drawings of FIGS. 33 to 38 are measurement results calculated with the parameters of case 3, respectively. FIG. 33 shows frequency coefficients, FIG. 34 shows instantaneous voltage, gauge differential voltage and voltage amplitude, and FIG. A synchronized phasor of the cosine function method, a synchronized phasor of the tangent function method and a symmetry breaking determination flag, FIG. 36 shows a synchronized phasor, FIG. 37 shows a voltage amplitude, and FIG. 38 shows a time synchronized phasor. The parameters for case 3 are as shown in Table 4 below. This parameter is defined as “G.2 Magnitude step test (10%)” included in the Benchmark test.

  First, in Case 3, the real instantaneous value function of the input waveform is expressed as follows.

Here, φ _C is the phase angle of the AC voltage before the sudden state change, and is calculated online.

  Further, the frequency coefficient when the input waveform shown in the above equation (315) is an instantaneous voltage value is obtained as follows.

  As shown in FIG. 33, it can be seen that stable values are obtained except for several points after the sudden change of state.

  Moreover, the gauge differential voltage in the steady state before the amplitude change is obtained as follows.

  Therefore, the voltage amplitude in the steady state before the amplitude change is obtained as follows.

  The result of the above formula is consistent with the measurement result of FIG. 34 and the input data of Table 4 above, and it can be seen that the measurement is correctly performed.

  The gauge differential voltage in the steady state after the amplitude change is obtained as follows.

  Therefore, the voltage amplitude in the steady state after the amplitude change is obtained as follows.

  It can be seen that the result of the above equation agrees with the measurement result of FIG. 34 and the input data of Table 4.

  Referring to FIG. 35, in the steady state, the AC voltage is symmetric, and the synchronized phasor of the cosine function method and the synchronized phasor of the tangent function method are completely the same. When the AC voltage changes suddenly, the results of the cosine function method synchronized phasor and the tangent function method synchronized phasor do not agree with each other, and it is shown that the symmetry is broken.

  In this way, by using the synchronized phasor measurement result of the cosine function method or the tangent function method, it is possible to determine whether or not the input waveform has symmetry. When the symmetry is broken, normal change can be maintained by performing synchronous phasor estimation calculation using equation (206).

  When there is symmetry, the voltage amplitude is obtained from the gauge differential voltage and the frequency coefficient. On the other hand, when the symmetry is broken, the already calculated voltage amplitude is latched. By doing so, as shown in FIG. 37, it is possible to prevent a vibrational transient state from occurring.

  In addition, as a comparison object, refer to Figure G.4-Magnitude step test example (simulation, 1 cycle FFT based algorithm) of P51 of Non-Patent Document 1. In this simulation, since the Fourier transform is performed, the voltage amplitude before the sudden change of the voltage amplitude is changed. Further, in Non-Patent Document 1, the actual frequency before and after the sudden change in voltage amplitude is the system rated frequency. On the other hand, in the present invention, a stable measurement result is obtained even though the actual frequency is 62.14 Hz.

  In addition, a time-synchronized phasor that is a difference between the current synchronized phasor and a point before one cycle of the rated frequency 60 Hz is obtained as follows.

  As shown in FIG. 38, it can be seen that the result of the above formula (theoretical value) and the measurement result of FIG. The absence of a transient state means that the synchronized phasor estimation calculation is correct.

  Next, the measurement results using the parameters of case 4 will be described with reference to the drawings of FIGS. 39 to 43 are measurement results calculated with the parameters of case 4, respectively. FIG. 39 shows frequency coefficients, FIG. 40 shows instantaneous voltage, gauge differential voltage and voltage amplitude, and FIG. A synchronized phasor of the cosine function method, a synchronized phasor of the tangent function method, and a symmetry breaking determination flag, FIG. 42 shows a synchronized phasor, and FIG. 43 shows a time synchronized phasor. The parameters for case 4 are as shown in Table 5 below. This parameter is defined as “G.3 Phase step test (90 °)” included in the Benchmark test.

  First, in Case 4, the real instantaneous value function of the input waveform is expressed as the following equation.

Here, φ _C is the phase angle of the AC voltage before the sudden state change, and is calculated online.

  Further, the frequency coefficient when the input waveform shown in the above equation (322) is an instantaneous voltage value is obtained as follows.

  As shown in FIG. 39, it can be seen that stable values are obtained except for several points after the sudden change of state.

  Moreover, the gauge differential voltage in the steady state before the amplitude change is obtained as follows.

  Therefore, the voltage amplitude in the steady state before the amplitude change is obtained as follows.

  It can be seen that the result of the above equation is consistent with the input data in Table 5 above.

  Referring to FIG. 41, in a steady state, the AC voltage is symmetric, and the synchronized phasor of the cosine function method and the synchronized phasor of the tangent function method are completely the same. When the AC voltage changes suddenly, the results of the cosine function method synchronized phasor and the tangent function method synchronized phasor do not agree with each other, and it is shown that the symmetry is broken.

  As can be seen from FIG. 42, when there is symmetry, the result of the synchronized phasor measurement of the cosine function method or the tangent function method may be used. When the symmetry is broken, the normal change is maintained by performing the synchronized phasor estimation calculation according to the equation (206). There is a 90 degree sudden change between the two steady states, but there is no oscillatory transient.

  In addition, a time-synchronized phasor that is a difference between the current synchronized phasor and a point before one cycle of the rated frequency 60 Hz is obtained as follows.

  However, the time-synchronized phasor changes as follows during one cycle after the phase is suddenly changed by 90 degrees.

  Next, measurement results using the parameters of case 5 will be described with reference to FIGS. 44 to 50. 44 to 50 show the measurement results calculated using the parameters of case 5, FIG. 44 shows the frequency coefficient, FIG. 45 shows the instantaneous voltage, gauge differential voltage and voltage amplitude, and FIG. The synchronized phasor of the cosine function method, the synchronized phasor of the tangent function method and the symmetry breaking discrimination flag, FIG. 47 shows the synchronized phasor, FIG. 48 shows the rotational phase angle, FIG. 49 shows the actual frequency, and FIG. 50 shows the time synchronized phasor. It is shown. The parameters for case 5 are as shown in Table 6 below. This parameter is defined as “G.4 Frequency step test (+5 Hz)” included in the Benchmark test.

  First, in Case 5, the real instantaneous value function of the input waveform is expressed as the following equation.

Here, φ _C is the phase angle of the AC voltage before the sudden state change, and is calculated online.

  In addition, in the frequency coefficient when the input waveform shown in the above equation (328) is an instantaneous voltage value, the frequency coefficient in the steady state before the frequency change is obtained as follows.

  On the other hand, the frequency coefficient in the steady state after the frequency change is obtained as follows.

  As shown in FIG. 44, it can be seen that stable values are obtained except for two points after the sudden change of state.

  The gauge differential voltage in the steady state before the frequency change is obtained as follows.

  On the other hand, the gauge differential voltage in the steady state after the frequency change is obtained as follows.

  Therefore, the voltage amplitude is obtained as follows.

  It can be seen that the result of the above equation is consistent with the input data in Table 6 above.

  Referring to FIG. 46, in the steady state, the AC voltage is symmetric, and the synchronized phasor of the cosine function method and the synchronized phasor of the tangent function method completely coincide with each other. When the AC voltage changes suddenly, the results of the cosine function method synchronized phasor and the tangent function method synchronized phasor do not agree with each other, and it is shown that the symmetry is broken.

  As can be seen from FIG. 47, when there is symmetry, the result of the synchronized phasor measurement of the cosine function method or the tangent function method may be used. When the symmetry is broken, the normal change is maintained by performing the synchronized phasor estimation calculation according to the equation (206).

  When there is symmetry, the correct rotational phase angle can be obtained by the frequency coefficient method. On the other hand, when the symmetry is broken, the already calculated rotational phase angle is latched. By doing so, as shown in FIG. 48, a vibrational transient state can be prevented.

  As shown in FIG. 49, it can be seen that the measurement results before and after the sudden frequency change coincide with the input data in Table 6. If there is symmetry, the frequency can be obtained correctly by the frequency coefficient method. On the other hand, when the symmetry is broken, the already calculated frequency is latched. By doing so, as shown in FIG. 49, it is possible to prevent a vibrational transient state from occurring.

  Further, in the steady state before the change, the time synchronization phasor which is the difference value between the current synchronization phasor and the synchronization phasor at the previous cycle is obtained as follows when the rated frequency is 60 Hz.

  In the steady state after the change, the time synchronization phasor, which is the difference value between the current synchronization phasor and the synchronization phasor at the previous cycle, is obtained as follows when the rated frequency is 60 Hz.

  As shown in FIG. 50, the measurement result of the time-synchronized phasor before and after the change agrees with the theoretical value.

  Next, simulation results using the parameters of case 6 will be described with reference to the drawing of FIG. FIG. 51 is a diagram showing the operation of the synchronization input device when executing a simulation using the parameters of case 6. The parameters for case 6 are as shown in Table 7 below, and the basic parameters necessary for the operation analysis of the synchronization input device are shown.

  According to the parameters of case 6 shown in Table 7, the voltage real number instantaneous value function at both ends is expressed as the following equation.

  Further, according to Table 7, the frequency difference between both terminals can be calculated as follows.

  Δf = 50.1-47.5 = 2.6 (Hz)

Further, the estimated synchronization time T _est can be calculated online using the above equation (276).

Table 8 below is a table showing a partial result of the simulation using the parameters of case 6, and FIG. 51 is a diagram showing the result. In this simulation, “T _CAL + T _COM ” (logic calculation time + control signal transmission communication time) shown in the equation (278) is set to 15 ms.

In Table 8 above, the synchronization input control delay time T _ASY is about 16.5 ms in the simulation step 19 and is longer than 15 ms of “T _CAL + T _COM ”. _est becomes a positive value, enabling synchronous input. On the other hand, in the simulation step 20, the value of the synchronization closing control delay time T _ASY is about 14.9 ms, and the synchronization closing predicted time T _est becomes a negative value. In this case, 2π is added to the spatial synchronization phasor to calculate the synchronization input prediction time T _est . In FIG. 51, when the control delay time indicated by the black triangle mark slightly exceeds 0.03S (30 ms), it jumps up greatly. This point corresponds to between simulation steps 19 and 20 in Table 8. .

  The conventional synchronous input device can be input only when the frequency difference between both ends is very small (for example, within 0.5 Hz). However, in the present invention, even when there is a large frequency difference such as 2.6 Hz. Synchronous input is possible. As described above, the synchronous input device according to the present invention can be input at a higher speed than the conventional synchronous input device.

(Embodiment 15)
Embodiment 1-14 of the embodiment, a frequency at least twice the actual frequency according sampling theorem defines a sampling frequency f _S, the calculation of the various symmetry groups using the required number of data obtained by the sampling frequency f _S I went. On the other hand, in the present embodiment, the sampling frequency (first sampling frequency) that means the reciprocal of the measurement period of the grid electricity quantity and the sampling frequency (first sampling frequency) that means the reciprocal of the extracted data period when calculating various symmetric groups. 2 sampling frequency) is proposed. Hereinafter, the former (first sampling frequency) is defined as a data collection sampling frequency, and the latter (second sampling frequency) is defined as a symmetric group sampling frequency. When defined in this way, the symmetric group sampling period that is the reciprocal of the symmetric group sampling frequency (second sampling frequency) corresponds to “T” described in Embodiment 1-14. If a data collection sampling period that is the reciprocal of the data collection sampling frequency (first sampling frequency) is represented by “T ₁ ”, a relationship of T> T ₁ is established between these T and T _1. .

FIG. 52 is a diagram illustrating a gauge voltage group and a gauge differential voltage group on a complex plane. In FIG. 52, the gauge differential voltage group {v ₂ (t), v ₂ (tT), v ₂ (t−2T)} constituted by the interval of the symmetrical group sampling period T defined above is a circle from the origin O. It is composed of four voltage vectors v ₁ (t), v ₁ (tT), v ₁ (t−2T), and v ₁ (t−3T) indicated by solid-line arrows directed toward the circumference. The gauge differential voltage group is also shown in FIG. 1, but here, in order to distinguish it from FIG. 1, the phase on the complex plane is shown by being shifted by 90 °. On the other hand, four voltage vectors v ₁ (tT ₁ ), v ₁ (tTT ₁ ), v ₁ (t-2T-T ₁ ), v ₁ (t-3T- T ₁ ) is delayed by the data collection sampling period T ₁ from the four voltage vectors v ₁ (t), v ₁ (tT), v ₁ (t-2T), and v ₁ (t-3T) indicated by solid arrows. Shows a set of components.

  Next, a calculation formula for calculating the frequency is derived using the gauge differential voltage group shown in FIG. The following explanation overlaps with the mathematical expressions (equations (1) to (16)) described with reference to FIG. 1, but in the sense that it holds even when the gauge differential voltage group is at an arbitrary position on the complex plane. I think the explanation is meaningful.

  First, the three differential voltage vectors shown in FIG. 52 can be expressed by the following equations.

  Here, V is the amplitude of the alternating current component of the instantaneous voltage. Further, ω is a rotational angular velocity and is expressed by the following equation.

Here, f is a real frequency. Further, T in the equation (337) is the symmetric group sampling period T defined above, and the following relationship is established with the symmetric group sampling frequency f _s .

(Frequency coefficient)
Similarly to the case described with reference to FIG. 1, the frequency coefficient f _c can be expressed using the following equation.

In the above equation, v ₂₁ , v ₂₂ , and v ₂₃ are the real part or imaginary part of the members of the gauge differential voltage group, respectively. For example, if it is a real part, it can be expressed as follows.

  Here, when the real part of the differential voltage vector is substituted into the numerator of the above equation (340), the calculation is performed as follows.

  Further, when the real part of the differential voltage vector is substituted into the denominator of the above equation (340), the following equation is calculated.

Above (342) and (343) where the frequency coefficient f _c as the cosine function value of the rotational phase angle obtained by the following equation.

The frequency coefficients f _c, as shown in the following (345) - (348) below can be obtained from the imaginary part of the differential voltage vector.

  Similar to the calculation result of the real part, the frequency coefficient is a cosine function value of the rotation phase angle. The above result is none other than that the gauge differential voltage group has symmetry and the frequency coefficient is a rotation invariant of the gauge differential voltage group.

(Rotation phase angle)
From above (344) or (348) wherein the rotational phase angle alpha, the frequency coefficients f _c, can be calculated as follows.

The frequency coefficient f _c satisfies the condition of the following expression.

  If the above conditional expression is not satisfied, it can be determined that the input waveform is not an AC waveform.

(Calculation of actual frequency by rotational phase angle)
The rotational phase angle α can be expressed as follows using the actual frequency f and the sampling frequency f _s .

Therefore, the (349) and (351) below, actual frequency f, using the sampling frequency f _s and the frequency coefficients f _c, can be calculated as follows.

  The results shown in the equations (349) to (352) are the same as the results of the above equations (13) to (16) derived using FIG. Therefore, it has been proved that the results shown in the above equations (13) to (16) hold even when the gauge differential voltage group is at an arbitrary position on the complex plane.

By the way, the concept of the embodiment 1-14 is to increase the number of data by reducing the sampling period (increasing the sampling frequency) and increasing the frequency of measurement using the increased continuous data. The basic idea was to calculate the amount of AC electricity, including the coefficient. However, in the method of simply increasing the number of data, the rotational phase angle α also decreases as the number of data increases, and if the harmonic noise is large, the calculation results vary due to the influence of the harmonic noise. It is also expected that the calculation accuracy cannot be improved. Therefore, even when the data necessary for the calculation is increased, the influence of the harmonic noise can be reduced while maintaining the preferable rotational phase angle α value so that the rotational phase angle α value does not decrease. The present embodiment introduces the concept of a symmetric group sampling period T (symmetric group sampling frequency f _s ) and a data collection sampling period T ₁ (data collection sampling frequency f ₁ ).

FIG. 53 is a diagram for explaining the relationship between the symmetric group sampling period T and the data collection sampling period T ₁ in more detail. In FIG. 53, there is a relationship represented by the following equation between the data collection sampling frequency f ₁ (data collection sampling period T ₁ ) and the symmetric group sampling frequency f _s (symmetric group sampling period T).

As shown in FIG. 53, the gauge differential voltage group 1 forming the differential voltage symmetric group at time t includes a gauge differential voltage v ₂₁ at time t, a gauge differential voltage v ₂₂ at time t-T, and a gauge at time t-2T. It is constituted by a differential voltage v _23, gauge differential voltage group 2 forming a differential voltage symmetric group at time t-T ₁ is the gauge difference in gauge differential voltage v ₂₁ ^', the time t-T-T ₁ at time t-T ₁ The voltage v ₂₂ ^′ and the gauge differential voltage v ₂₃ ^{′ at} time t−2T−T ₁ are configured. As can be understood from FIG. 53, the interval between the gauge differential voltage groups is the symmetric group sampling period T, whereas the interval between the members constituting each gauge differential voltage group is the data collection sampling period T ₁ . That is, by introducing the concept of a symmetric group sampling period T (symmetric group sampling frequency f _s ) and a data collection sampling period T ₁ (data collection sampling frequency f ₁ ), calculation is performed while maintaining a suitable rotational phase angle α. Therefore, it is possible to suppress the influence of harmonic noise by increasing the data required for.

(Frequency coefficient symmetry index)
Next, a method of using a frequency coefficient as an index for evaluating the symmetry of the input waveform will be described. First, a determination formula using the frequency coefficient symmetry index is defined as follows.

In the above equation, | _{fc (t) -fc0} | shown on the left side is a frequency coefficient symmetry index. In addition, _{fc (t)} in the frequency coefficient symmetry index is a current measurement value related to the frequency coefficient, and _fc0 is a processing value before one step related to the frequency coefficient (one step related to the data collection sampling period). is there. Further, f _{CBRK on} the right side is a threshold for determining symmetry breaking. The processing value f _c0 one step before the frequency coefficient has the following two types of possible values.

First, when it is determined that there is symmetry in the determination process one step before using the above equation (354), the measured value at that time becomes the processing value f _c0 . On the other hand, when it is determined that there is no symmetry in the determination process one step before (for example, when there is a large disturbance in the system, voltage flicker occurs due to voltage drop), the processing value f _c0 is Use the last measured value latched. That is, when the above equation (354) is established, the symmetry breaking is determined, and the measurement value of the previous step is latched as in the following equation.

In the above equation, f _t is the current measured value, and f _t0 is the measured value one step before.

  On the other hand, if the above equation (354) is not satisfied, it is determined that there is symmetry, and the measured value at that time is held.

(Rotation phase angle symmetry index)
Next, a method of using the rotational phase angle as an index for evaluating the symmetry of the input waveform will be described. First, a determination formula using a rotational phase angle symmetry index is defined as follows.

In the above equation, | α _t −α ₀ | shown on the left side is a rotational phase angle symmetry index. In addition, α _t in the rotational phase angle symmetry index is a current measured value related to the rotational phase angle, and α ₀ is a processing value before one step related to the rotational phase angle (one step related to the data collection sampling period). is there. In addition, α _{BRK on} the right side is a threshold for determining symmetry breaking. Note that the processing value α ₀ before one step related to the rotational phase angle has the following two types of patterns, similar to the processing value f _c0 one step before related to the frequency coefficient.

First, when it is determined that there is symmetry in the determination process one step before using the above equation (355), the measured value at that time becomes the processing value α ₀ . On the other hand, if it is determined that there is no symmetry in the determination process one step before, the process value α ₀ is the previous measurement value latched immediately before. That is, when the above expression (354) is established, the symmetry breaking is determined, and the measurement value one step before is latched. On the other hand, if the above equation (354) is not satisfied, it is determined that there is symmetry, and the measured value at that time is held.

  The two symmetry indices are referred to as temporal symmetry indices (indexes that are compared with different time sections with the same rotation invariant). On the other hand, the symmetry index described in Embodiment 1-14 is referred to as a spatial symmetry index (an index that is compared with different rotational invariant calculation formulas in the same time section). Note that the various symmetry indices, which are spatial symmetry indices described in Embodiment 1-14, are the frequency coefficient symmetry indices or rotational phase angle symmetry indices of the present embodiment, which are temporal symmetry indices. It can be constructed as a temporal symmetry index.

(Movement averaging with multiple symmetry groups)
As described above, in order to suppress (reduce) the influence of harmonic noise, moving average processing using a plurality of symmetrical groups is recommended. The moving averaging process using a plurality of symmetric groups can be performed using the following equation.

In the above equation, v ₂₁ , v ₂₂ , and v ₂₃ are instantaneous values (real part or imaginary part) of the differential voltage in the members of the gauge differential voltage group, respectively, and M is the designated number of the moving averaging process. Further, the increment of the time step width k corresponds to the data collection sampling period T ₁ . That is, every time the step size k increases by 1, the frequency coefficient is calculated by the member shifted by the data collection sampling period T ₁ .

  It should be noted that the moving average processing of the rotational phase angle α and the actual frequency f can be performed in the same manner, and can be performed using the calculation formulas shown in the following equations and the following equations, respectively.

(Frequency change rate)
The frequency change rate can be calculated using the following equation:

In the above equation, T ₀ is a predetermined time interval (e.g., 100 ms), f _t is the measured value of current related to the actual frequency (calc), f _t-T0 is the time T ₀ before regarding actual frequency point Measured value (calculated value). Note that the calculation processing according to the above equation (359) is calculated only when the two measured values have symmetry. On the other hand, if at least one of the two measured values does not have symmetry, the calculated value of the previous step is latched and held (stored).

  54 is a diagram showing a functional configuration of the frequency measurement device according to the fifteenth embodiment, and FIG. 55 is a flowchart showing a processing flow in the frequency measurement device shown in FIG. Note that this frequency measuring apparatus measures the frequency change rate in addition to the frequency.

  As shown in FIG. 54, the frequency measurement apparatus 801 according to the fifteenth embodiment includes an AC voltage instantaneous value data input unit 802, a frequency coefficient calculation unit 803, a symmetry breaking determination unit 804, a frequency latch unit 805, and a frequency calculation unit 806. A frequency change rate calculation unit 807, an interface 808, and a storage unit 809. Here, the interface 808 performs a process of outputting a calculation result or the like to a display device or an external device, and the storage unit 809 performs a process of storing measurement data, a calculation result, or the like.

  In the above configuration, the AC voltage / current instantaneous value data input unit 802 performs a process of reading the voltage instantaneous value from the instrument transformer (PT) provided in the power system (step S801). Note that the read voltage instantaneous value and current instantaneous value data are stored in the storage unit 809.

  The frequency coefficient calculation unit 803 calculates a frequency coefficient based on the calculation process described above (step S802). This frequency coefficient calculation process can be explained as follows when it is explained in a comprehensive manner including the concept of the calculation process described above. That is, the frequency coefficient calculation unit 803 is the voltage instantaneous value data obtained by sampling the AC voltage to be measured at a predetermined data collection sampling frequency, which is smaller than the data collection sampling frequency and satisfies the sampling theorem. Three-point differential voltage instants representing the distance between the tips of two adjacent voltage instant value data in at least four consecutive voltage instant value data extracted at a symmetric group sampling frequency that is at least twice the frequency of the AC voltage Among the value data, processing is performed to calculate a value obtained by normalizing the average value of the sum of the differential voltage instantaneous values other than the intermediate time with the differential voltage instantaneous value at the intermediate time as a frequency coefficient.

  The symmetry breaking determination unit 804 determines symmetry breaking using the determination formula of the frequency coefficient symmetry index or the rotational phase angle symmetry index described above (step S803). When the symmetry breaking is determined (step S803, Yes), the frequency latch unit 805 latches the measurement value (calculated value) (step S804), and proceeds to step S806. On the other hand, when the symmetry breaking is not determined (step S803, No), the frequency calculation unit 806 calculates the frequency (step S805).

  After the processing in step S804 or step S805, the frequency change rate calculation unit 807 calculates the frequency change rate (step S806).

  In the last step S807, it is determined whether or not to end the above-described overall flow. If not (No in step S807), the processes from step S801 to S806 are repeated.

  In the above description, the symmetry breaking is determined using the determination formula of the frequency coefficient symmetry index or the rotational phase angle symmetry index. However, the frequency coefficient symmetry index or the rotation phase that is the temporal symmetry index is determined. Symmetry breaking may be determined using voltage amplitude symmetry indices 1 to 4 as temporal symmetry indices generated following the angular symmetry index. When measuring not only the instantaneous voltage value of the power grid but also the instantaneous current value, other symmetry indices generated as the generated temporal symmetry index (for example, gauge power symmetry index, gauge differential power symmetry) The symmetry breaking may be determined using a sex index).

  Next, the usefulness and effects of the present invention will be described using numerical examples from cases 7 to 9. In each of cases 7 to 9, a 50 Hz power system is assumed, the data collection sampling frequency is set to 1000 Hz (1 ms step), and the symmetric group sampling frequency is set to 200 Hz (5 ms step).

  First, parameters of case 7 are as shown in Table 9 below.

  Based on Table 9, the voltage instantaneous value waveform is expressed as follows. The instantaneous voltage waveform at this time is as shown in FIG.

  FIG. 57 is a diagram illustrating frequency coefficients calculated using the parameters of case 7. In FIG. This frequency coefficient can be calculated as: In the calculation result of FIG. 57, in order to simulate the voltage flicker, the waveform operation forcibly increasing the voltage phase to 80 degrees is performed at the time of 0.05 seconds in the voltage instantaneous value waveform.

  As shown in FIG. 57, it can be seen that at several points after 0.05 seconds, the frequency coefficient is greatly shifted due to the influence of the sudden phase change.

  FIG. 58 is a diagram showing a rotational phase angle calculated using the parameters of case 7. In FIG. This rotational phase angle can be calculated as:

  As shown in FIG. 58, it can be seen that the rotational phase angle is greatly shifted due to the influence of the sudden phase change at several points after 0.05 seconds.

  FIG. 59 is a diagram illustrating a determination result of symmetry breaking calculated with the parameters of case 7. In FIG. This determination result is calculated for each step using the determination formula shown below.

  In the determination result shown in FIG. 59, the case where there is symmetry is indicated as “1”, and the case where there is no symmetry is indicated as “2”. As shown in FIG. 59, it can be seen that the symmetry is broken under the influence of the sudden phase change in the period of 0.05 to 0.07 seconds.

  FIG. 60 is a diagram illustrating a frequency (actual frequency) calculated using the parameters of case 7. In FIG. This frequency (actual frequency) can be calculated as follows.

  As shown in FIG. 60, it can be seen that a stable frequency measurement result is obtained even in the presence of voltage flicker.

  FIG. 61 is a diagram showing a frequency change rate calculated using the parameters of case 7. In FIG. As can be seen from FIG. 60, since the frequency value hardly fluctuates, it can be seen that the frequency change rate is almost zero as shown in FIG.

  Case 7 describes the simulation result when there is a voltage flicker, but Case 8 describes the simulation result when there is no voltage flicker and there is a frequency variation.

  First, parameters of case 8 are as shown in Table 10 below.

  Based on Table 10, the voltage instantaneous value waveform is expressed as follows. The instantaneous voltage waveform at this time is as shown in FIG.

In the above equation, φ ₀ is the initial voltage phase angle, and φ _C is the voltage phase angle at the time of 0.05 seconds. Δf is a frequency change for each simulation step, and is calculated as follows.

  FIG. 63 is a diagram illustrating frequency coefficients calculated using the parameters of case 8. In FIG. As shown in FIG. 63, it can be seen that the frequency coefficient value decreases after 0.05 seconds when the frequency starts to increase. Further, it can be seen that the frequency coefficient value fluctuates greatly at a specific point in time after 0.05 seconds (for example, 0.22 seconds and 0.34 seconds) due to the influence of the frequency fluctuation.

  FIG. 64 is a diagram showing the rotational phase angle calculated with the parameters of case 8. In FIG. As shown in FIG. 64, the fluctuation of the rotation phase angle also has the same tendency as the frequency coefficient. That is, the value of the rotational phase angle increases after 0.05 seconds when the frequency starts to increase. In addition, at a specific time point after 0.05 seconds (0.22 seconds, 0.34 seconds), the value of the rotational phase angle greatly varies under the influence of the frequency variation.

  FIG. 65 is a diagram showing a determination result of symmetry breaking calculated with the parameters of case 8. In FIG. This determination result is calculated for each step using the determination formula shown in the above equation (364). Similarly to FIG. 59, the case where there is symmetry is indicated as “1”, and the case where there is no symmetry is indicated as “2”.

  In the case 8, as shown in FIG. 65, it can be seen that, in the period after 0.05 seconds, the symmetric state and the asymmetric state are alternately repeated under the influence of the frequency fluctuation.

  FIG. 66 is a diagram illustrating the frequency (actual frequency) calculated using the parameters of case 8. In FIG. This frequency (actual frequency) can be calculated using the equation shown on the left side of the equation (365).

  As shown in FIG. 66, it can be seen that the measurement frequency follows the theoretical frequency. That is, it can be seen that the frequency after the fluctuation is reliably captured even if the frequency fluctuation occurs.

FIG. 67 is a diagram showing the frequency change rate calculated with the parameters of case 8. In FIG. This frequency change rate can be calculated using the above equation (360). The specified time interval T ₀ in the expression (360) is 50 ms.

  In Case 8, the frequency change rate is set to 1.5 Hz / S as shown in Table 10. Therefore, as shown in FIG. 67, although there is an error of about 0.1 Hz / S, it can be seen that the value of the frequency change rate can be captured at each time point after about 0.12 seconds.

  Next, the case 9 will be described. In case 9, a simulation result when there is voltage flicker and frequency variation will be described.

  First, the parameters of case 9 are as shown in Table 11 below.

  Based on Table 11, the voltage instantaneous value waveform is expressed as follows. Further, the voltage instantaneous value waveform at this time is as shown in FIG.

  The above equation (368) is the same as the equation (366) shown in case 8, but in this case 9, in order to simulate voltage flicker, 0.2 second in the voltage instantaneous value waveform as in case 1 is obtained. At the time, a waveform operation for forcibly increasing the voltage phase to 80 degrees is performed.

  FIG. 69 is a diagram illustrating frequency coefficients calculated using the parameters of case 9. In FIG. In FIG. 69, in order to illustrate the fluctuation due to the voltage flicker at the time of 0.2 seconds, the value on the vertical axis 1 scale is enlarged and displayed as compared with FIG. For this reason, the state in which the frequency coefficient decreases after 0.05 seconds when the frequency is increased cannot be displayed, but if the value on the vertical axis 1 scale is reduced and displayed, the waveform is the same as that in FIG. become. Further, the influence of voltage flicker has a waveform similar to that shown in FIG.

  FIG. 70 is a diagram showing the rotational phase angle calculated using the parameters of case 9, and is the same as the frequency coefficient shown in FIG. That is, in FIG. 70, in order to illustrate the fluctuation due to the voltage flicker at the time point of 0.2 seconds, the value of the vertical axis 1 scale is enlarged and displayed as compared with FIG. For this reason, the state in which the rotational phase angle increases after 0.05 seconds when the frequency is increased cannot be displayed. However, if the value of the vertical axis 1 scale is reduced and displayed, it is the same as FIG. It becomes a waveform. Further, the influence of voltage flicker has a waveform similar to that shown in FIG.

  FIG. 71 is a diagram showing a determination result of symmetry breaking calculated with the parameters of case 9. In FIG. This determination result is calculated for each step using the determination formula shown in the above equation (364). Similarly to FIGS. 59 and 65, the case where there is symmetry is shown as “1”, and the case where there is no symmetry is shown as “2”.

  In case 9, as shown in FIG. 71, it can be seen that, in the period after 0.05 seconds, the state is in a state of alternately repeating the symmetric state and the asymmetric state under the influence of frequency fluctuation. In the case 9, it can be seen that the symmetry breaking continues for a period of ten and several milliseconds after 0.2 seconds.

  FIG. 72 is a diagram showing the frequency (actual frequency) calculated with the parameters of case 9. In FIG. This frequency (actual frequency) can be calculated using the equation shown on the left side of the equation (365).

  As shown in FIG. 72, it can be seen that the measurement frequency follows the theoretical frequency. That is, it can be seen that the frequency after the fluctuation is reliably captured even if the frequency fluctuation occurs.

FIG. 73 is a diagram showing a frequency change rate calculated with the parameters of case 9. In FIG. This frequency change rate can be calculated using the above equation (360). The specified time interval T ₀ in the expression (360) is 50 ms.

  In Case 9, the frequency change rate is set to 1.5 Hz / S as shown in Table 11. Therefore, as shown in FIG. 67, although there is an error of about 0.6 Hz / S at the maximum, it can be seen that the value of the frequency change rate can be captured at each time point after about 0.12 seconds.

  As described above, according to the frequency measurement device and the frequency change rate measurement device according to the fifteenth embodiment, the data collection sampling frequency that is the sampling frequency of the measurement data that is the source of the data constituting the various symmetry groups, and the measurement Introduced the concept of symmetric group sampling frequency, which is the sampling frequency when extracting data constituting various symmetric groups from data, so it is necessary for calculation while setting the sampling interval of members constituting various symmetric groups to a preferable interval Measurement data can be increased, the measurement accuracy can be increased, and the influence of harmonic noise can be suppressed (reduced).

  As described above, according to the frequency measurement device and the frequency change rate measurement device according to the fifteenth embodiment, the moving average process can be performed in the data collection sampling cycle without changing the measurement data sampling cycle. Thus, the influence of harmonic noise can be suppressed (reduced) efficiently or effectively.

  As described above, the present invention is useful as an AC electrical quantity measuring device that enables highly accurate measurement of an AC electrical quantity even when the measurement target is operating outside the system rated frequency.

101 Power measuring device 102, 202, 302 AC voltage current instantaneous value data input unit 103, 203, 303, 403, 803 Frequency coefficient calculation unit 104, 206, 305 Gauge active power calculation unit 105, 207, 306 Gauge reactive power calculation unit 106 active power and reactive power calculation unit 107 apparent power calculation unit 108 power factor calculation unit 109, 213, 312, 413, 804 symmetry breaking discrimination unit 110, 216, 314, 419, 506, 711, 808 interface 111, 217, 315, 420, 507, 712, 809 Storage unit 201 Distance protection device 204, 407, 703, 806 Frequency calculation unit 205, 304 Gauge current calculation unit 208, 212 Resistance and inductance calculation unit 209, 308 Gauge differential current calculation unit 210, 309 gauge difference valid Force calculation unit 211, 310 Gauge difference reactive power calculation unit 214 Distance calculation unit 215, 313 Breaker trip unit 301 Step out protection device 307, 311 Step out center voltage calculation unit 401 Time synchronization phasor measurement device 402, 802 AC voltage instantaneous value Data input unit 404 Gauge differential voltage calculation unit 405 Voltage amplitude calculation unit 406 Rotation phase angle calculation unit 408 DC offset calculation unit 409 Gauge effective synchronization phasor calculation unit 410 Gauge invalid synchronization phasor calculation unit 411 Cosine function method synchronization phasor calculation unit 412 Tangent Synchronous phasor calculation unit 414 Synchronous phasor estimation unit 415 Rotation phase angle latch units 416 and 805 Frequency latch unit 417 Voltage amplitude latch unit 418 Time synchronization phasor calculation unit 501 Synchronization phasor measurement device 502 Spatial synchronization phasor measurement device 503 Synchronization phasor / Time Stamp receiver 504 Spatial synchronization phasor calculation unit 505 Control signal transmission units 508 and 603 Communication lines 601 and 602 Synchronization phasor measurement device 701 Synchronization input device 702 Voltage measurement unit 704 Voltage amplitude calculation unit 705 Voltage synchronization phasor calculation unit 706 Frequency comparison unit 707 Voltage amplitude comparison unit 708 Spatial synchronization phasor calculation unit 709 Synchronization input operation delay time calculation unit 710 Synchronization input operation execution unit 801 Frequency measurement device 807 Frequency change rate calculation unit

Claims (18)

The second voltage that is smaller than the first sampling frequency and is twice or more the frequency of the AC voltage, from among the voltage instantaneous value data obtained by sampling the AC voltage to be measured at a predetermined first sampling frequency. Among three differential voltage instantaneous value data representing the distance between the tips of two adjacent voltage instantaneous value data extracted from at least four consecutive voltage instantaneous value data extracted at the sampling frequency, a differential voltage instantaneous other than the intermediate time A frequency coefficient calculation unit that calculates a value obtained by normalizing an average value of the sum of values with a differential voltage instantaneous value at an intermediate time as a frequency coefficient;
A frequency calculation unit that calculates the frequency of the AC voltage using the second sampling frequency and the frequency coefficient;
An AC electric quantity measuring device comprising: Three points representing the tip-to-tip distance between two adjacent voltage instantaneous value data in at least four consecutive voltage instantaneous value data including the three differential voltage instantaneous value data used in calculating the frequency coefficient. A gauge difference voltage calculation unit that calculates a geometric average value of a difference between a square value of the difference voltage instantaneous value at the intermediate time and a difference voltage instantaneous value product other than the intermediate time as the gauge difference voltage among the difference voltage instantaneous value data; ,
A voltage amplitude calculation unit that calculates the amplitude of the AC voltage using the frequency coefficient and the gauge differential voltage;
The AC electric quantity measuring device according to claim 1, comprising:   DC that calculates a DC offset included in the AC voltage using the frequency coefficient and predetermined three voltage instantaneous value data among the four voltage instantaneous value data used when calculating the frequency coefficient The AC electric quantity measuring device according to claim 1, further comprising an offset calculating unit. Three points representing the tip-to-tip distance between two adjacent voltage instantaneous value data in at least four consecutive voltage instantaneous value data including the three differential voltage instantaneous value data used in calculating the frequency coefficient. A gauge difference voltage calculation unit that calculates a geometric average value of a difference between a square value of the difference voltage instantaneous value at the intermediate time and a difference voltage instantaneous value product other than the intermediate time as the gauge difference voltage among the difference voltage instantaneous value data; ,
The frequency coefficient calculated by the frequency coefficient calculation unit, the gauge differential voltage calculated by the gauge differential voltage calculation unit, and predetermined three points of the four voltage instantaneous value data used when calculating the frequency coefficient A DC offset calculation unit for calculating a DC offset included in the AC voltage using voltage instantaneous value data;
The AC electric quantity measuring device according to claim 1, comprising: From the square value of the component obtained by subtracting the DC offset from the voltage instantaneous value at the intermediate time among the three voltage instantaneous value data used when calculating the frequency coefficient, and the two voltage instantaneous values other than the intermediate time A gauge voltage calculation unit for calculating a geometric average value of a difference between the products obtained by subtracting the DC offsets as a gauge voltage;
A voltage amplitude calculation unit that calculates the amplitude of the AC voltage using the frequency coefficient and the gauge voltage;
The AC electric quantity measuring device according to claim 4, comprising: Gage is obtained by averaging the difference between the square value of the voltage instantaneous value at the intermediate time and the voltage instantaneous value product other than the intermediate time among the three voltage instantaneous value data used when calculating the frequency coefficient. A gauge voltage calculation unit that calculates the voltage;
Three points representing the tip-to-tip distance between two adjacent voltage instantaneous value data in at least four consecutive voltage instantaneous value data including the three differential voltage instantaneous value data used in calculating the frequency coefficient. A gauge difference voltage calculation unit that calculates a geometric average value of a difference between a square value of the difference voltage instantaneous value at the intermediate time and a difference voltage instantaneous value product other than the intermediate time as the gauge difference voltage among the difference voltage instantaneous value data; ,
The AC voltage using a determination index based on a deviation between the first rotational phase angle calculated using the frequency coefficient and the second rotational phase angle calculated using the gauge voltage and the gauge differential voltage. A symmetry breaking discriminating section for judging the waveform symmetry breaking;
The AC electric quantity measuring device according to claim 1, comprising: The geometric average value of the difference between the square value of the voltage instantaneous value at the intermediate time and the voltage instantaneous value product at the time other than the intermediate time among the three voltage instantaneous value data used in calculating the frequency coefficient is the gauge voltage. A gauge voltage calculation unit to calculate as
Three points representing the tip-to-tip distance between two adjacent voltage instantaneous value data in at least four consecutive voltage instantaneous value data including the three differential voltage instantaneous value data used in calculating the frequency coefficient. A gauge difference voltage calculation unit that calculates a geometric average value of a difference between a square value of the difference voltage instantaneous value at the intermediate time and a difference voltage instantaneous value product other than the intermediate time as the gauge difference voltage among the difference voltage instantaneous value data; ,
Using a determination index based on a deviation between a sine function value of a rotation phase angle half angle that can be calculated using the frequency coefficient and a sine function value of a rotation phase angle half angle that can be calculated using the gauge voltage and the gauge differential voltage A symmetry breaking discriminating unit for judging the symmetry breaking of the AC voltage waveform;
The AC electric quantity measuring device according to claim 1, comprising: The geometric average value of the difference between the square value of the voltage instantaneous value at the intermediate time and the voltage instantaneous value product at the time other than the intermediate time among the three voltage instantaneous value data used in calculating the frequency coefficient is the gauge voltage. A gauge voltage calculation unit to calculate as
Three points representing the tip-to-tip distance between two adjacent voltage instantaneous value data in at least four consecutive voltage instantaneous value data including the three differential voltage instantaneous value data used in calculating the frequency coefficient. A gauge difference voltage calculation unit that calculates a geometric average value of a difference between a square value of the difference voltage instantaneous value at the intermediate time and a difference voltage instantaneous value product other than the intermediate time as the gauge difference voltage among the difference voltage instantaneous value data; ,
Using the determination index based on the deviation between the first voltage amplitude calculated using the frequency coefficient and the gauge voltage and the second voltage amplitude calculated using the frequency coefficient and the gauge differential voltage A symmetry breaking discriminating section for judging the symmetry breaking of the AC voltage waveform;
The AC electric quantity measuring device according to claim 1, comprising: The geometric average value of the difference between the square value of the voltage instantaneous value at the intermediate time and the voltage instantaneous value product at the time other than the intermediate time among the three voltage instantaneous value data used in calculating the frequency coefficient is the gauge voltage. A gauge voltage calculation unit to calculate as
Three points representing the tip-to-tip distance between two adjacent voltage instantaneous value data in at least four consecutive voltage instantaneous value data including the three differential voltage instantaneous value data used in calculating the frequency coefficient. A gauge difference voltage calculation unit that calculates a geometric average value of a difference between a square value of the difference voltage instantaneous value at the intermediate time and a difference voltage instantaneous value product other than the intermediate time as the gauge difference voltage among the difference voltage instantaneous value data; ,
Of the three voltage instantaneous value data used when calculating the frequency coefficient, the voltage instantaneous value data of two points whose measurement time is late and the first fixed value on the same complex plane as the AC voltage to be measured A value obtained by a predetermined product difference calculation using a unit vector and a second fixed unit vector delayed by a rotation phase angle determined based on the frequency coefficient with respect to the first fixed unit vector is calculated as a gauge effective synchronous phasor. A gage effective synchronous phasor calculation unit,
Among the three voltage instantaneous value data used when calculating the effective synchronous phasor, the two voltage instantaneous value data whose measurement time is early, and the first and second used when calculating the gauge effective synchronous phasor, A gauge invalid synchronization phasor calculation unit that calculates a value obtained by a predetermined product difference calculation with the second fixed unit vector as a gauge invalid synchronization phasor;
Deviation between the first voltage amplitude calculated using the frequency coefficient, the gauge effective synchronization phasor and the gauge invalid synchronization phasor, and the second voltage amplitude calculated using the frequency coefficient and the gauge differential voltage A symmetry breaking discriminating unit for judging the breaking of symmetry of the alternating voltage waveform using a determination index based on:
The AC electric quantity measuring device according to claim 1, comprising: The geometric average value of the difference between the square value of the voltage instantaneous value at the intermediate time and the voltage instantaneous value product at the time other than the intermediate time among the three voltage instantaneous value data used in calculating the frequency coefficient is the gauge voltage. A gauge voltage calculation unit to calculate as
Three points representing the tip-to-tip distance between two adjacent voltage instantaneous value data in at least four consecutive voltage instantaneous value data including the three differential voltage instantaneous value data used in calculating the frequency coefficient. A gauge difference voltage calculation unit that calculates a geometric average value of a difference between a square value of the difference voltage instantaneous value at the intermediate time and a difference voltage instantaneous value product other than the intermediate time as the gauge difference voltage among the difference voltage instantaneous value data; ,
Of the three differential voltage instantaneous value data used in calculating the frequency coefficient, the differential voltage instantaneous value data of two points that are late in measurement time and the first on the same complex plane as the AC voltage to be measured. A value obtained by a predetermined product difference calculation using a fixed unit vector of the first fixed unit vector and a second fixed unit vector delayed by a rotational phase angle determined based on the frequency coefficient with respect to the first fixed unit vector Gauge difference effective synchronous phasor calculation unit for calculating as a phasor,
Used to calculate the differential voltage instantaneous value data of two points earlier in the measurement time among the three differential voltage instantaneous value data used when calculating the gauge differential effective synchronous phasor and the gauge differential effective synchronous phasor. A gauge difference invalid synchronization phasor calculation unit for calculating a value obtained by a predetermined product difference calculation using the first and second fixed unit vectors as a gauge difference invalid synchronization phasor;
A first voltage amplitude calculated using the frequency coefficient, the gauge difference effective synchronization phasor and the gauge difference invalid synchronization phasor; and a second voltage amplitude calculated using the frequency coefficient and the gauge difference voltage; A symmetry breaking discriminating section for judging the symmetry breaking of the alternating voltage waveform using a judgment index based on the deviation of
The AC electric quantity measuring device according to claim 1, comprising: The geometric average value of the difference between the square value of the voltage instantaneous value at the intermediate time and the voltage instantaneous value product at the time other than the intermediate time among the three voltage instantaneous value data used in calculating the frequency coefficient is the gauge voltage. A gauge voltage calculation unit to calculate as
Three points representing the tip-to-tip distance between two adjacent voltage instantaneous value data in at least four consecutive voltage instantaneous value data including the three differential voltage instantaneous value data used in calculating the frequency coefficient. A gauge difference voltage calculation unit that calculates a geometric average value of a difference between a square value of the difference voltage instantaneous value at the intermediate time and a difference voltage instantaneous value product other than the intermediate time as the gauge difference voltage among the difference voltage instantaneous value data; ,
Of the three voltage instantaneous value data used when calculating the frequency coefficient, the voltage instantaneous value data of two points whose measurement time is late and the first fixed value on the same complex plane as the AC voltage to be measured A value obtained by a predetermined product difference calculation using a unit vector and a second fixed unit vector delayed by a rotation phase angle determined based on the frequency coefficient with respect to the first fixed unit vector is calculated as a gauge effective synchronous phasor. A gage effective synchronous phasor calculation unit,
Of the three voltage instantaneous value data used when calculating the gauge effective synchronous phasor, the voltage instantaneous value data at two points earlier in the measurement time and the first voltage used when calculating the gauge effective synchronous phasor. A gauge invalid synchronization phasor calculation unit that calculates a value obtained by a predetermined product difference calculation with the second fixed unit vector as a gauge invalid synchronization phasor;
Of the three differential voltage instantaneous value data used to calculate the gauge effective synchronous phasor, the differential voltage instantaneous value data of two points with a later measurement time and the gauge effective synchronous phasor used to calculate the gauge effective synchronous phasor A gauge difference effective synchronization phasor calculation unit that calculates a value obtained by a predetermined product difference calculation using the first and second fixed unit vectors as a gauge difference effective synchronization phasor;
Used to calculate the differential voltage instantaneous value data of two points earlier in the measurement time among the three differential voltage instantaneous value data used when calculating the gauge differential effective synchronous phasor and the gauge differential effective synchronous phasor. A gauge difference invalid synchronization phasor calculation unit for calculating a value obtained by a predetermined product difference calculation using the first and second fixed unit vectors as a gauge difference invalid synchronization phasor;
First frequency amplitude calculated using the frequency coefficient, the gauge effective synchronization phasor and the gauge invalid synchronization phasor, and calculated using the frequency coefficient, the gauge difference effective synchronization phasor and the gauge difference invalid synchronization phasor. A symmetry breaking discriminating unit for judging a symmetry breaking of the AC voltage waveform using a determination index based on a deviation from the second voltage amplitude.
The AC electric quantity measuring device according to claim 1, comprising: The geometric average value of the difference between the square value of the voltage instantaneous value at the intermediate time and the voltage instantaneous value product at the time other than the intermediate time among the three voltage instantaneous value data used in calculating the frequency coefficient is the gauge voltage. A gauge voltage calculation unit to calculate as
The square value of the instantaneous current value at the intermediate time among the three instantaneous current value data sampled at the same time as the three instantaneous voltage values used when calculating the frequency coefficient, and other than the intermediate time A gauge current calculation unit that calculates a geometric average value of a difference from the instantaneous current value product as a gauge current;
Of the three voltage instantaneous value data used in calculating the frequency coefficient, two voltage instantaneous value data with an earlier measurement time and three points sampled at the same time as the three voltage instantaneous values. A gauge active power calculation unit that calculates a value obtained by a predetermined product difference calculation using differential current instantaneous value data at two points later in measurement time among current instantaneous value data;
Of the three voltage instantaneous value data used to calculate the gauge active power, two voltage instantaneous value data whose measurement time is late and three points sampled at the same time as the three voltage instantaneous values A gauge reactive power calculation unit for calculating a value obtained by a predetermined product difference calculation with differential current instantaneous value data of two points later in measurement time among current instantaneous value data of
A first calculated value calculated using the frequency coefficient, the gauge voltage, the gauge current, the gauge active power, and the gauge reactive power, and the frequency coefficient, the gauge active power, and the gauge reactive power. A symmetry breaking discriminating unit for judging a symmetry breaking of the AC voltage waveform using a determination index based on a deviation from the calculated second calculated value;
The AC electric quantity measuring device according to claim 1, comprising: Three points representing the tip-to-tip distance between two adjacent voltage instantaneous value data in at least four consecutive voltage instantaneous value data including the three differential voltage instantaneous value data used in calculating the frequency coefficient. A gauge difference voltage calculation unit that calculates a geometric average value of a difference between a square value of the difference voltage instantaneous value at the intermediate time and a difference voltage instantaneous value product other than the intermediate time as the gauge difference voltage among the difference voltage instantaneous value data; ,
Three points representing the tip-to-tip distance between two adjacent current instantaneous value data in the four current instantaneous value data sampled at the same time as the four voltage instantaneous value data used in calculating the frequency coefficient. Gauge difference current calculation part which calculates the geometric average value of the difference between the square value of the difference current instantaneous value at the intermediate time and the difference current instantaneous value product other than the intermediate time as the gauge difference current among the difference current instantaneous value data of When,
Of the three differential voltage instantaneous value data used to calculate the gauge differential voltage, two differential voltage instantaneous value data with an earlier measurement time, and the three points used to calculate the gauge differential current. A gauge difference active power calculation unit that calculates a value obtained by a predetermined product difference calculation using differential current instantaneous value data at two points later in the measurement time in the current instantaneous value data;
Of the three differential voltage instantaneous value data used to calculate the gauge differential active power, two differential voltage instantaneous value data with a later measurement time and 3 used to calculate the gauge differential active power. A gauge difference reactive power calculation unit that calculates a value obtained by a predetermined product difference calculation with the difference current instantaneous value data of two points later in the measurement time among the difference current instantaneous value data of the points, as a gauge difference reactive power;
A first calculated value calculated using the frequency coefficient, the gauge differential voltage, the gauge differential current, the gauge differential active power, and the gauge differential reactive power, the frequency coefficient, the gauge differential active power, and the gauge A symmetry breaking discriminating unit for judging a symmetry breaking of the AC voltage waveform using a determination index based on a deviation from the second calculated value calculated using the differential reactive power;
The AC electric quantity measuring device according to claim 1, comprising: The second voltage that is smaller than the first sampling frequency and is twice or more the frequency of the AC voltage, from among the voltage instantaneous value data obtained by sampling the AC voltage to be measured at a predetermined first sampling frequency. Among three differential voltage instantaneous value data representing the distance between the tips of two adjacent voltage instantaneous value data extracted from at least four consecutive voltage instantaneous value data extracted at the sampling frequency, a differential voltage instantaneous other than the intermediate time Calculating a value obtained by normalizing an average value of the sum of values with a differential voltage instantaneous value at an intermediate time as a frequency coefficient;
Calculating the frequency of the AC voltage using the second sampling frequency and the frequency coefficient;
A method for measuring the amount of alternating current electricity, comprising: Three points representing the tip-to-tip distance between two adjacent voltage instantaneous value data in at least four consecutive voltage instantaneous value data including the three differential voltage instantaneous value data used in calculating the frequency coefficient. Calculating the geometric average value of the difference between the square value of the differential voltage instantaneous value at the intermediate time and the differential voltage instantaneous value product other than the intermediate time as the gauge differential voltage among the differential voltage instantaneous value data;
Calculating the amplitude of the AC voltage using the frequency coefficient and the gauge differential voltage;
The AC electric quantity measuring method according to claim 14, comprising: A second current value that is smaller than the first sampling frequency and more than twice the frequency of the alternating current out of the instantaneous current value data obtained by sampling the alternating current to be measured at a predetermined first sampling frequency. The differential current instants other than the intermediate time out of the three differential current instant value data representing the distance between the tips of the adjacent two current instant value data in the continuous current instantaneous value data extracted at the sampling frequency. Calculating a value obtained by normalizing an average value of the sum of values with a differential current instantaneous value at an intermediate time as a frequency coefficient;
Calculating the frequency of the alternating current using the second sampling frequency and the frequency coefficient;
A method for measuring the amount of alternating current electricity, comprising: Three points representing the tip-to-tip distance between two adjacent current instantaneous value data in at least four consecutive current instantaneous value data including the three points of differential current instantaneous value data used in calculating the frequency coefficient. Calculating the geometric average value of the difference between the square value of the differential current instantaneous value at the intermediate time and the differential current instantaneous value product other than the intermediate time as the gauge differential current among the differential current instantaneous value data;
Calculating the amplitude of the alternating current using the frequency coefficient and the gauge differential current;
The AC electricity quantity measuring method according to claim 16, comprising:   The second voltage that is smaller than the first sampling frequency and is twice or more the frequency of the AC voltage, from among the voltage instantaneous value data obtained by sampling the AC voltage to be measured at a predetermined first sampling frequency. Among three differential voltage instantaneous value data representing the distance between the tips of two adjacent voltage instantaneous value data extracted from at least four consecutive voltage instantaneous value data extracted at the sampling frequency, a differential voltage instantaneous other than the intermediate time An AC electrical quantity measuring device comprising a frequency coefficient calculation unit that calculates a value obtained by normalizing an average value of the sum of values with a differential voltage instantaneous value at an intermediate time as a frequency coefficient.

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