CN104158220A - Method for controlling virtual reactance of photovoltaic grid-connected inverter - Google Patents

Abstract

A virtual reactance control method for a photovoltaic grid-connected inverter relates to the technical field of photovoltaic grid-connected inverter control. The problem of poor stability of existing photovoltaic grid-connected inverters is solved. The method includes the following steps: obtaining the virtual inductance, its equivalent internal resistance and virtual capacitance according to the actual grid impedance, the inverter output impedance and the stability criterion of the inverter output impedance; according to the virtual inductance and its equivalent The internal resistance, combined with the full-bridge gain to obtain the equivalent feedforward path transfer function of the virtual inductor; according to the capacitance of the virtual capacitor, combined with the full-bridge gain, the actual filter capacitor, filter inductor and its parasitic resistance, current loop transfer function and feedback The transfer function of the filter loop obtains the equivalent feedforward path transfer function of the virtual capacitor; the equivalent feedforward path transfer function of the virtual inductor and virtual capacitor is discretized to obtain a difference equation: the difference equation is superimposed on the output of the current loop. The invention is suitable for controlling photovoltaic grid-connected inverters.

Description

Virtual reactance control method for photovoltaic grid-connected inverter

technical field

The invention relates to the technical field of photovoltaic grid-connected inverter control.

Background technique

The power grid at the end of the power grid in remote areas, islands, etc. is usually designed for relatively small loads, and its power supply is mostly of medium and low voltage levels. In order to meet the load needs of distributed users, most of the transmission lines are long and the line reactance is large, so the power grid presents high Impedance characteristics, this kind of grid is usually called weak grid (weak grid). For a photovoltaic grid-connected inverter with a reasonable design in the normal grid, when the grid impedance becomes larger, the stability of the system will deteriorate, and the harmonics of the grid-connected current will increase. Therefore, when designing photovoltaic inverters used at the end of the grid or in remote areas, not only the working state of the normal grid must be considered, but also the stability of the system when the grid impedance increases, that is, the weak grid.

For the current source photovoltaic grid-connected inverter, it is hoped that the output impedance of the inverter should be as large as possible. By analyzing the output impedance characteristics of the LC type single-phase photovoltaic grid-connected inverter and the influence of different parameters on the output impedance of the inverter, it can be found that increasing the filter inductance will increase the output impedance in the high frequency band, which is conducive to improving system stability. ; But increasing the filter inductance will often lead to an increase in system size and cost. Further research has found that reducing the inverter output filter capacitor is also one of the effective measures to increase the inverter output impedance and thus enhance the system stability; but reducing Capacitors tend to increase the output ripple of the inverter and reduce the quality of grid-connected power, which will have a negative impact on the system.

Contents of the invention

In order to solve the problem of poor stability of existing photovoltaic grid-connected inverters, the present invention proposes a virtual reactance control method for photovoltaic grid-connected inverters.

The virtual reactance control method of a photovoltaic grid-connected inverter includes the following steps:

Step 1. Obtain the virtual inductance L _V according to the actual grid impedance Z _g , the output impedance Z _o (s) of the photovoltaic grid-connected inverter, and the amplitude-frequency characteristics and phase-frequency characteristics of the output impedance stability criterion of the photovoltaic grid-connected inverter , the equivalent internal resistance r _V of the virtual inductance and the virtual capacitance C _V ;

Step 2. According to the virtual inductance L _V and the equivalent internal resistance r _V of the virtual inductance, combined with the full-bridge gain K _PWM , obtain the equivalent feedforward path transfer function G _LV (s) of the virtual inductance;

Step 3. According to the capacitance C _V of the virtual capacitor, combined with the full-bridge gain K _PWM , the actual filter capacitor C _ac , the filter inductor L _ac and its parasitic resistance r _ac , the current loop transfer function G _i (s) and the feedback filter loop The transfer function G _a (s) obtains the equivalent feed-forward path transfer function of the virtual capacitor $G_{\mathrm{cv}}\left(\mathrm{the\; s}\right)=\frac{(C_{\mathrm{ac}}-C_v\mathrm{the\; s})(r_{\mathrm{ac}}+L_{\mathrm{ac}}\mathrm{the\; s}+K_{\mathrm{PWM}}{G}_i{G}_a)}{K_{\mathrm{PWM}}};$

Step 4. Discretize the equivalent feedforward path transfer function of the virtual inductor and the equivalent feedforward path transfer function of the virtual capacitor to obtain the difference equation:

$\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; V</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; V</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; PWM</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; V</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; PWM</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

z(n)=K ₁ v _O (n)+K ₂ v _O (n-1)-K ₃ v _O (n-2),

Among them, T _s is the sampling period, and K ₁ , K ₂ , and K ₃ are coefficients;

Step five, superimposing y(n), z(n) and the output x(n) of the current loop.

Beneficial effects: the control method proposed by the present invention improves the output impedance of the current-type photovoltaic grid-connected inverter by adding a virtual reactance control method instead of increasing the actual capacity of the filter inductor, and at the same time by adding a virtual capacitor in the control loop and If the original filter inductor is connected in series, the equivalent filter capacitance of the inverter will be reduced, which will increase the output impedance of the inverter, thereby enhancing system stability.

Description of drawings

Figure 1 is the equivalent structure diagram of the photovoltaic grid-connected inverter with virtual inductor added, V _dc is the DC bus voltage, S ₁ , S ₂ , S ₃ and S ₄ are full-bridge power switch tubes;

Figure 2 is the linear model of the system after adding the virtual inductor;

Figure 3 is an equivalent structure diagram of a photovoltaic grid-connected inverter after adding a virtual capacitor;

Fig. 4 is the linear model of the system after adding the virtual capacitor;

Figure 5 is an equivalent structure diagram of a photovoltaic grid-connected inverter after adding a virtual reactance;

Figure 6 is the linear model of the system after adding virtual reactance;

Fig. 7 is the linear model of virtual inductor feed-forward path;

Figure 8 is a comparison chart of inverter output impedance before and after adding virtual reactance. The inverter output impedance before adding virtual reactance is the Z _o1 curve, the inverter output impedance after adding virtual reactance is Z _o2 curve, and the Z _g curve is the actual Grid impedance;

Fig. 9 is a pole distribution diagram of the system open-loop transfer function before and after adding the virtual reactance control method;

Fig. 10 is the Nessler curve diagram of the system before adding the virtual reactance;

Figure 11 is the Nestle curve of the system after adding virtual reactance.

Detailed ways

Specific embodiments 1. This specific embodiment is described in conjunction with FIGS. 1-6 . The method for controlling virtual reactance of a photovoltaic grid-connected inverter described in this specific embodiment includes the following steps:

Step 1. Obtain the virtual inductance L _V according to the actual grid impedance Z _g , the output impedance Z _o (s) of the photovoltaic grid-connected inverter, and the amplitude-frequency characteristics and phase-frequency characteristics of the output impedance stability criterion of the photovoltaic grid-connected inverter , the equivalent internal resistance r _V of the virtual inductance and the virtual capacitance C _V ;

Step 2. According to the virtual inductance L _V and the equivalent internal resistance r _V of the virtual inductance, combined with the full-bridge gain K _PWM , obtain the equivalent feedforward path transfer function G _LV (s) of the virtual inductance;

Step 3. According to the capacitance C _V of the virtual capacitor, combined with the full-bridge gain K _PWM , the actual filter capacitor C _ac , the filter inductor L _ac and its parasitic resistance r _ac , the current loop transfer function G _i (s) and the feedback filter loop The transfer function G _a (s) obtains the equivalent feed-forward path transfer function of the virtual capacitor $G_{\mathrm{cv}}\left(\mathrm{the\; s}\right)=\frac{(C_{\mathrm{ac}}-C_v\mathrm{the\; s})(r_{\mathrm{ac}}+L_{\mathrm{ac}}\mathrm{the\; s}+K_{\mathrm{PWM}}{G}_i{G}_a)}{K_{\mathrm{PWM}}};$

Step 4. Discretize the equivalent feedforward path transfer function of the virtual inductor and the equivalent feedforward path transfer function of the virtual capacitor to obtain the difference equation:

$\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; V</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; V</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; PWM</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; V</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; PWM</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

z(n)=K ₁ v _O (n)+K ₂ v _O (n-1)-K ₃ v _O (n-2),

Among them, T _s is the sampling period, and K ₁ , K ₂ , and K ₃ are coefficients;

Step five, superimposing y(n), z(n) and the output x(n) of the current loop.

The present invention takes the LC type single-phase photovoltaic grid-connected inverter as an example. Figure 1 shows the equivalent structure diagram of the grid-connected inverter after adding virtual inductance. The inductance L _V in the dotted line box in the figure is the newly added The filter inductance component, the inductance is connected in series with the original filter inductance L _ac , according to the basic principle of increasing the inductance value of the inductance in series, after increasing the inductance L _V , the total filter inductance of the inverter becomes L _ac '=L _ac +L _V ; In order not to increase the volume and weight of the original photovoltaic grid-connected inverter, the inductance L _V is not an actual inductance, but a forward path is added in the control system, and the system linear model after adding the virtual inductance is shown in Figure 2 As shown, the dotted box in Figure 2 is the newly added control link, which can be regarded as a proportional differential link. From the control point of view, adding the forward path is equivalent to increasing the filter inductance from L _ac to L _ac + L _V ;

Reducing the output capacitance of the inverter is also one of the effective measures to improve system stability in the case of a weak grid, but reducing the capacitance will often lead to larger system output ripple and lower grid-connected power quality. For this reason, the present invention adds a virtual capacitor in series with the original filter inductance in the control loop, the equivalent filter capacitor of the inverter will be reduced, so that the output impedance of the inverter will increase, and then achieve For the purpose of enhancing system stability, the equivalent filter capacitor in this system becomes ${C_{\mathrm{ac}}}^{\&prime;}=\frac{C_{\mathrm{ac}}\&CenterDot;C_V}{C_{\mathrm{ac}}+C_V};$

Combining the above virtual inductance and virtual capacitance control methods is the virtual reactance control method proposed by the present invention. As shown in Figure 6, it can be seen that the method proposed by the present invention is equivalent to adding two A control loop to obtain the output control signals y(n) and z(n), and superimpose the control signal with the output signal x(n) of the current loop, and finally output the synthesized control signal to drive the power switch after SPWM modulation tube to achieve closed-loop control of the system.

Embodiment 2. The difference between this embodiment and the photovoltaic grid-connected inverter virtual reactance control method described in Embodiment 1 is that the actual grid impedance Z _g described in step 1 is obtained through impedance testing equipment or grid impedance. Obtained by online detection method.

Embodiment 3. The difference between this embodiment and the virtual reactance control method of the photovoltaic grid-connected inverter described in Embodiment 2 is that the output impedance Z _o (s) of the photovoltaic grid-connected inverter described in step 1 The expression is:

$\begin{array}{c}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{<span\; class="notranslate">\; |</span>}_{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}\\ <span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; QS</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}\mathrm{<span\; class="notranslate">\; Q</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}\mathrm{<span\; class="notranslate">\; Q</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; PWM</span>}}\mathrm{<span\; class="notranslate">\; Q</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; PWM</span>}}\mathrm{<span\; class="notranslate">\; Q</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; QS</span>}}^{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}\mathrm{<span\; class="notranslate">\; Q</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}\mathrm{<span\; class="notranslate">\; Q</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; P</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; PWM</span>}}{\mathrm{<span\; class="notranslate">\; Q\&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; PWM</span>}}{\mathrm{<span\; class="notranslate">\; Q\&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Q</span>}{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}}\end{array}<span\; class="notranslate">\; ,</span>$

Among them, ω _c is the cut-off corner frequency of the second-order low-pass filter, Q is the quality factor, C _ac is the actual filter capacitor, L _ac is the actual filter inductance, r _ac is the parasitic resistance of L _ac , K _PWM is the full-bridge gain , v _o is the output voltage of the photovoltaic grid-connected inverter, i _o is the output current of the photovoltaic grid-connected inverter, is the given value of the inductor current, K _P is the proportional coefficient of the current loop, and K _I is the current conversion integral coefficient.

Embodiment 4. The difference between this embodiment and the virtual reactance control method of the photovoltaic grid-connected inverter described in Embodiment 3 is that the output impedance stability criterion of the photovoltaic grid-connected inverter described in step 1 The expression is:

Among them, GM is the gain margin, and PM is the phase angle margin. When the actual grid impedance Z _g is constant, the amplitude-frequency characteristic of the output impedance of the photovoltaic grid-connected inverter satisfies |Z _g |+GM<|Z _o |, Its phase-frequency characteristics do not need to satisfy -180°+PM<∠Z _g -∠Z _o <180°-PM to ensure the stability of the power grid system; when the amplitude-frequency characteristics of the output impedance of the photovoltaic grid-connected inverter do not satisfy |Z _g |+GM<|Z _o |, then its phase-frequency characteristics must satisfy -180°+PM<∠Z _g -∠Z _o <180°-PM to ensure system stability.

Embodiment 5. The difference between this embodiment and the virtual reactance control method of the photovoltaic grid-connected inverter described in Embodiment 4 is that in step 1, according to the actual grid impedance Z _g , the photovoltaic grid-connected inverter The output impedance Z _o (s) and the amplitude-frequency characteristics and phase-frequency characteristics of the output impedance stability criterion of the photovoltaic grid-connected inverter are obtained to obtain the virtual inductance L _V , the equivalent internal resistance r _V of the virtual inductance and the virtual capacitance C The process of _V is: to ensure _that the actual grid impedance Z _g remains unchanged, and obtain the virtual inductance L _V and the virtual The capacitance C _V and the equivalent internal resistance r _V of the virtual inductance L _V are obtained in proportion to the equivalent internal resistance of the actual inductance.

Specific Embodiment 6. This specific embodiment is described in conjunction with Fig. 1-Fig. The virtual inductance L _V and the equivalent internal resistance r _V of the virtual inductance, combined with the full-bridge gain K _PWM , the process of obtaining the equivalent feedforward path transfer function G _LV (s) of the virtual inductance is:

Step 21: After multiplying the feedback output current information i _L and the equivalent feedforward path transfer function G _LV (s) of the virtual inductor, superimpose it with the current loop output to determine the equivalent feedforward path in the entire control loop The position in , and the linear model of the virtual inductance feed-forward path is obtained through this position;

Step 22. Determine the final control target after adding the feedforward path, that is, the equivalent target transfer function is $\frac{1}{(r_{\mathrm{ac}}+r_V)+(L_{\mathrm{ac}}+L_V)\mathrm{the\; s}};$

Step two and three, according to the structure diagram simplification method of the automatic control principle, the linear model of the virtual inductor feedforward path is simplified to obtain the transfer function This transfer function is equal to the equivalent target transfer function, resulting in the equivalent feedforward path transfer function of the virtual inductor

The principle of obtaining the virtual capacitance equivalent feedforward path transfer function G _CV (s) is similar to that of _GLV (s).

Embodiment 7. The difference between this embodiment and the virtual reactance control method of the photovoltaic grid-connected inverter described in Embodiment 6 is that the method described in step 4 $K_1=\frac{1}{K_{\mathrm{PWM}}{T}_{\mathrm{the\; s}}}\&Center\; Dot;(C_{\mathrm{ac}}{r}_{\mathrm{ac}}{T}_{\mathrm{the\; s}}+L_{\mathrm{ac}}{C}_{\mathrm{ac}}+C_{\mathrm{ac}}{K}_{\mathrm{PWM}}{G}_i{G}_a{T}_{\mathrm{the\; s}}-C_V{r}_{\mathrm{ac}}+\frac{L_{\mathrm{ac}}{C}_V}{T_{\mathrm{the\; s}}}+C_V{K}_{\mathrm{PWM}}{G}_i{G}_a),$ $K_2=\frac{1}{K_{\mathrm{PWM}}{T}_{\mathrm{the\; s}}}\&CenterDot;(C_V{r}_{\mathrm{ac}}+\frac{L_{\mathrm{ac}}{C}_V}{T_{\mathrm{the\; s}}}+C_V{K}_{\mathrm{PWM}}{G}_i{G}_a-L_{\mathrm{ac}}{C}_{\mathrm{ac}}),K_3=\frac{1}{K_{\mathrm{PWM}}{T}_{\mathrm{the\; s}}^2}\&Center\; Dot;L_{\mathrm{ac}}{C}_V.$

As shown in Figure 8, the inverter output impedance comparison chart before and after adding virtual reactance, it can be seen from the figure that after adding virtual reactance, the amplitude-frequency characteristics of the inverter output impedance are improved, and the output impedance amplitude of the inverter can be guaranteed in the middle and low frequency bands. The frequency characteristic curve satisfies the impedance stability criterion; Figure 9 shows the pole distribution diagram of the open-loop transfer function before and after adding the virtual reactance control method. After adding the virtual reactance, the poles of the open-loop transfer function of the system are farther away from the imaginary axis, and the system stability is improved; Figure 10 shows the Nysler curve diagram of the system before adding the virtual reactance. The Nyssler curve of the open-loop transfer function of the system surrounds the point (-1, j0). Stability criterion, so the system is unstable; Figure 11 shows the Nysler curve diagram of the system after adding virtual reactance, the system open-loop transfer transfer transfer transfer transfer function does not surround the (-1, j0) point, and the open-loop transfer transfer transfer transfer function does not exist Right half plane pole, so it can be judged that the system is stable at this time, which further proves that the virtual reactance control method proposed by the present invention can improve the stability of the system.

Claims (7)

1. The virtual reactance control method of photovoltaic grid-connected inverter, characterized in that, the control method comprises the following steps: Step 1. Obtain the virtual inductance L _V according to the actual grid impedance Z _g , the output impedance Z _o (s) of the photovoltaic grid-connected inverter, and the amplitude-frequency characteristics and phase-frequency characteristics of the output impedance stability criterion of the photovoltaic grid-connected inverter , the equivalent internal resistance r _V of the virtual inductance and the virtual capacitance C _V ; Step 2. According to the virtual inductance L _V and the equivalent internal resistance r _V of the virtual inductance, combined with the full-bridge gain K _PWM , obtain the equivalent feedforward path transfer function G _LV (s) of the virtual inductance; Step 3. According to the capacitance C _V of the virtual capacitor, combined with the full-bridge gain K _PWM , the actual filter capacitor C _ac , the filter inductor L _ac and its parasitic resistance r _ac , the current loop transfer function G _i (s) and the feedback filter loop The transfer function G _a (s) obtains the equivalent feed-forward path transfer function of the virtual capacitor $G_{\mathrm{cv}}\left(\mathrm{the\; s}\right)=\frac{(C_{\mathrm{ac}}-C_v\mathrm{the\; s})(r_{\mathrm{ac}}+L_{\mathrm{ac}}\mathrm{the\; s}+K_{\mathrm{PWM}}{G}_i{G}_a)}{K_{\mathrm{PWM}}};$ Step 4. Discretize the equivalent feedforward path transfer function of the virtual inductor and the equivalent feedforward path transfer function of the virtual capacitor to obtain the difference equation: $\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; V</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; V</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; PWM</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; V</span>}}}{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; PWM</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ z(n)=K ₁ v _O (n)+K ₂ v _O (n-1)-K ₃ v _O (n-2), Among them, T _s is the sampling period, and K ₁ , K ₂ , and K ₃ are coefficients; Step five, superimposing y(n), z(n) and the output x(n) of the current loop. 2. The virtual reactance control method of photovoltaic grid-connected inverter according to claim 1, characterized in that the actual grid impedance Z _g described in step 1 is obtained by impedance testing equipment or grid impedance online detection method. 3. The photovoltaic grid-connected inverter virtual reactance control method according to claim 2, wherein the expression of the photovoltaic grid-connected inverter output impedance Z _o (s) described in step 1 is: $\begin{array}{c}{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{<span\; class="notranslate">\; |</span>}_{{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}\\ <span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; QS</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}\mathrm{<span\; class="notranslate">\; Q</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}\mathrm{<span\; class="notranslate">\; Q</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; PWM</span>}}\mathrm{<span\; class="notranslate">\; Q</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; PWM</span>}}\mathrm{<span\; class="notranslate">\; Q</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; QS</span>}}^{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}\mathrm{<span\; class="notranslate">\; Q</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}\mathrm{<span\; class="notranslate">\; Q</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; P</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; PWM</span>}}{\mathrm{<span\; class="notranslate">\; Q\&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; S</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; PWM</span>}}{\mathrm{<span\; class="notranslate">\; Q\&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; ac</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; Q</span>}{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}}\end{array}<span\; class="notranslate">\; ,</span>$ Among them, ω _c is the cut-off corner frequency of the second-order low-pass filter, Q is the quality factor, C _ac is the actual filter capacitor, L _ac is the actual filter inductance, r _ac is the parasitic resistance of L _ac , K _PWM is the full-bridge gain , v _o is the output voltage of the photovoltaic grid-connected inverter, i _o is the output current of the photovoltaic grid-connected inverter, is the given value of the inductor current, K _P is the proportional coefficient of the current loop, and K _I is the current conversion integral coefficient. 4. The photovoltaic grid-connected inverter virtual reactance control method according to claim 3, wherein the expression of the photovoltaic grid-connected inverter output impedance stability criterion described in step 1 is: Among them, GM is the gain margin, and PM is the phase angle margin. When the actual grid impedance Z _g is constant, the amplitude-frequency characteristic of the output impedance of the photovoltaic grid-connected inverter satisfies |Z _g |+GM<|Z _o |, Its phase-frequency characteristics do not need to satisfy -180°+PM<∠Z _g -∠Z _o <180°-PM to ensure the stability of the power grid system; when the amplitude-frequency characteristics of the output impedance of the photovoltaic grid-connected inverter do not satisfy |Z _g |+GM<|Z _o |, then its phase-frequency characteristics must satisfy -180°+PM<∠Z _g -∠Z _o <180°-PM to ensure system stability. 5. The photovoltaic grid-connected inverter virtual reactance control method according to claim 4, characterized in that, according to the actual grid impedance Z _g and the photovoltaic grid-connected inverter output impedance Z _o (s) described in step 1 And the amplitude-frequency characteristics and phase-frequency characteristics of the photovoltaic grid-connected inverter output impedance stability criterion The process of obtaining virtual inductance L _V , equivalent internal resistance r _V of virtual inductance and virtual capacitance C _V is: The grid impedance Z _g remains unchanged, and the virtual inductance L _V and virtual capacitance C _V are obtained according to the expressions of gain margin GM, phase angle margin PM and photovoltaic grid-connected inverter output impedance Z _o (s), virtual inductance The equivalent internal resistance r _V of the quantity L _V is obtained in proportion to the equivalent internal resistance of the actual inductance. 6. The virtual reactance control method of photovoltaic grid-connected inverter according to claim 5, characterized in that, according to the virtual inductance L _V and the equivalent internal resistance r _V of the virtual inductance described in step 2, combined with Full-bridge gain K _PWM , the process of obtaining the equivalent feedforward path transfer function G _LV (s) of the virtual inductor is: Step 21: After multiplying the feedback output current information i _L and the equivalent feedforward path transfer function G _LV (s) of the virtual inductor, superimpose it with the current loop output to determine the equivalent feedforward path in the entire control loop The position in , and the linear model of the virtual inductance feed-forward path is obtained through this position; Step 22. Determine the final control target after adding the feedforward path, that is, the equivalent target transfer function is $\frac{1}{(r_{\mathrm{ac}}+r_V)+(L_{\mathrm{ac}}+L_V)\mathrm{the\; s}};$ Step two and three, according to the structure diagram simplification method of the automatic control principle, the linear model of the virtual inductor feedforward path is simplified to obtain the transfer function This transfer function is equal to the equivalent target transfer function, resulting in the equivalent feedforward path transfer function of the virtual inductor 7. The photovoltaic grid-connected inverter virtual reactance control method according to claim 1, characterized in that, the step 4 described $K_1=\frac{1}{K_{\mathrm{PWM}}{T}_{\mathrm{the\; s}}}\&CenterDot;(C_{\mathrm{ac}}{r}_{\mathrm{ac}}{T}_{\mathrm{the\; s}}+L_{\mathrm{ac}}{C}_{\mathrm{ac}}+C_{\mathrm{ac}}{K}_{\mathrm{PWM}}{G}_i{G}_a{T}_{\mathrm{the\; s}}-C_V{r}_{\mathrm{ac}}+\frac{L_{\mathrm{ac}}{C}_V}{T_{\mathrm{the\; s}}}+C_V{K}_{\mathrm{PWM}}{G}_i{G}_a),$ $K_2=\frac{1}{K_{\mathrm{PWM}}{T}_{\mathrm{the\; s}}}\&Center\; Dot;(C_V{r}_{\mathrm{ac}}+\frac{L_{\mathrm{ac}}{C}_V}{T_{\mathrm{the\; s}}}+C_V{K}_{\mathrm{PWM}}{G}_i{G}_a-L_{\mathrm{ac}}{C}_{\mathrm{ac}}),K_3=\frac{1}{K_{\mathrm{PWM}}{T}_{\mathrm{the\; s}}^2}\&CenterDot;L_{\mathrm{ac}}{C}_V.$