JP6416072B2 - Synchronous phasor measuring device and pulse generator - Google Patents

Description

  The present invention relates to a synchronized phasor measuring device and a pulse generating device.

  An apparatus for measuring a voltage / current phasor of an electric power system is generally called a synchronous phasor measurement unit (PMU: Phazor Measurement Unit) (see Non-Patent Document 1). In a conventional synchronous phasor measurement device, a method of analyzing the effective value and phase of the voltage / current of a power system using a recursive DFT (Discrete Fourier Transform) is generally used (see Non-Patent Document 2). However, if the system frequency deviates from the DFT design frequency (that is, the rated frequency), there is a problem that detection accuracy deteriorates because the detected effective value and phase have errors.

  The inventor of the present application has proposed a method of detecting a voltage / current phasor in high accuracy and in real time using the symmetry of an alternating voltage current in Patent Document 1. Specifically, this patent document discloses a calculation method using a gauge synchronized phasor group and a gauge differential synchronized phasor group (the meanings of these terms will be described later).

JP 2014-139541 A JP, 2014-71108, A Japanese Patent No. 5214074

"IEEE Standard for Synchrophasor Measurements for Power Systems", IEEE Power & Energy Society, 28 December 2011, IEEE Std C37.118.1-2011 Nakano et al., “Real-time power system frequency detection based on synchronous phasor measurement”, IEEJ Transaction C, 2002, Vol.122-C, No.12, p.2076-2082

  In order to monitor the stability of the power system using a plurality of synchronous phasor measuring devices, it is necessary to continuously measure the phasor amounts at a plurality of points. However, the synchronous phasor measuring device described in Patent Document 1 has a problem that the phasor amount cannot be calculated when the waveform of the electrical quantity to be detected temporarily deviates from a sine wave due to voltage flicker or the like. .

  The present invention has been made in consideration of the above problems, and an object of the present invention is to provide a synchronous phasor measuring device capable of continuously measuring the phasor amount even when there is a temporary system abnormality based on voltage flicker or the like. It is to be.

  The synchronous phasor measuring device according to the present invention includes an input unit to which instantaneous value data obtained by sampling the amount of electricity in the power system is sampled every first period, and an arithmetic processing unit. The arithmetic processing unit calculates the gage difference effective synchronization phasor and the gauge difference invalid synchronization phasor as invariants using the data of four consecutive points extracted from the instantaneous value data every second period larger than the first period. To do. Furthermore, the arithmetic processing unit does not include data at the sampling time at which the symmetry breaking occurs when calculating the phasor amount by averaging the gauge difference effective synchronization phasor and the gauge difference invalid synchronization phasor. .

  According to the present invention, it is possible to provide a synchronous phasor measuring device capable of continuously measuring a phasor amount even when there is a temporary system abnormality based on voltage flicker or the like.

It is a figure which shows the synchronous phasor on a complex plane. It is a figure which shows the cage synchronous phasor group on a complex plane. It is a figure which shows the cage difference synchronous phasor group on a complex plane. It is a figure which shows the gauge voltage group on a complex plane in the case of including a direct current component. It is a conceptual diagram of the invariant averaging process of the gauge difference synchronous phasor group on a complex plane. It is a flowchart for performing the invariant averaging process of a gauge symmetry group, and a power failure discrimination. It is a figure for demonstrating the space synchronous phasor on a complex plane. It is a figure for demonstrating the time synchronous phasor on a complex plane. It is a diagram showing a relationship between time synchronization cycle number corresponding to the phasor N _TP and the gauge number of sampling points N _g. It is a figure which shows the relationship between a synchronous phasor phase angle and elapsed time. It is a figure which shows the relationship between a time synchronous phasor and a gauge sampling point number. It is a figure which shows the synchronous phasor on a complex plane, a virtual reference | standard phasor, and these phase difference angles. It is a block diagram which shows the structure of a synchronous phasor measuring device. It is a flowchart which shows the measurement procedure of a synchronous phasor. It is a block diagram which shows the structure of a pulse generator. It is a flowchart which shows operation | movement of the pulse generator of FIG. It is a figure for demonstrating the production | generation method of a positive half wave. It is a figure for demonstrating the concept of said output command time calculation. It is a figure which shows the voltage instantaneous value in case 1, and the measurement result of alternating current amplitude. It is a figure which shows the theoretical frequency and the measurement frequency waveform in case 1. It is a figure which shows the measurement result of the frequency change rate in case 1. FIG. FIG. 6 is a measured voltage waveform diagram in a measured example of case 2; It is an enlarged view of the area for 0.1 second of FIG. It is a figure which shows the measurement result of a Fourier-transform spectrum when the actual measurement voltage waveform in the actual measurement example of case 2 is detected for 3 seconds with the sampling frequency of 4000 Hz. It is a figure which shows the measurement result of a synchronous phasor phase angle as verification 1 of the actual measurement example of case 2. FIG. FIG. 10 is a diagram illustrating a measurement result of a synchronous phasor real part in verification 1 of an actual measurement example of case 2. It is a figure which shows the measurement result of a time synchronous phasor as verification 1 of the actual measurement example of case 2. FIG. It is a figure which shows the measurement result of a voltage amplitude as verification 2 of the actual measurement example of case 2. FIG. It is a figure which shows the measurement result of a time synchronous phasor as verification 2 of the actual measurement example of case 2. FIG. It is a figure which shows the measurement result of an average frequency as verification 3 of the actual measurement example of case 2. FIG. It is a figure which shows the measurement result of a frequency change rate as verification 3 of the actual measurement example of case 2. FIG. It is a figure which shows the measurement result of a phase difference angle as verification 4 of the actual measurement example of case 2. FIG. It is an enlarged view of FIG. It is a figure which shows a pulse production | generation result as verification 5 of the measurement example of case 2. FIG. It is an enlarged view of FIG. It is a block diagram of the EAST10 electric power system model of the Institute of Electrical Engineers of Japan. It is a flowchart which shows the calculation procedure by the electric power system stability monitoring system of FIG. In case 3, it is a figure which shows the simulation result of the internal phase angle of the generator G1. FIG. 6 is a three-dimensional diagram showing measurement results of a plurality of spatially synchronized phasors before failure as verification 1 of case 3; FIG. 5 is a three-dimensional view showing measurement results of a plurality of spatially synchronized phasors immediately before step-out of the generator G1, as verification 1 of case 3. FIG. 6 is a three-dimensional diagram showing measurement results of a plurality of spatially synchronized phasors immediately after the step-out of the generator G1 as verification 1 of case 3. It is a figure which shows the instantaneous value waveform of the positive phase voltage of a node (11) and a node (21) as the verification 2 of case 3. FIG. It is a figure which shows the measurement result of the phase difference angle in a node (11) and a node (21) as the verification 2 of case 3. FIG. It is a figure which shows the measurement result of the space synchronous phasor between a node (11) and a node (21) as case 3 verification 2. FIG. It is a block diagram which shows the structure of a three-phase unbalanced electric quantity measuring apparatus. It is a flowchart which shows the arithmetic processing procedure of a three-phase unbalanced electric quantity measuring apparatus. In case 4, it is a figure which shows the measurement result of the real part and amplitude of A phase voltage instantaneous value, A phase voltage synchronous phasor. In Case 4, it is the figure which showed the measurement result of the A phase voltage synchronous phasor on the complex plane. In case 4, it is a figure which shows the measurement result of the phase angle of an A phase voltage synchronous phasor. In case 4, it is a figure which shows the measurement result of the real part and amplitude of a positive phase voltage synchronous phasor. In case 4, it is a figure which shows the measurement result of the real part and amplitude of a negative phase voltage synchronous phasor. In case 4, it is a figure which shows the measurement result of the real part and amplitude of a zero phase voltage synchronous phasor. FIG. 6 is a diagram illustrating a measurement result of a real part and an amplitude of a positive phase current synchronization phasor in case 4; In case 4, it is a figure which shows the measurement result of the real part and amplitude of a negative phase current synchronous phasor. In Case 4, it is a figure which shows the measurement result of the real part and amplitude of a zero phase current synchronous phasor.

  Hereinafter, each embodiment will be described in detail with reference to the drawings. In the following embodiments, first, the basic concept of the present disclosure that is the basis of each embodiment will be described. In the description of the basic concept, [1] Definition of terms, [2] Comparison between the present disclosure and the conventional theory, [3] Explanation of the gauge synchronized phasor group, [4] Construction of a real group table of the gauge synchronized phasor group, [5] Frequency coefficient (symmetry index of gauge synchronous phasor group) [6] Definition and calculation formula of gauge effective synchronous phasor, [7] Definition and calculation formula of gauge invalid synchronous phasor, [8] Real part, imaginary part, Formula for calculating phase angle and AC voltage amplitude (when using gauge synchronized phasor group), [9] Description of cage differential synchronized phasor group, [10] Construction of real group table of gauge differential synchronized phasor group, [11] Frequency coefficient (symmetry index of gauge differential synchronous phasor group), [12] Definition and calculation formula of gauge differential effective synchronous phasor, [13] Definition and calculation formula of gauge differential invalid synchronous phasor, [14] Real part, Imaginary number , Calculation formula of phase angle and AC voltage amplitude (when using gauge differential synchronous phasor group), [15] calculation of DC component of input waveform [16] averaging process of invariant of gauge symmetric group and blackout discrimination [17] Formulas for calculating power and impedance, [18] Definitions and formulas for spatially synchronized phasors, [19] Definitions and formulas for time-synchronized phasors, [20] Formulas for calculating frequency and frequency change rate, [21] Virtual Description will be made in the order of the setting of the reference phasor and the calculation formula of the phase difference angle.

  Next, in the first embodiment, a configuration of the synchronized phasor measurement device and a flowchart of calculation will be described. In the second embodiment, a pulse generation device will be described. In the third embodiment, as a case 1, a simulation result of the frequency and the frequency change rate when the frequency changes at a constant rate will be described.

  In the fourth embodiment, as a case 2, calculation results based on actually measured voltage waveforms will be described. Specifically, in the verification 1 of Case 2, the calculation result of the synchronized phasor when the symmetry breaking occurs will be described. In verification 2 of case 2, an example in which the length of the time width of the averaging process is changed will be described. In verification 3 of case 2, an example in which the number of cycles of the time synchronization phasor is changed will be described. In verification 4 of case 2, an example in which the phase difference angle is measured using a virtual reference phasor will be described. In verification 2 of case 2, the result of generating a positive half-wave pulse using the waveform of the power system will be described.

  In the fifth embodiment, a simulation result using a power system model called EAST10 of the Institute of Electrical Engineers will be described. In the sixth embodiment, the results of measuring the three-phase unbalanced electric quantity in the EAST10 model will be described.

  In the following description, the same or corresponding parts are denoted by the same reference numerals, and the description thereof may not be repeated. In the following, a symmetrical group with respect to voltage will be mainly described, but the same applies to other electric quantities such as current and power.

<Basic concept of the present disclosure>
[1. Definition of terms]
First, terms used in the present disclosure will be described.

(1) Synchronous phasor A voltage or current vector that rotates counterclockwise on a complex plane. That is, in this specification, the synchronized phasor is an alias for a rotating voltage vector or a rotating current vector. The synchronized phasor is a complex state variable having three variables: a synchronized phasor real part, a synchronized phasor imaginary part, and a synchronized phasor phase angle. Possible values of the synchronized phasor phase angle are between -180 degrees and +180 degrees.

(2) group theory
Includes mathematical theories to study symmetry.

(3) Symmetry group
A group composed of a plurality of vectors having symmetry rotating on a complex plane. A group composed of a plurality of vectors having symmetry that is stationary on a complex plane is included.

(4) invariant
Invariants are the property of systems that a symmetric group has that does not change under certain transformations. Invariants assumed in the present embodiment are not limited to these, but are not limited to the following: gauge rotation phase angle, frequency coefficient, gauge effective synchronization phasor, gauge invalid synchronization phasor, gauge difference effective synchronization phasor, gauge difference invalid synchronization There are phasors. If the invariants are known, the characteristics of the symmetric group can also be known.

(5) Data collecting rate
Sampling frequency at the time of data collection, the higher the better. In this specification, the data collection sampling frequency is represented by f ₁ and the data collection sampling period is represented by T ₁ . There is a relationship of T ₁ = 1 / f ₁ . In application to an actual device, it is necessary to select an appropriate data sampling frequency in consideration of hardware (H / W) limitations and data synchronization requests for a plurality of channels.

(6) Gauge sampling frequency
This is the sampling frequency used for the calculation of the gauge symmetry group, expressed by the symbol f _g , and its unit is hertz (Hz). Expressing gauge sampling period with T _g, a relationship of T _g = 1 / f _g. Hereinafter, the subscript “g” is not used, and it may be described as a gauge sampling frequency f and a gauge sampling period T.

(7) System nominal frequency
It means the rated frequency in the electric power system and is expressed by the symbol f ₀ and is typically 50 Hz or 60 Hz.

(8) Gauge rotation phase angle The rotation vector rotating on the complex plane means the angle (electrical angle) actually rotated in the gauge sampling period, and is expressed by the symbol α.

(9) Frequency coefficient This means the cosine function value of the gauge rotation phase angle and is expressed by the symbol f _C.

(10) Gauge voltage group A symmetric group rotating counterclockwise on a complex plane, which is composed of three rotation voltage vectors (synchronous phasors) that are adjacent to each other and have a time interval T in time series. means. The same symmetric group concept can be defined for current.

(11) Gauge-synchronized phasor unit group Adjacent to each other in time series with a time interval T (gauge sampling period) and stationary on a complex plane composed of voltage static vectors (unit static vectors) with three unit amplitudes Means a symmetrical group. The same concept of unit group can be defined for current.

(12) Gauge-synchronized phasor group A symmetric group composed of a gauge-voltage group rotating on a complex plane and a gauge-synchronized phasor unit group stationary on the same complex plane as the gauge voltage group. The same symmetric group concept can be defined for current.

(13) Gauge differential voltage group Rotating counterclockwise on a complex plane composed of three differentially synchronized phasors (differential rotational voltage vectors) adjacent to each other with a time interval T in time series. Means a symmetric group. Here, the differential synchronized phasor is defined as the difference between two synchronized phasors adjacent at a time interval T. Accordingly, the gauge differential voltage group is obtained by taking the difference between every two adjacent four synchronized phasors (rotational voltage vectors) that are adjacent to each other and have a time interval T in time series. The same symmetric group concept can be defined for current.

(14) Gauge differential synchronized phasor unit group This means a symmetrical group stationary on a complex plane composed of three differential voltage static vectors that are adjacent to each other and have a time interval T (gauge sampling period) and are continuous in time series. To do. Here, the differential voltage static vector is defined as the difference between the voltage static vectors of unit amplitude adjacent to each other at the time interval T (gauge sampling period). Therefore, the gauge differential synchronized phasor group takes the difference between every two adjacent voltage stationary vectors of four unit amplitudes having time interval T (gauge sampling period) adjacent to each other in time series. can get. The same concept of unit group can be defined for current.

(15) Gauge differential synchronized phasor group A symmetrical group composed of a gauge differential voltage group rotating on a complex plane and a gauge differential synchronized phasor unit group stationary on the same complex plane as the gauge differential voltage group. . The same symmetric group concept can be defined for current.

(16) Spatial synchronization phasor This is the difference in synchronization phasor phase angle between two nodes at the same time. Alternatively, it is defined as the phase difference of the synchronized phasor between two nodes at the same time. Possible values of the spatially synchronized phasor are between -180 degrees and +180 degrees.

(17) Time-synchronized phasor An integrated value of the phase angle at which the synchronized phasor has actually rotated from the time point before the current time to the present time is defined as the time-synchronized phasor. Therefore, the value that the time synchronization phasor can take is a value (positive number) greater than zero. The value obtained by dividing the time synchronization phasor by the specified period is defined as the phase velocity. Further, the fundamental frequency is calculated from the phase velocity.

  The above definition is different from that of Patent Document 1. In the case of Patent Document 1, the time-synchronized phasor is defined as a difference between a current synchronized phasor phase angle and a synchronized phasor phase angle at a time point that is a specified period before the current time. In this case, a possible value of the time synchronization phasor is between −180 degrees and +180 degrees.

(18) Phase difference angle This is the difference between the phase angle of the synchronized phasor on the complex plane and the phase angle of the virtual reference phasor. Possible values of the phase difference angle are between 0 degree and +180 degrees. By using this phase difference angle, it is possible to determine the power system step-out.

(19) Synchronous phasor measurement unit (PMU)
It is a device that measures synchronous phasors.

(20) Three-phase unbalanced electric quantity measuring device This is a device that measures the three-phase voltage and current of the power system and converts the measured three-phase voltage and current into normal phase, negative phase, and zero phase using the symmetric coordinate method. . In addition, when an antiphase and a zero phase component are zero, it will be in a three-phase equilibrium state.

(21) Pulse generator A device that generates a pulse signal. Specifically, the pulse generation device disclosed in this specification generates a pulse signal having the amplitude and frequency of the fundamental wave component of the input signal.

(22) Discrete Fourier transform (DFT)
Discrete Fourier transform, used for frequency analysis of discretized digital signals.

[2. Comparison between this disclosure and conventional theory]
First, the definition of the instantaneous frequency according to the IEEE standard is compared with the definition of the instantaneous frequency proposed by the present inventor. According to Equation (7) on page 8 of Non-Patent Document 1 (IEEE Std C37.118.1-2011), the fundamental wave x (t) is expressed by the following equation (A1) using the phase angle Ψ (t) and the amplitude Xm. ).

  Further, according to the equation (8) on page 8 of the same document, the frequency f (t) is defined as the following equation (A2) using the differential dψ (t) / dt of the phase angle ψ (t). The π represents the circumference ratio.

  Thus, the frequency f (t) is defined using the one-dimensional state variable Ψ (t). That is, the phase angle ψ is assumed to be a continuous function of time t, and the derivative of the function ψ (t) is defined as the instantaneous frequency f (t).

  In a general synchronous phasor measurement device (PMU), a phase difference and a frequency are measured by extracting a fundamental wave by DFT (see Non-Patent Document 2). For this reason, there is no analytical solution for frequency measurement of a pure sine wave even for input data (pure sine wave) of only the fundamental wave component.

  On the other hand, in the present disclosure, an instantaneous frequency based on a two-dimensional state variable is introduced without using the frequency definition of the above formula (2). First, the input waveform is digitized (quantized), and the instantaneous frequency is defined as in the following equation (A3) by introducing the symmetry principle based on the group theory concept for the quantized current and voltage. (See Patent Document 3).

Here, f _g is an arbitrary gauge sampling frequency, T _g is a gauge sampling period, and α is an angle (referred to as “gauge rotation phase angle”) that the synchronous phasor is rotated during the gauge sampling period T _g . If the input waveform is a pure sine wave, the fundamental frequency calculated with different number of cycles is the same, and there is an analytic solution for the fundamental frequency at the set gauge frequency f _g .

  Next, a comparison between a synchronous phasor calculation method based on the IEEE standard and a synchronous phasor calculation method proposed by the present disclosure will be described. As described above, in the IEEE standard disclosed in Non-Patent Document 1, the phase difference is calculated first based on the DFT, and then the frequency is calculated. Therefore, in general, there is no analytical solution of a synchronized phasor for a pure sine wave of an arbitrary frequency.

  On the other hand, in the synchronous phasor calculation method according to the present disclosure, as shown in Patent Document 1, even when a pure sine wave is input, an analytical solution of the synchronous phasor phase angle and the synchronous phasor is required. Specifically, it is as follows.

FIG. 1 is a diagram illustrating a synchronized phasor on a complex plane. The synchronized phasor v ₁ (t) is defined by a two-dimensional complex number as in the following equation (A4).

Here, V is the synchronized phasor amplitude, ω is the angular velocity, and φ is the synchronized phasor phase angle. The real part v _1re (t) and the imaginary part v _1im (t) of the synchronized phasor v ₁ (t) can be expressed as in the following equation (A5).

The angular velocity ω is expressed by the following equation (A6) using the instantaneous frequency f.

  In this way, when comparing the calculation method of the conventional synchronous phasor with the calculation method of the synchronous phasor proposed by the present disclosure, the latter has an analytical solution for a pure sine wave input signal of an arbitrary frequency. The existence is a great merit. In other words, in the conventional theory, a sine wave having a rated frequency of the power system is obtained with a symmetric transformation, whereas in the method proposed by the present disclosure, a pure sine wave having an arbitrary frequency (fundamental wave) ) For symmetric transformation.

  However, in an actual power system, various harmonic components exist due to various uncertain factors, and the fundamental wave itself is constantly changing. Therefore, in order to demonstrate the true value of the measurement method of synchronous phasor using the principle of symmetry, this disclosure describes the setting of symmetry breaking index, the expansion of the number of cycles to be measured, and the moving average processing of measurement results. By doing so, the influence of harmonic components is greatly reduced. Part of the above is disclosed in the patent document 1 by the present inventor, but in the present disclosure, by evolving the method related to the synchronous phasor measurement, the influence of the harmonic component is further reduced, The time resolution of the measurement of the fundamental frequency when the fundamental is changing is further increased.

  Specifically, first, an AC electric quantity (voltage and current) is obtained by using the gauge synchronous phasor group and the gauge differential synchronous phasor group, and thereby, the synchronous phasor is determined at high speed (detailed mathematical formula and Patent Document 1). Will be described later). Thereafter, a time-synchronized phasor (this definition is different from that of Patent Document 1) is calculated, and the fundamental frequency is calculated as in the following equation (A7) using the concept of phase velocity.

Here, f ₀ is a rated frequency of the power system or a moving average value of frequency measurement results from a time point a predetermined time before the current time to the current time. phi _TP (t) is newly proposed time synchronization phasor in the present disclosure (in integrated value of the phase angle synchronized phasor is rotated, therefore, the time synchronization phasor always greater than zero), T _TP corresponds to a time synchronization phasor This is the accumulated time. The integration time _TTP can be set arbitrarily. For example, the integration time may cycle greater than the fundamental wave, the cycle number N _TP corresponding to the integration time T _TP based on the rated frequency is determined. The larger the integration time T _TP (and hence the number of cycles N _TP ), the more the influence of harmonics can be reduced, but the detection time becomes longer. Selected.

  Furthermore, the difference of the synchronized phasor phase angles measured at the same time between any two nodes in the power system is defined as a spatially synchronized phasor. The spatially synchronized phasor is used for monitoring and controlling the stability of the power system.

  The method of the present disclosure can also be used to measure an unbalanced three-phase electricity quantity of a power system. As will be described in detail later, the effective value can be measured using a gauge invariant, and the instantaneous value can be calculated using a spiral vector symmetric coordinate method. On the other hand, in the conventional general method, the instantaneous value is calculated using αβ coordinate transformation, and the effective value is calculated using dq coordinate transformation.

  As described above, in the method of the present disclosure, unlike the IEEE standard (that is, the method of defining the fundamental wave in the real time domain), complex state variables (synchronized phasor real part, synchronized phasor imaginary part, synchronized phasor phase angle) are used. To define a synchronized phasor. Furthermore, these complex state variables that change from moment to moment are calculated in real time using the principle of symmetry. As a result, a high-speed and high-accuracy synchronous phasor measuring device (PMU) can be provided. Furthermore, the present disclosure proposes a sine wave pulse generation device using the above method.

  Table 1 below shows a comparison between a synchronized phasor measurement method according to the present disclosure and a conventional synchronized phasor measurement method based on the principle of symmetry.

[3. About Gauge Synchronized Phasers]
FIG. 2 is a diagram illustrating a cage-synchronized phasor group on a complex plane. With reference to FIG. 2, a phasor group represented by the following equation (B1) is assumed as three synchronized phasors on the complex plane.

  Here, t is time, V is AC voltage amplitude, T is a sampling time step size (ie, gauge sampling period) for calculating a symmetry group, α is a rotation phase angle corresponding to T, and φ is a synchronized phasor phase. It is a horn. A gauge voltage group is constituted by three synchronized phasors represented by the above formula (B1). The rotational phase angle α is an unknown number. In this specification, the rotational phase angle α represents an actually rotated angle and is always a positive number.

  Assume a unit vector group represented by the following equation (B2) as three unit vectors on the complex plane. A unit vector group represented by the following formula (B2) constitutes a gauge synchronous phasor unit group.

The rotational phase angle α ₀ used in the above equation (B2) is obtained as in the following equation (B3).

Here, f ₀ is an average frequency of the power system measured in a relatively long span (for example, several seconds up to the present time). When the apparatus is started, the rated frequency (50 Hz or 60 Hz) of the power system is set. f _g is the gauge sampling frequency.

A group constituted by the six vectors in FIG. 2 (that is, a gauge voltage group represented by the above equation (10) and a gauge synchronized phasor unit group represented by the above equation (11)) is referred to as a gauge synchronized phasor group. Define. It should be noted that the definition of the gauge synchronous phasor group is slightly different from the definition in Patent Document 1 previously filed by the present inventor. Specifically, in Patent Document 1, the gauge voltage group and the gauge synchronous phasor unit group use the same rotational phase angle α. On the other hand, in the definition of the present disclosure, the rotation phase angle α of the gauge voltage group is an unknown number, and the rotation phase angle α ₀ of the gauge synchronous phasor unit group is given in advance. The corresponding rotation phase angle or the rotation phase angle corresponding to the frequency averaged over a long span. Since the frequency of the actual power system constantly fluctuates, stable calculation can be performed by changing the above definition.

[4. Construction of real number group table of gauge synchronous phasor group]
In order to obtain the invariant calculation formula of the gauge synchronous phasor group, a real number group table of the gauge synchronous phasor group is generated as shown in Table 2 below.

In calculating each product in Table 2, first, the real part instantaneous value of each synchronized phasor is expressed by the following equation (B4). In the following equation, Re [v ₁ (t)] represents the real part of the synchronized phasor v ₁ (t).

Next, the real part instantaneous value of each unit vector is expressed by the following equation (B5).

  By substituting the real part instantaneous value of the voltage phasor of the above formula (B4) and the real part instantaneous value of the unit vector of the above formula (B5), each product of Table 2 is obtained as in the following formula (B6). .

  The following is a formula for calculating the invariant of the gauge-synchronized phasor group obtained by using each product of the real number group table in Table 2 above.

[5. Frequency coefficient (symmetry index of gauge synchronous phasor group)]
When the frequency coefficient cosα ₀ , which is one of invariants of the gauge synchronous phasor group, is obtained from the above equation (B6), the following equation (B7) is obtained. Since the approximate α ≒ α ₀ holds, it is when the derivation of the following formula (B7) was replaced with α ₀ in α.

  Using the above equation (B7), the symmetry index of the gauge synchronous phasor group represented by the following equation (B8) is defined. In the following formula (B8), | ... | represents an absolute value.

  When the above equation (B8) is satisfied, it means that the input waveform is greatly deviated from a pure sine wave, that is, the symmetry of the input waveform is broken due to sudden amplitude change, sudden phase change, or sudden frequency change. An index for determining this breaking of symmetry is a symmetry index. When the symmetry breaking of the gauge-synchronized phasor group is detected, the invariant calculation result at that time is not used for the calculation of the amplitude, phase, and frequency.

[6. Definition and calculation formula of gauge effective synchronous phasor]
As one of invariants, the gauge effective synchronous phasor SA _p is defined as in the following formula (B9). By substituting the related product of the real group table into the first equation of equation (B9) and further approximating α to α ₀ , the second equation is obtained. The gauge effective synchronous phasor SA _p has a formula similar to a calculation formula for calculating a gauge active power which is one of invariants from a gauge voltage group and a gauge current group (see, for example, Patent Document 1). ).

[7. Gauge Invalid Synchronized Phaser Definition and Calculation Formula]
As one of the invariants, the gauge invalid synchronization phasor SA _Q is defined as the following equation (B10). By substituting the relevant product of the real group table into the first equation of equation (B10) and further approximating α to α ₀ , the second equation is obtained. The gauge reactive synchronous phasor SA _Q has a formula similar to a calculation formula for calculating a gauge reactive power that is one of invariants from a gauge voltage group and a gauge current group (see, for example, Patent Document 1). ).

[8. Formulas for real part, imaginary part, phase angle, and AC voltage amplitude]
By using the above-described gauge effective synchronization phasor SA _p and gauge invalid synchronization phasor SA _Q and the definition of the synchronization phasor, the synchronization phasor real part v _re , the synchronization phasor imaginary part v _im , the synchronization phasor phase angle φ, and the AC voltage The amplitude V is calculated as in the following formulas (B11) to (B14).

In the above formulas (B11) to (B14), f _c is a frequency coefficient (= cos α). The range of the synchronized phasor phase angle φ in the formula (B13) is between −180 degrees and +180 degrees.

When the input voltage includes a DC voltage component, the real part v _re , the imaginary part v _im , the phase angle φ, and the AC voltage amplitude V include an error. In that case, the real number part v _re , the imaginary number part v _im , the phase angle φ, and the AC voltage amplitude V are calculated using a gauge difference synchronous phasor group described later.

[9. On cage differentially synchronized phasors on the complex plane]
FIG. 3 is a diagram illustrating a cage differential synchronization phasor group on a complex plane. With reference to FIG. 3, a phasor group represented by the following equation (C1) is assumed as three differentially synchronized phasors on the complex plane.

  Here, V is the AC voltage amplitude, ω is the rotational angular velocity, T is the symmetric group calculation sampling time step size (ie, the gauge sampling period), α is the rotational phase angle corresponding to T, and φ is the synchronized phasor phase angle. A gauge differential voltage group is constituted by the three differential synchronization phasors represented by the above formula (C1). The rotational phase angle α is an unknown number.

  As the three difference unit vectors on the complex plane, a difference unit vector group represented by the following equation (C2) is assumed. A gauge difference synchronous phasor unit group is constituted by three difference unit vectors represented by the following equation (C2).

A group consisting of six difference vectors in FIG. 3 (that is, a gauge difference voltage group represented by the above equation (C1) and a gauge difference synchronized phasor unit group represented by the above equation (C2)) is represented by a gauge difference. It is defined as a synchronized phasor group. As in the case of the gauge-synchronized phasor group, the definition of the gauge difference-synchronized phasor group is slightly different from the definition in Patent Document 1 previously filed by the present inventor. In Patent Literature 1, the gauge voltage group and the gauge synchronous phasor unit group use the same rotational phase angle α, whereas in the definition of the present disclosure, the rotational phase angle α of the gauge voltage group is an unknown value, The rotational phase angle α ₀ of the phasor unit group is given in advance. The latter rotational phase angle α ₀ is, for example, a rotational phase angle corresponding to the rated frequency of the power system or a rotational phase angle corresponding to a frequency averaged over a long span.

[10. Construction of real group table of gauge differential synchronized phasor group]
In order to obtain the invariant calculation formula of the gauge difference synchronized phasor group, a real number group table of the gauge difference synchronized phasor group is generated as follows.

In calculating each product in Table 3, the real part instantaneous values v ₂₁ , v ₂₂ , and v ₂₃ of each differential synchronized phasor are expressed by the following equation (C3), and the real part instantaneous value v of each difference unit vector: ₂₀₁ , v ₂₀₂ , and v ₂₀₃ are expressed as the following equation (C4).

  The real part instantaneous value of the difference synchronous phasor of the above expression (C3) and the real part instantaneous value of the difference unit vector of the above expression (C4) are substituted for each product of the real number group table of Table 3 above. Hereinafter, the invariant calculation formula of the gauge difference synchronous phasor group obtained by using each product of the real group table of Table 3 is shown.

[11. Frequency coefficient (symmetry index of gauge differential synchronized phasor group)]
From the calculation result of each product of the real group table of Table 3, the frequency coefficient cosα which is one of invariants of the gauge difference synchronized phasor group is obtained by the following equation (C5). Since the approximate α ≒ α ₀ holds, it is when the derivation of the following formula (C5) was replaced with α ₀ in α.

  Using the above equation (C5), the symmetry index of the gauge differential synchronized phasor group represented by the following equation (C6) is defined. In the following formula, | ... | represents an absolute value.

  When the above equation (17) holds, it means that the symmetry of the gauge difference synchronized phasor group is broken, and the invariant calculation result at that time is not used for the subsequent calculations.

[12. Definition and calculation formula of gauge difference effective synchronized phasor]
As one of the invariants, a gauge difference effective synchronization phasor SD _p is defined as the following equation (C7). By substituting the related product of the real group table of Table 3 into the first equation of equation (C7), and further approximating α to α ₀ , the second equation is obtained.

[13. Definition and formula of gauge difference invalid synchronized phasor]
One invariant, defined as the gauge differential disable synchronization following equation phasor SD _Q (C8). By substituting the related product of the real group table of Table 3 into the first expression of Expression (C8), and further approximating α to α ₀ , the second expression is obtained.

[14. Formulas for real part, imaginary part, phase angle, and AC voltage amplitude]
By using the above-described gauge difference effective synchronization phasor SD _p and gauge difference invalid synchronization phasor SD _Q and the definition of the synchronization phasor, the synchronization phasor real part v _re , the synchronization phasor imaginary part v _im , the synchronization phasor phase angle φ, and The AC voltage amplitude V is calculated as in the following formulas (C9) to (C12).

Here, in the above formulas (C9) to (C12), f _c is a frequency coefficient (= cos α). The range of the synchronized phasor phase angle φ in the equation (C11) is between −180 degrees and +180 degrees.

[15. Calculation of DC component of input waveform]
The above quantity calculated by the gauge differential synchronized phasor group is a value calculated only by the AC amount excluding the DC component of the input waveform. On the other hand, the DC component included in the input voltage can be calculated using the gauge voltage group in the gauge synchronous phasor group.

  FIG. 4 is a diagram illustrating a gauge voltage group on a complex plane when a DC component is included. Referring to FIG. 4, it is assumed that three voltage instantaneous values constituting the gauge voltage group are expressed by the following equation (C13).

Here, v _DC is a DC component, V is an AC voltage amplitude, α is a rotation phase angle, and t is time. The AC voltage amplitude V is calculated according to the above formula (C12) using a gauge differential synchronized phasor group. By using the above formula (C13), the following formula (C14) is established as a formula for calculating the frequency coefficient f _C (= cos α) of the gauge voltage group.

From the above equation (C14), the DC voltage v _DC is obtained as the following equation (C15).

[16. Invariant averaging of gauge symmetry group and blackout discrimination]
Since the synchronized phasor phase angle φ is constantly changing, the invariants of the synchronized phasor symmetry group expressed by the formula including the phase angle φ, such as the gauge differential effective synchronous phasor and the gauge differential invalid synchronous phasor, also always change over time. ing. Therefore, for these invariants, averaging cannot be calculated by a simple moving average. For this reason, a calculation device for performing the invariant averaging process is required. Hereinafter, it will be described in detail with reference to the drawings. The following description is the same for the gauge effective synchronization phasor and the gauge invalid synchronization phasor.

FIG. 5 is a conceptual diagram of the invariant averaging process of the gauge differential synchronized phasor group on the complex plane. Referring to FIG. 5, the invariants calculated for the current gauge differential voltage groups v ₂ (t), v ₂ (t−T), and v ₂ (t−2T), and one data collection sampling period ( T ₁₎ only prior to the gauge differential synchronized phasor group _{v 2 (t-T 1)} , v 2 (t-T-T 1), v averaging the calculated invariants for _{2 (t-2T-T 1} ) Processing will be described.

When calculating the current invariant, as in the above description, gauge differential synchronized phasor groups v ₂ (t), v ₂ (6) composed of six difference vectors represented by solid lines in FIG. t−T), v ₂ (t−2T), v ₂₀ (t), v ₂₀ (t−T), v ₂₀ (t−2T), and invariants (gauge difference effective synchronization phasor and gauge difference invalid synchronization) Phasor etc.). On the other hand, when calculating the invariant that is one data collection sampling period (T ₁ ) before the current time, first, the gage differential synchronized phasor unit group is one data collection sampling period (T ₁ ) before v _20. (t−T ₁ ), v ₂₀ (t−T−T ₁ ), and v ₂₀ (t−2T−T ₁ ). Using this gauge differential synchronized phasor unit group, that is, gauge differential synchronized phasor groups v ₂ (t−T ₁ ), v ₂ (t−T−T ₁ ), v ₂ (t −2T−T ₁ ), v ₂₀ (t−T ₁ ), v ₂₀ (t−T−T ₁ ), and v ₂₀ (t−2T−T ₁ ) are used to calculate the invariant.

Gauge differential synchronized phasor groups v ₂ (t), v ₂ (t−T), v ₂ (t−2T), v ₂₀ (t), v ₂₀ (t−T), v ₂₀ (t −2T) is rotated counterclockwise by the phase angle α ₁ corresponding to the data collection sampling period T ₁ , the gauge differential synchronized phasor groups v ₂ (t−T ₁ ) and v ₂ (t −T−T ₁ ), v ₂ (t−2T−T ₁ ), v ₂₀ (t−T ₁ ), v ₂₀ (t−T−T ₁ ), v ₂₀ (t−2T−T ₁ ) Therefore, it seems intuitively clear that each invariant is almost equal. As a result, it is possible to average the current invariant and the invariant one data sampling period before the current time.

  By applying the above method, it is possible to perform averaging processing of N invariants up to the present time (such as a gauge difference effective synchronization phasor and a gauge difference invalid synchronization phasor). Here, power system disturbances (disturbances from the steady state) include relatively large disturbances such as symmetry breaking and relatively small disturbances such as noise that does not cause symmetry breaking. There are two types. In the averaging processing of N invariants up to the present time, in order to ensure data accuracy, the data at the time when the symmetry breaking occurs is not used, and the data for which the symmetry breaking has not occurred is used. Only the averaging process is performed. Thereby, the influence of harmonic noise can be reduced.

The great advantage of such an averaging processing method is that the data up to one data collection sampling period before the current time even if the current calculation result cannot be used due to the symmetry breaking due to the influence of voltage flicker or the like. The current data can be estimated by performing the averaging process using. For example, in order to perform averaging processing of N invariants up to the present time, gauge differential synchronized phasor groups v ₂ (t−K · T ₁ ), v ₂ (t−T−k · T ₁ ), v ₂ (t−2T−k · T ₁ ), v ₂₀ (t−K · T ₁ ), v ₂₀ (t−T−k · T ₁ ), v ₂₀ (t−2T−k · T ₁ ) Suppose that invariants are calculated for k = 0, 1, 2,..., N−1). In this case, N-1 invariants of k = 1, 2,..., N−1 are calculated even if the data at the present time (k = 0) cannot be used due to the symmetry breaking. By averaging the results, it can be used as the current invariant.

  As described above, when the current data cannot be used due to the symmetry breaking, the data before the data acquisition sampling period (which may be after the moving average processing) is used for the synchrophasor amplitude and synchrophasor frequency. It can be used as it is (also referred to as latching data). The always-changing synchronized phasor phase angle is calculated from the gauge difference effective synchronized phasor and the gauge difference invalid synchronized phasor estimated using the above averaging process. As a result, the continuity of the synchronized phasor calculation can be guaranteed, so that, for example, real-time protection of the power system can be stably performed.

  In addition, in the case where the averaging process at the N points up to the present time described above is performed, it is possible to determine that a power failure has occurred when symmetry breaking occurs at all times.

  Hereinafter, the above-described averaging process will be generally described with reference to flowcharts. The following steps are realized by executing software stored in a memory by a computer (processor) constituting the synchronous phasor measuring device.

FIG. 6 is a flowchart for performing invariant averaging processing and power failure determination of the gauge symmetry group. Referring to FIG. 6, first, N gauge difference synchronized phasor groups at the N time points up to the current time point used for the averaging process are selected (step S121). The interval between successive time points is the data collection sampling period T ₁ . For example, in the case of N = 3, that is, the symmetric group at the present time (k = 0), the symmetric group at the time point T ₁ before (k = 1), and the time point (k = 3) before 2 × T ₁ The three symmetric groups including the symmetric group are expressed as the following formula (D1).

Next, the computer starts the calculation by initializing the count number k and the averaging process total number N _AVG (step S122). Specifically, initialization is performed as in the following equation (D2). The case where k = 0 corresponds to the current time, and k = p means the time before the current time p.

Next, the computer calculates the symmetry index of the k-th (k = 0, 1,..., N−1; initial value is k = 0) gauge differential synchronized phasor group (step S123). Specifically, the computer calculates the symmetry index f _CBRK from the instantaneous values of a plurality of elements constituting the k-th gauge differential synchronization phasor group according to the above-described equation (35). Next, the computer determines whether or not the symmetry is broken, that is, whether or not the symmetry index f _CBRK is greater than 1 (step S124).

When the symmetry is broken (YES in step S124), the computer does not perform invariant calculation using instantaneous values of a plurality of elements constituting the kth gauge difference synchronous phasor group, and performs an averaging process. The total number N _AVG is decreased by 1 (step S125). That is, as shown in the following formula (D2), N _AVG -1 is substituted for the N _AVG.

On the other hand, if the symmetry is not broken (NO in step S124), the computer uses the instantaneous values of a plurality of elements constituting the k-th gauge difference synchronized phasor group to calculate the above-described formulas (C7) and ( According to C8), a gauge difference effective synchronization phasor (step S126) and a gauge difference invalid synchronization phasor (step S127) are calculated. Further, the computer calculates the direct current component v _DC according to the above-described equation (C15) using the instantaneous values of a plurality of elements constituting the gauge voltage group corresponding to the k-th gauge differential synchronization phasor group.

  The above calculation is performed until the count number k reaches N−1 (YES in step S129), that is, while sequentially counting up the count number k for all of the N gauge differential synchronization phasor groups selected first ( Step S130) is repeated.

When the count number k reaches N−1, that is, as a result of the completion of the above calculation for all selected gauge difference synchronized phasor groups (YES in step S129), when the total number of averaging processes N _AVG is 0 ( In step S131, the computer determines that a power failure has occurred in the power system (step S132), and ends the process. In this case, the symmetry is broken for all gauge synchronous phasor groups. The power outage occurred at least N × T ₁ before.

On the other hand, when the average processing total number N _AVG is not 0 (NO in step S131), the computer calculates an average value SD _PAVG of the calculated N _AVG gauge difference effective synchronization phasors SD _P (step S133). The calculation formula is based on the following formula (D4). In the equation (D4), SD _p (K) is the Kth (K = 1, 2,..., N _AVG ) symmetry among N _AVG gauge differential synchronized phasor groups in which symmetry breaking has not occurred. It means the calculated gauge differential effective synchronization phasor SD _P with the group.

Subsequently, the computer calculates an average value SD _QAVG of the calculated N _AVG gauge difference invalid synchronization phasors SD _Q (step S134). The calculation formula is based on the following formula (D5). In Formula (D5), SD _Q (K) is the Kth (K = 1, 2,..., N _AVG ) symmetry among N _AVG gauge differential synchronized phasor groups in which symmetry breaking has not occurred. It means the gauge difference invalid synchronized phasor SD _Q calculated using the group.

Subsequently, the computer calculates an average value v _DCAVG of the calculated N _AVG DC components v _DC (step S135). The formula for calculating the average value of the DC component is according to the following formula (D6). In equation (D6), v _DC (K) is the Kth (K = 1, 2,..., N _AVG ) symmetry among N _AVG gauge differential synchronized phasor groups in which symmetry breaking has not occurred. It means the DC component v _DC calculated using the group.

Thus, the invariant calculation procedure is completed.

[17. Formula for calculating power and impedance]
Synchronous phasor real number part v _re (see equation (C9)) and synchronous phasor imaginary part v _im (see equation (C10)) obtained by the above calculation, and synchronous phasor real part of current obtained by similar calculation A method of calculating power and impedance using i _re and the synchronized phasor imaginary part i _im will be described. In the following description, a voltage synchronous phasor and a current electric phasor are defined as in the following equation (E1).

  The active power P and the reactive power Q are obtained by the following formula (E2) by definition. In the following expression, the superscript “*” represents a complex conjugate, Re {...} Represents a real part, and Im {.

  From the definition formula of the voltage synchronous phasor v (t) and the current synchronous phasor i (t) of the above equation (E1), the impedance Z can be calculated by the following equation (E3), and the resistance component R and the reactance component X are It can be calculated by equation (E4).

[18. Spatial synchronization phasor definition and formula]
In this specification, a spatially synchronized phasor is defined as a synchronized phasor phase angle between two nodes at the same time, or a phase difference between synchronized phasors between two nodes at the same time. Possible values of the spatially synchronized phasor are between -180 degrees and +180 degrees. The spatial synchronization phasor calculation method will be described below with reference to the drawings.

FIG. 7 is a diagram for explaining a spatially synchronized phasor on a complex plane. It is assumed that the voltage-synchronized phasor v ₁ (t) of node ₁ and the voltage-synchronized phasor v ₂ (t) of node 2 at the same time are given by the following equation (F1). In the following formula (F1), V ₁ and V ₂ are synchronous phasor amplitudes. In general, since the load of the power system and the amount of power generation are constantly changing, the angular frequency ω ₁ of the node ₁ and the angular frequency ω _{2 of the} node 2 at the same time are slightly different.

According to the cosine theorem, the spatial synchronization phasor φ _SP (t) that is the phase difference between the node 1 and the node 2 is given by the following equation (F2). In the following equation (F2), V ₁₂ is the difference-synchronized phasor amplitude between the node 1 and the node 2, and its square is given by the following equation (F3) by the Pythagorean theorem. In other words, the space-synchronized phasor φ _SP (t) is the real part and imaginary part of the phasor display of the quantity of electricity (voltage or current) measured at the same sampling time at each of the first and second nodes of the power system. , By using the cosine theorem. According to the definitions of the following equations (F2) and (F3), the possible values of the spatially synchronized phasor φ _SP (t) are 0 to +180 degrees.

Unlike the above calculation method, it is also possible to define a spatially synchronized phasor by the difference between the synchronized phasor phase angle φ ₁ of node ₁ and the synchronized phasor phase angle φ _{2 of} node 2 (in fact, a patent by the inventor of the present application). Reference 1 uses such a definition). However, if the spatially synchronized phasor is defined as the phase difference between φ ₁ and φ ₂ and the spatially synchronized phasor is calculated by the above equation (F2), the spatially synchronized phasor can be stably obtained with less error.

  A power system stability monitoring system can be constructed using the spatially synchronized phasor and the real-time frequency of each node. A specific simulation example will be described later with reference to FIGS.

[19. Time synchronization phasor definition and formula]
In this specification, the time-synchronized phasor is defined as an integrated value of the phase angles at which the synchronized phasor has actually rotated from the time point before the present time by a specified period _TTP to the present time. Therefore, the value that the time synchronization phasor can take is a value (positive number) greater than zero. Since it is different from the definition in Patent Document 1 by the inventor of the present application, attention is required. In Patent Document 1, a time-synchronized phasor is defined as a difference between a current synchronized phasor phase angle and a synchronized phasor phase angle at a time point a specified period before the current time. In this case, a possible value of the time synchronization phasor is between −180 degrees and +180 degrees.

FIG. 8 is a diagram for explaining a time-synchronized phasor on the complex plane. Referring to FIG. 8, time synchronization phasor φ _TP (t) is defined by the following equation (F4). In the following equation (F4), φ (t) is the current synchronized phasor phase angle, φ (t−T _TP ) is the synchronized phasor phase angle just before the present time by the designated period T _TP , and N _TP is the designated period. T _TP synchronization in phasor is the number of cycles of rotation.

The designated period _TTP is represented by a positive integer multiple of the data collection sampling period T ₁ as shown in the following equation (F5). This positive integer is referred to as the gauge sampling point number N _g .

Figure 9 is a diagram showing the relationship between the time synchronization cycle number corresponding to the phasor N _TP and the gauge number of sampling points N _g. Referring to FIG. 9, the data collection sampling frequency is 4000 Hz, and the system frequency is 60 Hz. Theoretically, all of the gauge number of sampling points N _g 9, the measured synchronization phasor of phase angle difference (i.e., φ (t) -φ (t -T TP)) and by the number of cycles N _TP, time it should be possible to calculate the synchronized phasor phi _TP. However, since the measurement point also varies when the frequency varies, a shift may occur in the cycle number _NTP . Therefore, it is desirable to determine the number of cycles in the vicinity of the intermediate point (points A, B, and C in FIG. 9) of the stepped step in FIG. 9 corresponding to the rated frequency of the power system. Table 4 is a table showing the relationship between the gauge number of sampling points N _g and cycle number N _TP of the time synchronization phasor.

FIG. 10 is a diagram illustrating the relationship between the synchronized phasor phase angle and the elapsed time. Referring to FIG. 10, the synchronized phasor phase angle varies between −180 degrees and +180 degrees. On the other hand, the time-synchronized phasor is a positive real number and increases with time. If the number of cycles _NTP is different, different time-synchronized phasors _φTP are obtained for the same synchronized phasor phase angles φ (t) and φ (t− _TTP ). In the case of FIG. 10, the number of cycles N _TP is 2, and the time synchronization phasor φ _TP is given by φ (t) −φ (t−T _TP ) + 4π.

FIG. 11 is a diagram illustrating the relationship between the time synchronization phasor and the number of gauge sampling points. Referring to FIG. 11, the data collection sampling frequency is 4000 Hz. Even with the same gauge sampling point N _g , the time synchronization phasor φ _TP [deg] is different when the system frequency is different. FIG. 11 shows the relationship between the time-synchronized phasor φ _TP [deg] and the number of gauge sampling points N _g when the system frequencies are 65 Hz, 60 Hz, and 55 Hz. Time synchronization phasor phi _TP higher system frequency increases.

[20. Calculation formula of frequency and frequency change rate]
Using the time-synchronized phasor φ _TP (t) calculated according to the above, the frequency f (t) and the frequency change rate ROCOF (rate of change of frequency) are respectively calculated as the following equations (F6) and (F7). be able to. In the following equation, f (t) is the current frequency, and f (t−T _TP ) is the frequency before the current time by the specified period T _TP . f ₀ is a rated frequency of the power system or a moving average value of frequency measurement results from a time point a predetermined time before the current time to the current time.

[21. Virtual reference phasor setting and phase difference calculation formula]
In the following, assuming a virtual reference phasor rotating at a constant initial speed, the phase difference angle between the currently measured sync phaser and the virtual reference sync phaser is calculated, and the frequency and frequency change rate are calculated using the phase difference angle. Present the calculation method. By using the phase difference angle, the harmonic component can be confirmed as will be described later with reference to FIGS. 32 and 33, and step out can be determined as will be described later with reference to FIG.

FIG. 12 is a diagram illustrating a synchronized phasor, a virtual reference phasor, and their phase difference angles on a complex plane. Referring to FIG. 12, the current synchronized phasor v ₁ (t) is expressed by the following equation (G1). In the following equation (G1), v ₁ , ω ₁ , and φ ₁ are the current synchronous phasor amplitude, angular frequency, and initial phase angle, respectively.

The current virtual reference phasor v ₀ (t) is expressed by the following equation (G2). The virtual reference phasor is defined as a fixed value of the amplitude, angular frequency, and initial phase of the synchronized phasor at a certain time. In the following equation (G2), v ₀ , ω ₀ , and φ ₀ are the amplitude, angular frequency, and initial phase angle of the virtual reference phasor that are measured at the time of setting the virtual reference phasor and fixed to the measured values.

The phase difference angle φ _d (t) is the phase difference between the current synchronized phasor v ₁ (t) and the virtual reference phasor v ₀ (t), and is defined by the following equation (G3) using the cosine theorem. Can do. In the equation (G3), V ₁₀ is the amplitude of the differential synchronized phasor obtained by the difference between the synchronized phasor v ₁ (t) and the virtual reference phasor v ₀ (t), and its square is expressed by the following equation (G4). expressed. That is, the phase difference angle φ _d (t) is the values of the real and imaginary parts of the virtual reference phasor rotating at a constant initial speed in the complex plane, and the real and imaginary parts of the synchronized phasor at the current sampling time. Calculated by using the value and the cosine theorem. From the following definition formulas (G3) and (G4), the possible value of the phase difference angle φ _d (t) is between 0 degree and +180 degrees.

According to the definition of the virtual reference phasor, it can be seen that the phase difference angle φ _d is zero when the frequency of the input signal does not change. When the frequency of the input signal changes, the phase difference angle also changes. The greater the change rate of the frequency, the greater the change rate of the phase difference angle. The frequency change Δf can be expressed as the following equation (G5) using the phase difference angle φ _d (t).

In the equation (G5), T _d is an elapsed time from the setting time of the virtual reference phasor to the present time. sgn is a code representing +1 or −1, and is defined as +1 (acceleration) when the time synchronization phasor φ _TP (t) is increased as in the following equation (G6), and the time synchronization phasor φ _TP ( It is defined as -1 (deceleration) when t) is decreasing.

By using the frequency change Δf in the above equation (G5), the current frequency f is calculated by adding the frequency change Δf to the frequency (rotational speed) f ₀ of the virtual reference phasor (f = f ₀ + Δf). Furthermore, the frequency change rate ROCOF (t) can be obtained as in the following equation (G7).

<Embodiment 1>
Embodiment 1 demonstrates the structure and operation | movement of the synchronous phasor measuring apparatus 100 connected to an electric power grid | system. As described above, regarding the calculation of the real part, the imaginary part, the phase angle, and the amplitude of the synchronized phasor, the same calculation result can be obtained in the gauge synchronized phasor group and the gauge differential synchronized phasor group. However, in the latter case, since all the elements constituting the symmetry group are difference vectors, the influence on the measurement result of the DC component of the input signal can be greatly reduced. For this reason, the following synchronized phasor measuring device 100 uses a gauge differential synchronized phasor group.

  FIG. 13 is a block diagram showing a configuration of the synchronous phasor measuring device. In the following, the measurement of the voltage-synchronized phasor will be mainly described, but the measurement of the current-synchronized phasor can be similarly performed. Referring to FIG. 13, synchronous phasor measuring device 100 includes voltage instantaneous value data input unit 101, calculation processing unit 120, calculation information transmission unit (and calculation information reception unit) 113, interface unit 114, and storage unit. 115 and a GPS receiver 116.

The voltage instantaneous value data input unit 101 is connected to the voltage transformer PT and continuously acquires voltage information from the power system. The acquired voltage information is converted into a digital signal by a built-in A / D converter, and finally, time-series voltage data for each data collection sampling period T ₁ is obtained.

  The arithmetic processing unit 120 is configured by a CPU (Central Processing Unit), and performs various arithmetic processes by operating according to a program stored in the storage unit 115. In terms of functionality, the arithmetic processing unit 120 includes an invariant averaging processing unit 102, a real part calculation unit 103 of a synchronized phasor, an imaginary part calculation unit 104 of a synchronized phasor, and a phase angle calculation unit 105 of a synchronized phasor. The amplitude calculation unit of the synchronized phasor, the space synchronization phasor calculation unit 107, the time synchronization phasor calculation unit 108, the frequency calculation unit 109, the frequency change rate calculation unit 110, the phase difference angle calculation unit 111, and the gauge difference synchronization phasor A rotation phase angle correction unit 112 of a unit group. The operation of each functional unit will be described with reference to the flowchart of FIG.

  The calculation information transmission unit (and calculation information reception unit) 113 is connected to another synchronous phasor measurement device (not shown) or a central monitoring system (for example, the power system stability monitoring system 201 in FIG. 36) via a communication line (not shown). ), For example, the calculation result in the arithmetic processing unit 120 is transmitted and received.

  The interface unit 114 is provided for connection with a user interface or an external device. The storage unit 115 stores the input voltage instantaneous value data, the above calculation result, and the like. The GPS receiver receives a time synchronization signal from a GPS satellite for time synchronization. The time synchronization method is not limited to GPS, and for example, a time synchronization signal may be transmitted from the central monitoring system to each synchronized phasor measurement device via a communication line.

  FIG. 14 is a flowchart showing the measurement procedure of the synchronized phasor. Referring to FIGS. 13 and 14, first, voltage instantaneous value data input unit 101 acquires an instantaneous voltage value from the power system (step S101). The acquired voltage instantaneous value is converted into time-series digital data.

  Next, the invariant averaging processing unit 102 calculates the average value of the gauge difference effective synchronization phasor, the average value of the gauge difference invalid synchronization phasor, and the average value of the DC component according to the flowchart described in FIG. 6 (step S102). ).

  Next, the real part calculation unit 103 of the synchronized phasor calculates the real part of the synchronized phasor according to the aforementioned equation (38) (step S103). The imaginary part calculation unit 104 calculates the imaginary part of the synchronized phasor according to the above equation (39) (step S104). The phase angle calculation unit calculates the phase angle of the synchronized phasor according to the above equation (39) (step S105). The synchronized phasor rotates counterclockwise on the complex plane, and the range of change of the phase angle of the synchronized phasor is −180 degrees to +180 degrees. Further, the amplitude calculator 106 calculates the synchronized phasor amplitude according to the above-described equation (41) (step S106). The calculations in steps S103 to S106 may be performed in any order.

  Next, the time synchronization phasor calculation unit 108 calculates a time synchronization phasor according to the above-described equation (83) (step S107). The frequency calculation unit 109 calculates the fundamental frequency according to the above equation (85) (step S108). The frequency change rate calculation unit 110 calculates the frequency change rate according to the above equation (86) (step S109).

  Next, the phase difference angle calculation unit 111 calculates the phase difference angle according to the above formula (92), calculates the change in frequency according to the above formula (94), and calculates the frequency change rate according to the above formula (96). (Step S110).

Next, the rotation phase angle correction unit 112 corrects the rotation phase angle α ₀ of the gauge difference synchronized phasor unit group (step S111). Specifically, the following procedure is followed. First, the rotational phase angle correction unit 112 performs a moving average of M frequencies calculated at M time points up to the present time according to the following equation (H1). In the following equation (H1), M is the designated moving average number, and T ₁ is the data collection sampling period.

The rotational phase angle α ₀ is obtained by the following equation (H2) using the above average value f ₀ (t) of the frequency and the gauge sampling frequency f _g .

  Next, the calculation information transmission part 113 transmits the information regarding the calculated synchronous phasor, and utilizes it for a wide area protection control system (step S112). When calculating a spatially synchronized phasor, the calculation information receiving unit 113 receives information on the synchronized phasor calculated from another synchronized phasor measuring device. In the next step S113, the space synchronization phasor calculation unit 107 calculates a space synchronization phasor according to the above-described equation (F2).

  When the calculation of the synchronized phasor is not completed (NO in step S114), the process returns to step S101, and the above calculation is repeated every data collection sampling period T1.

<Embodiment 2>
In Embodiment 2, a pulse generation device will be described. In the field of electronic circuits, a rectangular wave having a certain width is called a pulse, and is used for a clock signal or a synchronization signal. A square wave is mathematically expressed as a superposition of sine waves of a plurality of frequencies (so-called Fourier analysis). Here, the proposed pulse generation device generates a half wave of the fundamental wave out of the input signal waveform (the fundamental wave is the main component, but includes a harmonic component and a direct current component). The frequency and amplitude of the fundamental wave are reproduced with high accuracy).

  FIG. 15 is a block diagram illustrating a configuration of the pulse generation device. Referring to FIG. 15, pulse generation device 400 includes a sine wave input unit 401, a positive half wave generation unit 402 as a pulse generation unit, a designated output command unit 403, and a pulse output unit 404. The operation of each component will be described with reference to the flowchart of FIG.

  FIG. 16 is a flowchart showing the operation of the pulse generation device of FIG. Referring to FIGS. 15 and 16, sine wave input unit 401 receives an input of an AC voltage or an AC current from a power system, for example (step S401). The input AC voltage and AC current are mainly composed of fundamental waves, but contain harmonic components and DC components.

  Next, the positive half wave generation unit 402 is a positive half wave having the same frequency and the same amplitude as the fundamental wave of the input AC voltage and AC current (in the sense of a positive half wave of a sine wave) (Step S402). Specifically, the following method is used. In the following, a case where an alternating current is input is described, but the same applies to an alternating voltage.

FIG. 17 is a diagram for explaining a method of generating a positive half wave. FIG. 17 shows current phasors i ₁ (t) and i ₁ (t−T) when there is a DC component i _DC on the complex plane. In FIG. 17, I is the current amplitude, α is the gauge rotation phase angle, and i _DC is the positive half-wave output current. The instantaneous values i ₁₁ and i ₁₂ of the current phasors i ₁ (t) and i ₁ (t−T) are expressed by the following formula (I1).

The following positive half-wave output formula (I2) is obtained by modifying the time variable t in the above formula (I1) to be eliminated. In the following formula (I2), f _C is a frequency coefficient. The frequency coefficient f _C and the current amplitude I are calculated using the gauge differential synchronization phasor group, that is, according to the above (C5) and (C12) (but by replacing the voltage with the current).

  Alternatively, when the input AC voltage or AC current is generated almost exclusively by the fundamental wave, the positive half wave of the input sine wave may be output as it is. The output condition is given by the following equation (I3) using the synchronized phasor phase angle φ (t) of the input signal.

  Referring to FIGS. 15 and 16 again, designated output command unit 403 calculates a designated output command time for pulse output according to the following equation (I4) (step S403).

Here, T _pulse is a specified pulse output interval time, T ₀ is an input signal period, and T _output is a specified output command time. FIG. 18 is a diagram for explaining the concept of the above-described output command time calculation. By designating the pulse output interval time T _pulse , the designated output command unit 403 commands the _output of the next pulse after the designated output command time T _output has elapsed from the previous pulse output.

  Next, when receiving the pulse output command from the designated output command unit 403, the pulse output unit 404 outputs the pulse signal generated by the positive half wave generation unit 402 (step S404). If a pulse output end command has not been received (NO in step S405), the above steps S401 to S404 are repeated.

<Embodiment 3>
In the third embodiment, a case (case 1) in which the calculation of the frequency and the frequency change rate by the above method is verified by simulation will be described. Specifically, in case 1, a simulation was performed in which the input signal was a sine wave and the frequency was changed at a constant rate from a specified time. Table 5 shows the parameters of case 1.

The input signal of case 1 is expressed by the following equation.

The simulation result will be described below.

  FIG. 19 is a diagram illustrating the instantaneous voltage value and the measurement result of the AC amplitude in case 1. As shown in FIG. 19, the frequency is a steady value of 60 Hz up to 0.1 second. Thereafter, the frequency increases at a rate of 0.5 Hz per second. It can be seen that the synchrophasor amplitude calculated by the proposed synchrophasor measurement method agrees with the theoretical value.

  FIG. 20 is a diagram illustrating a theoretical frequency and a measurement frequency waveform in Case 1. Both the frequency calculated by the time-synchronized phasor method and the virtual reference phasor method have been proven to follow the fluctuation of the theoretical frequency at high speed and to measure the frequency with high accuracy.

  FIG. 21 is a diagram showing the measurement result of the frequency change rate in case 1. FIG. Both the frequency change rate calculated by the time-synchronized phasor method and the virtual reference phasor method have been proven to follow the fluctuation of the theoretical frequency change rate at high speed and to measure a highly accurate frequency. Note that the measurement result by the time-synchronized phasor method has a comparatively large measurement error although it is transient before and after the frequency suddenly changes.

<Embodiment 4>
In the fourth embodiment, five cases (case 2) in which various proposed methods are verified using actually measured input data will be described. Table 6 shows parameters of the measurement example of Case 2.

  FIG. 22 is an actual measurement voltage waveform diagram in an actual measurement example of case 2. FIG. FIG. 22 shows a measured voltage waveform detected for 3 seconds at a data collection sampling frequency of 4000 Hz. Since the amplitudes of the voltage waveforms are not uniform, it can be seen that this data includes abundant harmonic components.

  FIG. 23 is an enlarged view of the 0.1 second section of FIG. When an enlarged view of the 0.1 second section shown in FIG. 23 is observed, it looks like a clean sine wave, but it can be seen that the height of the amplitude is slightly different.

FIG. 24 is a diagram illustrating a measurement result of a Fourier transform spectrum when an actual measurement voltage waveform in an actual measurement example of case 2 is detected for 3 seconds at a sampling frequency of 4000 Hz. FIG. 24 shows an enlarged view up to 420 Hz. From the Fourier transform result, it can be seen that the actually measured data has abundant harmonic components.
[Verification 1 of actual measurement example of Case 2]
Hereinafter, a description will be given of measurement results when discontinuity occurs in the time-synchronized phasor due to symmetry breaking.

  FIG. 25 is a diagram illustrating a measurement result of the synchronized phasor phase angle as verification 1 of the actual measurement example of case 2. Referring to FIG. 25, the measurement result of the phase angle in the case where the invariant averaging process is not performed using only one symmetry group is indicated by a triangle mark. It can be seen that the value of the synchronized phasor phase angle has suddenly changed because the symmetry is broken around 0.0245 seconds. For this reason, the continuity of calculation results cannot be maintained.

  On the other hand, the calculation result of the phase angle when the invariant averaging process is performed using 10 symmetry groups is indicated by square marks. It can be seen that even when the symmetry is broken around 0.0245 seconds, there is no sudden change in the synchronized phasor phase angle, and the continuity of the calculation results can be maintained.

  FIG. 26 is a diagram illustrating a measurement result of the real part of the synchronized phasor in the verification 1 of the actual measurement example of the case 2. Referring to FIG. 26, the measurement result of the real part of the synchronized phasor when the invariant averaging process is not performed using only one symmetry group is indicated by a triangle. It can be seen that the value of the real part of the synchronized phasor suddenly changed because the symmetry was broken around 0.0245 seconds. For this reason, the continuity of calculation results cannot be maintained.

  On the other hand, the calculation result of the synchronous phasor real part when the invariant averaging process is performed using 10 symmetry groups is indicated by a square mark. It can be seen that even if the symmetry is broken around 0.0245 seconds, the real part of the synchronized phasor does not change suddenly and the continuity of the calculation results can be maintained.

  For comparison, the actual measured voltage instantaneous value is indicated by a circle. It can be seen that due to the influence of the harmonic component, it is far from the curve of the real part of the synchronous phasor of the square mark which is a pure sine wave.

  FIG. 27 is a diagram illustrating the measurement result of the time-synchronized phasor as verification 1 of the actual measurement example of case 2. With reference to FIG. 27, the measurement result of the time-synchronized phasor when the invariant averaging process is not performed using only one symmetry group is indicated by a triangle. It can be seen that the value of the time-synchronized phasor suddenly changed because the symmetry was broken around 0.0245 seconds and 0.041 seconds. For this reason, the continuity of calculation results cannot be maintained.

  On the other hand, the calculation results of the time-synchronized phasor when the invariant averaging process is performed using 10 symmetry groups are indicated by square marks. It can be seen that even when the symmetry is broken around 0.0245 seconds and 0.041 seconds, the synchronous phasor real part does not change suddenly and the continuity of the calculation results can be maintained. Furthermore, it can be seen that the fluctuation range of the time-synchronized phasor is reduced by performing the invariant averaging process.

[Verification 2 of actual measurement example of Case 2]
Hereinafter, an example in which the length of the time width of the averaging process is changed in the actual measurement example of case 2 will be described.

  FIG. 28 is a diagram illustrating a voltage amplitude measurement result as verification 2 of the actual measurement example of case 2. FIG. Referring to FIG. 28, when the invariant averaging process is performed using 60 symmetric groups, the voltage is compared with the case where the invariant averaging process is performed using 12 symmetric groups. It can be seen that the amplitude fluctuation range is small.

  FIG. 29 is a diagram illustrating the measurement result of the time-synchronized phasor as verification 2 of the actual measurement example of case 2. Referring to FIG. 29, when invariant averaging is performed using 60 symmetric groups, time is inferior to when invariant averaging is performed using 12 symmetric groups. It can be seen that the fluctuation range of the synchronized phasor is small.

[Verification 3 of measurement example of Case 2]
Hereinafter, an example in which the designated period (that is, the number of cycles) of the time synchronization phasor is changed in the actual measurement example of Case 2 will be described.

  FIG. 30 is a diagram illustrating an average frequency measurement result as verification 3 of the actual measurement example of case 2. Referring to FIG. 30, the measurement result of the average frequency when the designated period of the time synchronization phasor is 3 cycles has a smaller fluctuation range than the measurement result of the average frequency when the designation period of the time synchronization phasor is 1 cycle. Can be confirmed.

  FIG. 31 is a diagram illustrating a measurement result of the frequency change rate as verification 3 of the actual measurement example of case 2. Referring to FIG. 31, the measurement result of the frequency change rate when the designated period of the time-synchronized phasor is 10 cycles has a fluctuation range larger than the measurement result of the frequency change rate when the designated period of the time-synchronized phasor is 3 cycles. It can be confirmed that it is getting smaller.

[Verification 4 of measurement example of Case 2]
Hereinafter, an example in which the phase difference angle is measured using the virtual reference phasor in the actual measurement example of case 2 will be described.

  FIG. 32 is a diagram illustrating a phase difference measurement result as verification 4 of the actual measurement example of case 2. FIG. 33 is an enlarged view of FIG. 32 and 33, the data collection sampling frequency of the actually measured data is 4000 Hz. It can be seen that the phase difference angle oscillates as a result of the fact that the phase difference angle cannot be determined because the power system contains harmonic components of 2000 Hz or higher. It can be seen that the cause of voltage flicker is due to high frequency harmonic components.

[Verification 5 of measurement example of Case 2]
Hereinafter, in the actual measurement example of Case 2, the result of generating a positive half-wave pulse using the waveform of the power system will be described.

  FIG. 34 is a diagram illustrating a pulse generation result as verification 5 of the actual measurement example of case 2. FIG. FIG. 35 is an enlarged view of FIG. 34 and 35, the rated frequency is 60 Hz, and the data collection sampling frequency is 4000 Hz. A positive half-wave pulse of a sine wave having a pulse interval of 0.5 seconds was generated using an AC signal actually measured in the power system described with reference to FIGS. As can be seen from the above measurement results, even though the input data of the power system used contains abundant harmonic components, pulse output of only the fundamental wave can be realized without using any filter. I understand that.

<Embodiment 5>
In the fifth embodiment, a simulation result using a standard model of an electric power system called EAST10 of the Institute of Electrical Engineers will be described.

  FIG. 36 is a configuration diagram of the EAST10 power system model of the Institute of Electrical Engineers of Japan. As shown in FIG. 36, the model power system is provided with generators G1 to G10, a synchronized phasor measuring device PMU, and a power system stability monitoring system 201. The power system stability monitoring system 201 is configured based on a computer, acquires a measurement result of a synchronized phasor by communicating with each synchronized phasor measurement device PMU, and determines the stability of the power system based on the acquired measurement result. judge. Furthermore, the three-phase unbalanced electric quantity measuring device described in the sixth embodiment is connected to the node (21).

  FIG. 37 is a flowchart showing a calculation procedure by the power system stability monitoring system of FIG.

  Referring to FIGS. 36 and 37, first, power system stability monitoring system 201 receives the synchronized phasor information of each PMU (step S201). Next, the power system stability monitoring system 201 calculates a spatially synchronized phasor for all power systems (step S202). Next, the power system stability monitoring system 201 displays the calculated spatially synchronized phasor result in a three-dimensional view (step S203). Next, the power system stability monitoring system 201 determines whether or not a step-out has occurred by comparing with a set value, and issues a warning if it is determined that a step-out has occurred (step S204). If an end command has not been received (NO in step S205), the above steps S201 to S204 are repeated.

[Case 3: Simulation result of grid fault]
As case 3, the result of the simulation about the EAST10 power system model is shown. Table 3 shows the simulation parameters. Below, the measurement result of the several space synchronous phasor of generator G1-G10 is shown with a three-dimensional figure.

  FIG. 38 shows the simulation result of the internal phase angle of the generator G1 in case 3. Referring to FIG. 38, it can be confirmed that the phase angle increases from the initial value and the generator G1 gradually steps out.

  FIG. 39 is a three-dimensional view showing measurement results of a plurality of spatially synchronized phasors before failure as verification 1 of case 3. Referring to FIG. 39, it can be confirmed that all the spatially synchronized phasors in the power system are fluctuated within a certain range before the failure.

  FIG. 40 is a three-dimensional diagram showing the measurement results of a plurality of space-synchronized phasors immediately before step-out of the generator G1 as verification 1 of case 3. Referring to FIG. 40, it can be seen that immediately before the generator G1 steps out, the spatially synchronized phasor between the output node of the generator G1 and the output node of another generator is increased.

  FIG. 41 is a three-dimensional view showing measurement results of a plurality of spatially synchronized phasors immediately after the step-out of the generator G1 as verification 1 of case 3. Referring to FIG. 41, it can be seen that immediately after the generator G1 has stepped out, the spatially synchronized phasor between the output node of the generator G1 and the output node of another generator has reversed and stepped out.

  FIG. 42 is a diagram illustrating instantaneous value waveforms of positive phase voltages of the node (11) and the node (21) as verification 2 of case 3. Referring to FIG. 42, it can be seen that a failure has occurred since time 1 second.

  FIG. 43 is a diagram illustrating measurement results of phase difference angles at the node (11) and the node (21) as verification 2 of case 3. Referring to FIG. 43, node (11) has a phase difference angle of 180 degrees at point A (near time 1.65 seconds), leading to step-out, and node (21) is point C (near time 2.05 seconds). ), The phase difference angle becomes 180 degrees, and it can be seen that step-out has occurred. Node (11) is in the second step-out at point D.

  FIG. 44 is a diagram illustrating a measurement result of the spatial synchronization phasor between the node (11) and the node (21) as the case 3 verification 2. Referring to FIG. 44, it can be seen that the phase difference between the node (11) and the node (21) reaches 180 degrees around the time 1.8 seconds.

<Embodiment 6>
In the sixth embodiment, a measurement result using the three-phase unbalanced electric quantity measuring device 301 of FIG. 36 will be described. The three-phase unbalanced electric quantity measuring device 301 is an extension of the function of the synchronous phasor measuring device described so far.

[Configuration and operation of three-phase unbalanced electricity measurement device]
FIG. 45 is a block diagram showing a configuration of a three-phase unbalanced electric quantity measuring device. Referring to FIG. 45, three-phase unbalanced electric quantity measuring device 301 includes an instantaneous value data input unit 302, a calculation processing unit 313, a calculation information transmission unit 310, an interface unit 311, and a storage unit 312. .

  The instantaneous value data input unit 302 receives input of A-phase / B-phase / C-phase voltage / current instantaneous value data from the voltage transformer PT and the current transformer CT connected to the three-phase transmission line of the power system.

  The arithmetic processing unit 313 is configured by a CPU, and performs various arithmetic processes by operating according to a program stored in the storage unit 312. Functionally, the arithmetic processing unit 313 includes an A-phase / B-phase / C-phase voltage-synchronized phasor calculating unit 303, a positive-phase / reverse-phase / zero-phase voltage-synchronized phasor calculating unit 304, and an A-phase / B-phase. Phase / C-phase current synchronous phasor calculation unit 305, positive phase / reverse phase / zero phase current synchronous phasor calculation unit 306, normal phase / reverse phase / zero phase active power calculation unit 307, normal phase / reverse phase A phase / zero phase reactive power calculation unit 308 and a normal phase / reverse phase / zero phase power factor calculation unit 309 are included. The operation of each functional unit will be described with reference to the flowchart of FIG.

  The calculation information transmission unit (and calculation information reception unit) 310 communicates with another synchronized phasor measurement device (not shown) or the power system stability monitoring system 201 of FIG. 36 via a communication line (not shown), for example. The calculation result in the arithmetic processing unit 313 is transmitted and received.

  The interface unit 311 is provided for connection with a user interface or an external device. The storage unit 312 stores the input voltage instantaneous value data, the above calculation result, and the like.

FIG. 46 is a flowchart showing a calculation processing procedure of the three-phase unbalanced electric quantity measuring device. First, in the instantaneous value data input unit 302, instantaneous value data of A phase / B phase / C phase voltage (A phase instantaneous value voltage: v _Are , B phase instantaneous value voltage: v shown by the following equation (K1): _Bre , C-phase instantaneous value voltage v _Cre ) is input (step S301). In the following equation (K1), V _A , V _B and V _C are the voltage amplitudes of the A phase, B phase and C phase, respectively, and φ _VA , φ _VB and φ _VC are the A phase, B phase and C phase voltages, respectively. The initial phase angle.

Similarly, the instantaneous value data input unit 302 has instantaneous value data (A phase instantaneous value current: i _Are , B phase instantaneous value current: A phase / B phase / C phase current shown by the following equation (K2)). i _Bre and C phase instantaneous value current i _Cre ) are input (step S301). In the following equation (K2), I _A , I _B , and I _C are current amplitudes of the A phase, B phase, and C phase, respectively, and φ _IA , φ _IB , and φ _IC are A phase, B phase, and C phase currents, respectively. The initial phase angle.

Next, the voltage synchronization phasor calculation unit 303 calculates the voltage synchronization phasor of A phase / B phase / C phase (step S302). The A-phase / B-phase / C-phase voltage-synchronized phasors v _A , v _B , v _C are calculated according to the following equation (K3).

The real part v _Are , the imaginary part v _Aim , the amplitude V _A and the phase angle φ _VA of the A-phase voltage synchronous phasor used in the above formula (K3) are calculated according to the following formula (K4) as described above. . In the equation (K4), SD _VAP , SD _VAQ , and f _C are the A-phase voltage gauge difference effective synchronization phasor, the A-phase voltage gauge difference invalid synchronization phasor, and the frequency coefficient.

Real part v _Bre , imaginary part v _Bim , amplitude V _B , and phase angle φ _{VB of B-} phase voltage-synchronized phasor, and real part v _Cre , imaginary part v _Cim , amplitude V _C , and phase angle of C-phase voltage-synchronized phasor φ _VC can be calculated using the same formula as above. More specifically, in the case of the B phase, the gauge difference effective synchronization phasor SD _VBP and the gauge difference invalid synchronization phasor of the B phase voltage in place of the A phase voltage gauge difference effective synchronization phasor SD _VAP and the gauge difference invalid synchronization phasor SD _VAQ. SD _VBQ is used, and in the case of a C-phase voltage, a gauge difference effective synchronization phasor SD _VCP and a gauge difference invalid synchronization phasor SD _VCQ of the C phase voltage are used.

Next, the voltage-synchronized phasor calculating unit 304 calculates a normal-phase / reverse-phase / zero-phase voltage-synchronized phasor (step S303). Positive phase / reverse phase / zero-phase voltage synchronized phasor v _0, v _1, v ₂ is the voltage of the A-phase / B-phase / C phase synchronous phasor v _A by the following equation (K5), v _B, and v _C Calculated by transforming coordinates. The symmetric coordinate conversion coefficient in the equation (K5) is expressed by the following equation (K6).

Next, the current synchronous phasor calculation unit 305 calculates an A phase / B phase / C phase current synchronous phasor (step S304). The A-phase / B-phase / C-phase current-synchronized phasors i _A , i _B and i _C are calculated according to the following equation (K7).

The real part i _Are , the imaginary part i _Aim , the amplitude I _A, and the phase angle φ _IA of the A-phase current synchronous phasor used in the above formula (K7) are calculated according to the following formula (K8) as described above. . In the equation (K8), SD _IAP , SD _IAQ , and f _C are the A-phase current gauge difference effective synchronization phasor, the A-phase current gauge difference invalid synchronization phasor, and the frequency coefficient.

Real part i _Bre , imaginary part i _Bim , amplitude I _B , and phase angle φ _{IB of} the _B phase current synchronous phasor, and real part i _Cre , imaginary part i _Cim , amplitude I _C , and phase angle of the C phase current synchronous phasor φ _IC can be calculated using the same formula as above. Specifically, in the case of the B phase, the gauge difference effective synchronization phasor SD _IBP and the gauge difference invalid synchronization phasor SD _IBQ of the B phase current are used, and in the case of the C phase current, the gauge difference effective synchronization phasor SD _ICP of the C phase current and Gauge differential invalid synchronous phasor SD _ICQ is used.

Next, the current synchronous phasor calculating unit 306 calculates a normal phase / reverse phase / zero phase current synchronous phasor (step S305). The positive / negative / zero-phase current-synchronized phasors i ₀ , i ₁ , i ₂ represent the A-phase / B-phase / C-phase current-synchronized phasors i _A , i _B , i _C as in the following equation (K9) Calculated by transforming coordinates. The symmetric coordinate conversion coefficient in the equation (K9) is expressed by the aforementioned equation (K6).

Next, the active power calculation unit 307 calculates active power P ₀ , P ₁ , P ₂ of the positive phase / reverse phase / zero phase (step S306), and the reactive power calculation unit 308 calculates the normal phase / reverse phase / zero phase. The reactive powers Q ₀ , Q ₁ , and Q ₂ are calculated (step S308). The active power P ₀ , P ₁ , P ₂ of the positive / negative / zero phase is calculated according to the following equation (K10), and the reactive power Q ₀ , Q ₁ , Q ₂ of the positive / negative / zero phase is Calculated according to equation (K11).

Next, the power factor calculation unit 309, based on the calculated active powers P ₀ , P ₁ , P ₂ and reactive powers Q ₀ , Q ₁ , Q ₂ , the power factor PF _{0 of the} normal phase / reverse phase / zero phase. , PF ₁ , PF ₂ are calculated (step S308). The power factors PF ₀ , PF ₁ , PF ₂ of the normal phase / reverse phase / zero phase are calculated according to the following equation (K12).

  Thereafter, if there is no termination command (NO in step S309), the above steps S301 to S308 are repeated.

[Case 4: Simulation example of three-phase unbalanced electricity measurement]
As Case 4, the result of measuring the three-phase unbalanced electric quantity for the EAST10 power system model of FIG. 36 will be described. Table 8 shows the parameters used in the simulation of Case 4. The measurement of the three-phase unbalanced electric quantity is performed by the three-phase unbalanced electric quantity measuring device 301 described with reference to FIGS. 36, 45, and 46. The conventional general method requires coordinate transformation such as αβ change and dq transformation to calculate the fundamental wave, but the method using the symmetric group of the present disclosure does not require such transformation. .

  FIG. 47 is a diagram illustrating the instantaneous value of the A phase voltage, the real part of the A phase voltage synchronized phasor, and the measurement result of the amplitude in case 4. Referring to FIG. 47, a graph of the A phase voltage instantaneous value is indicated by a triangular mark, a graph of a real part of the A phase voltage synchronous phasor is indicated by a square mark, and an amplitude graph of the A phase voltage synchronous phasor is indicated by a solid line (no mark). ). When the time shown in the figure is 0.1 second, a failure occurs in the power system, and when it is 0.2 seconds, the state returns to a steady state (failure is cleared).

  As shown in FIG. 47, it can be confirmed that the A-phase voltage instantaneous value has a large sudden change before and after the occurrence of the failure and before and after the failure is cleared. The real part of the phase A voltage-synchronized phasor overlaps with the instantaneous value of the A phase voltage in the steady state, but changes gradually immediately after the failure occurs and immediately after the failure is cleared, and changes suddenly like the instantaneous value of the A phase voltage. Not. This is because the measurement result of the synchronized phasor is averaged. In the averaging process, if the symmetry of the symmetry group is broken due to a sudden voltage change, the time at which the symmetry is broken is displayed. This is because the measured value is not used for the averaging process. It can be confirmed that the amplitude of the phase A voltage synchronized phasor is an envelope of the real part of the phase A voltage synchronized phasor.

  FIG. 48 is a diagram showing a measurement result of the A-phase voltage synchronous phasor on the complex plane in Case 4. As shown in FIG. 48, it can be seen that the phase A voltage synchronous phasor rotates on the circumference as a circular vector in a stable state and changes in a spiral vector shape in a transient state.

  FIG. 49 is a diagram illustrating a measurement result of the phase angle of the A-phase voltage synchronized phasor in Case 4. It can be seen that the phase angle of the A-phase voltage synchronized phasor changes periodically and uniformly in the range of −180 degrees to +180 degrees.

  FIG. 50 is a diagram illustrating measurement results of the real part and the amplitude of the positive phase voltage synchronous phasor in case 4. In FIG. 50, the graph of the real part of the positive phase voltage synchronization phasor is indicated by a triangle, the amplitude of the positive phase voltage synchronization phasor is indicated by a thin solid line, and the theoretical value of the amplitude of the positive phase voltage is indicated by a thick solid line.

  As shown in FIG. 50, the amplitude of the positive phase voltage synchronous phasor coincides with the theoretical value of the amplitude of the positive phase voltage and has a constant value in the steady state. On the other hand, the amplitude of the positive-phase voltage-synchronized phasor changes gently in the transient state immediately after the failure occurs and immediately after the failure is cleared, and does not change abruptly like the theoretical value of the positive-phase voltage amplitude. I know that there is.

  FIG. 51 is a diagram illustrating measurement results of the real part and the amplitude of the negative phase voltage synchronization phasor in case 4. In FIG. 51, the graph of the real part of the negative phase voltage synchronous phasor is indicated by a triangle, the amplitude of the negative phase voltage synchronous phasor is indicated by a thin solid line, and the theoretical value of the negative phase voltage amplitude is indicated by a thick solid line.

  As shown in FIG. 51, the amplitude of the negative phase voltage-synchronized phasor is zero in the steady state, and coincides with the theoretical value of the amplitude of the negative phase voltage. On the other hand, the amplitude of the negative-phase voltage-synchronized phasor changes gradually in the transient state immediately after the occurrence of the failure and immediately after the failure is cleared, and does not change abruptly as the theoretical value of the negative-phase voltage amplitude. I know that there is.

  FIG. 52 is a diagram illustrating measurement results of the real part and amplitude of the zero-phase voltage synchronized phasor in case 4. In FIG. 52, the graph of the real part of the zero phase voltage synchronized phasor is indicated by a triangle, the amplitude of the zero phase voltage synchronized phasor is indicated by a thin solid line, and the theoretical value of the amplitude of the zero phase voltage is indicated by a thick solid line.

  As shown in FIG. 52, the amplitude of the zero-phase voltage-synchronized phasor is zero in the steady state and matches the theoretical value of the amplitude of the zero-phase voltage. On the other hand, the amplitude of the zero-phase voltage-synchronized phasor changes slowly in the transient state immediately after the failure occurs and immediately after the failure is cleared, and does not change abruptly like the theoretical value of the zero-phase voltage amplitude, and there is a certain delay with respect to the theoretical value. I know that there is.

  FIG. 53 is a diagram illustrating the measurement result of the real part and the amplitude of the positive phase current synchronization phasor in case 4. FIG. The graph of the real part of the positive phase current synchronous phasor is indicated by a triangle, the amplitude of the positive phase current synchronous phasor is indicated by a thin solid line, and the theoretical value of the positive phase current amplitude is indicated by a thick solid line.

  As shown in FIG. 53, the amplitude of the positive phase current synchronous phasor coincides with the theoretical value of the positive phase current amplitude in a steady state and has a constant value. On the other hand, the amplitude of the positive-phase current-synchronized phasor changes slowly in the transient state immediately after the failure occurs and immediately after the failure is cleared, and does not change abruptly like the theoretical value of the positive-phase current amplitude. I know that there is.

  FIG. 54 is a diagram illustrating the measurement result of the real part and the amplitude of the negative phase current synchronization phasor in case 4. FIG. In FIG. 54, the graph of the real part of the negative phase current synchronous phasor is indicated by a triangle, the amplitude of the negative phase current synchronous phasor is indicated by a thin solid line, and the theoretical value of the negative phase current amplitude is indicated by a thick solid line.

  As shown in FIG. 54, the amplitude of the negative-phase current synchronization phasor is zero in the steady state, and matches the theoretical value of the negative-phase current amplitude. On the other hand, the amplitude of the negative-phase current-synchronized phasor changes slowly in the transient state immediately after the failure occurs and immediately after the failure is cleared, and does not change abruptly as the theoretical value of the negative-phase current amplitude. I know that there is.

  FIG. 55 is a diagram illustrating the measurement result of the real part and the amplitude of the zero-phase current synchronous phasor in Case 4. In FIG. 55, the graph of the real part of the zero phase current synchronous phasor is indicated by a triangle, the amplitude of the zero phase current synchronous phasor is indicated by a thin solid line, and the theoretical value of the amplitude of the zero phase current is indicated by a thick solid line.

  As shown in FIG. 55, the amplitude of the zero-phase current synchronous phasor is zero in the steady state, and matches the theoretical value of the amplitude of the zero-phase current. On the other hand, the amplitude of the zero-phase current-synchronized phasor changes gently in the transient state immediately after the failure occurs and immediately after the failure is cleared, and does not change abruptly like the theoretical value of the zero-phase current amplitude. I know that there is.

  The embodiment disclosed this time must be considered as illustrative in all points and not restrictive. The scope of the present invention is defined by the terms of the claims, rather than the description above, and is intended to include any modifications within the scope and meaning equivalent to the terms of the claims.

DESCRIPTION OF SYMBOLS 100 Synchronous phasor measuring apparatus, 101 Voltage instantaneous value data input part, 102 Invariant averaging process part, 103 Real part calculation part, 104 Imaginary part calculation part, 105 Phase angle calculation part, 106 Amplitude calculation part, 107 Spatial synchronous phasor calculation Unit, 108 time synchronization phasor calculation unit, 109 frequency calculation unit, 110 frequency change rate calculation unit, 111 phase difference angle calculation unit, 112 rotation phase angle correction unit, 113, 310 calculation information transmission unit (calculation information reception unit), 114, 311 interface unit, 115, 312 storage unit, 120, 313 arithmetic processing unit, 201 power system stability monitoring system, 301 three-phase unbalanced electric quantity measuring device, 302 instantaneous value data input unit, 303, 304 voltage synchronous phasor calculation unit , 305, 306 Current synchronous phasor calculation unit, 307 active power calculation unit, 308 reactive power calculation , 309 power factor calculation unit, 400 a pulse generator, 401 sinusoidal input unit, 402 a positive half-wave generating unit, 403 designated output instruction unit, 404 a pulse output unit, SA _Q gauge disable synchronization phasor, SA _p gauge effective synchronization phasor, SD _P gauge differential valid synchronous phasor, SD _Q gauge differential invalid synchronous phasor, T, T _g gauge sampling period, T ₁ data collection sampling period, f, f _g gauge sampling frequency, i _im , v _im synchronous phasor imaginary part, i _re , v _re Synchronous phasor real part.

Claims (10)

An input unit for inputting instantaneous value data obtained by sampling the amount of electricity in the power system every first period T ₁ ;
An arithmetic processing unit,
The arithmetic processing unit extracts three points of first data v ₁₁ (t), which are extracted from the instantaneous value data for each second period T greater than the first period T ₁ and continuous from the current sampling time t. v ₁₂ (t−T), v ₁₃ (t−2T), and the real part of three fixed unit vector groups arranged at intervals of the second period on the complex plane when the quantity of electricity is displayed as a phasor From v ₁₀₁ , v ₁₀₂ , and v ₁₀₃ , a frequency coefficient f _C is calculated according to the following equation (L1):

The arithmetic processing unit, when the absolute value of the frequency coefficient f _C is less than 1, the gauge effective synchronization phasor SA _p represented by the following expression (L2) and the gauge invalid synchronization phasor SA represented by the following expression (L3) Calculate _q

The arithmetic processing unit performs an averaging process on the gauge effective synchronization phasor SA _p and the gauge invalid synchronization phasor SA _q to each k from k = 1 to k = N−1 (N is an integer of 2 or more). On the other hand, the first data v ₁₁ (t−k · T ₁ ), v ₁₂ (t−T−k · T ₁ ), v at the sampling time k times before the first period T ₁ from the current sampling time t. ₁₃ (t−2T−k · T ₁ ) and real parts v ₁₀₁ , v ₁₀₂ , v when the unit vector group is rotated clockwise on the complex plane by an angle corresponding to time k · T _{1. 103} , the frequency coefficient f _C is calculated according to the above equation (L1), and the gauge effective synchronous phasor SA _p represented by the above equation (L2) when the absolute value of the calculated frequency coefficient f _C is less than 1. And a gauge invalid synchronized phasor SA _q represented by the above formula (L3),
The arithmetic processing unit averages the gauge effective synchronization phasor SA _p and the gauge invalid synchronization phasor SA _q calculated up to the current sampling time, and uses the averaged gauge effective synchronization phasor SA _p and gauge invalid synchronization phasor SA _q. A synchronous phasor measuring device for determining a phasor amount of the electric quantity at a current sampling time. The real part v _re , the imaginary part v _im , and the phase angle φ in the phasor display of the quantity of electricity are obtained by using the averaged gauge effective synchronization phasor SA _p , gauge invalid synchronization phasor SA _q , and frequency coefficient f _C. Calculated according to the following formulas (L4) to (L6),

The synchronous phasor measuring device according to claim 1. An input unit for inputting instantaneous value data obtained by sampling the amount of electricity in the power system every first period T ₁ ;
An arithmetic processing unit,
The arithmetic processing unit uses the first data of four points that are extracted from the instantaneous value data for each second period T that is greater than the first period T ₁ and that is continuous from the current sampling time t. The second data v ₂₁ (t), v ₂₂ (t−T), v ₂₃ (t−2T) of three consecutive points obtained by the difference between two adjacent points of one data are obtained,
The arithmetic processing unit uses two fixed unit vector groups arranged at intervals of the second period T on a complex plane when the electric quantity is displayed as a phasor, and uses two adjacent vector vectors of the unit vector group. Find the real parts v ₂₀₁ , v ₂₀₂ , v ₂₀₃ of the three difference vectors obtained by the difference between them,
The arithmetic processing unit includes the second data v ₂₁ (t), v ₂₂ (t−T), and v ₂₃ (t−2T) of the three points and the real parts v ₂₀₁ and v _{202 of the} three difference vectors. , V ₂₀₃ to calculate the frequency coefficient f _C according to the following equation (L7):

The arithmetic processing unit, when the absolute value of the frequency coefficient f _C is less than 1, the gauge difference effective synchronization phasor SD _p represented by the following equation (L8) and the gauge difference invalid synchronization represented by the following equation (L9): Calculate phasor SD _q ,

In order to perform the averaging process of the gauge difference effective synchronization phasor SD _p and the gauge difference invalid synchronization phasor SD _q , each of the arithmetic processing units includes k = 1 to k = N−1 (N is an integer of 2 or more). Second data v ₂₁ (t−k · T ₁ ), v ₂₂ (t−T−k · T ₁ ) at a sampling time k times before the first cycle T ₁ from the current sampling time t with respect to k, v ₂₃ (t−2T−k · T ₁ ) and the difference vector between adjacent vectors when the unit vector group is rotated clockwise on the complex plane by an angle corresponding to time k · T ₁ . The frequency coefficient f _C is calculated from the real part v ₂₀₁ , v ₂₀₂ , v ₂₀₃ according to the above expression (L7), and when the absolute value of the calculated frequency coefficient f _C is less than 1, the above expression (L8) invalid gauge difference represented by gauge differential effective synchrophasor SD _p and the above formula (L9) represented To calculate the period phasor SD _q,
The arithmetic processing unit averages the gauge difference effective synchronization phasor SD _p and the gauge difference invalid synchronization phasor SD _q calculated up to the current sampling time, and averages the gauge difference effective synchronization phasor SD _p and the gauge difference invalid synchronization phasor. A synchronous phasor measurement device that determines a phasor amount of the electric quantity at the current time using SD _q . The real part v _re , the imaginary part v _im , and the phase angle φ in the phasor display of the quantity of electricity are the averaged gauge difference effective synchronization phasor SD _p , gauge difference invalid synchronization phasor SD _q , and frequency coefficient f _C. Is calculated according to the following formulas (L10) to (L12),

The synchronous phasor measuring device according to claim 3.   The arithmetic processing unit subtracts the phase angle in the phasor display of the electrical quantity at the specified sampling time from the phase angle in the phasor display of the electrical quantity at the current sampling time, and the specified sampling 5. The time-synchronized phasor that is an integrated value of the phase change amount from the designated sampling time to the current sampling time is calculated based on the number of cycles from the time to the current sampling time. The described synchronized phasor measuring device.   The arithmetic processing unit includes values of a real part and an imaginary part of a virtual reference phasor rotating at a constant initial speed in the complex plane, and a real part in a phasor display of the electric quantity calculated at a current sampling time. And calculating a phase difference angle that is a phase difference between the virtual reference phasor and the phasor amount of the electric quantity at a current sampling time by using a value of an imaginary part and a cosine theorem. Synchronous phasor measuring device.   The synchronous phasor measurement device according to claim 6, wherein the arithmetic processing unit calculates at least one of a frequency of the electric quantity and a frequency change rate based on the phase difference angle.   The arithmetic processing unit uses the values of the real part and the imaginary part of the phasor display of the electric quantity measured at the same sampling time in each of the first node and the second node of the power system, and the cosine theorem, The synchronized phasor measuring device according to claim 2 or 4, wherein a spatially synchronized phasor that is a phase difference between the first node and the second node is calculated. The amount of electricity includes each of a positive phase voltage, a negative phase voltage, a zero phase voltage, a positive phase current, a negative phase current, and a zero phase current of the power system,
The arithmetic processing unit calculates a phasor amount for each of the positive phase voltage, the negative phase voltage, the zero phase voltage, the positive phase current, the negative phase current, and the zero phase current,
5. The calculation unit according to claim 1, wherein the arithmetic processing unit calculates active power and reactive power of each of a positive phase, a negative phase, and a zero phase based on the calculated amount of each phasor. Synchronous phasor measuring device. An input unit for inputting instantaneous value data obtained by sampling the amount of electricity in the power system every first period T ₁ ;
A pulse generator,
The pulse generation unit uses the first data of four points that are extracted from the instantaneous value data for each second period T that is greater than the first period T ₁ and that is continuous from the current sampling time t. The second data v ₂₁ (t), v ₂₂ (t−T), v ₂₃ (t−2T) of three consecutive points obtained by the difference between two adjacent points of one data are obtained,
The pulse generation unit uses two fixed unit vector groups arranged at intervals of the second period T on the complex plane when the electricity quantity is displayed in a phasor, and uses two adjacent vector vectors of the unit vector group. Find the real parts v ₂₀₁ , v ₂₀₂ , v ₂₀₃ of the three difference vectors obtained by the difference between them,
The pulse generation unit includes the second data v ₂₁ (t), v ₂₂ (t−T), and v ₂₃ (t−2T) of the three points, and the real parts v ₂₀₁ and v _{202 of the} three difference vectors. , V ₂₀₃ to calculate the frequency coefficient f _C according to the following equation (L7):

The pulse generation unit calculates a gauge difference effective synchronization phasor SD _p represented by the following equation (L8) and a gauge difference invalid synchronization phasor SD _q represented by the following equation (L9):

The pulse generator uses the calculated gauge difference effective synchronization phasor SD _p and gauge difference invalid synchronization phasor SD _q to calculate the amplitude V of the electric quantity according to the following equation (L13):

The pulse generator uses the first data v ₁₁ (t), v ₁₂ (t−T), the frequency coefficient f _C, and the amplitude V to generate an output pulse v _OUT according to the following equation (L14). ,

Pulse generator.