JP2012029543A - Electric power conversion system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To suppress a beat phenomenon irrespective of a variation of an operation period, etc.SOLUTION: The electric power conversion system provided with means to adjust an output voltage in accordance with a pulsation component of a DC intermediate voltage comprises state equation calculating means 200 to calculate a state equation by using at least a carrier period where PWM control of an inverter is carried out, the DC intermediate voltage and a control delay correction time of the inverter. The calculating means 200 includes: means 201 to calculate a coefficient of a matrix exponential function by using the carrier period; difference equation calculating means 202 which has the DC intermediate voltage and the matrix exponential function as inputs, has at least two independent state variables expressing a secondary or greater transfer function, and at the same time calculates the state equation in which one of the state variables is an extraction value of the pulsation component of the DC intermediate voltage to output at least two state variables; phase correction amount calculating means 205 for calculating the pulsation component by performing linear combination on the state variables upon phase correction; gains 203 and 204; trigonometric functions 206 and 207; and addition means 209, etc.

Description

  The present invention relates to a power converter for driving an AC motor mounted on an AC electric vehicle, for example, at a variable speed, and more specifically, a converter such as a PWM converter that converts an AC voltage into a DC voltage, and a DC output voltage of the converter. And an inverter such as a VVVF inverter for converting to a variable voltage / variable frequency AC voltage.

FIG. 8 shows a vehicular power conversion device having substantially the same configuration as the conventional technology described in Patent Document 1.
This power conversion device includes a main circuit and a control device. The main circuit includes a single-phase AC power supply 101, a PWM converter 102, a DC smoothing capacitor 103, and a VVVF inverter 104 that outputs an AC voltage having a variable voltage and a variable frequency. The AC motor 105 is provided.
The control device includes a voltage detection unit 111, a current detection unit 112, an analog / digital (A / D) conversion unit 121, a band pass filter 122, a parameter adjustment unit 123, gain calculation units 124 and 125, a vector control unit 131, A vector analyzer 132, a gate signal generating unit 133, a primary frequency generating unit 134, an average value calculating unit 135, an integrating unit 136, a multiplying unit 141, and an adding unit 142 are provided.

In this prior art, first, a method for generating a gate signal applied to the inverter 104 will be described.
According to Patent Document 1, the vector control unit 131 detects the current flowing through the AC motor 105 by the current detection unit 112, and based on the detected value, the voltage of the rotational coordinate axes (d, q axes) synchronized with the primary frequency. Command values v _d ^* and v _q ^* are output.
The voltage across the capacitor 103 (DC intermediate voltage) detected by the voltage detection means 111 is converted into a digital signal v _dc by the analog / digital conversion means 121 and input to the average value calculation means 135. The average value calculation means 135 calculates the average value v _dcav of the DC intermediate voltage. The average value v _dcav and the voltage command values v _d ^* , v _q ^* are input to the vector analyzer 132, and the vector analyzer 132 calculates the phase angle α of the output voltage of the inverter 104 and the modulation factor command value λ ₀ .

The modulation factor command value λ ₀ is corrected by a multiplication unit 141 with a gain command value K _λ of a modulation ratio output from a gain calculation unit 124 described later to become a modulation factor command value λ ₁ , and this modulation factor command value λ ₁ Is input to the gate signal generating means 133.

Further, the primary frequency generation means 134 calculates the frequency command value of the AC voltage applied to the AC motor 105. Specifically, when AC motor 105 is an induction motor, a primary frequency is generated in consideration of the slip frequency from the detected speed value or estimated speed value of the motor, and when AC motor 105 is a synchronous motor, the motor is The primary frequency ω ₁ is generated according to the type of the motor, such as using the detected speed value.
The integrating means 136 integrates the primary frequency ω ₁ and outputs an angle θ ₀ . The angle θ ₁ is calculated by adding the angle θ ₀ and Δθ from the gain calculating means 125 described later by the adding means 142, and the angle θ ₁ is input to the gate signal generating means 133.
Based on the phase angle α, the modulation factor command value λ ₁ and the angle θ ₁ , the gate signal generation unit 133 generates and outputs a gate signal for the semiconductor switching element of the inverter 104 by PWM control.

  By the way, in a power conversion device that rectifies a single-phase AC voltage such as a single-phase AC power source 101 by a converter 102 and uses it as a power source, generally, a pulsating component having a frequency twice the power source frequency is included in a DC intermediate voltage. It is known to be included. When the frequency of the output voltage of the inverter 104 is close to the frequency of the pulsating component, the output voltage of the inverter 104 includes a direct current component or a low frequency component, and a large load current may flow through the alternating current motor 105. . This phenomenon is called a beat phenomenon.

Next, a method for suppressing the beat phenomenon disclosed in Patent Document 1 will be described.
The DC intermediate voltage v _dc as a digital signal output from the analog / digital conversion means 121 is input to the band pass filter 122. The band pass filter 122 extracts a voltage having a frequency component twice the power supply frequency included in the DC intermediate voltage, and outputs this voltage as a pulsation component Δv _dc . This pulsation component Δv _dc is input to gain calculation means 124 and 125.

The characteristics of the bandpass filter 122 are determined by the adjustment parameters (center frequency f ₀ , gain G) input from the parameter adjusting means 123. The characteristics of the bandpass filter 122 are as shown in FIG. 9, for example. Yes. According to FIG. 9, the value of the output of the filter is set to be a leading phase at the frequency of the pulsation component Δv _dc , and the time corresponding to the leading phase cancels the control delay of the control device of the inverter 104. Is set to
The parameter adjusting means 123 performs primary approximation or linear approximation according to the primary frequency ω ₁ in order to make the time for canceling the control delay variable, and calculates and outputs the center frequency f ₀ and the gain G.
The gain calculator 124 calculates the gain command value K _λ according to the pulsation component Δv _dc output from the bandpass filter 122, and the multiplier 141 modulates the modulation factor λ ₀ by the gain command value K _λ. By correcting to the rate λ ₁ , the direct current component and the low frequency component superimposed on the output voltage of the inverter 104 are canceled to suppress the beat phenomenon.

Here, when the inverter 104 operates in a so-called one-pulse mode in which only one pulse is output in one cycle of the AC voltage fundamental wave, the modulation factor is fixed to 1, so that the modulation is performed using the gain calculation means 124. The rate cannot be adjusted.
In such a case, the gain calculation means 125 calculates Δθ according to the pulsation component Δv _dc of the DC intermediate voltage so that the voltage time products in the positive and negative polarity periods of the output voltage are equal, and uses this Δθ. By adjusting the angle θ ₁ of the output voltage of the inverter 104, the beat phenomenon is suppressed.

As described above, in this conventional technique, the parameter adjusting means 123 makes the characteristics of the bandpass filter 122 variable according to the primary frequency (inverter frequency) ω ₁ , thereby suppressing the beat phenomenon over a wide range of inverter frequencies. Making it possible.

JP 2009-273330 A (paragraphs [0016] to [0023], FIG. 1, etc.)

When synchronous PWM control is performed to synchronize the phase of the output voltage fundamental wave and the pulse pattern of the output voltage as in the prior art described above, the calculation cycle of the pulse pattern changes according to the inverter frequency, especially before and after pulse switching. The calculation cycle varies greatly. If the calculation cycle varies in this manner, the phase characteristic among the characteristics of the bandpass filter 122 is adversely affected, the compensation accuracy for the control delay described above is deteriorated, and the effect of suppressing the beat phenomenon is reduced.
Therefore, a problem to be solved by the present invention is to provide a power conversion device capable of suppressing the beat phenomenon regardless of fluctuations in the calculation cycle.

In order to solve the above problems, an invention according to claim 1 is directed to a converter for converting an AC voltage into a DC voltage, a DC smoothing capacitor connected to the DC side of the converter, and a DC intermediate voltage across the DC smoothing capacitor. Voltage detecting means for detecting the DC intermediate voltage, an inverter for converting the DC intermediate voltage into an AC voltage and supplying the load to the load, and means for adjusting the output voltage of the inverter according to a pulsation component of the DC intermediate voltage. In the power converter,
A state equation calculating means for calculating a state equation using at least a carrier cycle for PWM control of the inverter, the DC intermediate voltage, and a correction time for correcting a control delay of the inverter;
The state equation calculation means includes:
Means for calculating a coefficient of a matrix exponential function using the carrier period;
The DC intermediate voltage and the matrix exponential function are input, and at least two independent state variables expressing a transfer function of second order or higher are included, and one state variable is an extracted value of the pulsating component of the DC intermediate voltage A difference equation calculation means for calculating a state equation as a difference equation and outputting the at least two state variables;
Means for obtaining the pulsation component by linearly combining these state variables with a phase correction amount based on a phase correction amount based on the correction time; and
It is equipped with.

  The invention according to claim 2 detects the phase difference between the pulsating component of the DC intermediate voltage and a value obtained by multiplying the state variable, which is an extracted value of the pulsating component, by a gain in the power conversion device according to claim 1. And means for calculating a parameter corresponding to the resonance frequency of the state equation based on the phase difference, and calculating a coefficient of the matrix exponential function using the parameter.

According to the first aspect of the present invention, the beat phenomenon can be suppressed even when the calculation cycle of the pulse pattern changes due to pulse switching or the like, as compared with the prior art.
According to the second aspect of the present invention, even when the power supply frequency fluctuates and a deviation occurs between the frequency of the pulsating component and the resonance frequency of the filter, the resonance frequency is automatically adjusted to cause the beat phenomenon. Can be suppressed.

It is a lineblock diagram of the power converter concerning a 1st embodiment of the present invention. It is a block diagram of the state equation calculating means in FIG. FIG. 3 is a Bode diagram of a transfer function of one gain output in FIG. 2. It is a block diagram of the power converter device which concerns on 2nd Embodiment of this invention. It is a block diagram of the resonance frequency adjustment means in FIG. It is a figure which shows the timing which the timing generation means in FIG. 5 outputs a 1st trigger signal, and the output signal of a sampling means. It is a figure which shows the timing which the timing production | generation means in FIG. 5 outputs a 2nd trigger signal, and the output signal of an amplitude calculating means. It is a block diagram which shows the power converter device for vehicles of the structure substantially the same as the prior art described in patent document 1. It is a figure which shows the frequency characteristic of the band pass filter in FIG.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
FIG. 1 is a configuration diagram of the power conversion device according to the first embodiment of the present invention, and its main circuit is a single-phase AC power source 101, a PWM converter 102, a DC smoothing capacitor 103, a VVVF inverter, as in FIG. 104, an AC motor 105.
On the other hand, in the control device, portions having the same functions as those in FIG. 8 are denoted by the same reference numerals, and description thereof is omitted. Hereinafter, portions different from those in FIG.

That is, in the first embodiment, the bandpass filter 122, the parameter adjusting unit 123, the gain calculating unit 125, and the adding unit 142 in FIG. 8 are removed, and the state equation calculating unit 200 and the correction time adjusting unit 210 are added. .
The state equation calculation unit 200 in FIG. 1 includes a DC intermediate voltage v _dc output from the analog / digital conversion unit 121, an average value v _dcav of the DC intermediate voltage calculated by the average value calculation unit 135, and a gate signal generation. The PWM control carrier period t _c supplied from the means 133 and the correction time t _d output from the correction time adjustment means 210 are input, and the pulsation component Δv _dc of the DC intermediate voltage is calculated and input to the gain calculation means 124. It is designed to output. The correction time t _d is intended to offset the response delay time of the inverter control device.

FIG. 2 is a detailed configuration diagram of the state equation calculation means 200. The state equation calculating means 200 includes a coefficient calculating means 201 for calculating a matrix exponential function e ^Atc, which will be described later, based on the carrier period t _c , and a state variable x ₁ , based on the DC intermediate voltage v _dc and the matrix exponential function e ^Atc . a difference equation calculating means 202 for calculating the x _2, the state variables _x 1, gain is multiplied by each of the _{x 2} 203 and 204, a subtraction unit 208 for subtracting the average value _{v DCAV} the DC link voltage from the output of the gain 203, A trigonometric function 206 to which the output of the subtracting means 208 is input, a trigonometric function 207 to which the output of the gain 204 is input, an adding means 209 for calculating the pulsating component Δv _dc by adding the outputs of the trigonometric functions 206 and 207, and a phase correction amount calculation means 205. give controlled delayed correction time t _d by calculating a phase correction amount β trigonometric functions 206 and 207 It has been.

Equation 1 is a state equation representing a transfer function having a denominator of second order and a numerator of first order. When this is calculated, the variable x ₂ corresponds to the output of the bandpass filter for the input u. In Equation 1, ω _c corresponds to the angular frequency of the single-phase power source.

2 calculates the matrix exponential function e ^Atc of the matrix A in Equation 1 using Equation 2. In Equation 2, t _c is a carrier period and I is a unit matrix.

Or for loading and Equation 2 to calculate each time is high, among the parameters of the matrix A, if it is not necessary to change the omega _c and zeta, the carrier period (operation cycle) t _c, will advance what e ^Atc This may be approximated as a polynomial in t _c .

Also, the matrix exponential function e ^Atc can be obtained using the eigenvalues λ ₁ and λ ₂ and the eigenvector of the matrix A.
The eigenvalues of the matrix A are λ ₁ = −ω _c (ζ + √ (ζ ² −1)) and λ ₂ = −ω _c (ζ−√ (ζ ² −1)). If the eigenvectors for this are v ₁ and v ₂ , TAT ⁻¹ = diag {e ^λ1 , e ^λ2 } can be calculated using the matrix T = [v ₁ , v ₂ ]. Therefore, e ^Atc can be ^obtained from Equation 3 using T and e ^λ1 and e ^λ2 .

但し、ｂ：［０ １］^Ｔ，ｔ：キャリア周期（演算周期）である。 The difference equation calculation means 202 in FIG. 2 calculates the state equation shown in Equation 1 as a difference equation. For example, the value x ((k + 1) t) of the next state variable can be calculated as shown in Equation 4. According to this equation, the bandpass in the continuous system as shown in FIG. 8 even in the sampling system as shown in FIG. A behavior similar to that of the filter 122 can be realized.

Where b: [0 1] ^T , t: carrier period (calculation period).

When the pulse pattern calculation cycle changes, the difference equation calculation means 202 calculates the difference equation as follows.
That is, when the calculation cycle before the change is t ₁ and the calculation cycle after the change is t ₂ , the matrix exponential function e ^At2 after the change of the calculation cycle is obtained by the calculation of Equation 5 using the coefficient calculation unit 201. deep.

  By calculating the difference equation as described above, the characteristics as a band-pass filter can be kept constant even immediately after the calculation cycle changes greatly, such as when switching pulses, so that the effect of suppressing the beat phenomenon can be maintained. it can.

The gains 203 and 204 have values g ₁ and g ₂ such that the state variables x ₁ and x ₂ are the same predetermined gain (0 [dB]) with respect to the component of the resonance frequency ω _c , respectively. Set. When the DC component is included in the state variable x ₁ , the DC component is removed by subtracting the average value v _dcav of the DC intermediate voltage from the output of the gain 203 by the subtracting unit 208.

FIG. 3 is a Bode diagram of the transfer function of the output of the gain 204 when ω _c = 753.6 [rad / s] and ζ = 0.1.
As shown in FIG. 3, since the amplitude at the resonance frequency ω _c is 0 [dB] and the phase is 0 degree, the component of the state variable x _{2 at} the resonance frequency ω _c does not change in amplitude or phase. Can pass through.

On the other hand, the state variable x ₁ has a differential relationship with respect to x ₂ as is apparent from Equation 1, and it can be seen that the phase of the component of the resonance frequency ω _c differs by 90 degrees. By linearly combining the two state variables _x 1, _{x 2} via trigonometric functions 206, 207 and the adding means 209, the pulsating component Delta] v _dc with arbitrary phase relative to the input DC link voltage _{v dc} Can be generated.

The phase correction amount calculation means 205 and the trigonometric functions 206 and 207 perform the same action as the parameter adjustment means 123 in the prior art of FIG. 8, and change the phase according to the correction time t _{d for} which control delay is to be compensated. . That is, the phase correction amount β is output by dividing the correction time t _d by the resonance frequency ω _c , and the trigonometric functions 206 and 207 are calculated using the phase correction amount β.

Assuming that the pulsation component included in the DC intermediate voltage v _dc is Msin (ω _c t + φ), the output of the gain 204 is Msin (ω _c t + φ), and the output of the subtracter 208 is Mcos (ω _c t + φ). It becomes. For this reason, the pulsation component Δv _dc via the trigonometric functions 206 and 207 and the adding means 209 is expressed by Equation 6.

Since Equation 6 is equal to Equation 7, a value obtained by changing the phase of the input signal Msin (ω _c t + φ) by β can be obtained as the pulsation component Δv _dc from the state equation calculation unit 200.

The pulsation component Δv _dc output from the state equation calculation means 200 is input to the gain adjustment means 124 as shown in FIG. 1, and the modulation factor λ ₀ is corrected by the gain command value K _λ as shown in FIG. Adjust the amplitude of the output voltage.

Next, a second embodiment of the present invention will be described with reference to FIG.
The second embodiment differs from the first embodiment of FIG. 1 in that the resonance frequency is based on the DC intermediate voltage v _dc and its average value v _dcav and the output signal g ₂ x ₂ from the state equation calculation means 200. Resonance frequency adjusting means 220 for calculating and outputting ω _c1 is provided, and the resonance frequency ω _c1 is inputted to the state equation calculating means 200 together with the DC intermediate voltage v _dc and its average value v _{dcav and the} correction time t _d. It is a point. Based on the input resonance frequency ω _c1 , the state equation calculation unit 200 calculates the matrix exponential function e ^Atc by the internal coefficient calculation unit 201 as in FIG.

Hereinafter, an example in which the resonance frequency ω _c1 is output by the resonance frequency adjusting unit 220 in accordance with the frequency of the pulsating component of the DC intermediate voltage will be described.
FIG. 5 is a detailed configuration diagram of the resonance frequency adjusting means 220. The resonance frequency adjusting means 220 includes a subtracting means 226 for obtaining a deviation between the DC intermediate voltage v _dc and its average value v _dcav , a timing generating means 222 to which the pulsation component Msin (ωt) as the deviation is input, and a state equation A sampling means 221 that outputs a signal Msin (φ) based on the output signal g ₂ x ₂ of the gain 204 in the calculation means 200 and the first trigger signal Trg ₁ from the timing generation means 222, and the pulsating component Msin ( ωt) and the second trigger signal Trg ₂ from the timing generation means 222, the amplitude calculation means 223 that outputs the amplitude M, and the output of the sampling means 221 are divided by the output of the amplitude calculation means 223 to obtain sin (φ ), A gain 225 multiplied by sin (φ), and a resonance frequency that is the output thereof By adding the several deviation Δω and the resonance frequency omega _c and an addition means 227 for outputting a resonant frequency omega _c1.

In the above configuration, the sampling unit 221 receives the trigger signal Trg ₁ from the timing generation unit 222 and simultaneously records and holds the value of the output signal g ₂ x ₂ of the gain 204.
As described above, the timing generation unit 222 receives a pulsation component which is a deviation between the DC intermediate voltage v _dc and the average value v _{dcav thereof,} and _supplies the first trigger signal Trg ₁ to the sampling unit 221 and the second The trigger signal Trg ₂ is supplied to the amplitude calculation means 223.

Now, it is assumed that the pulsation component input to the timing generation unit 222 can be expressed by the following Equation 8.

The timing generation means 222 observes the slope of the pulsating component and its zero cross, generates the first trigger signal Trg ₁ at the timing when the slope of the pulsating component is positive and the pulsating component becomes zero, The sampling means 221 is supplied. For this reason, the output signal of the sampling means 221 is Msin (φ).
On the other hand, the timing generation unit 222 generates the second trigger signal Trg ₂ at the same time as the inclination of the pulsation component changes from positive to negative, and supplies it to the amplitude calculation unit 223.
At the same time as the trigger signal Trg ₂ is input, the amplitude calculation means 223 calculates the magnitude of the pulsating component that is the input signal, and outputs this as the amplitude M.

6 is a diagram illustrating the timing at which the timing generation unit 222 outputs the _first trigger signal Trg ₁ and the output signal of the sampling unit 221. FIG. 7 illustrates the timing generation unit 222 as the second trigger. and when to output a signal Trg _2, a diagram showing an output signal of the amplitude calculating unit 223.

In FIG. 5, the output sin (φ) of the dividing means 224 is input to the gain 225. The gain 225 multiplies the sin (φ) by a gain (−ζω _c ) composed of the braking coefficient ζ and the resonance frequency ω _c included in the above-described equation 1, and outputs the result as the resonance frequency deviation Δω. This resonance frequency deviation Δω is added to the resonance frequency ω _c so far by the adding means 227 and supplied to the state equation calculation means 200 of FIG. 4 as a new resonance frequency ω _c1 .

Next, the reason why the new resonance frequency ω _c1 is obtained from the frequency of the pulsating component in this way will be described below.
FIG. 3 shows the frequency characteristic of the output of the gain 204 in the state equation calculation means 200 as described above, and the input is the DC intermediate voltage v _dc . In this embodiment, it is assumed that the resonance frequency ω _c is not equal to the frequency ω of the pulsating component of the DC intermediate voltage.
According to FIG. 3, the phase advances with respect to the low frequency signal than the resonant frequency omega _c, it can be seen that the phase is delayed with respect to signal higher than the resonant frequency omega _c. As a result, the phase of the pulsating component shown in Formula 8 changes, and the output of the gain 204 becomes Formula 9.

As described above, when the timing generation unit 222 generates the trigger signal Trg ₁ , Msin (ωt) = 0 and ωt = 2nπ. Therefore, the output of the sampling means 221 is Msin (φ), and the output of the dividing means 224 is sin (φ).

Further, when the phase characteristic of FIG. 3 is expressed in a complex number format, Expression 10 is obtained. However, ω in Formula 10 is the angular frequency on the horizontal axis in FIG.

If the angular frequency omega of the pulsating component and the resonance frequency omega _c are not equal, it can be seen that the imaginary part of equation 10 is no longer zero. If this frequency deviation is defined as Δω = ω−ω _c , the approximation of Expression 11 holds when the deviation Δω is sufficiently smaller than the original resonance frequency ω _c .

The imaginary component of the phase characteristic is equal to sin (φ) that is the output of the dividing means 224 in FIG.
Therefore, from Equation 11, the approximate frequency deviation Δω can be obtained by multiplying sin (φ) by (−ζω _c ) with the gain 225, and this addition Δ227 is used to add the deviation Δω to the original resonance frequency. By adding to ω _c , a new resonance frequency ω _c1 is obtained.
In the state equation calculation unit 200 of FIG. 4, the matrix exponential function e ^Atc is calculated by the coefficient calculation unit 201 based on the resonance frequency ω _c1 .

DESCRIPTION OF SYMBOLS 101: Single phase alternating current power supply 102: PWM converter 103: DC smoothing capacitor 104: VVVF inverter 105: AC motor 111: Voltage detection means 112: Current detection means 121: Analog / digital conversion means 124: Gain calculation means 131: Vector control means 132: Vector analyzer 133: Gate signal generation means 134: Primary frequency generation means 135: Average value calculation means 136: Integration means 141: Multiplication means 200: State equation calculation means 201: Coefficient calculation means 202: Difference equation calculation means 203, 204 : Gain 205: Phase correction amount calculation means 206, 207: Trigonometric function 208: Subtraction means 209: Addition means 210: Correction time adjustment means 220: Resonance frequency adjustment means 221: Sampling means 222: Timing generation means 22 3: Amplitude calculation means 224: Division means 225: Gain 226: Subtraction means 227: Addition means

Claims (2)

A converter for converting an AC voltage into a DC voltage; a DC smoothing capacitor connected to the DC side of the converter; voltage detection means for detecting a DC intermediate voltage at both ends of the DC smoothing capacitor; and the DC intermediate voltage as an AC voltage In an electric power converter comprising:
A state equation calculating means for calculating a state equation using at least a carrier cycle for PWM control of the inverter, the DC intermediate voltage, and a correction time for correcting a control delay of the inverter;
This equation of state calculation means
Means for calculating a coefficient of a matrix exponential function using the carrier period;
The DC intermediate voltage and the matrix exponential function are input, and at least two independent state variables expressing a transfer function of second order or higher are included, and one state variable is an extracted value of the pulsating component of the DC intermediate voltage A difference equation calculation means for calculating a state equation as a difference equation and outputting the at least two state variables;
Means for obtaining the pulsation component by linearly combining these state variables with a phase correction amount based on a phase correction amount based on the correction time; and
A power conversion device comprising: In the power converter device according to claim 1,
Means for detecting a phase difference between a pulsating component of the DC intermediate voltage and a value obtained by multiplying a state variable that is an extracted value of the pulsating component by a gain;
Means for calculating a parameter corresponding to the resonance frequency of the state equation based on the phase difference;
With
A power conversion apparatus that calculates a coefficient of the matrix exponential function using the parameter.

Images