JP2022108842A - Method for measuring output admittance of subsystem configuring three-phase electric power system - Google Patents

Abstract

To provide a method capable of measuring output admittance of a subsystem with a simpler configuration than before.SOLUTION: A method according to the invention comprises: a step S1 of generating a perturbation signal; a step S2 of converting a voltage va that oscillates according to the perturbation signal and a voltage vb that does not oscillate into voltages vu, vv, vw; a step 3 of measuring currents iu, iv, iw and the voltages vu, vv, vw while voltages vu-vw, vv-vw are applied to u and v phases of a subsystem; a step S4 of converting the currents iu, iv, iw obtained in step S3 into currents ia, ib; a step S5 of converting the voltages vu, vv, vw obtained in step S3 into voltages va, vb; a step S6 of obtaining matrix elements Yaa, Yba of output admittance based on the relation between the currents ia, ib obtained in step S4 and the voltages va, vb obtained in step S5; and steps S9 to S14 of obtaining matrix elements Yab, Ybb of the output admittance in the same way.SELECTED DRAWING: Figure 5

Description

The present invention relates to a method for measuring the output admittance of one of a plurality of subsystems making up a three-phase power system.

The impedance method is suitable for analyzing the stability of a three-phase power system such as a grid-connected three-phase inverter system. In the impedance method, the output impedances or output admittances (hereinafter referred to as "output impedances, etc.") of multiple subsystems that make up a three-phase power system are defined as the Nyquist stability condition, which is a stability criterion that considers the interaction between subsystems. apply to Therefore, in order to analyze the stability of the system by the impedance method, the output impedance of the subsystem is required.

In the stability analysis at the system design stage, analytically obtained subsystem output impedance, etc. can be used. must. For this reason, various techniques for measuring the output impedance of a subsystem are being studied. For example, Non-Patent Document 1 describes a method of applying (injecting) a voltage from the outside to a power line of each phase that connects a voltage source that is a subsystem and a load, and measuring the voltage of each phase. (especially see Figure 3-12 on page 57).

Z. Shen, "Online Measurement of Three-phase AC Power System Impedance in Synchronous Coordinates," Ph. D. dissertation, Virginia Polytechnic Institute and State University, 2012

The conventional method described in Non-Patent Document 1 requires three transformers in order to apply a voltage to each phase power line. Therefore, this method has the problem that the wiring between the three transformers and their drive circuits is complicated and the cost is high.

SUMMARY OF THE INVENTION The present invention has been made in view of such circumstances, and provides a method for measuring the output admittance of a subsystem with the same accuracy as the conventional method with a simpler configuration than the conventional method. The challenge is to

In order to solve the above problems, according to the present invention, there is provided a method for measuring the output admittance of a subsystem that constitutes a three-phase power system, comprising: (1) a first step of generating a perturbation signal that oscillates with a predetermined amplitude; , (2) a second step of converting the two-phase voltage v _a oscillating according to the perturbation signal and the non-oscillating two-phase voltage v _b into three-phase voltages v _u , v _v , and v _w ; 3) Of the u-phase, v-phase and w-phase of the subsystem, while applying the voltage v _u −v _w and the voltage v _v −v _w to the u-phase and v-phase, respectively, the current i _u of each phase by measurement, a third step of obtaining _{i v} , i _w and voltages _{v u} , _{v v} , v _w ; _a fourth step of obtaining a and i _b ; (5) a fifth step of converting the voltages v _u , v _v , and v _w obtained in the third step to obtain two-phase system voltages v _a and v _b ; (6) Based on the relationship between the currents i _a and i _b obtained in the fourth step and the voltages v _a and v _b obtained in the fifth step, Y _aa and Y _ba , which are the matrix elements of the output admittance, are obtained. (7) _a seventh step of converting the two-phase system voltage vb that oscillates according to the perturbation signal and the two-phase system voltage _va that does not oscillate into three-phase system voltages _vu , _vv , and _vw ; and (8) of the u-phase, v-phase and w-phase of the subsystem, while applying the voltage v _u −v _w and the voltage v _v −v _w to the u-phase and v-phase, respectively, and measuring the current of each phase an eighth step of obtaining _iu , _iv , _iw and voltages _vu , _vv , _vw ; and (9) converting the currents _iu , _iv , _iw obtained in the eighth step into and (10 ₎ converting the voltages _vu , _vv , and _vw obtained in the eighth step to obtain two-phase system _{voltages va} and _vb . (11) Based on the relationship between the currents i _a , i _b obtained in the ninth step and the voltages v _a , v _b obtained in the tenth step, the matrix elements Y _ab , Y _bb of the output admittance and an eleventh step of obtaining .

The above method repeatedly executes the second to sixth steps while changing the frequency of vibration within a predetermined measurement frequency range, and then, while changing the frequency of vibration within the measurement frequency range, the seventh to eleventh steps. The steps may be repeatedly executed.

In the above method, for example, the transformations in the second and seventh steps are performed by equation (3-1), the transformations in the fourth and ninth steps are performed by equation (3-2), and the fifth and tenth steps are Conversion of steps may be performed by equation (3-3).

Further, in the above method, for example, the conversion of the second step and the seventh step is performed by equation (4-1), the conversion of the fourth step and the ninth step is performed by equation (4-2), and the fifth step and The conversion in the tenth step may be performed using equation (4-3).

According to the present invention, it is possible to provide a method capable of measuring the output admittance of a subsystem with an accuracy equivalent to that of the conventional method with a simpler configuration than the conventional method.

BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a diagram showing a three-phase power system to which the measurement method according to the first embodiment of the invention can be applied; FIG. 2 is a diagram showing an example of a specific configuration of a voltage applying section shown in FIG. 1; FIG. 4 is a diagram showing a three-phase power system to which the measurement method according to the second embodiment of the invention can be applied; 4 is a block diagram of a PLL included in the signal processing unit shown in FIG. 3; FIG. It is a flow chart of the measuring method concerning the present invention. FIG. 2 is a circuit diagram of a three-phase power system to be measured in first and second measurement examples; 7 is a graph showing measurement results (Z _dd , Z _dq ) of a first measurement example; 7 is a graph showing measurement results (Z _qd , Z _qq ) of a first measurement example; 9 is a graph showing measurement results (Z _αα , Z _ββ ) of a second measurement example; FIG. 11 is a circuit diagram of a three-phase power system that is a measurement target in a third measurement example; 9 is a graph showing measurement results (Y _dd , Y _dq ) of a third measurement example; 9 is a graph showing measurement results (Y _qd , Y _qq ) of a third measurement example;

[Measurement principle]
First, the measurement principle of the method for measuring the output admittance of a subsystem constituting a three-phase power system (hereinafter simply referred to as the "measurement method") according to the present invention will be described.

The instantaneous value vector of the voltage applied to the u-, v-, and w-phase power lines that connect the two subsystems that make up the three-phase power system is represented by [v~ _u v~ _v v~ _w ] ^T (where T is a transposed symbol). , the instantaneous value vector of the current generated by this application is [i~ _ui ~ _vi ~ _w ] ^T , and these phasors are expressed in capital letters. ) and equation (2).

ただし、Ｃ_ａｂは変換行列であり、２次の単位行列をＩ_２とすると、Ｃ_ａｂおよびＣ_ａｂ ^Ｔの間には次式が成立する。

Further, the conversion of the instantaneous value voltage from the three-phase (u, v, w) system to the two-phase (a, b) system and its inverse conversion can be performed by equations (3) and (4). The conversion of the instantaneous value current from the phase system to the two-phase system and its inverse conversion can be performed by equations (5) and (6).

However, C _ab is a transformation matrix, and the following equation holds between C _ab and C _ab ^T , where I ₂ is a secondary unit matrix.

また、ｄｑ変換により２相系への変換を行う場合、および逆ｄｑ変換により３相系への変換を行う場合は、変換行列Ｃ_ａｂとして次式のＣ_ｄｑを使用すればよい。ただし、θは、同期座標の位相角である。

When conversion to a two-phase system is performed by αβ conversion, and when conversion to a three-phase system is performed by inverse αβ conversion, C _αβ in the following equation may be used as the conversion matrix C _ab .

Further, when converting to a two-phase system by dq transformation, and when converting to a three-phase system by inverse dq transformation, C _dq of the following equation may be used as the transformation matrix C _ab . where θ is the phase angle of the synchronous coordinates.

なお、３相電力システムが相間で対称な場合は、インピーダンスおよびアドミタンスも対称なので、Ｚ_ａｂ＝－Ｚ_ｂａ、Ｚ_ａａ＝Ｚ_ｂｂ、Ｙ_ａｂ＝－Ｙ_ｂａおよびＹ_ａａ＝Ｙ_ｂｂが成立する。 The two-phase system impedance matrix and admittance matrix can be defined by equations (10) and (11).

Note that if the three-phase power system is symmetrical between phases, then Z _ab =−Z _ba , Z _aa =Z _bb , Y _ab =−Y _ba and Y _aa =Y _bb since the impedance and admittance are also symmetrical.

ここで、２相系のインピーダンス行列およびアドミタンス行列の間には、次式の関係がある。

Using the symbol ^m that indicates a matrix and the symbol ^v that indicates a vector, equation (10) can be rewritten in the form of equation (12), and equation (11) can be transformed into equation (13). can be rewritten in the form of

Here, there is the following relationship between the impedance matrix and the admittance matrix of the two-phase system.

In order to obtain the elements of the admittance matrix shown in equation (11), one of V~ _a and V~ _b should be oscillated with a predetermined amplitude and the other amplitude should be set to zero. For example, _{if Ia and Ib are measured} while _{Va ≠} 0 and Vb ₌ 0, the matrix element Y _aa can be obtained, and the matrix element Y _ba can be obtained by the formula "I~ _b /V~ _a ". Conversely, _{if Ia and Ib are measured} while _Va = 0 and Vb ≠ 0, the matrix element _Yab can be obtained by the formula " _Ia / _Vb ". The matrix element _Ybb can be obtained by "I~ _b /V~ _b ".

As described above, since the impedance matrix Z ^mab and the admittance matrix Y _mab have the relationship of Equation (14), each element (Y ^aa , _Yab , Y _ba , Y _{bb ) of the} admittance matrix Y ^mab is obtained, each element (Z ^aa , Z _ab , Z _ba , Z _bb ) of the impedance matrix Z _mab can also be easily _obtained by calculation.

[First embodiment]
Next, a first embodiment of the present invention will be described with reference to the accompanying drawings.

FIG. 1 shows a system to which the measurement method according to the first embodiment can be applied. As shown in the figure, this system comprises a first subsystem 10, a second subsystem 11, u-, v-, and w-phase power lines that enable three-phase power exchange between them, frequency It includes a characteristic analysis section 12, a signal processing section 13, and a voltage application section 14 interposed in a power line. It can be said that this system is obtained by adding a frequency characteristic analysis section 12, a signal processing section 13 and a voltage application section 14 to a three-phase power system consisting of two subsystems 10 and 11 and power lines. The frequency characteristic analyzer 12 finally outputs the measured output admittance Y ^m _αβ (or output impedance Z ^m _αβ ) of the second subsystem 11 .

The frequency characteristic analyzer 12 is composed of a commercially available frequency characteristic analyzer (FRA, Frequency Response Analyzer). The signal processor 13 is composed of a commercially available digital signal processor (DSP). The sampling frequency of the signal processing unit 13 is 100 kHz. As shown in FIG. 2, the voltage application unit 14 includes a first transformer Tu interposed in the _u -phase power line, a second transformer Tv interposed in the _v -phase power line, and a signal processing unit Drive circuits 15 and 16 drive the transformers T _u and T _v based on the signal output from 13 . No transformer is interposed in the w-phase power line.

The frequency characteristic analysis unit 12, the signal processing unit 13, and the voltage application unit 14 measure and output the output admittance Y ^m _αβ (Z ^m _αβ ) according to the flow shown in FIG.

First, in step S1, the frequency characteristic analysis unit 12 generates a perturbation signal that oscillates with a predetermined amplitude. The initial value of the vibration frequency f is f ₁ (for example, 10 Hz), which is the lower limit of the measurement frequency.

In step S2, the signal processing unit 13 generates an oscillating two-phase voltage v _a (in this embodiment, the voltage v _α ) and a non-oscillating two-phase voltage v _b (in this embodiment, voltage v _β ) are converted into three-phase system voltages v _u , v _v , and v _w (in this embodiment, inverse αβ conversion). The conversion formulas are formulas (4) and (8).

In step S3, based on the signals relating to the voltages v _u , v _v , and v _w output from the signal processing unit 13, the voltage applying unit 14 applies the voltage v _u −v _w and the voltage v Apply _v −v _w . More specifically, the drive circuit 15 drives the first transformer T _u so that the voltage v _u −v _w is applied to the u-phase power line, and the voltage v _v −v _w is applied to the v-phase power line. Thus, the drive circuit 16 drives the second transformer _Tv .

In step S3, the instantaneous values i _u , i _v , and i _w of the currents flowing through the power lines of each phase are obtained by measurement. Here, to "determine the instantaneous current values _iu , _iv , and _iw by measurement", not only _iu , _iv , and _iw are measured, but also _iu , _iv , and _iw Measurement of two of them and calculation of the remaining one by the signal processing unit 13 are also included. As shown in FIG. 1, in this embodiment, _iv is obtained from the measured i _u and i _w .

In step S3, the instantaneous values v _u , v _v , and v _w of the power line voltages of the respective phases are obtained by measurement between the voltage application unit 14 and the second subsystem 11 . Here, "determining the instantaneous voltage values _vu , _vv , and _vw by measurement" includes not only measuring each of _vu , _vv , and _vw , but also interphase voltage _vuv (= _vu −v _v ), v _vw (=v _v −v _w ), and v _uw (=v _u −v _w ) are measured, and the signal processing unit 13 calculates v _u , v _v , v _w shall also include seeking As shown in FIG. 1, in this embodiment, v _u , v _v , and v _w are calculated from the measured v _uv and v _vw .

In step S4, the signal processing unit 13 converts the instantaneous current values _iu , _iv , and _iw obtained in step S3 to two-phase system currents _ia , _ib (currents i _α , i _β ) (in this embodiment, αβ conversion). The conversion formulas are formulas (5) and (8).

In step S5, the signal processing unit 13 converts the voltage instantaneous values vu, _vv , and _vw obtained in step S3 to two-phase system voltages va and _{vb (} in this embodiment, voltages _vα and _{v β} ) (in this embodiment, αβ conversion). The conversion formulas are formulas (3) and (8). Since only the voltage v _α is oscillated in step S2, the voltage v _β obtained in this step is zero.

In step S6, the frequency characteristic analysis unit 12 analyzes the currents i _a and i _b (currents i _α and i _β in this embodiment) obtained in step S4 and the voltages v _a and v _b (in this embodiment) obtained in step S5. In the _{example , Y aa ,} ^Y _ba ⁽ In this embodiment, Y _αα , Y _βα ) are obtained.

In step S7, it is determined whether or not the current vibration frequency f has reached f ₂ (for example, 10 kHz), which is the upper limit of the measurement frequency. If the vibration frequency f has not reached f2, a predetermined Δf is added to f ₍ step S8). Then, steps S1 to S7 are executed for the vibration frequency f after addition. Steps S1 to S8 _are repeatedly executed until the vibration frequency f reaches f2. In other words, steps S1 to S8 are repeatedly performed until Y _aa and Y _ba are obtained in the entire range of measurement frequencies (f ₁ to f ₂ ). Δf may be a constant value or a variable value. The same applies to Δf in step S15, which will be described later.

In step S9, similarly to step S1, the frequency characteristic analysis unit 12 generates a perturbation signal that oscillates with a predetermined amplitude. _The initial value of the vibration frequency f is f1.

In step S10, unlike step S2, the signal processing unit 13 does not oscillate with the two-phase voltage v _b (voltage v _β in this embodiment) that oscillates according to the perturbation signal output from the frequency characteristic analysis unit 12. Two-phase system voltage v _a (voltage v _α in this embodiment) is converted into three-phase system voltages v _u , v _v , and v _w (inverse αβ conversion in this embodiment). The conversion formulas are formulas (4) and (8).

Steps S11-S13 are equivalent to steps S3-S5.

In step S14, the frequency characteristic analysis unit 12 analyzes the currents i _a and i _b (currents i _α and i _β in this embodiment) obtained in step S12 and the voltages v _a and v _b (in this embodiment) obtained in step S13. In the _{example ,} ^Y _{ab ,} ^Y _{bb (} In this embodiment, Y _αβ , Y _ββ ) are obtained.

_In step S15, it is determined whether or not the current vibration frequency f has reached f2. If the vibration frequency f has not reached f2, Δf is added to f ₍ step S16). Then, steps S9 to S15 are executed for the vibration frequency f after addition. Steps S9 to S16 _are repeatedly executed until the vibration frequency f reaches f2. In other words, steps S9 to S16 are repeatedly performed until Y _ab and Y _bb are obtained in the entire range of measurement frequencies (f ₁ to f ₂ ).

As described above, the frequency characteristic analysis unit 12, the signal processing unit 13, and the voltage application unit ₁₄ determine the output admittance Y ^m _{αβ (} Y _αα , Y _αβ , Y _βα , Y _ββ ) are measured. The frequency characteristic analysis unit 12 may output the measured output admittance Y ^m _αβ as it is, or convert it into an output impedance Z ^m _αβ and output it. A conversion formula is Formula (14).

In the measurement method according to the first embodiment of the present invention, only two transformers are required for voltage application. Therefore, according to the measuring method according to the present embodiment, the output admittance of the subsystem can be measured with a simpler configuration than the conventional one.

Note that f ₁ and f ₂ that define the range of measurement frequencies can be changed arbitrarily. For example, f ₁ and f ₂ may be 100 kHz and 100 Hz, and the vibration frequency f may be decreased by a predetermined amount each time steps S8 and S16 are executed.

Further, the voltage applying unit 14 may be configured to apply voltage to the u- and w-phase power lines, or may be configured to apply voltage to the v- and w-phase power lines. In a symmetric system, applying voltages v _u −v _w , v _v −v _w to the u, v phases, applying voltages v _u −v _v , v _w −v _v to the u, w phases, and Applying voltages v _v −v _u and v _w −v _u to the v and w phases is equivalent.

[Second embodiment]
Next, a second embodiment of the present invention will be described with reference to the accompanying drawings.

FIG. 3 shows a system to which the measuring method according to the second embodiment can be applied. As shown in the figure, in this system, the signal processing unit 13 uses interphase voltages v^ _uv and v^ _vw between the first subsystem 10 and the voltage applying unit 14, and the signal processing unit 13 In the first embodiment, dq conversion (inverse dq conversion) is performed instead of αβ conversion (inverse αβ conversion), and the frequency characteristic analysis unit 12 outputs the output admittance Y ^m _dq (or the output impedance Z ^m _dq ). Although different from the example system, they are identical in other respects.

The signal processing unit 13 uses, for example, a known phase-locked loop (PLL, Phase Locked Loop). The voltages _v̂u , _v̂v , and _v̂w input to this loop are obtained from the phase-to-phase voltages _v̂uv and _v̂vw . ω ₀ is the fundamental angular frequency to be measured, and T is the sampling time of the signal processor 13 . As described above, the sampling frequency of the signal processor 13 is 100 kHz, so the sampling time T is 10 μs.

In steps S2 and S10, the signal processing unit 13 converts the two-phase system voltage to the three-phase system voltage (inverse dq conversion in this embodiment) by using equation (9) instead of equation (8). use. Further, in steps S4, S5, S12, and S13, the signal processing unit 13 also converts the voltage/current of the three-phase system into the voltage/current of the two-phase system (dq conversion in this embodiment) using the formula Use equation (9) instead of (8).

The measurement method according to the second embodiment of the present invention also provides the same effects as the measurement method according to the first embodiment.

Note that when the signal processing unit 13 also controls the object to be measured, the phase angle θ in equation (9) is known to the signal processing unit 13 . Therefore, in this case, the measurement of the phase-to-phase voltages _{v̂uv and v̂vw and} the synchronization control using the phase-locked loop can be omitted.

[Measurement example]
Next, measurement examples using the measurement methods according to the first and second embodiments of the present invention will be described.

(First measurement example)
In the first measurement example, using the measurement method according to the second embodiment of the present invention, the output admittance Y ^m _dq (Y _dd , Y _dq , Y _qd , Y _qq ) were measured and converted to the output impedance Z ^m _dq (Z _dd , Z _dq , Z _qd , Z _qq ). As shown in the figure, the second subsystem 11 is a three-phase RL load with R=30Ω, L=5mH, and ω ₀ =2π×60.

7 and 8 show analysis results (solid lines), simulation results (⋄ symbols), and measurement results (broken lines). The analytical results and simulation results were in good agreement for any of Z _dd , Z _dq , Z _qd and Z _qq . Also, for Z _dd and Z _qq , three of the analysis results, simulation results and measurement results generally agreed.

Note that the analytical values of Z _dd , Z _dq , Z _qd and Z _qq are as shown in Equation (16).

(Second measurement example)
In the second measurement example, using the measurement method according to the first embodiment of the present invention, the output admittance Y ^m _αβ (Y _αα , Y _αβ , Y _βα , Y _ββ ) were measured and converted to output impedance Z ^m _αβ (Z _αα , Z _αβ , Z _βα , Z _ββ ). As in the first measurement example, the second subsystem 11 is a 3-phase RL load with R=30Ω, L=5mH and ω ₀ =2π×60.

FIG. 9 shows the analysis result (solid line), the simulation result (⋄ mark), and the measurement result (broken line). As shown in the figure, for both Z _αα and Z _ββ , the analysis results, simulation results, and measurement results generally agreed.

Note that the analytical values of Z _αα and Z _ββ are as shown in equation (17).

(Third measurement example)
In the third measurement example, using the measurement method according to the second embodiment of the present invention, the output admittance Y ^m _dq (Y _dd , Y _dq , Y _qd , Y _qq ) were measured. As shown in the figure, the second subsystem 11 is a three-phase inverter with a filter, and its circuit parameters are as shown in the table below. This three-phase inverter is controlled by a state feedback control system that includes a sinusoidal compensator.

11 and 12 show the analysis results (solid lines), the simulation results (⋄ symbols), and the measurement results (broken lines). As shown in the figure, for _Ydd , the analysis results, simulation results, and measurement results generally agreed with each other in terms of both amplitude and phase. Although the accuracy is slightly lower than that of _Ydd , the analysis results, simulation results, and measurement results of _Yqq also agree with each other in terms of both amplitude and phase. Since Y _dq and Y _qd have amplitudes smaller than Y _dd and Y _qq by 30 dB or more, it seems that the difference between the analysis result and the measurement result is large. However, the measurement results of the amplitudes of Y _dq and Y _qd showed the same trend as the analysis results.

Although detailed description is omitted, the state equation of the two-phase (α, β) system at time t is represented by equation (18), and the state variable vector x _αβ in equation (18) is represented by equation (19). Then, the analytic value of the output admittance Y ^m _αβ can be obtained by equations (20) and (21).

また、ｕ_αβ、ｉ_ｏαβ、ｉ_Ｌαβ、ｖ_Ｃαβ、ｋ^ｍ _ｆαβおよびＧ^ｍ _ｓは、制御入力、出力電流、フィルタインダクタ電流、フィルタキャパシタ電圧、状態フィードバックゲインおよび正弦波補償器の伝達関数である。 However, the continuous system coefficient matrix A _c , the continuous system input coefficient vector b _c , the continuous system disturbance coefficient vector h _c and the continuous system output coefficient vector c _c are as shown in Equation (22).

Also, u _αβ , i _oαβ , i _Lαβ , v _Cαβ , ^{km fαβ} and G _ms are the transfer _functions of the control input, output current, filter inductor current, filter capacitor voltage, state feedback gain and sinusoidal compensator .

10 First Subsystem 11 Second Subsystem 12 Frequency Characteristic Analysis Section 13 Signal Processing Section 14 Voltage Application Section 15 Drive Circuit 16 Drive Circuit _Tu First Transformer _Tv Second Transformer

Claims (4)

A method for measuring the output admittance of a subsystem constituting a three-phase power system, comprising:
a first step of generating a perturbation signal oscillating at a predetermined amplitude;
_{a second step of converting the two-phase system voltage v a that oscillates according to the perturbation signal and the two-phase system voltage v b that} does not oscillate into three-phase system voltages v _u , v _v , and v _w ;
While applying the voltage v _u −v _w and the voltage v _v −v _w to the u phase and the v phase of the u phase, the v phase and the w phase of the subsystem, the currents i _u and i of each phase are measured. a third step of obtaining _v , i _w and voltages v _u , v _v , v _w ;
a fourth step of converting the currents i _u , i _v , i _w obtained in the third step to obtain two-phase system currents i _a , i _b ;
a fifth step of converting the voltages v _u , v _v , v _w obtained in the third step to obtain two-phase system voltages v _a , v _b ;
A sixth step of obtaining Y _aa and Y _ba , which are the matrix elements of the output admittance, based on the relationship between the currents i _a and i _b obtained in the fourth step and the voltages v _a and v _b obtained in the fifth step. When,
_a seventh step of converting the two-phase system voltage _vb that oscillates according to the perturbation signal and the two-phase system voltage va that does not oscillate into three-phase system voltages _vu , _vv , and _vw ;
While applying the voltage v _u −v _w and the voltage v _v −v _w to the u phase and the v phase of the u phase, the v phase and the w phase of the subsystem, the currents i _u and i of each phase are measured. an eighth step of obtaining _v , i _w and voltages v _u , v _v , v _w ;
a ninth step of converting the currents i _u , _iv , i _w obtained in the eighth step to obtain two-phase system currents i _a , _ib ;
a tenth step of converting the voltages v _u , v _v , v _w obtained in the eighth step to obtain two-phase system voltages v _a , v _b ;
An eleventh step of _{obtaining Yab} and _Ybb , which are the matrix elements of the output admittance, based on the relationship between the currents _ia and _ib obtained in the ninth step and the voltages va and _vb obtained in the tenth step. and Repeating steps 2 to 6 while changing the frequency of vibration within a predetermined measurement frequency range, and then performing steps 7 to 11 while changing the frequency of vibration within the measurement frequency range. 2. The method of claim 1, wherein the method is performed repeatedly. The transformations in the 2nd and 7th steps are performed by the equation (3-1), the transformations in the 4th and 9th steps are performed by the equation (3-2), and the transformations in the 5th and 10th steps are performed by the equation ( 3-3).

The transformations in the 2nd and 7th steps are performed by the equation (4-1), the transformations in the 4th and 9th steps are performed by the equation (4-2), and the transformations in the 5th and 10th steps are performed by the equation ( 4-3).

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