JP6033030B2 - Electric quantity measuring device, electric quantity measuring method, insulation monitoring device and impedance measuring device using these devices and methods - Google Patents

Description

  The present invention relates to an electric quantity measuring device, an electric quantity measuring method, an insulation monitoring device, and an impedance measuring device.

  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 (wide area protection control measurement system) and patent document 2 (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 Document 3 is a prior patent invention by the inventor of the present application, and the contents of this invention will be described later as appropriate.

JP 2009-65766 A JP 2009-71637 A Japanese Patent No. 4874438

“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 these methods calculate 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.

  On the other hand, the inventor of the present application has discovered the symmetry of alternating voltage / alternating current, has made a proposal to introduce the group theory of symmetry theory into the alternating current system, and has been patent-registered in Japan (Patent Document 3). . In addition, in this patent document 3, although the measuring method of alternating current electric quantity is disclosed, it is desired to measure not only the alternating current electric quantity but also the direct current electric quantity superimposed on the alternating current electric quantity.

  The present invention has been made in view of the above, and even when the object to be measured is operating outside the system rated frequency, highly accurate measurement of electric quantity (AC electric quantity and DC electric quantity) is performed. It is an object of the present invention to provide an electrical quantity measuring device and an electrical quantity measuring method that enable the above, and to provide an insulation monitoring device and an impedance measuring device using these devices and methods.

  In order to solve the above-described problems and achieve the object, the present invention provides the first sampling from the voltage instantaneous value data obtained by sampling the AC voltage of the system to be measured at a predetermined first sampling frequency. 3 representing the distance between the tips of two adjacent voltage instantaneous value data in at least four consecutive voltage instantaneous value data extracted at a second sampling frequency that is smaller than the frequency and equal to or higher than the frequency of the AC voltage. Based on the differential voltage instantaneous value data of the point and the three differential current instantaneous value data corresponding to the three differential voltage instantaneous value data, the differential voltage instantaneous value data or the differential current instantaneous value data is A frequency coefficient calculation unit that calculates a cosine function value of a rotational phase angle rotated on a complex plane during one cycle of two sampling frequencies as a frequency coefficient; Of the three differential voltage instantaneous value data and the three differential current instantaneous value data used when calculating the frequency coefficient, the first differential voltage instantaneous value at the intermediate time and the first differential current instantaneous at the intermediate time A second product of the second differential voltage instantaneous value on the advance side of the intermediate time and the second differential current instantaneous value on the delay side of the intermediate time, and a second product of the delay side of the intermediate time. A gauge difference active power calculation unit that calculates a value obtained by subtracting an average value of the third product of the difference voltage instantaneous value of 3 and the third product of the third difference current instantaneous value on the leading side as the gauge difference active power; An active power calculation unit that calculates the active power of the grid based on the gauge differential active power.

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

FIG. 1 is a diagram for explaining the symmetry between the rotational phase angle and the real-time frequency. FIG. 2A is a diagram (time-space vector diagram) illustrating a group of gauge powers on a complex plane. FIG. 2-2 is a diagram (vector product space diagram) showing the vector product elements of the gauge power group on the complex plane. FIG. 2-3 is a diagram for explaining the relationship between the gauge sampling period T and the data collection sampling period T ₁ . FIG. 2-4 is a characteristic diagram regarding an invariant obtained using a gauge power group. FIG. 2-5 is a diagram illustrating a rotational power group on a complex plane. FIG. 2-6 is a diagram illustrating a vector product element of the rotational power group on a complex plane. FIG. 2-7 is a diagram illustrating a gauge differential power group on a complex plane. FIG. 2-8 is a diagram illustrating vector product elements of the gauge differential power group on a complex plane. FIG. 2-9 is a diagram illustrating a rotational difference power group on the complex plane. FIG. 2-10 is a diagram showing the vector product elements of the rotational difference power group on the complex plane. FIG. 2-11 is a frequency gain characteristic diagram of active power at a gauge sampling frequency of 200 Hz. FIG. 2-12 is a frequency gain characteristic diagram of reactive power at a gauge sampling frequency of 200 Hz. FIG. 2-13 is a frequency gain characteristic diagram of the phase angle between voltage and current at a gauge sampling frequency of 200 Hz. FIG. 3A is a diagram for explaining a concept of processing in the insulation monitoring apparatus according to the first embodiment. FIG. 3-2 is a diagram illustrating a functional configuration of the insulation monitoring apparatus according to the first embodiment. FIG. 3-3 is a flowchart illustrating a process flow in the insulation monitoring apparatus according to the first embodiment. FIG. 3-4 is a diagram illustrating a voltage instantaneous value waveform in the present simulation. FIG. 3-5 is a diagram illustrating an instantaneous current value waveform in this simulation. 3-6 is a figure which shows the measurement result of the frequency coefficient in this simulation. 3-7 is a figure which shows the measurement result of the gauge difference active power in this simulation. 3-8 is a figure which shows the calculation result of the gauge difference reactive power in this simulation. 3-9 is a figure which shows the measurement result of the voltage-current phase angle in this simulation. FIG. 4-1 is a diagram illustrating a functional configuration of the impedance measuring apparatus according to the second embodiment. FIG. 4-2 is a flowchart of a process flow in the impedance measuring apparatus according to the second embodiment. FIG. 4-3 is a diagram illustrating a voltage instantaneous value waveform in this simulation. FIGS. 4-4 is a figure which shows each waveform of the electric current instantaneous value and gauge difference electric current in this simulation. 4-5 is a figure which shows the measurement result of the frequency coefficient in this simulation. 4-6 is a figure which shows the measurement result of the rotation phase angle in this simulation. 4-7 is a figure which shows the measurement result of the active power in this simulation. 4-8 is a figure which shows the measurement result of the reactive power in this simulation. 4-9 is a figure which shows the measurement result of the resistance value in this simulation. 4-10 is a figure which shows the measurement result of the inductance in this simulation.

  DESCRIPTION OF EMBODIMENTS Hereinafter, an electrical quantity measuring device and an electrical quantity measuring method according to an embodiment of the present invention, and an insulation monitoring device and an impedance measuring device using these devices and methods will be described with reference to the accompanying drawings. In addition, this invention is not limited by embodiment shown below.

(Meaning of terms)
First, terms used in the specification of the present application will be described in describing the electric quantity measuring device and the electric quantity measuring method according to the present embodiment.

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.
Symmetry group: a group having symmetry rotating on a complex plane.
Invariant: a parameter that does not change before and after the symmetry group rotates. Examples of the invariant in the present application include a rotational phase angle, a frequency coefficient, a gauge voltage, a gauge differential voltage, a gauge active power, a gauge reactive power, a gauge differential active power, and a gauge differential reactive power. If the invariants are known, the characteristics of the symmetric group can also be known.
Vector group table: A table (table) represented by the product (multiplication) of predetermined members (vector variables) in a symmetric group. This is a roadmap for examining invariants of symmetric groups.
Real group table: A table (table) represented by the product (multiplication) of predetermined members (real variables) in a symmetric group.
Real-time 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. In the present application, the real-time frequency is expressed by f. The unit of the real-time frequency f is hertz (Hz). In addition, the angular frequency ω in an electric circuit or the like is represented by ω = 2πf, and its unit is (rad / s).
Data collection Sampling frequency: a data collection time of the sampling frequency (first sampling frequency), represented by the symbol f _1. The data collection sampling frequency f ₁ is higher is better accuracy. Similar to the gauge sampling period T described below, the data collection sampling period T ₁ is represented by T ₁ = 1 / f ₁ as the reciprocal of the data collection sampling frequency f ₁ .
Gauge sampling frequency: a sampling frequency (second sampling frequency) used for calculation of the gauge symmetry group, and represented by the symbol f _S. Therefore, the gauge sampling period T is expressed as T = 1 / f _S as the reciprocal of the gauge sampling frequency f _S. Note that there is a relationship of T> T ₁ between T and T ₁ .
System frequency: Basically, it means the rated frequency in the power system, and there are two types, 50 Hz and 60 Hz.
Rotation phase angle: A voltage rotation vector (sometimes simply referred to as a “voltage vector”) or a current rotation vector (sometimes simply referred to as a “current vector”) rotates on a complex plane during one cycle of the gauge sample frequency. The phase angle is represented by α. Note that the rotational phase angle α is a frequency-dependent amount. As will be described later, when α is a positive number, α = 2π (f / f _S ) is calculated, and when α is a negative number, α = Calculate with 2π {(f / f _S ) −1}. When α is zero, there is a relationship of f = f _S / 2 between the gauge sampling frequency f _S and the real time frequency f.
Frequency coefficient: A cosine function value of the rotational phase angle α, expressed as f _C. All gauge symmetry groups of the present application have respective frequency coefficient calculation formulas. Note that if the frequency coefficient f _C is used as a symmetry index, it is possible to determine whether or not the current is AC.
Moving average process: A simple average process using a predetermined number of recent data. Note that the influence of measurement error and additive Gaussian noise can be reduced by performing the moving average process.
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.
Rotational voltage group: A symmetric group composed of two consecutive voltage vectors. The actually measured voltage instantaneous value corresponds to the real part of the voltage vector.
Rotational differential voltage group: A symmetrical group composed of two consecutive differential voltage vectors.
Gauge power group: A symmetric group composed of three consecutive voltage vectors and three consecutive current vectors.
Gauge active power: This is the active power (invariant) calculated by the formula found from the vector product space diagram of the gauge power group.
Gauge reactive power: Reactive power (invariant) calculated by a formula found from the vector product space diagram of the gauge power group.
Gauge differential power group: A symmetric group composed of three consecutive differential voltage vectors and three consecutive differential current vectors.
Gauge differential active power: Active power (invariant) calculated by a formula found from the vector product space diagram of the gauge differential power group.
Gauge differential reactive power: Reactive power (invariant) calculated by the formula found from the vector product space diagram of the gauge power group.
Rotational power group: A power group obtained by reducing the voltage vector and the current vector, which are constituent members of the gauge power group, by one, that is, a symmetric group composed of two consecutive voltage vectors and two consecutive current vectors.
Rotational differential power group: A differential power group in which the differential voltage vector and differential current vector, which are constituent members of the gauge differential power group, are each reduced by one, that is, composed of two consecutive differential voltage vectors and two consecutive differential current vectors Symmetry group.
-Broken symmetry: The input waveform is broken from a pure sine wave. The symmetry of the input waveform is broken by sudden amplitude change, sudden phase change, or sudden frequency change. An index for determining (detecting) this breaking of symmetry is a symmetry index.

(Summary of the present invention)
The present invention is an invention relating to an electric quantity measuring device which is a basic technology of a smart grid, and one of the gist thereof is to handle a frequency domain and an instantaneous value domain simultaneously through a rotational phase angle, and more specifically, The structure of the AC voltage and AC current and the DC component (DC voltage and DC current) included in these AC voltage and AC 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) is calculated using various symmetric groups (vector symmetric groups) on the complex plane defined above. , Amplitude, phase angle between voltage currents, phase angle difference) and time-dependent amount (voltage current instantaneous value) are analyzed simultaneously.

  The top concept of the present invention is the symmetry between the rotational phase angle and the real-time frequency (see FIG. 1). According to the present invention, the frequency in the entire region corresponding to the gauge sampling frequency can be measured by introducing a rotation phase angle that takes a negative value (hereinafter referred to as “negative number rotation phase angle”) (in the conventional method, , Only a frequency less than half of the sampling frequency (in the present invention, the gauge sampling frequency) can be determined. That is, according to the symmetry group measurement theory of the present invention, the measurement range is doubled as compared with the prior art.

  Further, the second gist of the present invention is to generate a vector group table of a symmetric group, examine a structure of the symmetric group in a vector product space, and then generate a real group table of the same symmetric group. It is to lead the calculation formula. A vector group table is a roadmap for examining invariants of symmetric groups. The inventor of the present application has found various invariants such as a frequency coefficient and a gauge voltage in the gauge differential voltage group in the previous applications. However, there was no general answer, such as how many invariants of the symmetric group, and how each invariant calculation formula is structured.

  On the other hand, in the present invention, by proposing two types of group tables, a new invariant (a newly defined invariant) corresponding to the upper concept of the invariant can be found. When applying the present invention to a specific application, a practical invariant may be selected from the listed invariants.

  The third gist of the present invention is to propose a method for separating the gauge sampling frequency and the data collection sampling frequency. If this method is used, high-speed and highly accurate measurement is possible.

  Furthermore, the fourth gist of the present invention is to propose a method for measuring not only the AC electricity quantity but also the DC electricity quantity. Due to this feature, in the present invention, the conventional invention name “AC electric quantity measurement (method)” is changed to “electric quantity measuring device (method)”.

Next, an electric quantity measuring device and an electric quantity measuring method according to the present embodiment will be described. In this description, first, the concept (algorithm) of the electric quantity measurement technique forming the gist of the present embodiment will be described, and then the configuration and operation of the electric quantity measurement apparatus according to the present embodiment which is an application apparatus of this technique. In addition, as applications to which these devices and methods are applied, an insulation monitoring device for electric equipment such as a transmission line, a power and impedance measuring device, and a three-phase circuit measuring device 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.

(Symmetry of rotational phase angle and real-time frequency)
FIG. 1 is a diagram for explaining the symmetry between the rotational phase angle and the real-time frequency. For example, in Patent Document 3 and the like, a calculation method based on the following relational expression is developed.

In the above equation, f is a real-time frequency, f _S is a gauge sampling frequency, and α is a rotational phase angle. Further, the rotational phase angle α is a positive number from zero to π, and the measurement range is also ½ or less of the gauge sampling frequency which is the same as the limit of the sampling theorem. Thereafter, the present inventor has found that the following relational expression is true if a negative rotational phase angle from minus π to zero is introduced.

  From the above two formulas, as shown in FIG. 1, it is possible to establish a one-to-one symmetrical relationship between the rotation phase angle and the real-time frequency by using the gauge sampling frequency as a mirror, and as a result, measurement of the sampling theorem The range can be doubled. Thus, the method of the present application extends the calculation range not only in the frequency domain but also in the instantaneous value domain via the rotational phase angle. On the other hand, the sampling theorem can be said to be an algorithm only in the frequency domain based on the Fourier transform.

  Summarizing the above two equations, the expression of the rotational phase angle using the real-time frequency is as follows.

  From the above equation, it can be seen that the positive rotation phase angle (first equation) and the negative rotation phase angle (second equation) are symmetrical with respect to zero. As can be seen from this equation, symmetry exists in the mathematical expressions throughout the present application. Symmetry is a guideline of the present application.

  Similarly, the expression of the real-time frequency using the rotational phase angle is as follows.

  As is clear from the above two equations, if the rotational phase angle is known, the real-time frequency can also be known. Furthermore, if the real-time frequency is known, it is possible to perform other highly accurate electric quantity measurements having a frequency correction function by calculating the symmetry group.

  In the following, we propose a method to generate several symmetry groups, determine the rotational phase angle and other invariants of the symmetry group, and measure various electric quantities.

(Gauge power group on complex plane)
FIG. 2A is a diagram illustrating a gauge power group on a complex plane. Three voltage rotation vectors on the complex plane shown in FIG. 2A can be expressed by the following equations.

  The above equation is a gauge voltage group.

  In the above equation, V is the AC voltage amplitude, ω is the rotational angular velocity, T is the step size of the gauge sampling frequency, α is the rotational phase angle at T (range is between −180 degrees and +180 degrees), and φ is the voltage-current phase. It is a horn.

  Also, the three current rotation vectors on the complex plane shown in FIG. 2A can be expressed by the following equation.

  The above equation is a gauge current group.

  In the above equation, I is the alternating current amplitude, and the other symbols are as described in the section of the voltage rotation vector.

In FIG. 2A, two voltage rotation vectors v ₁ (t) and v ₁ (t−2T) on both sides have symmetry with respect to an intermediate voltage rotation vector v ₁ (tT). Also, the two current rotation vectors i ₁ (t) and i ₁ (t−2T) on both sides have symmetry with respect to the intermediate current rotation vector i ₁ (tT). Further, there is a symmetry that the same voltage-current phase angle φ exists between each of the three voltage rotation vectors and each of the corresponding three current vectors. Further, at another time, these six rotation vectors (three voltage rotation vectors and three current rotation vectors) rotate, and even if they are in different places, the rotation phase angle α and the voltage-current phase angle φ does not change. This property is referred to as rotation invariance, and an assembly (structure) of six rotation vectors (three voltage rotation vectors and three current rotation vectors) having such rotation invariance properties is a cage power group. It is defined as From the above, it can be seen that the three voltage rotation vectors are the gauge voltage group, and the three current rotation vectors are the gauge current group, and therefore the gauge power group is composed of the gauge voltage group and the gauge current group.

(Vector group table of gauge power group)
In order to examine the invariant of the gauge power group, a vector group table of the gauge power group as shown in Table 1 below is constructed.

  The voltage rotation vector and the current rotation vector shown in the vector group table are complex state variables. The symbol “x” in the above table means that the element on the front side and the element on the front side are multiplied. At this time, each product element of the vector group table of the gauge power group can be expressed as the following equation.

  Fig. 2-2 shows each element based on the above equation on the complex plane. Here, a space generated by a product operation of two vectors is called a vector product space. In this vector product space, each vector product element rotates counterclockwise at an angular velocity of 2ω. In the following description, five symmetries are selected.

The first set having symmetry is v ₁ (t−2T) i ₁ (t), v ₁ (tT) i ₁ (tT) and v ₁ (t) i ₁ located on the intermediate axis of each rotation vector. This is a set of (t-2T), and the results of the vector multiplication of the three are equal as shown in the following equation.

  As will be apparent from the calculation formula described later, the gauge active power that has been proposed before (for example, Patent Document 3 above) is constituted by this set.

The second set having symmetry is a set of v ₁ (tT) i ₁ (t) and v ₁ (t) i ₁ (tT) located on the left side of the intermediate axis. The result of vector multiplication of is equal.

  As will be apparent from the calculation formula described later, the gauge reactive power that has been proposed before (for example, Patent Document 3 above) is constituted by this set.

The third set having symmetry is a set of v ₁ (t-2T) i ₁ (tT) and v ₁ (tT) i ₁ (t-2T) located on the right side of the intermediate axis. Thus, the result of vector multiplication of both is equal.

  As will be apparent from the calculation formula described later, this set can constitute another symmetrical group for calculating the gauge reactive power.

The fourth set having symmetry is v ₁ (tT) i ₁ (t) and v ₁ (t) i ₁ (t-2T) located on both sides of the intermediate axis, and v ₁ (t-2T) i ₁ (tT) and v ₁ (tT) i ₁ (t-2T), both of which (each having two vectors) have a phase difference α with respect to the intermediate axis. As will be apparent from the calculation formula described later, another set of symmetry for calculating the frequency coefficient can be constituted by these sets.

The fifth set having symmetry is a set of v ₁ (t) i ₁ (t) and v ₁ (t-2T) i ₁ (t-2T) located on both sides of the intermediate axis. It has a phase difference 2α with respect to the axis. According to the calculation formula described later, another symmetry group for calculating another gauge active power can be configured by the three members of this set and the intermediate rotation vector v ₁ (tT) i ₁ (tT).

  In this way, by using the vector product space diagram created using the vector group table of the gauge power group, the symmetry of the gauge power group can be intuitively examined.

(Real number group table of gauge power group)
In order to derive the invariable calculation formula of the gauge power group, a real number group table of the gauge power group as shown in Table 2 below is constructed. In addition, as each voltage instantaneous value in the following real number group table, although each real part of a voltage rotation vector and a current rotation vector is used, each imaginary part may be used.

  Next, the real number group table of the gauge power group will be described. First, the instantaneous value elements of the voltage rotation vector and the current rotation vector, which are constituent elements of the set in Table 2, can be expressed by the following equations and the following equations.

  In the above equations, “Re” represents the real part of the complex number. Further, each product element shown in Table 2 can be expressed by the following equation using the above two equations.

  Next, calculation formulas for various invariants by the gauge power group will be described using each product element of the real number group table of the gauge power group.

(Calculation formula of frequency coefficient by gauge power group)
Below, the calculation formula of the frequency coefficient by a gauge power group is demonstrated.

  The inventor of the present application first calculated the following equation with reference to the time-space vector diagram of the gauge power group shown in FIG. 2A in order to derive the equation for calculating the frequency coefficient proposed in Patent Document 3 and the like.

On the other hand, a quadruple value of the product of the product element v ₁₂ i ₁₂ and the rotational phase angle cosine value cos α can be expressed by the following equation.

From the above two equations, the frequency coefficient f _C by the gauge power group can be calculated using the following equation.

  In the above description, the equation transformation is performed using the real part of the voltage rotation vector and the current rotation vector as the instantaneous voltage value, but the same is true even if the equation modification is performed using the imaginary part of the voltage rotation vector and the current rotation vector. Results are obtained. The same applies to the other invariants of the gauge power group and the invariants of the other symmetric groups in the present invention, and the same calculation result is derived whether the real part or the imaginary part of the rotation vector is used. Therefore, hereinafter, only the case where the real number instantaneous value is used will be described, and the description using the imaginary number instantaneous value will be omitted.

(Gauge power group symmetry index (first formula))
The following formula is proposed as a symmetry index of the gauge power group.

Here, if the above equation is satisfied, v ₁ (t), v ₁ (tT), v ₁ (t-2T), i ₁ (t), i ₁ (tT), i ₁ (t-2T) The symmetry of the constructed gauge power group is broken. For this reason, when the symmetry of the gauge power group is broken, the calculated value before the symmetry is broken is latched. On the other hand, if the above equation is not satisfied, it is determined that the symmetry is not broken, and the calculation using the symmetry group is continued.

(Rotation phase angle by gauge power group)
From the above formula, the rotational phase angle can be calculated using the following formula.

(Moving average of rotation phase angle)
In order to reduce the influence of noise when calculating the rotational phase angle, for example, it is effective to perform a moving average process as shown in the following equation.

In the above equation, T ₁ is a data collection sampling period (details will be described later), and M is the number of data (data collection sampling points) for moving average processing including the current time.

(Real-time frequency by gauge power group)
From the above formula, the real-time frequency can be calculated using the following formula:

In the above equation, f is a real-time frequency, and f _S is a gauge sampling frequency (details will be described later).

(Moving average processing of real-time frequency)
In order to reduce the influence of noise when calculating the real-time frequency, it is effective to perform, for example, a moving average process as shown in the following equation.

In the above equation, T ₁ is a data collection sampling period, and M is the number of data for moving average processing including the current time (the number of data collection sampling points).

(Separation of data collection sampling frequency and gauge sampling frequency)
By the way, as in the case of the above-mentioned Patent Document 3 and the like, when increasing the accuracy of measurement, the number of data is increased by decreasing the sampling cycle (increasing the sampling frequency), and using the increased continuous data. The basic idea was to calculate various AC electrical quantities including frequency coefficients. However, in the method of simply increasing the number of data, the rotation phase angle also decreases as the number of data increases, and when the harmonic noise is large, the calculation results vary under the influence of the harmonic noise, It is also expected that the calculation accuracy cannot be increased. 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 value so that the rotational phase angle value does not decrease. The present invention introduces the concepts of a gauge sampling period T (gauge sampling frequency f _S ) and a data collection sampling period T ₁ (data collection sampling frequency f ₁ ).

FIG. 2-3 is a diagram for explaining the relationship between the gauge sampling period T and the data collection sampling period T ₁ . In FIG. 2-3, there is a relationship represented by the following equation between the gauge sampling frequency f _S (gauge sampling period T) and the data collection sampling frequency f ₁ (data collection sampling period T ₁ ).

  In the above formula, n is a positive integer, and the example of FIG. 2-3 illustrates the case where n = 4.

  In FIG. 2-3, the members of the gauge voltage group (gauge voltage group 1) at the present time (time t) are as follows.

In addition, it is as a member of the following gauge voltage group (gauge voltage group 2) than the current time T ₁ time before (time t-T _1).

As can be understood from FIG. 2-3, the interval between the gauge voltage groups (the interval between the gauge voltage group 1 and the gauge voltage group 2) is the data collection sampling period T ₁ , whereas the members constituting each gauge voltage group The interval between them is a gauge sampling period T. That is, by introducing the concepts of the gauge sampling period T (gauge sampling frequency f _S ) and the data collection sampling period T ₁ (data collection sampling frequency f ₁ ), it is necessary for the calculation while maintaining a suitable rotational phase angle α. It is possible to suppress the influence of harmonic noise by increasing the data.

In addition to this concept, when the concept of the negative rotation phase angle proposed in the present application is used in combination, the same effect as that obtained when the data collection sampling frequency f ₁ is further doubled can be obtained. In practice, it goes without saying that an appropriate and appropriate data collection sampling frequency and gauge sampling frequency are selected according to the requirements of the system.

  If the data collection sampling frequency can be set as high as possible by selecting hardware considering cost performance (for example, 4 kHz is recommended for international and standard protection relay devices). The output of the result can be performed at a high speed, and the influence of the harmonic noise can be greatly reduced by using the moving average process for the output result together.

  In this way, by introducing the concept of processing that distinguishes the data collection sampling frequency and the gauge sampling frequency, it is possible to suppress disturbances (small disturbances) that are always present in the power system.

(Gauge active power definition and calculation formula)
The inventor of the present application knows the following equation as a calculation formula representing the gauge active power from the “vector product space diagram of the gauge power group” shown in FIG. 2-2, and the related product of the real group table in the calculation formula. The formula was transformed by substituting.

  From the above equation, the gauge active power can be calculated using the following equation.

  The following equation is also established by the above equation.

In the above equation, V _g is the gauge voltage and I _g is the gauge current.

  The following equation is also established by the definition of the power factor.

(Gauge reactive power definition and calculation formula)
Similarly to the gauge active power, the gauge reactive power can also be derived based on the following equation modification found from the “vector product space diagram of gauge power group” shown in FIG.

  From the above equation, the gauge reactive power can be calculated using the following equation.

(Moving average processing of gauge active power and gauge reactive power)
When calculating the gauge active power and the gauge reactive power, it is effective to perform, for example, a moving average process as shown in the following equation in order to reduce the influence of noise.

In the above equation, T ₁ is the data collection sampling period, and M is the number of data collection sampling points including the current time. The gauge active power calculation formula in the sum code can be expressed as the following formula.

  Also, the gauge reactive power calculation formula in the sum code can be expressed as the following formula.

(Calculation formula of active power and reactive power by gauge power group)
First, the definition expression of the active power, active power P _A can be calculated using the following equation.

同様に、無効電力の定義式により、無効電力Ｑ_Aは次式を用いて計算することができる。

Similarly, the reactive power Q _A can be calculated using the following formula according to the reactive power definition formula.

(Moving average of active power and reactive power)
As with other amounts of electricity, when calculating active power and reactive power, for example, it is effective to perform a moving average process as shown in the following equation in order to reduce the influence of noise.

(Calculation formula of phase angle between voltage and current by gauge power group)
From the above equations (20) and (23), the tangent function value of the voltage-current phase angle φ can be expressed as the following equation.

  Therefore, the voltage-current phase angle φ can be calculated using the following equation.

  The voltage-current phase angle φ changes in the range of −180 degrees to +180 degrees.

(Calculation formula of apparent power by gauge power group)
According to the definition formula of the apparent power, the apparent power S can be calculated using the following formula.

(Power factor calculation formula by gauge power group)
From the power factor definition, the power factor PF can be calculated using the following equation:

(Calculation formula of impedance by gauge power group)
According to the gauge power group, it is also possible to calculate the impedance. Specifically, the equation representing the impedance can be expressed as the following equation.

  From the above equation, the resistance component of the impedance can be calculated using the following equation.

  Similarly, the reactance component of impedance can be calculated using the following equation:

  In order to reduce the influence of circuit noise, the following moving average process may be performed in the same manner as other electric quantities.

(Calculation formula of inductance component by gauge power group)
When the reactance component of the impedance is positive (plus), it can be calculated using the following equation, and when the reactance component is negative (minus), it can be calculated using the following equation.

(Calculation formula of capacitance component by gauge power group)
Similarly, when the reactance component of the impedance is negative (minus), it can be calculated using the following equation.

(Comparison with Patent Document 3 (hereinafter referred to as “prior invention”) relating to gauge active power and gauge reactive power)
First, regarding the gauge active power, the present invention proposes an invariant of the gauge power group represented by the following equation.

  In the present invention, an invariant of a gauge power group different from the above formula is proposed.

  The following relational expression is established by the above two formulas.

  On the other hand, in the invention of the prior application, the gauge effective power is defined as follows.

  Therefore, it can be said that the prior invention is a part of the gauge effective power of the present invention. Furthermore, since the gauge effective power of the present invention does not have a term of sinφ, the calculation formula is simplified.

  The above discussion was about gauge active power, but gauge reactive power will be examined in the same way. First, in the present invention, an invariant of the gauge power group represented by the following equation is proposed.

  In conclusion, the expressions representing the gauge reactive power of the present invention and the prior invention are the same. However, in the present invention, four product elements are used, whereas in the prior invention, two product elements are used. Therefore, the calculation formula of the present invention that can use a large amount of data has an advantage of excellent smoothing effect of the calculation result, and the calculation formula of the present invention is recommended.

(Other formulas for calculating gauge active power)
The inventor of the present application has found the following expression as another calculation expression representing the gauge active power from the “vector product space diagram of the gauge power group” shown in FIG. 2-2, and relates the real number group table to the calculation expression. The product was transformed by substituting the product.

  As is apparent from the above formula modification, the following gauge active power calculation formula is established.

  Note that, as can be understood by paying attention to the subscripts of the product elements in the above equation, the order of the subscripts in each product element is the same for the voltage component and the current component. Therefore, when performing computer data processing, there is an aspect more advantageous than that of the prior invention.

  Further, if necessary, the following moving average process may be performed in the same manner as other electric quantities.

  The gauge active power calculation formula in the sum code can be expressed as the following formula.

  If the two formulas for calculating the gauge active power described above are solved simultaneously, the following formula is established.

From the above equation, the following equation can be defined as another calculation equation representing the frequency coefficient f _C.

It should be noted that the frequency measurement range of the above equation is not more than a quarter of the gauge sampling frequency f _S (the rotation phase angle α is not more than 90 degrees).

(Symmetry index of gauge power group (second formula))
The above formula (49), that is, the square calculation value of the frequency coefficient f _C by the gauge power group can be used as a symmetry index of the gauge power group as in the following formula.

Here, if the above equation is satisfied, v ₁ (t), v ₁ (tT), v ₁ (t-2T), i ₁ (t), i ₁ (tT), i ₁ (t-2T) The symmetry of the constructed gauge power group is broken. For this reason, when the symmetry of the gauge power group is broken, the calculated value before the symmetry is broken is latched. On the other hand, if the above equation is not satisfied, it is determined that the symmetry is not broken, and the calculation using the symmetry group is continued.

(Other formulas for calculating gauge reactive power)
Similar to the gauge active power, the following formula is proposed as another calculation formula for the gauge reactive power.

  If the above equation is used, the reactive power can be obtained using the following equation.

  In the case of the above formula, a point where the denominator is zero (a point where the rotational phase angle α is 90 degrees) is a singular point, so care must be taken.

  As described above, various invariants could be found by the group table of the gauge power group and the four-side arithmetic operation for the gauge power group.

FIG. 2-4 is a characteristic diagram regarding invariants obtained using the gauge power group. As shown in FIG. 2-4, the gauge active power P _g , gauge reactive power Q _g , active power P, and reactive power Q are geometrical via a rotational phase angle α and a voltage-current phase angle φ. There is a relationship. As can be understood from this relationship, in the present invention, the gauge active power with P _g and gauge reactive power Q _g, when by-series instantaneous values of active power P and reactive power Q and a frequency automatic correction function The calculation has been realized.

  From this point, we propose a rotating power group that can reduce the number of voltage rotation vectors and current rotation vectors that are constituent members of the gauge power group and reduce the number of each by one. Note that the rotational power group here is a symmetric group composed of two voltage rotation vectors and two current rotation vectors obtained by reducing the number of voltage rotation vectors and current rotation vectors by one, respectively.

(Rotational power group on complex plane)
FIG. 2-5 is a diagram illustrating a rotational power group on a complex plane. Two voltage rotation vectors and two current rotation vectors on the complex plane shown in FIG. 2-5 can be expressed by the following equations and the following equations.

  The above equation (54) represents a rotational voltage group, and the above equation (55) represents a rotational current group.

  In the above two formulas, V is the AC voltage amplitude, I is the AC current amplitude, ω is the rotational angular velocity, T is the gauge sampling frequency step size, α is the rotational phase angle at T, and φ is the voltage-current phase angle. It is.

2-5, the two voltage rotation vectors v ₁ (t) and v ₁ (tT) and the two current rotation vectors i ₁ (t) and i ₁ (tT) are symmetrical with each other. Have. In addition, the two voltage rotation vectors and the two current rotation vectors have a symmetry that the voltage-current phase angle φ is the same. In addition, these four voltage rotation vectors and current rotation vectors can be used between these two voltage rotation vectors and between two current rotation vectors at different times and at different locations. Neither the rotation phase angle α nor the phase angle between each voltage rotation vector and the corresponding current rotation vector (voltage-current phase angle φ) changes. That is, this rotational power group is also a structure having the property of rotational invariance like the cage power group described above. From the above, it can be seen that the two voltage rotation vectors are the rotation voltage group, and the two current rotation vectors are the rotation current group, and therefore the rotation power group is composed of the rotation voltage group and the rotation current group.

(Vector group table of rotational power group)
In order to examine the invariants of the rotational power group, a vector group table of the rotational power group as shown in Table 3 below is constructed.

  The voltage rotation vector shown in the above vector group table is a complex state variable. The symbol “x” in the above table means that the element on the front side and the element on the front side are multiplied. At this time, each product element of the vector group table of the rotational power group can be expressed as follows.

  Fig. 2-6 shows a vector product element based on the above equation on the complex plane. Here, a space generated by a product operation of two vectors is called a vector product space. In this vector product space, each vector product element rotates counterclockwise at an angular velocity of 2ω.

Here, two sets having symmetry will be described. First, the first set is a set of v ₁ (t) i ₁ (tT) and v ₁ (tT) i ₁ (t) located on the intermediate axis. Takes the same value. Although details will be described later, reactive power can be calculated with this set.

The second set is a set of v ₁ (t) i ₁ (t) and v ₁ (tT) i ₁ (tT) having a phase difference α with respect to the intermediate axis. Although details will be described later, the active power can be calculated from this set and the frequency coefficient.

(Real number group table of rotating power group)
In order to derive the invariable calculation formula of the rotational power group, a real number group table of the rotational power group as shown in Table 4 below is constructed. As described above, as the instantaneous voltage value and the instantaneous current value in the real number group table, the real part of each rotation vector or the imaginary part may be used.

  Next, the real number group table of the rotational power group will be described. First, each instantaneous value element which is a component of the set of Table 4 can be expressed by the following formula (voltage element) and the following formula (current element).

  From the above equation, each product element shown in Table 4 can be expressed as the following equation.

  Next, calculation formulas for various invariants related to the rotational power group will be described using each product element of the real number group table of the rotational power group.

(Calculation formula for sine function and cosine function value of voltage / current phase angle by rotating power group)
First, in the rotating power group, the following equation is established.

  From the above equation, the calculation formula of the sine function value of the voltage-current phase angle φ is obtained as follows.

  In the rotational power group, the following formula and the following formula are also established.

  Here, if both sides of the equation (64) are multiplied by the cosine function value of the rotation phase angle α, the following equation is obtained.

  Then, by solving the simultaneous equations of these equations (63) and (64), the following equation is obtained as an equation representing the cosine function value of the voltage-current phase angle φ.

(Calculation formula of active power and reactive power by rotating power group)
The following expression representing the effective power is obtained by the expression modification of the expression (65).

  In order to reduce noise, a moving average process represented by the following equation may be performed.

In the above formula, M is the number of data (data collection sampling points) for the moving average process including the current time. In addition, each calculation formula of vi _add1 (t, k) and vi _add2 (t, k) in the Σ symbol of the above formula is expressed by the following formula.

  Further, the following equation representing reactive power is obtained by similar equation modification.

  In order to reduce noise, a moving average process represented by the following equation may be performed.

In the above formula, M is the number of data (data collection sampling points) for the moving average process including the current time. Also, the calculation formula of vi _sub (t, k) within the Σ symbol in the above formula is expressed by the following formula.

(Calculation formula of voltage / current phase angle by rotating power group)
First, the calculation formula of the tangent function value of the voltage-current phase angle φ can be expressed by the following formula.

  From the above equation, the voltage / current phase angle φ can be expressed as follows.

(Calculation formula of apparent power by rotating power group)
According to the definition of the apparent power, the calculation formula of the apparent power can be expressed by the following formula.

  Moreover, the calculation formula of a power factor can be represented by following Formula by the definition of a power factor.

(Equation for calculating the impedance of rotating power group)
The impedance can be calculated from the rotational power group. Of the impedance components, the calculation formula for the resistance component can be expressed by the following equation.

  Moreover, the calculation formula of the reactance component of the impedance can be expressed by the following formula.

  Further, in order to reduce the influence of circuit noise, moving average processing may be performed in the same manner as other electric quantities. Note that formula expansion here is omitted.

  Similarly to the case where the gauge power group is used, the inductance component (reactance component is positive (plus)) and the capacitance component (reactance component is negative (minus)) can be calculated using the rotating power group. The calculation formula is the same as that for the gauge power group, and the development of the formula here is omitted.

(Gauge differential power group on complex plane)
FIG. 2-7 is a diagram illustrating a gauge differential power group on a complex plane. 2-7, the three differential voltage rotation vectors on the complex plane can be expressed by the following equations.

  The above equation is a gauge differential voltage group.

In the above equation, V is the AC voltage amplitude, ω is the rotational angular velocity, T is the step size of the gauge sampling frequency for several hours, and α is the rotational phase angle at T. Figure 2-7 shows three differential voltage rotation vector _{v 2 (t), v 2} (tT), v 2 (t-2T) at the two differential voltage on opposite sides rotation vector v ₂ (t) , V ₂ (t−2T) are symmetrical with respect to the differential voltage rotation vector v ₂ (tT) located at the center. Further, these three differential voltage rotation vectors rotate at different times, and the rotation phase angle α, which is the phase angle difference between the two, does not change even if they are in different locations. For this reason, it has the same rotation invariance property as the gauge power group, and these three differential voltage rotation vectors are defined as a cage differential power group.

  2-7, the three differential current rotation vectors on the complex plane can be expressed by the following equations.

  The above equation is a gauge differential current group.

Similar to the differential voltage rotation vector, two differential current pressure rotation vectors i ₂ (t), i ₂ (tT), and i ₂ (t-2T) shown in FIG. The differential current rotation vectors i ₂ (t) and i ₂ (t−2T) have symmetry with respect to the differential current rotation vector i ₂ (tT) located at the center. Further, these three differential current rotation vectors rotate at different times, and the rotational phase angle α which is the phase angle difference between the two does not change even if they are in different locations. For this reason, it has a rotation invariant property similar to the gauge current group, and these three differential current rotation vectors are defined as a cage differential power group.

  2-7, the three differential voltage rotation vectors and the three differential current vectors have symmetry with respect to the intermediate difference vector. Also, the same voltage-current phase angle is symmetrical between the three differential voltage rotation vectors and the three differential current vectors. Further, at another time, the structure constituted by these six differential rotation vectors rotates, and the rotation phase angle α and the voltage-current phase angle φ of this structure do not change even if they are in different places. Therefore, the shape of the structure does not change. This property is called rotational invariance. It turns out that it has rotation invariance like a gauge electric power group. A structure constituted by these six differential rotation vectors is defined as a cage differential power group. As described above, the three differential voltage rotation vectors are the gauge differential voltage group, and the three differential current rotation vectors are the gauge differential current group. Therefore, the gauge differential power group is composed of the gauge differential voltage group and the gauge differential current group. I understand that

(Vector group table of gauge differential power group)
In order to examine the invariant of the gauge differential power group, a vector group table of the gauge differential power group as shown in Table 5 below is constructed.

  The differential power rotation vector in the above vector group table is a complex state variable. The symbol “x” in the above table means that the element on the front side and the element on the front side are multiplied. At this time, each product element of the vector group table of the gauge differential power group can be expressed as the following equation.

  Moreover, if the calculation of the right side of the above formula is advanced, it can be simplified as the following formula.

  Fig. 2-8 shows a vector product element based on the above equation on the complex plane. Each vector product element rotates counterclockwise at an angular velocity of 2ω. In the following description, five symmetries are selected.

The first set having symmetry is v ₂ (t−2T) i ₂ (t), v ₂ (t, which is located on the intermediate axis of each rotation vector (the real axis (Re axis) in the example of FIG. 2-8). tT) i ₂ (tT) and v ₂ (t) i ₂ (t−2T), and the result of the vector multiplication of the three is equal as shown in the following equation.

The second set having symmetry is a set of v ₂ (tT) i ₂ (t) and v ₂ (t) i ₂ (tT) located on the left side of the intermediate axis. Are equal as It should be noted that another symmetry group for calculating the gauge differential reactive power can be configured with this set by a calculation formula described later.

The third set having symmetry is a set of v ₂ (t-2T) i ₂ (tT) and v ₂ (tT) i ₂ (t-2T) located on the right side of the intermediate axis, and the vector of both The result of the product is equal as

The fourth set of symmetry is v ₂ (tT) i ₂ (t) and v ₂ (t) i ₂ (tT) and v ₂ (t-2T) i ₂ ( tT) and v ₂ (tT) i ₂ (t−2T), both having two vectors, each having a phase difference α with respect to the intermediate axis. As will be apparent from the calculation formula described later, another set of symmetry for calculating the frequency coefficient can be constituted by these sets.

The fifth set having symmetry is a set of v ₂ (t) i ₂ (t) and v ₂ (t-2T) i ₂ (t-2T) located on both sides of the intermediate axis. It has a phase difference 2α with respect to the axis.

(Real number group table of gauge differential power group)
In order to derive the invariable calculation formula of the gauge differential power group, a real group table of the gauge differential power group as shown in Table 6 below is constructed.

  Next, the real number group table of the gauge differential power group will be described. First, the real part instantaneous value of the differential voltage rotation vector, which is a component of the set of Table 6, can be expressed by the following equation.

  In the above equation, “Re” indicates the real part of the complex number. Further, the real part instantaneous value of the differential current rotation vector, which is a component of the set of Table 6, can be expressed by the following equation.

  Substituting the instantaneous values of the above two formulas into the real number group table, each product element of the real number group table of the gauge differential power group is expressed as follows.

  Next, calculation formulas for various invariants related to the gauge differential power group will be described using each product element of the real number group table of the gauge differential power group.

(Calculation formula of frequency coefficient by gauge differential power group)
Below, the calculation formula of the frequency coefficient by a gauge difference electric power group is demonstrated. The inventor of the present application refers to the space vector diagram of the gauge differential power group shown in FIG. 2-8 and performs the following equation modification in order to derive the relationship between the calculation formula of the frequency coefficient and the real number group table. The product element of the real group table shown in Table 6 was substituted into the format.

Further, the expansion formula of the next product element 4v ₂₂ i ₂₂ cos α is as follows.

From the above two formulas, the frequency coefficient f _C of the gauge differential power group can be calculated as in the following formula.

(Symmetry index of gauge differential power group (first calculation formula))
The following formula is proposed as a symmetry index of the gauge differential power group.

If the above equation is satisfied, v ₂ (t), v ₂ (tT), v ₂ (t-2T) and i ₂ (t), i ₂ (tT), i ₂ (t-2T) The symmetry of the constructed gauge differential power group is broken. For this reason, when the symmetry of the gauge differential power group is broken, the calculated value before the symmetry is broken is latched. On the other hand, if the above equation is not satisfied, it is determined that the symmetry is not broken and the current calculated value is used.

(Rotation phase angle and real-time frequency by gauge differential power group)
The calculation formulas for the rotational phase angle and the real-time frequency by the gauge differential power group are the same as the calculation formulas for the rotational phase angle and the real-time frequency by the gauge power group, and thus description thereof is omitted here.

(Gauge differential active power definition and calculation formula)
The inventor of the present application has found the following formula as a calculation formula representing the gauge differential active power from the “vector product space diagram of the gauge differential power group” shown in FIG.

  Substituting the relevant product of the real group table of the gauge differential power group into the above formula, the following formula is obtained.

  From the above equation, the gauge differential power value can be calculated using the following equation.

  Also, it can be seen from the above formula that the following formula holds.

In the above equation, V _gd and I _gd are a gauge differential voltage and a gauge differential current, respectively.

  Furthermore, it can be seen that the following equation is established by the definition of the power factor.

(Gauge differential reactive power definition and calculation formula)
The inventor of the present application has found the following formula as a calculation formula representing the gauge differential reactive power from the “vector product space diagram of the gauge differential power group” shown in FIG.

  Substituting the relevant product of the real group table of the gauge differential power group into the above formula, the following formula is obtained.

  From the above equation, the gauge differential power value can be calculated using the following equation.

(Gauge differential active power and moving average processing of gauge differential active power)
When calculating the gauge differential active power and the gauge differential active power, it is effective to perform, for example, a moving average process as shown in the following equation in order to reduce the influence of noise.

  In the above equation, M is the number of data collection sampling points including the current time. In addition, each calculation formula of the gauge differential active power and the gauge differential active power in the sum code can be expressed as the following formula and the following formula.

(Calculation formula of active power and reactive power by gauge differential power group)
Using the above equation, the real power P _D by gauge differential power group can be calculated using the following equation.

Further, based on the result of the above formula and the definition of power, the reactive power Q _D by the gauge differential power group can be calculated using the following formula.

(Moving average processing of gauge differential active power and gauge differential reactive power)
When calculating the gauge difference active power and the gauge difference reactive power, it is effective to perform, for example, a moving average process as shown in the following equation in order to reduce the influence of noise.

In the above equation, T ₁ is the data collection sampling period, and M is the number of data collection sampling points including the current time.

(Calculation formula of phase angle between voltage and current by gauge differential power group)
From the above equation, the sine function value of the voltage-current phase angle φ can be obtained as follows.

  Therefore, the voltage-current phase angle φ is obtained as follows.

  The range of the voltage-current phase angle φ is between −180 degrees and +180 degrees.

(Calculation formula of apparent power and power factor by gauge differential power group)
By the above formula and the definition of the apparent power, the apparent power S by the gauge differential power group can be calculated using the following formula.

  Further, the power factor PF based on the gauge differential power group can be calculated using the following equation based on the above-described equation and the definition of the power factor.

(Calculation formula of impedance by gauge differential power group)
Similar to the gauge power group, the impedance can be calculated using the gauge differential power group. Specifically, the equation representing the impedance can be expressed as the following equation.

  From the above equation, the resistance component of the impedance can be calculated using the following equation.

  Similarly, the reactance component of impedance can be calculated using the following equation:

  In order to reduce the influence of circuit noise, the following moving average process may be performed in the same manner as other electric quantities.

(Calculation formula of inductance component and capacitance component by gauge power group)
Similar to the gauge power group, the inductance component and the capacitance component can be calculated using the gauge differential power group. In addition, since it becomes the same expression expansion, expression expansion here is abbreviate | omitted.

(Comparison between the invariant according to the present invention and the prior invention)
First, the present invention proposes the following invariants of the gauge differential power group.

  The present invention also proposes an invariant of the next gauge differential power group different from the above formula.

  Here, the following relational expression is established from the above two expressions.

  On the other hand, the gauge differential active power in the prior invention (Patent Document 3) is as follows.

  From the above equation, it can be understood that the gauge differential active power of the prior invention is part of the gauge differential active power of the present invention. In addition, it can be said that the calculation is simple because there is no term of sinφ in the formula of the present invention.

  For the gauge differential reactive power that is one of the invariants of the gauge differential power group, the same formula as in the prior application invention is used. Specifically, it is the following formula.

  As can be understood from the above equation (99), the present invention uses four product elements, and the prior invention is different in that it uses two product elements. Use of many product elements in the same symmetric group space is considered to have a smoothing effect on the calculation result. Therefore, the present invention is recommended over the calculation formula of the prior invention.

(Other invariants of gauge differential power group)
Also, for the gauge differential active power, another calculation formula different from the above formula can be assumed. For example, the following formula may be used.

If the frequency coefficient f _C is used instead of the rotational phase angle α, it can be expressed as the following equation.

  If necessary, the moving average process shown in the following equation may be performed to reduce noise.

In the above equation, M is the number of data (the number of data collection sampling points) for moving average processing including the current time. Further, the calculation formula of P _gd (t, k) within the Σ symbol in the above formula is expressed by the following formula.

  In addition, if the two calculation formulas regarding the gauge differential active power described above are solved simultaneously, the following calculation formula is derived.

The above formula leads to a calculation formula for the frequency coefficient f _C shown in the following formula.

However, the frequency measurement range of the above equation is ¼ or less of the gauge sampling frequency f _S (the rotational phase angle α is 90 degrees or less).

(Symmetry index of gauge differential power group (second calculation formula))
As a symmetry index of the gauge differential power group, the following formula different from the first calculation formula is proposed.

If the above equation is satisfied, then v ₂ (t), v ₂ (tT), v ₂ (t-2T), i ₂ (t), i ₂ (tT), i ₂ (t-2T) The symmetry of the constructed gauge differential power group is broken. For this reason, when the symmetry of the gauge differential power group is broken, the calculated value before the symmetry is broken is latched. On the other hand, if the above equation is not satisfied, it is determined that the symmetry is not broken, and the calculation using the symmetry group is continued.

  Thus, it is considered that various invariants can be found by using the group table of the gauge differential power group and can be used when necessary. In addition, since various quantities calculated | required by a gauge difference electric power group are calculated by the difference value of an instantaneous value, there exists a merit that the influence of a direct-current component becomes small.

  From here, a rotational differential power group is proposed in which the number of differential voltage rotation vectors and differential current rotation vectors, which are members of the gauge differential power group, is reduced by one, and calculation output can be performed at higher speed. Note that the rotation difference power group here, that is, a power group composed of two rotation difference vectors obtained by reducing the number of rotation difference vectors by one is referred to as a rotation difference voltage group.

(Rotational differential power group on complex plane)
FIG. 2-9 is a diagram illustrating a rotational difference power group on the complex plane. The two differential voltage rotation vectors and the two differential current rotation vectors on the complex plane shown in FIG. 2-9 can be expressed by the following equations and the following equations, respectively.

  The equation (127) represents a rotation difference voltage group, and the equation (128) represents a rotation difference current group.

  In the above two equations, V is an AC voltage amplitude, I is an AC current amplitude, ω is a rotation angular velocity, T is a step size of a gauge sampling frequency for several hours, α is a rotation phase angle at T (from −180 degrees to +180 degrees). Φ) is the phase angle between voltage and current.

  In FIG. 2-9, two differential voltage rotation vectors and two differential current rotation vectors have symmetry. Further, the two differential voltage rotation vectors and the two differential current vectors have the same voltage-current phase angle. Further, the four differential rotation vectors, which are structures composed of the two differential voltage rotation vectors and the two differential current rotation vectors, can be obtained at different times and at different locations. The rotation phase angle α and the voltage-current phase angle φ in each of the differential rotation vectors do not change. That is, these four differential rotation vectors are also structures having the property of rotation invariance as described above. As described above, the two differential voltage rotation vectors are the rotation difference voltage group, the two differential current rotation vectors are the rotation difference current group, and therefore the rotation difference power group is composed of the rotation difference voltage group and the rotation difference current group. I understand that

(Vector group table of rotational differential power group)
In order to examine the invariants of the rotation difference power group, a vector group table of the rotation difference power group as shown in Table 7 below is constructed.

  The voltage / current rotation vector shown in the vector group table is a complex state variable. The symbol “x” in the above table means that the element on the front side and the element on the front side are multiplied. At this time, each product element of the vector group table of the rotational difference power group can be expressed as the following equation.

  Moreover, if the calculation of the right side of the above formula is advanced, it can be simplified as the following formula.

  FIG. 2-10 shows a vector product element based on the above equation on the complex plane. Here, a space generated by a product operation of two vectors is called a vector product space. Using this vector product space, we can see the symmetry inherent in AC sine waves. In the vector product space, each vector product element rotates counterclockwise at an angular velocity of 2ω. In the following description, two symmetries are selected.

The first set having symmetry is a set of v ₂ (t) i ₂ (tT) and v ₂ (tT) i ₂ (t) located on the intermediate axis of each rotation vector, and The result of vector multiplication of both is equal.

  As will be apparent from the calculation formula described later, reactive power can be directly calculated by this set.

A second set having symmetry is a set of v ₂ (t) i ₂ (t) and v ₂ (tT) i ₂ (tT), and has a phase difference α with respect to the intermediate axis. As will be apparent from the calculation formula described later, the active power can be calculated from this set and the frequency coefficient.

(Real number group table of rotational difference power group)
In order to derive the invariable calculation formula of the rotation difference power group, a real number group table of the rotation difference power group as shown in Table 8 below is constructed.

  Next, the real number group table of the rotational difference power group will be described. First, the real part instantaneous value of the differential voltage rotation vector, which is a constituent element of Table 8, can be expressed by the following equation.

  In the above equation, “Re” indicates the real part of the complex number. Further, the real part instantaneous value of the differential current rotation vector, which is a constituent element of Table 8, can be expressed by the following equation.

  Substituting the instantaneous values of the above two formulas into the real number group table, each product element of the real number group table of the gauge differential power group is expressed as follows.

  Next, calculation formulas such as active power, reactive power, and phase angle between voltage and current will be described using each product element of the real number group table of the rotational difference power group.

(Calculation formulas for sine function and cosine function values of voltage / current phase angle by rotational differential power group)
First, in the rotation differential power group, the following equation is established.

  From the above equation, the calculation formula of the sine function value of the voltage-current phase angle φ is obtained as follows.

  Further, in the rotational difference power group, the following formula and the following formula are also established.

  Here, if both sides of the equation (138) are multiplied by the cosine function value of the rotation phase angle α, the following equation is obtained.

  Then, by solving the simultaneous equations of these equations (137) and (138), the following equation is obtained as an equation representing the cosine function value of the voltage-current phase angle φ.

(Calculation formulas for active power and reactive power by rotational differential power group)
First, the active power P can be calculated using the following formula by the definition formula of the active power and the formula derived above.

  In order to reduce the influence of noise, it is effective to perform a moving average process as shown in the following equation, for example.

Further, each calculation formula of vi _2add1 (t, k) and vi _2add2 (t, k) within the Σ symbol in the above formula is expressed by the following formula.

  From the above equation, the reactive power Q can be calculated using the following equation.

  In order to reduce the influence of noise, it is effective to perform a moving average process as shown in the following equation, for example.

Each calculation formula of vi _sub (t, k) within the Σ symbol in the above formula is expressed by the following formula.

(Calculation formula of phase angle between voltage and current by rotational differential power group)
From the above equation, the tangent function value of the phase angle between the voltage and current is obtained as the following equation.

  Therefore, the voltage-current phase angle φ is obtained as follows.

  The range of the voltage-current phase angle φ is between −180 degrees and +180 degrees.

(Calculation formula of apparent power and power factor by rotational differential power group)
By the above formula and the definition of the apparent power, the apparent power S by the gauge differential power group can be calculated using the following formula.

  Further, the power factor PF based on the gauge differential power group can be calculated using the following equation based on the above-described equation and the definition of the power factor.

(Impedance calculation formula using rotational differential power group)
Impedance can be calculated from the rotational differential power group. Here, the resistance component of the impedance can be calculated using the following equation.

  Similarly, the reactance component of impedance can be calculated using the following equation:

  In addition, the inductance component and the capacitance component can be calculated using the reactance component of the above equation. The calculation formula is the same as that of the gauge power group, for example, and the formula development here is omitted.

  Further, in order to reduce the influence of noise, it is effective to perform a moving average process as with other electric quantities.

(Calculation formula of rotational phase angle and real-time frequency using multiple symmetry groups)
Here, calculation formulas of the rotational phase angle and the real-time frequency using the gauge power group and the gauge differential power group will be described.

  First, there is a relationship of the following formula among the gauge effective power, the gauge differential effective power, and the rotation phase angle.

  From the above equation, the rotational phase angle is obtained as follows.

  Therefore, the real-time frequency can be obtained using the following equation based on the definition equation of the rotational phase angle.

  A similar expression can be derived using gauge reactive power and gauge differential reactive power.

  First, there is a relationship of the following formula among the gauge reactive power, the gauge differential reactive power, and the rotation phase angle.

  From the above equation, the rotational phase angle is obtained as follows.

  Therefore, the real-time frequency can be obtained using the following equation based on the definition equation of the rotational phase angle.

  When the real-time frequency deviates significantly from the power system frequency, it is possible to determine the symmetry breaking of the fundamental waveform by using the above formula (155) or (157). Although the expression expansion is omitted, it goes without saying that the same determination can be made when the rotational phase angle is a negative number.

(Calculation formula for AC active energy and AC reactive energy)
The AC active energy can be calculated using the following equation and the following equation.

In the above equation, t is the measurement time, and W _P1 and W _P2 are the forward direction AC active power amount and the reverse direction (reverse power flow) AC active power amount, respectively.

  The AC reactive energy can be calculated using the following equation and the following equation.

In the above equation, t is the measurement time, and W _Q1 and W _Q2 are the forward AC reactive energy and the reverse (reverse power flow) AC reactive energy, respectively. If the method of this invention is used, there exists an advantage that the reactive energy meter currently required becomes unnecessary.

  Next, based on the simulation results shown in FIGS. 2-11 to 2-13, the frequency gain characteristics according to the method of the present application will be considered. 2-11 is a frequency gain characteristic diagram of active power at a gauge sampling frequency of 200 Hz, FIG. 2-12 is a frequency gain characteristic diagram of reactive power at a gauge sampling frequency of 200 Hz, and FIG. FIG. 6 is a frequency gain characteristic diagram of a phase angle between voltage and current at a gauge sampling frequency of 200 Hz.

The simulation conditions shown in FIGS. 2-11 to 2-13 are as follows.
・ Gauge sampling frequency: 200Hz
・ Input waveform: sine wave ・ Input waveform frequency: variable from 0 to 200Hz ・ AC voltage amplitude: 1.0V
・ AC current amplitude: 0.8A
・ AC voltage initial phase angle: 30 degrees

  As shown in FIGS. 2-11 to 2-13, it can be seen that the frequency gain value at the active power, reactive power, and voltage-current phase angle is “1”, which matches the theoretical value.

  The various calculation formulas presented above can be applied to various apparatuses. Therefore, two embodiments are presented as application examples. One is an insulation monitoring device, and the other is an impedance measurement device. Needless to say, the present invention is not limited to these embodiments.

Embodiment 1 FIG.
3A is a diagram for explaining a concept of processing in the insulation monitoring apparatus according to the first embodiment, and FIG. 3B is a diagram illustrating a functional configuration of the insulation monitoring apparatus according to the first embodiment. Yes, FIG. 3-3 is a flowchart showing the flow of processing in this insulation monitoring apparatus.

  First, in the equivalent circuit without leakage current shown in FIG. 3A, the power supply voltage v can be expressed by the following equation.

In the above equation, V is the voltage amplitude, and φ ₀ is the voltage initial phase angle. Further, ω is an angular frequency and is expressed by the following equation using the real-time frequency f.

  Further, according to Ohm's law, the vector current on the power supply side is expressed as follows.

In the above equation, R ₀ , R, and L are equivalent ground resistance, equivalent resistance, and equivalent inductance, respectively. I ₀ is the current amplitude.

In an electrical facility such as a power transmission line, when the insulation performance is good, it can be shown as an equivalent circuit having no leakage current as shown in FIG. In this case, since the electrical equipment insulation performance is good, the equivalent ground resistance R ₀ has a very large value, and the leakage current i _0leak is almost zero as shown in the following equation.

As shown in the voltage-current vector diagram of FIG. 3A, the phase angle φ ₀ between the voltage and current has a large value.

  On the other hand, FIG. 3B is an equivalent circuit having a leakage current and a voltage-current vector diagram. In this equivalent circuit, the power supply voltage v can be expressed by the following equation.

In the above equation, V is a voltage amplitude, φ ₁ is a voltage initial phase angle, and ω is an angular frequency.

  Further, according to Ohm's law, the vector current on the power supply side is expressed as follows.

In the above equation, R ₁ is equivalent ground resistance, I ₁ is current amplitude, and ω is angular frequency.

In electrical equipment such as a power transmission line, when the insulation performance is poor, the equivalent ground resistance R ₁ shown in FIG. 3-1 (a) is a very small value, and the leakage current i _1leak is as shown in the following equation. The value is greater than or equal to the value.

At this time, as shown in the voltage-current vector diagram (FIG. 3B), the phase angle φ ₁ between the voltage and current is also reduced. By utilizing this principle, an insulation monitoring device can be configured. Specifically, the phase angle between the voltage and current at the power supply end is measured and compared with a threshold value, and if the measured phase angle between the voltage and current is equal to or less than the threshold value, it may be determined that the insulation performance is degraded. .

  Although the equivalent circuit of FIG. 3A is shown as a single-phase circuit, it is needless to say that it can be applied to circuits other than the single-phase circuit (for example, a three-phase circuit). If applied to a three-phase circuit, calculate the positive phase, negative phase and zero phase components in the three-phase voltage and current, and the phase angle in each component, that is, the phase angle between the positive-phase voltage and current, The phase angle between the negative phase voltage current and the phase angle between the zero phase voltage current may be calculated and compared with a predetermined threshold value.

  Conventionally, there is an insulation monitoring device using an Igr detection method. This method is a method of injecting a signal having a frequency different from the commercial frequency and separating a leakage current component flowing from the detected current to the ground capacitance. The present invention is advantageous in terms of hardware cost because it is a technique that does not require an injection current unlike the Igr detection method. In addition, about the apparatus of the type | system | group which inject | pours the signal of a frequency different from a commercial frequency like the Igr detection system, you may comprise an apparatus also applying the calculation formula of this application.

  Next, the insulation monitoring apparatus according to the first embodiment to which the above principle is applied will be described with reference to FIGS. 3-2 and 3-3.

  As shown in FIG. 3-2, the insulation monitoring apparatus D101 according to the first embodiment includes an alternating voltage current instantaneous value data input unit D102, a frequency coefficient calculation unit (hereinafter simply referred to as “frequency coefficient calculation unit”) of the gauge differential power group. D103, symmetry breaking discriminating unit D104, frequency coefficient moving average processing unit (hereinafter referred to as "first moving average processing unit") D105, gauge difference active power calculating unit D106, and moving average processing of gauge difference active power Unit (hereinafter referred to as “second moving average processing unit”) D107, gauge differential reactive power calculation unit D108, moving average processing unit of gauge differential reactive power (hereinafter referred to as “third moving average processing unit”) D109, Voltage-current phase angle calculation unit D110, voltage-current phase angle moving average processing unit (hereinafter referred to as "fourth moving average processing unit") D111, insulation monitoring information output unit D112 Interfaces D113 and configured to include a storage unit D 114. Here, the interface D113 performs a process of outputting a calculation result or the like to a display device or an external device, and the storage unit D114 performs a process of storing measurement data, a calculation result, or the like.

(Step SD101)
In the above configuration, the AC voltage / current instantaneous value data input unit D102 performs a process of reading the voltage instantaneous value from the instrument transformer (PT) and the current instantaneous value from the current transformer (CT) provided in the power system. Do. The read voltage instantaneous value and current instantaneous value data are stored in the storage unit D114.

(Step SD102)
For example, the frequency coefficient calculation unit D103 calculates the frequency coefficient using the following equation, which is shown again, based on the above calculation process using the gauge differential power group.

In the above equation, v ₂₁ , v ₂₂ , and v ₂₃ are differential voltage instantaneous values, which are calculated using the following equations.

In the above equation, v ₁₁ , v ₁₂ , v ₁₃ , v ₁₄ are instantaneous voltage values corresponding to the gauge sampling frequency. Further, i ₂₁ , i ₂₂ , and i ₂₃ are differential current instantaneous values, which are calculated using the following equations.

In the above equation, i ₁₁ , i ₁₂ , i ₁₃ , i ₁₄ are instantaneous current values corresponding to the gauge sampling frequency. T is a gauge sampling period and is calculated using the following equation.

The frequency coefficient calculation process can be explained as follows when it is explained in general according to the concept of the calculation process described above. That is, the frequency coefficient calculation unit D103 is selected from the instantaneous voltage data obtained by sampling the alternating voltage to be measured at a predetermined data collection sampling frequency, and is smaller than the data collection sampling frequency and equal to or higher than the frequency of the alternating voltage. Three-point differential voltage instantaneous value data (v ₂₁ , v ₂₂ , v) representing the distance between the tips of two adjacent voltage instantaneous value data in at least four consecutive voltage instantaneous value data extracted at the gauge sampling frequency ₂₃ ) and three points of differential current instantaneous value data (i ₂₁ , i ₂₂ , i ₂₃ ) corresponding to the three points of differential voltage instantaneous value data (v ₂₁ , v ₂₂ , v ₂₃ ), Rotational phase angle (α) obtained by rotating differential voltage instantaneous value data or differential current instantaneous value data on a complex plane during one cycle of the gauge sampling frequency is calculated. Both performs processing for calculating the calculated rotational phase angle cosine function value of (alpha) as a frequency coefficient (f _C).

(Step SD103)
The symmetry breaking determination unit D104 determines the symmetry breaking by using the above-described symmetry index determination formula (represented below) of the gauge differential power group.

(Step SD104)
If the above equation holds (Yes at step SD103), it is determined that the symmetry is broken, and the previous frequency coefficient value is latched and used, for example, using the following equation.

T ₁ is a data collection sampling period and is calculated using the following equation.

  On the other hand, if the above equation (170) is not satisfied (No at step SD103), it is determined that the symmetry is not broken, and the process proceeds to step SD105 without latching the frequency coefficient value.

(Step SD105)
The first moving average processing unit D105 performs the moving average processing of the frequency coefficient using the following equation that is shown again.

(Step SD106)
The gauge difference active power calculation unit D106 calculates the gauge difference active power using the following formula that will be described again.

(Step SD107)
The second moving average processing unit D107 performs a moving average process on the gauge differential active power using, for example, the following equation.

(Step SD108)
The gauge difference reactive power calculation unit D108 calculates the gauge difference reactive power using the following equation that is re-displayed.

(Step SD109)
The third moving average processing unit D109 performs a moving average process on the gauge differential reactive power using, for example, the following equation.

(Step SD110)
The voltage-current phase angle calculation unit D110 calculates the voltage-current phase angle using the following equation.

(Step SD111)
For example, the fourth moving average processing unit D111 performs a moving average process on the phase angle between voltage and current using the following equation.

(Step SD112)
The insulation monitoring device D101 outputs the calculated voltage-current phase angle as insulation monitoring information. Moreover, the insulation monitoring apparatus D101 outputs an alarm warning using the following formula.

(Step SD113)
The insulation monitoring apparatus D101 determines whether or not the process is complete. If the process is not complete (No in step SD113), the process returns to step SD101. On the other hand, if the process is finished (step SD113, Yes), the flow exits.

  Next, the usefulness and effect of the insulation monitoring apparatus according to the first embodiment will be described based on the simulation result using the numerical example of case 1.

  First, parameters of case 1 are as shown in Table 9 below. In case 1, the equivalent ground resistance is changed from the time of setting, and the phase angle between the voltage and current corresponding to the change is monitored in real time.

  Based on Table 9, the simulation is set. First, the angular frequency is obtained as follows.

  When the initial phase angle of the power supply voltage is zero, the rotation vector voltage is expressed by the following equation.

  If it does so, the power supply side electric current before fluctuation | variation generation | occurrence | production will be calculated | required like following Formula.

  As shown in the above equation, the voltage-current phase angle before the occurrence of fluctuation is 72.33 degrees (1.2623 radians). Next, the power supply side current after the occurrence of fluctuation is obtained as follows.

  As shown in the above equation, the phase angle between voltage and current after occurrence of fluctuation is 14.82 degrees (0.2587 radians).

  From these results, the voltage / current functions before and after the occurrence of fluctuations in this simulation are expressed as the following equations and the following equations.

  The waveforms of the above two formulas are shown in FIGS. 3-4 and 3-5. In these figures, for the sake of simplicity, the waveforms before and after the fluctuation are abruptly connected in a time of 0.1 seconds. However, by solving the system characteristic equation based on the spiral vector theory, a voltage or current transient solution is obtained. It is also possible to draw a current waveform that is closer to reality.

  3-6 is a figure which shows the measurement result of the frequency coefficient in this simulation. Except for the transient state after the occurrence of fluctuation, the frequency coefficient is obtained as follows.

  According to FIGS. 3-6, although the fixed error has arisen in the measurement result in the fixed time immediately after a state change, it turns out that it corresponds with a theoretical value except the time slot | zone.

  Moreover, FIG. 3-7 is a figure which shows the measurement result of the gauge difference active power in this simulation. Before the occurrence of the fluctuation, the equivalent ground resistance has a very large value, so that the value is small as calculated by the gauge differential active power, which is expressed by the following equation.

  On the other hand, after the occurrence of fluctuation, the equivalent ground resistance changes to a small value, resulting in leakage current. As a result, the gauge differential active power changes to a large value as calculated by the following equation.

  Moreover, FIG. 3-8 is a figure which shows the calculation result of the gauge difference reactive power in this simulation. The calculation results of the gauge differential reactive power before and after the occurrence of fluctuation are as follows:

  As shown in FIG. 3-8, the value of the gauge differential reactive power does not change much before and after the occurrence of fluctuations, except in the transient state period. The reason for this is that the cause of the leakage current is due to a decrease in the equivalent ground resistance, and the change in the reactance (inductance, capacitance) component of the system is small.

  3-9 is a figure which shows the measurement result of the voltage-current phase angle in this simulation. The calculation results of the phase angle between voltage and current before and after the occurrence of fluctuation are as follows:

Also, the alarm occurrence threshold φ _SET for the voltage-current phase angle is set to a value of the following equation, for example.

  In this case, for example, according to this simulation, as shown in FIG. 3-9, it is possible to output an alarm alarm of insulation decrease due to leakage current in a time of about 40 ms after the state change.

Embodiment 2. FIG.
Next, an impedance measuring device will be described as an application example of the various calculation formulas described above. FIG. 4-1 is a diagram illustrating a functional configuration of the impedance measuring apparatus according to the second embodiment, and FIG. 4-2 is a flowchart illustrating a processing flow in the impedance measuring apparatus.

  As shown in FIG. 4A, the impedance measuring apparatus D201 according to the second embodiment includes an AC voltage / current instantaneous value data input unit D202, a frequency coefficient calculation unit of a gauge differential power group (hereinafter simply referred to as “frequency coefficient calculation unit”). D203, symmetry breaking determination unit D204, frequency coefficient moving average processing unit (hereinafter referred to as "first moving average processing unit") D205, rotational phase angle calculation unit D206, rotational phase angle moving average processing unit ( (Hereinafter referred to as “second moving average processing section”) D207, gauge difference current calculation section D208, moving average processing section for gauge difference current (hereinafter referred to as “third moving average processing section”) D209, gauge difference effective / Reactive power calculation unit D210, gauge difference active / reactive power moving average processing unit (hereinafter referred to as “fourth moving average processing unit”) D211, active / reactive power calculation unit D2 2. Active / reactive power moving average processing unit (hereinafter referred to as “fifth moving average processing unit”) D213, resistance / reactance calculation unit D214, resistance / reactance moving average processing unit (hereinafter referred to as “sixth moving average”) D215, an interface D216, and a storage unit D217. Here, the interface D216 performs a process of outputting a calculation result or the like to a display device or an external device, and the storage unit D217 performs a process of storing measurement data, a calculation result, or the like.

(Step SD201)
In the above configuration, the AC voltage / current instantaneous value data input unit D202 performs a process of reading the voltage instantaneous value from the transformer for a meter (PT) provided in the power system and the current instantaneous value from the current transformer (CT). Do. Note that the read voltage instantaneous value and current instantaneous value data are stored in the storage unit D217.

(Step SD202)
For example, the frequency coefficient calculation unit D203 calculates the frequency coefficient using the following equation, which is shown again, based on the above calculation process using the gauge differential power group.

In the above equation, v ₂₁ , v ₂₂ , and v ₂₃ are differential voltage instantaneous values, which are calculated using the following equations.

In the above equation, v ₁₁ , v ₁₂ , v ₁₃ , v ₁₄ are instantaneous voltage values corresponding to the gauge sampling frequency. Further, i ₂₁ , i ₂₂ , and i ₂₃ are differential current instantaneous values, which are calculated using the following equations.

In the above equation, i ₁₁ , i ₁₂ , i ₁₃ , i ₁₄ are instantaneous current values corresponding to the gauge sampling frequency. T is a gauge sampling period and is calculated using the following equation.

  The frequency coefficient calculation process is the same as or equivalent to the process of the first embodiment described above, and detailed description thereof is omitted here.

(Step SD203)
The symmetry breaking determination unit D204 determines the symmetry breaking by using the above-described symmetry index determination formula (represented below) of the gauge differential power group.

(Step SD204)
If the above equation holds (Yes at step SD203), it is determined that the symmetry is broken, and the previous frequency coefficient value is latched and used, for example, using the following equation.

T ₁ is a data collection sampling period and is calculated using the following equation.

  On the other hand, if the above equation (199) is not satisfied (No in step SD203), it is determined that the symmetry is not broken, and the process proceeds to step SD205 without latching the frequency coefficient value.

(Step SD205)
The first moving average processing unit D205 performs the moving average processing of the frequency coefficient using the following equation that will be described again.

(Step SD206)
The rotational phase angle calculation unit D206 calculates the rotational phase angle using the following equation that will be described again.

(Step SD207)
The second moving average processing unit D207 performs a moving average process of the rotational phase angle using the following equation again.

(Step SD208)
The gauge differential current calculation unit D208 calculates the gauge differential current using the following equation.

(Step SD209)
The third moving average processing unit D209 performs a moving average process of the gauge differential current using the following equation.

(Step SD210)
The gauge difference active / reactive power calculation unit D210 calculates the gauge difference active / reactive power using the following formula and the following formula that are re-displayed.

(Step SD211)
The 4th moving average process part D211 performs the moving average process regarding a gauge difference effective / reactive power using the following formula and the following formula which are repeated.

(Step SD212)
The active / reactive power calculation unit D212 calculates the active / reactive power using the following formula and the following formula that are re-displayed.

(Step SD213)
The 5th moving average process part D213 performs the moving average process regarding active / reactive power using a following formula.

(Step SD214)
The resistance / reactance calculation unit D214 calculates the resistance component and reactance component of the impedance using the following equation and the following equation.

  When the sign of the reactance component is positive (plus), the inductance component can be calculated using, for example, the following equation.

In the above equation, α is the rotational phase angle and f _S is the gauge sampling frequency.

  When the sign of the reactance component is negative (minus), the capacitance component can be calculated using, for example, the following equation.

(Step SD215)
The sixth moving average processing unit D215 performs moving average processing on resistance and reactance (inductance in the following equation) components using the following equation.

(Step SD216)
The impedance measuring apparatus D201 determines whether or not the process is complete. If the process is not complete (No in step SD216), the process returns to step SD201. On the other hand, if the process is finished (step SD216, Yes), the process exits this flow.

  In the second embodiment, the impedance measuring device has been described as an application example. However, it is needless to say that the power measuring device may be configured to measure active power or reactive power. When configured as a pure power measuring device, the resistance / reactance calculation unit D214 and the sixth moving average processing unit D215 can be omitted.

  Next, the usefulness and effect of the impedance measuring apparatus according to the second embodiment will be described based on the simulation result using the numerical example of case 2.

  First, the parameters of case 2 are as shown in Table 10 below.

  Based on Table 10, the simulation is set. First, the angular frequency is obtained as follows.

  When the initial phase angle of the power supply voltage is zero, the rotation vector voltage is expressed by the following equation.

  Then, the current flowing through the circuit is obtained as follows.

  As shown in the above equation, the phase angle between the voltage and current is 75.26 degrees (1.3135 radians). Next, theoretical values of active power and reactive power are obtained as follows.

  From the result of the above equation, the voltage / current function in this simulation is expressed as the following equation.

  Here, the waveform of the voltage instantaneous value in the above equation is shown in FIG. In this case, since the input frequency is 60.5 Hz and not the rated frequency (60 Hz), it can be seen that the plot position in the figure is shifted and the change in the phase angle is nonlinear.

  The waveform of the instantaneous current value and the gauge differential current in the above equation (223) is shown in FIG. 4-4. In this case, since the input frequency is 60.5 Hz and not the rated frequency (60 Hz), it can be seen that the plot position in the figure is shifted and the change in the phase angle is nonlinear.

  When the gauge differential current immediately after the start of data accumulation is set to zero, the calculation result shown in the following expression is obtained by the subsequent calculation process, and the value is plotted in FIG. 4-4.

  4-5 is a figure which shows the measurement result of the frequency coefficient in this simulation. This frequency coefficient is obtained as follows.

  FIGS. 4-6 is a figure which shows the measurement result of the rotation phase angle in this simulation. This rotational phase angle is obtained as follows.

  Since the gauge sampling frequency (125 Hz) is about twice the real time frequency (60.5 Hz), the rotational phase angle has a large value.

  Although not shown, the gauge differential active power is calculated as follows:

  FIGS. 4-7 is a figure which shows the measurement result of the active power in this simulation. This active power is obtained by the following equation.

  As shown in FIGS. 4-7, it turns out that the measurement result and theoretical value of active power correspond.

  Although not shown, the gauge differential reactive power is calculated as follows.

  Moreover, FIG. 4-8 is a figure which shows the measurement result of the reactive power in this simulation. This reactive power is obtained by the following equation.

  As shown in FIG. 4-8, it can be seen that the measurement result of the reactive power agrees with the theoretical value.

  Moreover, FIG. 4-9 is a figure which shows the measurement result of the resistance value in this simulation. The resistance value at this time is obtained as in the following equation.

  As shown in FIG. 4-9, it can be seen that the measurement result of the resistance value agrees with the theoretical value.

  Further, FIG. 4-10 is a diagram showing a measurement result of inductance in this simulation. The inductance at this time is obtained as follows.

  As shown in FIG. 4-10, it can be seen that the measurement result of the inductance agrees with the theoretical value.

  Note that the configuration shown in the above embodiment is an example of the configuration of the present invention, and can be combined with another known technique, and a part thereof is omitted without departing from the gist of the present invention. Needless to say, it is possible to change the configuration.

  For example, in the insulation monitoring device of the first embodiment, the rotation phase angle is not particularly calculated, and only the frequency coefficient is calculated by the gauge differential power group. In the impedance measurement device of the second embodiment, the frequency is first calculated by the gauge differential power group. The coefficient is calculated, and then the rotational phase angle is calculated from the frequency coefficient. First, the rotational phase angle is calculated from the gauge differential voltage group included in the gauge differential power group, and this rotational phase angle is calculated. It may be used to calculate the frequency coefficient.

  In Embodiments 1 and 2, the frequency coefficient is calculated using the gauge differential power group, but a gauge power group may be used instead of the gauge differential power group.

  In the first and second embodiments, the calculation of the real-time frequency is omitted, but a real-time frequency calculation unit may be provided.

  As described above, the present invention is useful as an electric quantity measuring device that enables highly accurate measurement of electric quantity even when the object to be measured is operating outside the system rated frequency.

D101 insulation monitoring device, D102, D202 AC voltage current instantaneous value data input unit, D103 frequency coefficient calculation unit, D203 frequency coefficient calculation unit, D104, D204 symmetry breaking determination unit, D105, D205 moving average processing unit of frequency coefficient (first 1 moving average processing unit), D106 gauge difference active power calculation unit, D107 gauge difference active power moving average processing unit (second moving average processing unit), D108 gauge difference reactive power calculation unit, D109 gauge difference reactive power Moving average processing unit (third moving average processing unit), D110 voltage-current phase angle calculation unit, D111 voltage-current phase angle moving average processing unit (fourth moving average processing unit), D112 insulation monitoring information output unit , D113, D216 interface, D114, D217 storage unit, D201 impedance D206 rotational phase angle calculation unit, D207 rotational phase angle moving average processing unit (second moving average processing unit), D208 gauge differential current calculation unit, D209 gauge differential current moving average processing unit (third moving unit) Average processing unit), D210 Gauge difference active / reactive power calculation unit, D211 Gauge difference active / reactive power moving average processing unit (fourth moving average processing unit), D212 Effective / reactive power calculation unit, D213 Active / reactive power Moving average processing unit (fifth moving average processing unit), D214 resistance / reactance calculation unit, D215 resistance / reactance moving average processing unit (sixth moving average processing unit).

Claims (18)

Second sampling that is smaller than the first sampling frequency and equal to or higher than the frequency of the AC voltage, from among the voltage instantaneous value data obtained by sampling the AC voltage of the system to be measured at a predetermined first sampling frequency. The differential voltage instantaneous value data of three points representing the tip-to-tip distance between two adjacent voltage instantaneous value data of at least four consecutive voltage instantaneous value data extracted by frequency, and the differential voltage instantaneous value data of the three points Rotational phase in which the differential voltage instantaneous value data or the differential current instantaneous value data is rotated on a complex plane during one cycle of the second sampling frequency based on the three differential current instantaneous value data corresponding to A frequency coefficient calculator that calculates the cosine function value of the angle as a frequency coefficient;
Of the three differential voltage instantaneous value data and the three differential current instantaneous value data used when calculating the frequency coefficient, the first differential voltage instantaneous value at the intermediate time and the first differential current instantaneous at the intermediate time A second product of the second differential voltage instantaneous value on the advance side of the intermediate time and the second differential current instantaneous value on the delay side of the intermediate time, and a second product of the delay side of the intermediate time. A gauge difference active power calculation unit that calculates a value obtained by subtracting an average value of the third product of the difference voltage instantaneous value of 3 and the third product of the third difference current instantaneous value on the advance side as a gauge difference active power;
An active power calculator that calculates the active power of the system based on the frequency coefficient and the gauge differential active power;
An electrical quantity measuring device comprising: Average value of the fourth product of the second differential voltage instantaneous value and the first differential current instantaneous value and the fifth product of the first differential voltage instantaneous value and the second differential current instantaneous value From the sixth product of the first differential voltage instantaneous value and the third differential current instantaneous value, and the seventh product of the third differential voltage instantaneous value and the first differential current instantaneous value A gauge difference reactive power calculation unit that calculates a value obtained by subtracting the average value as a gauge difference reactive power;
A reactive power calculator that calculates reactive power of the system based on the frequency coefficient and the gauge differential reactive power;
The electrical quantity measuring device according to claim 1, further comprising: The electrical quantity measuring device according to claim 2 , further comprising a voltage-current phase angle calculation unit that calculates a voltage-current phase angle in the system based on the gauge difference active power and the gauge difference reactive power. .   The electrical quantity measuring device according to claim 2, wherein apparent power of the system is calculated from the active power and the reactive power.   The electrical quantity measuring device according to claim 2, wherein a power factor of the system is calculated from the active power and the reactive power. Second sampling that is smaller than the first sampling frequency and equal to or higher than the frequency of the AC voltage, from among the voltage instantaneous value data obtained by sampling the AC voltage of the system to be measured at a predetermined first sampling frequency. The differential voltage instantaneous value data of three points representing the tip-to-tip distance between two adjacent voltage instantaneous value data of at least four consecutive voltage instantaneous value data extracted by frequency, and the differential voltage instantaneous value data of the three points Rotational phase in which the differential voltage instantaneous value data or the differential current instantaneous value data is rotated on a complex plane during one cycle of the second sampling frequency based on the three differential current instantaneous value data corresponding to A frequency coefficient calculator that calculates the cosine function value of the angle as a frequency coefficient;
Of the three differential voltage instantaneous value data and the three differential current instantaneous value data used when calculating the frequency coefficient, the first differential voltage instantaneous value at the intermediate time and the first differential current instantaneous at the intermediate time The value obtained by subtracting the second product of the second differential voltage instantaneous value on the advance side and the second differential current instantaneous value on the delay side from the intermediate time from the first product with the value is the first gauge difference effective A value obtained by subtracting the third product of the third differential voltage instantaneous value lagging from the intermediate time and the third differential current instantaneous value of the leading side from the first product is calculated as the second power. A gauge difference active power calculation unit that calculates the gauge difference active power and calculates the average value of the first and second gauge difference active powers as the gauge difference active power;
An active power calculator that calculates the active power of the system based on the frequency coefficient and the gauge differential active power;
An electrical quantity measuring device comprising: Average value of the fourth product of the second differential voltage instantaneous value and the first differential current instantaneous value and the fifth product of the first differential voltage instantaneous value and the second differential current instantaneous value From the sixth product of the first differential voltage instantaneous value and the third differential current instantaneous value, and the seventh product of the third differential voltage instantaneous value and the first differential current instantaneous value A gauge difference reactive power calculation unit that calculates a value obtained by subtracting the average value as a gauge difference reactive power;
A reactive power calculator that calculates reactive power of the system based on the frequency coefficient and the gauge differential reactive power;
The electrical quantity measuring device according to claim 6, further comprising:   The electrical quantity measurement according to claim 1 or 6, further comprising a symmetry breaking discriminating unit that judges the breaking of symmetry of the waveform of the AC voltage using a calculation formula when using the frequency coefficient as a determination index. apparatus. The electric quantity measuring device according to claim 7 ,
Using the frequency coefficient, the gauge differential active power, and the gauge differential reactive power to calculate a phase angle between the AC voltage and the AC current flowing in and out of the system, and based on the calculated phase angle, An insulation monitoring apparatus characterized by determining insulation.   Of the three differential current instantaneous value data used in calculating the frequency coefficient, the second differential current instantaneous value and the third differential current are calculated from the square value of the first differential current instantaneous value. The electric quantity measuring device according to claim 2, further comprising a gauge difference current calculation unit that calculates a square root of a value obtained by subtracting a product of the instantaneous value as a gauge difference current. The electric quantity measuring device according to claim 10,
An impedance measuring apparatus that calculates a resistance component of impedance in the system based on the gauge differential active power and gauge differential current. The electric quantity measuring device according to claim 10,
An impedance measuring apparatus, wherein a reactance component of impedance in the system is calculated based on the frequency coefficient, the gauge differential reactive power, and a gauge differential current. Second sampling that is smaller than the first sampling frequency and equal to or higher than the frequency of the AC voltage, from among the voltage instantaneous value data obtained by sampling the AC voltage of the system to be measured at a predetermined first sampling frequency. The differential voltage instantaneous value data of three points representing the tip-to-tip distance between two adjacent voltage instantaneous value data of at least four consecutive voltage instantaneous value data extracted by frequency, and the differential voltage instantaneous value data of the three points Rotational phase in which the differential voltage instantaneous value data or the differential current instantaneous value data is rotated on a complex plane during one cycle of the second sampling frequency based on the three differential current instantaneous value data corresponding to A frequency coefficient calculation unit that calculates an angle and calculates a cosine function value of the calculated rotation phase angle as a frequency coefficient;
A frequency calculating unit for calculating a real-time frequency of the system integration using the frequency coefficients and said second sampling frequency,
Equipped with a,
When the real-time frequency is smaller than ½ of the second sampling frequency, the rotational phase angle takes a positive value,
An electrical quantity measurement wherein the rotational phase angle takes a negative value when the real-time frequency is greater than ½ of the second sampling frequency and smaller than the second sampling frequency. apparatus. The electrical quantity measuring device according to claim 13 , wherein the real-time frequency is calculated as ½ of the second sampling frequency when the rotational phase angle takes a value of zero.   Effective power for calculating the active power of the system based on the rotation phase angle and the differential voltage instantaneous value data of three consecutive points of the four voltage instantaneous value data used in calculating the rotation phase angle The electric quantity measuring device according to claim 13, further comprising a power calculating unit. Second sampling that is smaller than the first sampling frequency and equal to or higher than the frequency of the AC voltage, from among the voltage instantaneous value data obtained by sampling the AC voltage of the system to be measured at a predetermined first sampling frequency. The differential voltage instantaneous value data of three points representing the tip-to-tip distance between two adjacent voltage instantaneous value data of at least four consecutive voltage instantaneous value data extracted by frequency, and the differential voltage instantaneous value data of the three points corresponding to three points on the basis of the difference current instantaneous values of the differential voltage instantaneous value data or the differential current instantaneous value data is rotated on the complex plane during a cycle of said second sampling frequency, the When the real-time frequency of the system is smaller than ½ of the second sampling frequency, it takes a positive value and the real-time frequency of the system Greater than 1/2 the frequency of the second sampling frequency, and wherein with the second and if smaller than the sampling frequency for calculating the rotation phase angle takes a negative value, the cosine function of the rotational phase angle calculated Calculating a value as a frequency coefficient;
Calculating the real-time frequency of the system using the second sampling frequency and the frequency coefficient;
A method of measuring electricity, comprising: Second sampling that is smaller than the first sampling frequency and equal to or higher than the frequency of the AC voltage, from among the voltage instantaneous value data obtained by sampling the AC voltage of the system to be measured at a predetermined first sampling frequency. The differential voltage instantaneous value data of three points representing the tip-to-tip distance between two adjacent voltage instantaneous value data of at least four consecutive voltage instantaneous value data extracted by frequency, and the differential voltage instantaneous value data of the three points Rotational phase in which the differential voltage instantaneous value data or the differential current instantaneous value data is rotated on a complex plane during one cycle of the second sampling frequency based on the three differential current instantaneous value data corresponding to Calculating a cosine function value of the angle as a frequency coefficient;
Of the three differential voltage instantaneous value data and the three differential current instantaneous value data used when calculating the frequency coefficient, the first differential voltage instantaneous value at the intermediate time and the first differential current instantaneous at the intermediate time A second product of the second differential voltage instantaneous value on the advance side of the intermediate time and the second differential current instantaneous value on the delay side of the intermediate time, and a second product of the delay side of the intermediate time. Calculating a value obtained by subtracting the average value of the third product of the differential voltage instantaneous value of 3 and the third product of the leading third differential current instantaneous value as the gauge differential active power;
Calculating active power of the system based on the frequency coefficient and the gauge differential active power;
A method of measuring electricity, comprising: Second sampling that is smaller than the first sampling frequency and equal to or higher than the frequency of the AC voltage, from among the voltage instantaneous value data obtained by sampling the AC voltage of the system to be measured at a predetermined first sampling frequency. The differential voltage instantaneous value data of three points representing the tip-to-tip distance between two adjacent voltage instantaneous value data of at least four consecutive voltage instantaneous value data extracted by frequency, and the differential voltage instantaneous value data of the three points Rotational phase in which the differential voltage instantaneous value data or the differential current instantaneous value data is rotated on a complex plane during one cycle of the second sampling frequency based on the three differential current instantaneous value data corresponding to Calculating a cosine function value of the angle as a frequency coefficient;
Of the three differential voltage instantaneous value data and the three differential current instantaneous value data used when calculating the frequency coefficient, the first differential voltage instantaneous value at the intermediate time and the first differential current instantaneous at the intermediate time The value obtained by subtracting the second product of the second differential voltage instantaneous value on the advance side and the second differential current instantaneous value on the delay side from the intermediate time from the first product with the value is the first gauge difference effective A value obtained by subtracting the third product of the third differential voltage instantaneous value lagging from the intermediate time and the third differential current instantaneous value of the leading side from the first product is calculated as the second power. Calculating as gauge difference active power, and calculating an average value of these first and second gauge difference active powers as gauge difference active power;
Calculating active power of the system based on the frequency coefficient and the gauge differential active power;
A method of measuring electricity, comprising:

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