STABILITY CONTROL METHOD FOR VIRTUAL SYNCHRONOUS GENERATOR IN STRONG GRID BASED ON INDUCTANCE-CURRENT DIFFERENTIAL FEEDBACK

Abstract

A stability control method for a virtual synchronous generator (VSG) in a strong grid based on an inductance-current differential feedback is provided. A grid-connected topological structure of a VSG using the control method includes a direct-current (DC)-side voltage source, a three-phase inverter, a three-phase grid impedance and a three-phase grid. By controlling the VSG and controlling the inductance-current differential feedback, the method suppresses the oscillation of the output power from the VSG in the strong grid and implements the stable operation of an inner-loop-free VSG in the strong grid, without adding the physical inductance, increasing the cost of the filter and additionally providing a grid-side current sensor.

Claims

1. A stability control method for a virtual synchronous generator (VSG) in a strong grid based on an inductance-current differential feedback, wherein a topological structure of a VSG using the control method comprises a direct-current (DC)-side voltage source, a three-phase inverter, a three-phase grid impedance and a three-phase grid; the DC-side voltage source is connected to the three-phase inverter, and the three-phase inverter is connected to the three-phase grid through the three-phase grid impedance; the three-phase inverter is composed of a three-phase full-bridge inverter circuit, a three-phase inductance-capacitance (LC) filter, a three-phase voltage-current sensor, and a three-phase inverter controller; the three-phase full-bridge inverter circuit is connected to the three-phase LC filter; the three-phase voltage-current sensor samples three-phase voltages of a filter capacitance and three-phase currents of a filter inductance in the three-phase LC filter, and transmits a sampled signal to the three-phase inverter controller; and the three-phase inverter controller performs control and computation, and outputs a pulse width modulation (PWM) signal to control the three-phase full-bridge inverter circuit; the stability control method in the strong grid comprises a round of computation for controlling the VSG and a round of computation for controlling the inductance-current differential feedback in each computation cycle T.sub.compute of the three-phase inverter controller, wherein T.sub.compute=1/f.sub.compute, and f.sub.compute a computed frequency of the three-phase inverter controller; and the round of computation for controlling the VSG and the round of computation for controlling the inductance-current differential feedback comprise the following steps: step 1: respectively labeling the filter capacitance and the filter inductance in the three-phase LC filter as an inverter-side filter capacitance and an inverter-side filter inductance, wherein the three-phase voltage-current sensor samples the three-phase voltages U.sub.a, U.sub.b, U.sub.c of the inverter-side filter capacitance and the three-phase currents I.sub.La, I.sub.Lb, I.sub.Lc of the inverter-side filter inductance, and transmits a sampled signal to the three-phase inverter controller; step 2: obtaining, by the three-phase inverter controller, according to the three-phase voltages U.sub.a, U.sub.b, U.sub.c of the inverter-side filter capacitance in step 1, two-phase voltages U.sub.α, U.sub.β of the inverter-side filter capacitance in a static coordinate system through an equation for transforming voltages in a three-phase static coordinate system into voltages in a two-phase static coordinate system; and obtaining, by the three-phase inverter controller, according to the three-phase currents I.sub.La, I.sub.Lb, I.sub.Lc of the inverter-side filter inductance in step 1, two-phase currents I.sub.Lα, I.sub.Lα of the inverter-side filter inductance in the static coordinate system according to an equation for transforming currents in the three-phase static coordinate system into currents in the two-phase static coordinate system; step 3: obtaining, by the three-phase inverter controller, according to the two-phase voltages U.sub.α, U.sub.β of the inverter-side filter capacitance in the static coordinate system and the two-phase currents I.sub.Lα, I.sub.Lα the inverter-side filter inductance in the static coordinate system in step 2, an output active power P of the three-phase inverter and an output reactive power Q of the three-phase inverter through an equation for computing an instantaneous power, the equation for computing the instantaneous power being:
P=U.sub.αI.sub.Lα+U.sub.βI.sub.Lβ
Q=U.sub.βI.sub.Lα−U.sub.αI.sub.Lβ step 4: labeling a reactive power axis as a q-axis and an active power axis as a d-axis; and obtaining, by the three-phase inverter controller, according to the two-phase voltages U.sub.α, U.sub.β of the inverter-side filter capacitance in the static coordinate system in step 2, a d-axis voltage U.sub.d of the inverter-side filter capacitance and a q-axis voltage U.sub.q of the inverter-side filter capacitance through an equation for transforming the voltages in the two-phase static coordinate system into voltages in a two-phase rotating coordinate system, and obtaining a phase angle θ.sub.PLL of an A-phase voltage of the inverter-side filter capacitance through a phase-locked equation of a phase-locked loop (PLL) in a single synchronous coordinate system; step 5: obtaining, by the three-phase inverter controller, according to the output active power P of the three-phase inverter in step 3, an angle θ.sub.m of a modulated wave output from the VSG through an equation for computing an active power loop; and obtaining, by the three-phase inverter controller, according to the output reactive power Q of the three-phase inverter in step 3 and the d-axis voltage U.sub.d of the inverter-side filter capacitance in step 4, an amplitude U.sub.m_VSG of the modulated wave output from the VSG through an equation for calculating a reactive power loop, the equation for computing the active power loop being: ${\theta }_m=\frac{P_{\mathrm{set}}-P+{\omega }_n^2{D}_p}{J{\omega }_n{s}^2+{\omega }_n{D}_{p}s}$ the equation for computing the reactive power loop being: $U_{\mathrm{m\_VSG}}=\frac{1}{K_q\times s}\left[D_q\times \left(U_{\mathrm{nAmp}}-U_d\right)+\left(Q_{\mathrm{set}}-Q\right)\right]$ wherein, P.sub.set is a set value of the output active power of the three-phase inverter, ω.sub.n is a rated angular frequency of the three-phase grid, D.sub.P is a frequency droop coefficient of the VSG, J is a virtual rotational inertia of the VSG, U.sub.nAmP is a rated phase voltage amplitude of the three-phase grid, Q.sub.set is a set value of the output reactive power of the three-phase inverter, D.sub.q is a voltage droop coefficient of the VSG, K.sub.q is an inertia coefficient for controlling the reactive power, and s is a Laplace operator; step 6: obtaining, by the three-phase inverter controller, according to the amplitude U.sub.m_VSG of the modulated wave output from the VSG and the angle θ.sub.m of the modulated wave output from the VSG in step 5, output three-phase modulation voltages U.sub.mA_VSG, U.sub.mB_VSG, U.sub.mC_VSG of the VSG through an equation for computing the modulated wave of the VSG, the equation for computing the modulated wave of the VSG being: $U_{\mathrm{mA\_VSG}}=U_{\mathrm{m\_VSG}}\times \cos \left({\theta }_m\right)U_{\mathrm{mB\_VSG}}=U_{\mathrm{m\_VSG}}\times \cos \left({\theta }_m-\frac{2}{3}\pi \right)U_{\mathrm{mC\_VSG}}=U_{\mathrm{m\_VSG}}\times \cos \left({\theta }_m+\frac{2}{3}\pi \right)$ step 7: obtaining, by the three-phase inverter controller, according to the three-phase currents I.sub.La, I.sub.Lb, I.sub.Lc of the inverter-side filter inductance in step 1, increments ΔU.sub.mA, ΔU.sub.mB, ΔU.sub.mC of the output three-phase modulation voltages caused by a virtual series-connection inductance through an equation for computing the inductance-current differential feedback, the equation for computing the inductance-current differential feedback being:
ΔU.sub.mA=−sL.sub.virI.sub.La
ΔU.sub.mB=−sL.sub.virI.sub.Lb
ΔU.sub.mC=−sL.sub.virI.sub.Lc wherein, L.sub.vir is the virtual series-connection inductance; step 8: computing, by the three-phase inverter controller, according to the output three-phase modulation voltages U.sub.mA_VSG, U.sub.mB_VSG, U.sub.mC_VSG of the VSG in step 6 and the increments ΔU.sub.mA, ΔU.sub.mB, ΔU.sub.mC of the output three-phase modulation voltages caused by the virtual series-connection inductance in step 7, output three-phase modulation voltages U.sub.mA, U.sub.mB, U.sub.mC of the three-phase inverter through a following computational equation:
U.sub.mA=U.sub.mA_VSG+ΔU.sub.mA
U.sub.mB=U.sub.mB_VSG+ΔU.sub.mB
U.sub.mC=U.sub.mC_VSG+ΔU.sub.mC, and step 9: controlling, by the three-phase inverter controller, according to the output three-phase modulation voltages U.sub.mA, U.sub.mB, U.sub.mC of the three-phase inverter in step 8, transmission of a PWM modulated wave and outputting a PWM signal, and controlling the three-phase full-bridge inverter circuit through the PWM signal to transmit output electrical energy of the three-phase inverter to the three-phase grid.

2. The stability control method for the VSG in the strong grid based on the inductance-current differential feedback according to claim 1, wherein the equation for transforming the voltages in the three-phase static coordinate system into the voltages in the two-phase static coordinate system in step 2 is: $\left[\begin{array}{c}{U}_{\alpha }\\ U_{\beta }\end{array}\right]=\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\end{array}\right]\left[\begin{array}{c}{U}_a\\ U_b\\ U_c\end{array}\right],$ and the equation for transforming the currents in the three-phase static coordinate system into the currents in the two-phase static coordinate system in step 2 is: $\left[\begin{array}{c}{I}_{L\alpha }\\ I_{L\beta }\end{array}\right]=\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\end{array}\right]\left[\begin{array}{c}{I}_{La}\\ I_{\mathrm{Lb}}\\ I_{\mathrm{Lc}}\end{array}\right].$

3. The stability control method for the VSG in the strong grid based on the inductance-current differential feedback according to claim 1, wherein the equation for transforming the voltages in the two-phase static coordinate system into the voltages in the two-phase rotating coordinate system in step 4 is:
U.sub.d=cos(θ.sub.PLL_Last)×U.sub.α+sin(θ.sub.PLL_Last)×U.sub.β
U.sub.q=sin(θ.sub.PLL_Last)×U.sub.α+cos(θ.sub.PLL_Last)×U.sub.β, and the phase-locked equation of the PLL in the single synchronous coordinate system in step 4 is: ${\theta }_{\mathrm{PLL}}=U_q\times \left(k_{\mathrm{p\_PLL}}+\frac{k_{\mathrm{i\_PLL}}}{s}\right)\times \frac{1}{s}$ wherein, θ.sub.PLL-Last is a phase angle of an A-phase voltage of the inverter-side filter capacitance obtained through the phase-locked equation of the PLL in the single synchronous coordinate system in a last computation cycle, k.sub.p_PLL is a coefficient of a proportional controller for the PLL in the single synchronous coordinate system, and k.sub.i_PLL is a coefficient of an integral controller for the PLL in the single synchronous coordinate system.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0046] FIG. 1 is a topological graph of a main circuit for a VSG and an inverter according to the present disclosure;

[0047] FIG. 2 is a control block diagram of a VSG according to the present disclosure;

[0048] FIG. 3 is a control block diagram of an inductance-current differential feedback according to the present disclosure;

[0049] FIG. 4 illustrates waveforms of a grid-connected voltage and a grid-connected current of a VSF not using the method of the present disclosure in a strong grid; and

[0050] FIG. 5 illustrates waveforms of a grid-connected voltage and a grid-connected current of a VSF using the method of the present disclosure in a strong grid.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0051] The embodiments of the present disclosure will be specifically described below with reference to the accompanying drawings.

[0052] FIG. 1 is a topological graph of a main circuit for a VSG and an inverter according to the present disclosure. As shown in FIG. 1, a topological structure of the VSG using the control method of the present disclosure includes a DC-side voltage source 10, a three-phase inverter 60, a three-phase grid impedance 70 and a three-phase grid 80, where the DC-side voltage source 10 is connected to the three-phase inverter 60, and the three-phase inverter 60 is connected to the three-phase grid 80 through the three-phase grid impedance 70; the three-phase inverter 60 is composed of a three-phase full-bridge inverter circuit 20, a three-phase LC filter 30, a three-phase voltage-current sensor 40, and a three-phase inverter controller 50; the three-phase full-bridge inverter circuit 20 is connected to the three-phase LC filter 30; the three-phase voltage-current sensor 40 samples three-phase voltages of a filter capacitance and three-phase currents of a filter inductance in the three-phase LC filter 30, and transmits a sampled signal to the three-phase inverter controller 50; and the three-phase inverter controller 50 performs control and computation, and outputs a PWM signal to control the three-phase full-bridge inverter circuit 20.

[0053] In FIG. 1, V.sub.dc is the DC-side voltage of the DC-side voltage source 10, L.sub.f is the bridge arm side inductance of the three-phase LC filter 30, C.sub.f is the filter capacitance in the three-phase LC filter 30, R.sub.g is the resistance in the three-phase grid impedance 70, L.sub.g is the inductance in the three-phase grid impedance 70, Grid is the three-phase grid 80, and PCC is a point of common coupling.

[0054] In the embodiment, the main circuit of the inverter involves the following parameters: The DC-side voltage V.sub.dc is 800 V, the rated output line voltage of the inverter is 380 V/50 Hz, the rated power of the inverter is 100 kW, the inverter-side filter capacitance C.sub.f has a capacitance of 270 uF, the inverter-side filter inductance L.sub.f has an inductance of 0.56 mH, the three-phase grid impedance has an inductance of L.sub.g=0.6 mH, and the three-phase grid has a resistance of R.sub.g=0.05Ω.

[0055] The stability control method for a VSG in a strong grid based on an inductance-current differential feedback includes a round of computation for controlling the VSG and a round of computation for controlling the inductance-current differential feedback in each computation cycle T.sub.compute of the three-phase inverter controller 50, T.sub.compute=1/f.sub.compute, f.sub.compute being a computed frequency of the three-phase inverter controller 50. In the embodiment, f.sub.compute=5000 Hz.

[0056] The round of computation for controlling the VSG and the round of computation for controlling the inductance-current differential feedback include the following steps:

[0057] Step 1: Respectively label the capacitance and the inductance in the three-phase LC filter 30 as an inverter-side filter capacitance and an inverter-side filter inductance, where the three-phase voltage-current sensor 40 samples the three-phase voltages U.sub.a, U.sub.b, U.sub.c of the inverter-side filter capacitance and the three-phase currents I.sub.La, I.sub.Lb, I.sub.Lc inverter-side filter inductance, and transmits the sampled signal to the three-phase inverter controller 50.

[0058] Step 2: Obtain, by the three-phase inverter controller 50, according to the three-phase voltages U.sub.a, U.sub.b, U.sub.c of the inverter-side filter capacitance in Step 1, two-phase voltages U.sub.α, U.sub.β of the inverter-side filter capacitance in a static coordinate system through an equation for transforming the voltages in a three-phase static coordinate system into the voltages in a two-phase static coordinate system; and obtain, by the three-phase inverter controller, according to the three-phase currents I.sub.La, I.sub.Lb, I.sub.Lc of the inverter-side filter inductance in Step 1, two-phase currents I.sub.Lα, I.sub.Lα of the inverter-side filter inductance in the static coordinate system according to an equation for transforming the currents in the three-phase static coordinate system into the currents in the two-phase static coordinate system.

[0059] The equation for transforming the voltages in the three-phase static coordinate system into the voltages in the two-phase static coordinate system is:

[00007]$\left[\begin{array}{c}{U}_{\alpha }\\ U_{\beta }\end{array}\right]=\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\end{array}\right]\left[\begin{array}{c}{U}_a\\ U_b\\ U_c\end{array}\right]$

[0060] The equation for transforming the currents in the three-phase static coordinate system into the currents in the two-phase static coordinate system is:

[00008]$\left[\begin{array}{c}{I}_{L\alpha }\\ I_{L\beta }\end{array}\right]=\left[\begin{array}{ccc}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\end{array}\right]\left[\begin{array}{c}{I}_{La}\\ I_{\mathrm{Lb}}\\ I_{\mathrm{Lc}}\end{array}\right].$

[0061] Step 3: Obtain, by the three-phase inverter controller 50, according to the two-phase voltages U.sub.α, U.sub.β of the inverter-side filter capacitance in the static coordinate system and the two-phase currents I.sub.Lα, I.sub.Lβ of the inverter-side filter inductance in the static coordinate system in Step 2, an output active power P of the three-phase inverter and an output reactive power Q of the three-phase inverter through an equation for computing an instantaneous power.

[0062] The equation for computing the instantaneous power is:

P=U.sub.αI.sub.Lα+U.sub.βI.sub.Lβ

Q=U.sub.βI.sub.Lα−U.sub.αI.sub.Lβ

[0063] Step 4: Label a reactive power axis as a q-axis and an active power axis as a d-axis; and obtain, by the three-phase inverter controller 50, according to the two-phase voltages U.sub.α, U.sub.β of the inverter-side filter capacitance in the static coordinate system in Step 2, a d-axis voltage U.sub.d of the inverter-side filter capacitance and a q-axis voltage U.sub.q of the inverter-side filter capacitance through an equation for transforming the voltages in the two-phase static coordinate system into the voltages in a two-phase rotating coordinate system, and obtain a phase angle θ.sub.PLL of an A-phase voltage of the inverter-side filter capacitance through a phase-locked equation of a phase-locked loop (PLL) in a single synchronous coordinate system.

[0064] The equation for transforming the voltages in the two-phase static coordinate system into the voltages in the two-phase rotating coordinate system is:

U.sub.d=cos(θ.sub.PLL_Last)×U.sub.α+sin(θ.sub.PLL_Last)×U.sub.β

U.sub.q=sin(θ.sub.PLL_Last)×U.sub.α+cos(θ.sub.PLL_Last)×U.sub.β

[0065] The phase-locked equation of the PLL in the single synchronous coordinate system in Step 4 is:

[00009]${\theta }_{\mathrm{PLL}}=U_q\times \left(k_{\mathrm{p\_PLL}}+\frac{k_{\mathrm{i\_PLL}}}{s}\right)\times \frac{1}{s}$

[0066] where, θ.sub.PLL_Last is a phase angle of an A-phase voltage of the inverter-side filter capacitance obtained through the phase-locked equation of the PLL in the single synchronous coordinate system in a last computation cycle, k.sub.p_PLL is a coefficient of a proportional controller for the PLL in the single synchronous coordinate system, and k.sub.i_PLL is a coefficient of an integral controller for the PLL in the single synchronous coordinate system. In the embodiment, k.sub.p_PLL=1.0637, and k.sub.i_PLL=176.0135.

[0067] Step 5: Obtain, by the three-phase inverter controller 50, according to the output active power P of the three-phase inverter in Step 3, an angle θ.sub.m of a modulated wave output from the VSG, through an equation for computing an active power loop; and obtain, by the three-phase inverter controller 50, according to the output reactive power Q of the three-phase inverter in Step 3 and the d-axis voltage U.sub.d of the inverter-side filter capacitance in Step 4, an amplitude U.sub.m_VSG of the modulated wave output from the VSG, through an equation for calculating a reactive power loop.

[0068] The equation for computing the active power loop is:

[00010]${\theta }_m=\frac{P_{\mathrm{set}}-P+{\omega }_n^2{D}_p}{J{\omega }_n{s}^2+{\omega }_n{D}_{p}s}$

[0069] The equation for computing the reactive power loop is:

[00011]$U_{\mathrm{m\_VSG}}=\frac{1}{K_q\times s}\left[D_q\times \left(U_{\mathrm{nAmp}}-U_d\right)+\left(Q_{\mathrm{set}}-Q\right)\right]$

[0070] where, P.sub.set is a set value of the output active power of the three-phase inverter, ω.sub.n is a rated angular frequency of the three-phase grid 80, D.sub.p is a frequency droop coefficient of the VSG, J is a virtual rotational inertia of the VSG, U.sub.nAmP is a rated phase voltage amplitude of the three-phase grid 80, Q.sub.set is a set value of the output reactive power of the three-phase inverter, D.sub.q is a voltage droop coefficient of the VSG, K.sub.q is an inertia coefficient for controlling the reactive power, and s is a Laplace operator. In the embodiment, P.sub.set=100 kW, ω.sub.n=314.1593 rad/s, D.sub.p=50, J=.sub.0.057 kg×m.sup.2, U.sub.nAmp=311.08V, Q.sub.set=0 Var, D.sub.q=3210, and K.sub.q=120.

[0071] Step 6: Obtain, by the three-phase inverter controller 50, according to the amplitude U.sub.m_VSG of the modulated wave output from the VSG and the angle θ.sub.m of the modulated wave output from the VSG in Step 5, output three-phase modulation voltages U.sub.mA_VSG, U.sub.mB_VSG, U.sub.mC_VSG of the VSG through an equation for computing the modulated wave of the VSG.

[0072] The equation for computing the modulated wave of the VSG is:

[00012]$U_{\mathrm{mA\_VSG}}=U_{\mathrm{m\_VSG}}\times \cos \left({\theta }_m\right)U_{\mathrm{mB\_VSG}}=U_{\mathrm{m\_VSG}}\times \cos \left({\theta }_m-\frac{2}{3}\pi \right)U_{\mathrm{mC\_VSG}}=U_{\mathrm{m\_VSG}}\times \cos \left({\theta }_m+\frac{2}{3}\pi \right)$

[0073] The above describes the steps in the computation for controlling the VSG. FIG. 2 illustrates the control block diagram of the computation for controlling the VSG.

[0074] Step 7: Obtain, by the three-phase inverter controller 50, according to the three-phase currents I.sub.La, I.sub.Lb, I.sub.Lc of the inverter-side filter inductance in Step 1, increments ΔU.sub.mA, ΔU.sub.mB, ΔU.sub.mC of the three-phase modulation voltages due to a virtual series-connection inductance through an equation for computing the inductance-current differential feedback, the equation for computing the inductance-current differential feedback being:

ΔU.sub.mA=−sL.sub.virI.sub.La

ΔU.sub.mB=−sL.sub.virI.sub.Lb

ΔU.sub.mC=−sL.sub.virI.sub.Lc

[0075] where, L.sub.vir is the virtual series-connection inductance.

[0076] Step 8: Compute, by the three-phase inverter controller 50, according to the output three-phase modulation voltages U.sub.mA_VSG, U.sub.mB_VSG, U.sub.mC_VSG of the VSG in Step 6 and the increments ΔU.sub.mA, ΔU.sub.mB, ΔU.sub.mC of the three-phase modulation voltages due to the virtual series-connection inductance in Step 7, output three-phase modulation voltages U.sub.mA, U.sub.mB, U.sub.mC of the three-phase inverter with a following computational equation:

U.sub.mA=U.sub.mA_VSG+ΔU.sub.mA

U.sub.mB=U.sub.mB_VSG+ΔU.sub.mB

U.sub.mC=U.sub.mC_VSG+ΔU.sub.mC

[0077] Step 7 to Step 8 show the computation for controlling the inductance-current differential feedback. FIG. 3 illustrates the control block diagram of the computation for controlling the inductance-current differential feedback.

[0078] Step 9: Control, by the three-phase inverter controller 50, according to the output three-phase modulation voltages U.sub.mA, U.sub.mB, U.sub.mC of the three-phase inverter in Step 8, transmission of a PWM modulated wave and outputting the PWM signal, and control the three-phase full-bridge inverter circuit 20 through the PWM signal to transmit output electrical energy of the three-phase inverter to the three-phase grid 80.

[0079] FIG. 4 illustrates waveforms of a grid-connected voltage and a grid-connected current of a VSF not using the method of the present disclosure in a strong grid. As can be seen from FIG. 4, both the grid-connected voltage and the grid-connected current are oscillating, indicating that the VSG not controlled with the inductance-current differential feedback cannot operate stably in the strong grid.

[0080] FIG. 5 illustrates waveforms of a grid-connected voltage and a grid-connected current of a VSF using the method of the present disclosure in a strong grid. As can be seen from FIG. 5, both the grid-connected voltage and the grid-connected current are not oscillating, with good waveforms. It is indicated that the VSG can operate stably in the strong power grid through the stability control method for a virtual synchronous generator in a strong grid based on an inductance-current differential feedback.