DUAL-MODE COMBINED CONTROL METHOD FOR MULTI-INVERTER SYSTEM BASED ON DOUBLE SPLIT TRANSFORMER

Abstract

A dual-mode combined control method for a multi-inverter system based on a double split transformer is provided. For an extremely-weak grid, the method provides the dual-mode combined control method for a multi-inverter system based on a double split transformer. According to the method, the equivalent grid impedance at a point of common coupling (PCC) of one grid-connected inverter (GCI) in the multi-inverter system based on the double split transformer is obtained with a grid impedance identification algorithm, and the system sequentially operates in a full current source mode, a hybrid mode, and a full voltage source mode according to a gradually increasing equivalent grid impedance, thereby effectively improving the stability of the multi-inverter system based on the double split transformer during variation of the strength of the grid. The method ensures that the system can still operate stably in the extremely-weak grid.

Claims

1. A dual-mode combined control method for a multi-inverter system based on a double split transformer, wherein the multi-inverter system based on the double split transformer in the control method comprises two identical grid-connected inverters (GCIs), and the dual-mode combined control method comprises a full current source mode, a hybrid mode, and a full voltage source mode; the control method comprises the following steps: step 1: selecting a first GCI of the two identical GCIs from the multi-inverter system, labeling the first GCI as a 1 # GCI and a second GCI of the two identical GCIs as a 2 # GCI, acquiring an equivalent grid impedance at a point of common coupling (PCC) of the 1 # GCI with a grid impedance identification algorithm, and labeling the equivalent grid impedance as a reference equivalent grid impedance Z.sub.g_est; and step 2: setting a lower boundary value λ.sub.1 of the equivalent grid impedance and an upper boundary value λ.sub.2 of the equivalent grid impedance, and performing the following determinations and operations according to the reference equivalent grid impedance Z.sub.g_est in step 1: determining, in response to Z.sub.g_est≤λ.sub.1, that a power grid is in a strong grid state, setting the multi-inverter system to operate in the full current source mode, and ending a control process; determining, in response to λ.sub.1<Z.sub.g_est≤λ.sub.2, that the power grid is in a weak grid state, setting the multi-inverter system to operate in the hybrid mode, and ending the control process; and determining, in response to Z.sub.g_est>λ.sub.2, that the power grid is in an extremely-weak grid state, setting the multi-inverter system to operate in the full voltage source mode, and ending the control process; and the full current source mode means that the two identical GCIs operate in a current source mode; the hybrid mode means that the first GCI operates in the current source mode, and the second GCI operates in a voltage source mode; the full voltage source mode means that the two identical GCIs operate in the voltage source mode; and each of the two identical GCIs is a three-phase full-bridge GCI.

2. The dual-mode combined control method for the multi-inverter system based on the double split transformer according to claim 1, wherein the current source mode comprises the following control steps: step 2.1: sampling output grid-connected currents i.sub.ga, i.sub.gb, i.sub.gc, and sampling PCC voltages u.sub.pcca, u.sub.pccb, u.sub.pccc; step 2.2: obtaining, according to the PCC voltages u.sub.pcca, u.sub.pccb, u.sub.pccc sampled in step 2.1, dq-axis components u.sub.pccd, u.sub.pccq for the PCC voltages through a transformation equation from a three-phase static coordinate system to a two-phase rotating coordinate system; and obtaining a phase angle θ of each of the PCC voltages u.sub.pcca, u.sub.pcca, u.sub.pccc through a phase-locked loop (PLL), a transformation equation for transforming the PCC voltages from the three-phase static coordinate system to the two-phase rotating coordinate system being: $u_{pccd}=\frac{2}{3}\left[u_{\mathrm{pcca}}\cos \theta +u_{pccb}\cos \left(\theta -\frac{2\pi }{3}\right)+u_{pccc}\cos \left(\theta +\frac{2\pi }{3}\right)\right]u_{pccq}=-\frac{2}{3}\left[u_{\mathrm{pcca}}\sin \theta +u_{pccb}\sin \left(\theta -\frac{2\pi }{3}\right)+u_{pccc}\sin \left(\theta +\frac{2\pi }{3}\right)\right]$ and an equation for calculating the phase angle θ of each of the PCC voltages being: $\theta =\frac{{\omega }_0-\left(K_{p_{-}PLL}+K_{i_{-}PLL}/s\right).Math.u_{pccq}}{s}$ wherein, ω.sub.0 is a rated angular frequency of each of the PCC voltages, K.sub.p_PLL is a proportional coefficient of a proportional-integral (PI) controller in the PLL, K.sub.i_PLL is an integral coefficient of the PI controller in the PLL, and s is a Laplace operator; step 2.3: transforming, according to the phase angle θ of each of the PCC voltages in step 2.2, the output grid-connected currents i.sub.ga, i.sub.gb, i.sub.gc sampled in step 2.1 into dq-axis components i.sub.gq, i.sub.gq for the output grid-connected currents in the two-phase rotating coordinate system through the transformation equation from the three-phase static coordinate system to the two-phase rotating coordinate system, a transformation equation for transforming the output grid-connected currents from the three-phase static coordinate system to the two-phase rotating coordinate system being: $i_{gd}=\frac{2}{3}\left[i_{ga}\cos \theta +i_{\mathrm{gb}}\cos \left(\theta -\frac{2\pi }{3}\right)+i_{gc}\cos \left(\theta +\frac{2\pi }{3}\right)\right]i_{gq}=-\frac{2}{3}\left[i_{ga}\sin \theta +i_{\mathrm{gb}}\sin \left(\theta -\frac{2\pi }{3}\right)+i_{gc}\sin \left(\theta +\frac{2\pi }{3}\right)\right]$ step 2.4: setting reference signals i.sub.gdref, i.sub.gqref for the output grid-connected currents, and obtaining control signals u.sub.d, u.sub.q through a grid current closed-loop control equation according to the dq-axis components i.sub.gd, i.sub.gq for the output grid-connected currents in step 2.3, the grid current closed-loop control equation being: $u_d=\left(K_p+\frac{K_i}{s}\right).Math.\left(i_{gdref}-i_{gd}\right)u_q=\left(K_p+\frac{K_i}{s}\right).Math.\left(i_{gqref}-i_{gq}\right)$ wherein, K.sub.p is a proportional coefficient of a PI controller in the grid current closed-loop control equation, and K.sub.i is an integral coefficient of the PI controller in the grid current closed-loop control equation; step 2.5: transforming, according to the phase angle θ of each of the PCC voltages in step 2.2, the control signals u.sub.d, u.sub.q in step 2.4 into components u.sub.a, u.sub.b, u.sub.c for the control signals in the three-phase static coordinate system through a transformation equation from the two-phase rotating coordinate system to the three-phase static coordinate system, a transformation equation for transforming the control signals from the two-phase rotating coordinate system to the three-phase static coordinate system being: $u_a=u_d\cos \theta -u_q\sin \theta u_b=u_d\cos \left(\theta -\frac{2\pi }{3}\right)-u_q\sin \left(\theta -\frac{2\pi }{3}\right)u_c=u_d\cos \left(\theta +\frac{2\pi }{3}\right)-u_q\sin \left(\theta +\frac{2\pi }{3}\right)$ and step 2.6: adding the components u.sub.a, u.sub.b, u.sub.c in the three-phase static coordinate system in step 2.5 and the PCC voltages u.sub.pcca, u.sub.pccb, u.sub.pccc in step 2.1, respectively, to obtain bridge arm voltage control signals u.sub.a+u.sub.pcca, u.sub.b+u.sub.pccb, u.sub.c+u.sub.pccc of the three-phase full-bridge GCI, performing a space vector pulse width modulation (SVPWM) to generate a switching signal for a power device of the three-phase full-bridge GCI, and controlling connection and disconnection of the power device of the three-phase full-bridge GCI through a driving circuit.

3. The dual-mode combined control method for the multi-inverter system based on the double split transformer according to claim 1, wherein the voltage source mode comprises the following control steps: step 3.1: sampling output grid-connected currents i.sub.ga, i.sub.gb, i.sub.gc, and sampling PCC voltages u.sub.pcca, u.sub.pccb, u.sub.pccc; step 3.2: obtaining, according to the output grid-connected currents i.sub.ga, i.sub.gb, i.sub.gc sampled in step 3.1, αβ-axis components i.sub.gα, i.sub.gβ for the output grid-connected currents through a transformation equation from a three-phase static coordinate system to a two-phase static coordinate system; and obtaining, according to the PCC voltages u.sub.pcca, u.sub.pccb, u.sub.pccc sampled in step 3.1, αβ-axis components u.sub.pccα, u.sub.pccβ for the PCC voltages through the transformation equation from the three-phase static coordinate system to the two-phase static coordinate system, a transformation equation for transforming the output grid-connected currents from the three-phase static coordinate system to the two-phase static coordinate system being: $i_{g\alpha }=\frac{2}{3}\left(i_{ga}-\frac{1}{2}{i}_{gb}-\frac{1}{2}{i}_{gc}\right)i_{g\beta }=\frac{2}{3}\left(\frac{\sqrt{3}}{2}{i}_{gb}-\frac{\sqrt{3}}{2}{i}_{gc}\right)$ and a transformation equation for transforming the PCC voltages from the three-phase static coordinate system to the two-phase static coordinate system being: $u_{pcc\alpha }=\frac{2}{3}\left(u_{\mathrm{pcca}}-\frac{1}{2}{u}_{\mathrm{pccb}}-\frac{1}{2}{u}_{\mathrm{pccc}}\right)u_{pcc\beta }=\frac{2}{3}\left(\frac{\sqrt{3}}{2}{u}_{pccb}-\frac{\sqrt{3}}{2}{u}_{pccc}\right)$ step 3.3: according to the αβ-axis components i.sub.gα, i.sub.gβ for the output grid-connected currents and the αβ-axis components u.sub.pccα, u.sub.pccβ for the PCC voltages in step 3.2, obtaining an average active power P through an equation for calculating the average active power, and obtaining an average reactive power Q through an equation for calculating the average reactive power, the equation for calculating the average active power being: $\overline{P}=\frac{1.5}{\tau s+1}\left(u_{pcc\alpha }{i}_{g\alpha }+u_{pcc\beta }{i}_{g\beta }\right)$ and the equation for calculating the average reactive power being: $\overline{Q}=\frac{1.5}{\tau s+1}\left(u_{pcc\alpha }{i}_{g\beta }-u_{pcc\beta }{i}_{g\alpha }\right)$ wherein, τ is a time constant of a first-order low-pass filter, and s is a Laplace operator; step 3.4: obtaining, according to the average active power P in step 3.3, an output angular frequency ω of the three-phase full-bridge GCI through an active power-frequency droop control equation, the active power-frequency droop control equation being:
ω=ω.sub.n+D.sub.p(P.sub.n−P) wherein, P.sub.n is a given active power reference of the three-phase full-bridge GCI, ω.sub.n is a rated angular frequency of the three-phase full-bridge GCI corresponding to the given active power reference P.sub.n, and D.sub.p is a droop coefficient of an active power loop; and integrating the output angular frequency ω of the three-phase full-bridge GCI to obtain an output phase angle θ.sub.0 of the three-phase full-bridge GCI, by the following equation: ${\theta }_0=\frac{\omega }{s}$ step 3.5: obtaining, according to the PCC voltages u.sub.pcca, u.sub.pccb, u.sub.pccc sampled in step 3.1, and the output phase angle θ.sub.0 of the three-phase full-bridge GCI in step 3.4, dq-axis components u.sub.pccd, u.sub.pccq for the PCC voltages through a transformation equation from the three-phase static coordinate system to a two-phase rotating coordinate system, a transformation equation for transforming the PCC voltages from the three-phase static coordinate system to the two-phase rotating coordinate system being: $u_{pccd}=\frac{2}{3}\left[u_{pcca}\cos {\theta }_0+u_{pccb}\cos \left({\theta }_0-\frac{2\pi }{3}\right)+u_{pccc}\cos \left({\theta }_0+\frac{2\pi }{3}\right)\right]u_{pccq}=-\frac{2}{3}\left[u_{pcca}\sin {\theta }_0+u_{pccb}\sin \left({\theta }_0-\frac{2\pi }{3}\right)+u_{pccc}\sin \left({\theta }_0+\frac{2\pi }{3}\right)\right]$ step 3.6: obtaining, according to the output grid-connected currents i.sub.ga, i.sub.gb, i.sub.gc sampled in step 3.1, and the output phase angle θ.sub.0 of the three-phase full-bridge GCI in step 3.4, dq-axis components i.sub.gd, i.sub.gq for the output grid-connected currents through the transformation equation from the three-phase static coordinate system to the two-phase rotating coordinate system, a transformation equation for transforming the output grid-connected currents from the three-phase static coordinate system to the two-phase rotating coordinate system being: $i_{gd}=\frac{2}{3}\left[i_{\mathrm{ga}}\cos {\theta }_0+i_{gb}\cos \left({\theta }_0-\frac{2\pi }{3}\right)+i_{gc}\cos \left({\theta }_0+\frac{2\pi }{3}\right)\right]i_{gq}=-\frac{2}{3}\left[i_{\mathrm{ga}}\sin {\theta }_0+i_{gb}\sin \left({\theta }_0-\frac{2\pi }{3}\right)+i_{gc}\sin \left({\theta }_0+\frac{2\pi }{3}\right)\right]$ step 3.7: obtaining, according to the output average reactive power Q of the three-phase full-bridge GCI in step 3.3, reference values u.sub.pccdref, u.sub.pccqref of the dq-axis components for the PCC voltages of the three-phase full-bridge GCI through a reactive power-amplitude droop control equation, the reactive power-amplitude droop control equation being:
u.sub.pccdref=U.sub.n+D.sub.q(Q.sub.n−Q)
u.sub.pccqref=0 wherein, U.sub.n is a rated output voltage of the three-phase full-bridge GCI corresponding to a given reactive power reference Q.sub.n, and D.sub.q is a droop coefficient of a reactive power loop; step 3.8: obtaining reference signals i.sub.gdref, i.sub.gqref for the output grid-connected currents through a voltage loop control equation according to the dq-axis components u.sub.pccd, u.sub.pccq for the PCC voltages in step 3.5 and the reference values u.sub.pccdref, u.sub.pccqref of the dq-axis components for the PCC voltages in step 3.7; the voltage loop control equation being: $i_{\mathrm{gdref}}=\left(K_{p1}+\frac{K_{i1}}{s}\right).Math.\left(u_{\mathrm{pccdref}}-u_{\mathrm{pccd}}\right)i_{\mathrm{gqref}}=\left(K_{p1}+\frac{K_{i1}}{s}\right).Math.\left(u_{\mathrm{pccqref}}-u_{\mathrm{pccq}}\right)$ wherein, K.sub.p1 is a proportional coefficient of a PI controller in the voltage loop control equation, and K.sub.i1 is an integral coefficient of the PI controller in the voltage loop control equation; step 3.9: obtaining control signals u.sub.d, u.sub.q through a current loop control equation according to the reference signals i.sub.gdref, i.sub.gqref for the output grid-connected currents in step 3.8 and the dq-axis components i.sub.gd, i.sub.gq for the output grid-connected currents in step 3.6, the current loop control equation being: $u_d=\left(K_{p2}+\frac{K_{i2}}{s}\right).Math.\left(i_{gdref}-i_{gd}\right)u_q=\left(K_{p2}+\frac{K_{i2}}{s}\right).Math.\left(i_{gqref}-i_{gq}\right)$ wherein, K.sub.p2 is a proportional coefficient of a PI controller in the current loop control equation, and K.sub.i2 is an integral coefficient of the PI controller in the current loop control equation; step 3.10: transforming, according to the output phase angle θ.sub.0 of the three-phase full-bridge GCI in step 3.4, the control signals u.sub.d, u.sub.q in step 3.9 into components u.sub.a, u.sub.b, u.sub.c for the control signals in the three-phase static coordinate system through a transformation equation from the two-phase rotating coordinate system to the three-phase static coordinate system, a transformation equation for transforming the control signals from the two-phase rotating coordinate system to the three-phase static coordinate system being: $u_a=u_d\cos {\theta }_0-u_q\sin {\theta }_0{u}_b=u_d\cos \left({\theta }_0-\frac{2\pi }{3}\right)-u_q\sin \left({\theta }_0-\frac{2\pi }{3}\right)u_c=u_d\cos \left({\theta }_0+\frac{2\pi }{3}\right)-u_q\sin \left({\theta }_0+\frac{2\pi }{3}\right)$ and step 3.11: adding the components u.sub.a, u.sub.b, u.sub.c in the three-phase static coordinate system in step 3.10 and the PCC voltages u.sub.pcca, u.sub.pccb, u.sub.pccc in step 3.1, respectively, to obtain bridge arm voltage control signals u.sub.a+u.sub.pcca, u.sub.b+u.sub.pccb, u.sub.c+u.sub.pccc of the three-phase full-bridge GCI, generating switching signals for a power device of the three-phase full-bridge GCI through a space vector pulse width modulation (SVPWM), and controlling opening and closing of the power device of the three-phase full-bridge GCI through a driving circuit.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0071] FIG. 1 is a schematic structural view of a multi-inverter system based on a double split transformer according to the present invention;

[0072] FIG. 2 is a topological structure of a single GCI in a multi-inverter system based on a double split transformer according to the present invention;

[0073] FIG. 3 is a flow chart for implementation according to the present invention;

[0074] FIG. 4 is a schematic view of a control strategy when a single GCI in a multi-inverter system based on a double split transformer in a weak grid operates in a current source mode;

[0075] FIG. 5 is a schematic view of a control strategy when a single GCI in a multi-inverter system based on a double split transformer in a weak grid operates in a voltage source mode;

[0076] FIG. 6 is a block diagram of a grid impedance identification algorithm based on uncharacteristic harmonic injection according to the present invention;

[0077] FIG. 7 illustrates an experimental waveform of a dual-mode combined control strategy for a multi-inverter system based on a double split transformer;

[0078] FIG. 8 illustrates an experimental waveform of a time period t.sub.1-t.sub.2 in FIG. 7;

[0079] FIG. 9 illustrates an experimental waveform of a time period t.sub.2-t.sub.3 in FIG. 7; and

[0080] FIG. 10 illustrates an experimental waveform of a time period t.sub.3-t.sub.4 in FIG. 7.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0081] The embodiment of the present invention provides a dual-mode combined control method for a multi-inverter system based on a double split transformer, to solve the stability problem when the multi-inverter system based on the double split transformer in the extremely-weak grid operates in the conventional single current source mode or hybrid mode. According to this method, the equivalent grid impedance at a PCC of one GCI in the multi-inverter system based on the double split transformer is obtained with a grid impedance identification algorithm, and when the equivalent grid impedance gradually increases, namely the power grid respectively operates in the strong grid, weak grid and extremely-weak grid, the system sequentially operates in a full current source mode, a hybrid mode, and a full voltage source mode, thereby effectively improving the stability of the multi-inverter system based on the double split transformer during variation of the strength of the grid. The present invention is implemented simply, and greatly increases the stability margin of the multi-inverter system based on the double split transformer during the drastic fluctuation of the grid impedance; and particularly, the present invention ensures that the system can still operate stably in the extremely-weak grid, and makes the system more adaptable to the power grid.

[0082] The technical solutions in the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0083] FIG. 1 illustrates a schematic structural view of a multi-inverter system based on a double split transformer according to the present invention. The multi-inverter system includes two identical GCIs; the GCIs each are connected to a photovoltaic cell panel; and one double split transformer is connected to the multi-inverter system composed of two GCIs.

[0084] FIG. 2 illustrates a topological structure of a single GCI in a multi-inverter system based on a double split transformer according to the present invention. As can be seen from FIG. 2, the single GCI is a three-phase full-bridge GCI, and the topological structure includes a direct-current (DC)-side filter capacitor C.sub.dc, a topology of a three-phase bridge inverter, an inverter-side inductor L.sub.1, a filter capacitor C, a damping resistor R.sub.d, a grid-side inductor L.sub.2 and a PCC. In the embodiment, C.sub.dc=600 μF, L.sub.1=0.9 mH, C=20 μF, R.sub.d=0.6Ω, and L.sub.2=0.05 mH.

[0085] FIG. 3 is a flow chart for implementation according to the present invention; As shown in FIG. 3, the dual-mode combined control method includes a full current source mode, a hybrid mode, and a full voltage source mode.

[0086] Specifically, the control method includes the following steps:

[0087] Step 1: Select any GCI from the multi-inverter system, label the GCI as a 1 # GCI and the other GCI as a 2 # GCI, acquire an equivalent grid impedance at a PCC of the 1 # GCI with a grid impedance identification algorithm, and label the equivalent grid impedance as a reference equivalent grid impedance Z.sub.g_est.

[0088] Step 2: Set a lower boundary value λ.sub.1 of equivalent grid impedance and an upper boundary value λ.sub.2 of equivalent grid impedance, and perform the following determinations and operations according to the reference equivalent grid impedance Z.sub.g_est in Step 1:

[0089] Determine, in response to Z.sub.g_est≤λ.sub.1, that a power grid is in a strong grid state, set the multi-inverter system to operate in the full current source mode, and end a control process.

[0090] Determine, in response to λ.sub.1<Z.sub.g_est≤λ.sub.2, that the power grid is in a weak grid state, set the multi-inverter system to operate in the hybrid mode, and end a control process.

[0091] Determine, in response to Z.sub.g_est>λ.sub.2 that the power grid is in an extremely-weak grid state, , set the multi-inverter system to operate in the full voltage source mode, and end a control process.

[0092] The full current source mode means that the two GCIs operate in a current source mode; the hybrid mode means that one GCI operates in the current source mode, and the other GCI operates in a voltage source mode; and the full voltage source mode means that the two GCIs operate in the voltage source mode.

[0093] In the embodiment of the present invention, λ.sub.1=0.98 mH, and λ.sub.2=2 mH.

[0094] FIG. 4 is a schematic view of a control strategy when a single GCI in a multi-inverter system based on a double split transformer in a weak grid operates in a current source mode. As shown in FIG. 4, the GCI operating in the current source mode is controlled with the following steps:

[0095] Step 2.1: Sample output grid-connected currents i.sub.ga, i.sub.gb, i.sub.gc, and sample PCC voltages u.sub.pcca, u.sub.pccb, u.sub.pccc. In the embodiment of the present invention, the current sensor has a sample proportion of 29, and the voltage sensor has a sample proportion of 400.

[0096] Step 2.2: Obtain, according to the sampled PCC voltages u.sub.pcca, u.sub.pccb, u.sub.pccc in Step 2.1, dq-axis components u.sub.pccd, u.sub.pccq for the PCC voltages through a transformation equation from a three-phase static coordinate system to a two-phase rotating coordinate system; and obtain a phase angle θ of each of the PCC voltages u.sub.pcca, u.sub.pccb, u.sub.pccc through a PLL.

[0097] A transformation equation for transforming the PCC voltages from the three-phase static coordinate system to the two-phase rotating coordinate system is:

[00016]$u_{pccd}=\frac{2}{3}\left[u_{pcca}\cos \theta +u_{pccb}\cos \left(\theta -\frac{2\pi }{3}\right)+u_{pccc}\cos \left(\theta +\frac{2\pi }{3}\right)\right]$$u_{pccq}=-\frac{2}{3}\left[u_{pcca}\sin \theta +u_{pccb}\sin \left(\theta -\frac{2\pi }{3}\right)+u_{pccc}\sin \left(\theta +\frac{2\pi }{3}\right)\right]$

[0098] An equation for calculating the phase angle θ of each of the PCC voltages is:

[00017]$\theta =\frac{{\omega }_0-\left(K_{\mathrm{p\_PLL}}+K_{\mathrm{i\_PLL}}/s\right).Math.u_{pccq}}{s}$

[0099] where, ω.sub.0 is a rated angular frequency of each of the PCC voltages, K.sub.p_PLL is a proportional coefficient of a PI controller in the PLL, K.sub.i_PLL is an integral coefficient of the PI controller in the PLL, and s is a Laplace operator. In the embodiment of the present invention, ω.sub.0=314 rad/s, K.sub.p_pLL=0.3, and K.sub.i_PLL=36.

[0100] Step 2.3: Transform, according to the phase angle θ of each of the PCC voltages in Step 2.2, the sampled output grid-connected currents i.sub.ga, i.sub.gb, i.sub.gc in Step 2.1 into dq-axis components i.sub.gd, i.sub.gq for the output grid-connected currents in the two-phase rotating coordinate system through the transformation equation from the three-phase static coordinate system to the two-phase rotating coordinate system.

[0101] A transformation equation for transforming the output grid-connected currents from the three-phase static coordinate system to the two-phase rotating coordinate system is:

[00018]$i_{gd}=\frac{2}{3}\left[i_{ga}\cos \theta +i_{gb}\cos \left(\theta -\frac{2\pi }{3}\right)+i_{gc}\cos \left(\theta +\frac{2\pi }{3}\right)\right]$$i_{gq}=-\frac{2}{3}\left[i_{ga}\sin \theta +i_{gb}\sin \left(\theta -\frac{2\pi }{3}\right)+i_{gc}\sin \left(\theta +\frac{2\pi }{3}\right)\right]$

[0102] Step 2.4: Set reference signals i.sub.gdref, i.sub.gqref for the output grid-connected currents, and obtain control signals u.sub.d, u.sub.q through a grid current closed-loop control equation according to the dq-axis components i.sub.gd, i.sub.gq for the output grid-connected currents in step 2.3.

[0103] The grid current closed-loop control equation is:

[00019]$u_d=\left(K_p+\frac{K_i}{s}\right).Math.\left(i_{gdref}-i_{gd}\right)$$u_q=\left(K_p+\frac{K_i}{s}\right).Math.\left(i_{gqref}-i_{gq}\right)$

[0104] where, K.sub.p is a proportional coefficient of a PI controller in the grid current closed-loop control equation, and K.sub.i is an integral coefficient of the PI controller in the grid current closed-loop control equation. In the embodiment of the present invention, K.sub.p=67.2, and K.sub.i=180,000.

[0105] Step 2.5: Transform, according to the phase angle θ of each of the PCC voltages in Step 2.2, the control signals u.sub.d, u.sub.q in Step 2.4 into components u.sub.a, u.sub.b, u.sub.c for the control signals in the three-phase static coordinate system through a transformation equation from the two-phase rotating coordinate system to the three-phase static coordinate system.

[0106] A transformation equation for transforming the control signals from the two-phase rotating coordinate system to the three-phase static coordinate system is:

[00020]$u_a=u_d\cos \theta -u_q\sin \theta$$u_b=u_d\cos \left(\theta -\frac{2\pi }{3}\right)-u_q\sin \left(\theta -\frac{2\pi }{3}\right)$$u_c=u_d\cos \left(\theta +\frac{2\pi }{3}\right)-u_q\sin \left(\theta +\frac{2\pi }{3}\right)$

[0107] Step 2.6: Add the components u.sub.a, u.sub.b, u.sub.c in the three-phase static coordinate system in Step 2.5 and the PCC voltages u.sub.pcca, u.sub.pccb, u.sub.pccc in Step 2.1, respectively, to obtain bridge arm voltage control signals u.sub.a+u.sub.pcca, u.sub.b+u.sub.pccb, u.sub.c+u.sub.ccc of the three-phase full-bridge GCI, perform SVPWM to generate a switching signal for a power device of the GCI, and control connection and disconnection of the power device of the three-phase full-bridge GCI through a driving circuit.

[0108] FIG. 5 is a schematic view of a control strategy when a single GCI in a multi-inverter system in a weak grid operates in a voltage source mode. As shown in FIG. 5, the GCI operating in the voltage source mode is controlled with the following steps:

[0109] Step 3.1: Sample output grid-connected currents i.sub.ga, i.sub.gb, i.sub.gc, and sample PCC voltages u.sub.pcca, u.sub.pccb, u.sub.pccc.

[0110] Step 3.2: Obtain, according to the sampled output grid-connected currents i.sub.ga, i.sub.gb, i.sub.gc in Step 3.1, αβ-axis components i.sub.gα, i.sub.gβ for the output grid-connected currents through a transformation equation from a three-phase static coordinate system to a two-phase static coordinate system; and obtain, according to the sampled PCC voltages u.sub.pcca, u.sub.pccb, u.sub.pccc in Step 3.1, αβ-axis components u.sub.pccα, u.sub.pccβ for the PCC voltages through the transformation equation from the three-phase static coordinate system to the two-phase static coordinate system.

[0111] A transformation equation for transforming the output grid-connected currents from the three-phase static coordinate system to the two-phase static coordinate system is:

[00021]$i_{g\alpha }=\frac{2}{3}\left(i_{ga}-\frac{1}{2}{i}_{gb}-\frac{1}{2}{i}_{gc}\right)$$i_{g\beta }=\frac{2}{3}\left(\frac{\sqrt{3}}{2}{i}_{gb}-\frac{\sqrt{3}}{2}{i}_{gc}\right)$

[0112] A transformation equation for transforming the PCC voltages from the three-phase static coordinate system to the two-phase static coordinate system is:

[00022]$u_{\mathrm{pcc}\alpha }=\frac{2}{3}\left(u_{\mathrm{pcca}}-\frac{1}{2}{u}_{\mathrm{pccb}}-\frac{1}{2}{u}_{\mathrm{pcc}}\right)$$u_{pcc\beta }=\frac{2}{3}\left(\frac{\sqrt{3}}{2}{u}_{pccb}-\frac{\sqrt{3}}{2}{u}_{pccc}\right)$

[0113] Step 3.3: According to the αβ-axis output components i.sub.gα, i.sub.gβ for the output grid-connected currents, and the αβ-axis components u.sub.pccα, u.sub.pccβ for the PCC voltages in Step 3.2, obtain an average active power P through an equation for calculating the average active power, and obtain an average reactive power Q through an equation for calculating the average reactive power.

[0114] The equation for calculating the average active power is:

[00023]$\overline{P}=\frac{1.5}{\tau s+1}\left(u_{pcc\alpha }{i}_{g\alpha }+u_{pcc\beta }{i}_{g\beta }\right)$

[0115] The equation for calculating the average reactive power is:

[00024]$\overline{Q}=\frac{1.5}{\tau s+1}\left(u_{pcc\alpha }{i}_{g\beta }-u_{pcc\beta }{i}_{g\alpha }\right)$

[0116] where, τ is the time constant of a first-order low-pass filter, and s is a Laplace operator. In the embodiment of the present invention, τ=0.00667 s.

[0117] Step 3.4: Obtain, according to the average active power P in Step 3.3, an output angular frequency ω of the GCI through an active power-frequency droop control equation, the active power-frequency droop control equation being:

ω=ω.sub.n+D.sub.p(P.sub.n−P)

[0118] where, P.sub.n is a given active power reference of the GCI, ω.sub.n is a rated angular frequency of the GCI corresponding to the given active power reference P.sub.n, and D.sub.p is a droop coefficient of an active power loop. In the embodiment of the present invention, ω.sub.n=314 rad/s, P.sub.n=100 kW, and D.sub.p=0.0001.

[0119] Integrate the output angular frequency ω of the GCI to obtain an output phase angle θ.sub.0 of the GCI, namely:

[00025]${\theta }_0=\frac{\omega }{s}$

[0120] Step 3.5: Obtain, according to the sampled PCC voltages u.sub.pcca, u.sub.pccb, u.sub.pccc in Step 3.1, and the output phase angle θ.sub.0 of the GCI in Step 3.4, dq-axis components u.sub.pccd, u.sub.pccq for the PCC voltages through a transformation equation from the three-phase static coordinate system to a two-phase rotating coordinate system.

[0121] A transformation equation for transforming the PCC voltages from the three-phase static coordinate system to the two-phase rotating coordinate system is:

[00026]$u_{pccd}=\frac{2}{3}\left[u_{pcca}\cos {\theta }_0+u_{pccb}\cos \left({\theta }_0-\frac{2\pi }{3}\right)+u_{pccc}\cos \left({\theta }_0+\frac{2\pi }{3}\right)\right]$$u_{pccq}=-\frac{2}{3}\left[u_{pcca}\sin {\theta }_0+u_{pccb}\sin \left({\theta }_0-\frac{2\pi }{3}\right)+u_{pccc}\sin \left({\theta }_0+\frac{2\pi }{3}\right)\right]$

[0122] Step 3.6: Obtain, according to the sampled output grid-connected currents i.sub.ga, i.sub.gb, i.sub.gc in Step 3.1, and the output phase angle θ.sub.0 of the GCI in Step 3.4, dq-axis components i.sub.gd, i.sub.gq for the output grid-connected currents through the transformation equation from the three-phase static coordinate system to the two-phase rotating coordinate system.

[0123] A transformation equation for transforming the output grid-connected currents from the three-phase static coordinate system to the two-phase rotating coordinate system is:

[00027]$i_{gd}=\frac{2}{3}\left[i_{ga}\cos {\theta }_0+i_{gb}\cos \left({\theta }_0-\frac{2\pi }{3}\right)+i_{gc}\cos \left({\theta }_0+\frac{2\pi }{3}\right)\right]$$i_{gq}=-\frac{2}{3}\left[i_{ga}\sin {\theta }_0+i_{gb}\sin \left({\theta }_0-\frac{2\pi }{3}\right)+i_{gc}\sin \left({\theta }_0+\frac{2\pi }{3}\right)\right]$

[0124] Step 3.7: Obtain, according to the output average reactive power Q of the GCI in Step 3.3, reference values u.sub.pccdref, u.sub.pccqref of the dq-axis components for the PCC voltages of the GCI through a reactive power-amplitude droop control equation, the reactive power-amplitude droop control equation being:

u.sub.pccdref=U.sub.n+D.sub.q(Q.sub.n−Q)

u.sub.pccqref=0

[0125] where, U.sub.n is a rated output voltage of the GCI corresponding to a given reactive power reference Q.sub.n, and D.sub.q is a droop coefficient of a reactive power loop. In the embodiment of the present invention, U.sub.n=220 V, Q.sub.n=0, and D.sub.q=0.0001.

[0126] Step 3.8: Obtain reference signals i.sub.gdref, i.sub.gqref for the output grid-connected currents through a voltage loop control equation according to the dq-axis components u.sub.pccd, u.sub.pccq for the PCC voltages in Step 3.5 and the reference values u.sub.pccdref, U.sub.pccqref of the dq-axis components for the PCC voltages in Step 3.7.

[0127] The voltage loop control equation is:

[00028]$i_{\mathrm{gdref}}=\left(K_{p1}+\frac{K_{i1}}{s}\right).Math.\left(u_{\mathrm{pccdref}}-u_{\mathrm{pccd}}\right)i_{\mathrm{gqref}}=\left(K_{p1}+\frac{K_{i1}}{s}\right).Math.\left(u_{\mathrm{pccqref}}-u_{\mathrm{pccq}}\right)$

[0128] where, K.sub.p1 is a proportional coefficient of a PI controller in the voltage loop control equation, and K.sub.i1 is an integral coefficient of the PI controller in the voltage loop control equation. In the embodiment of the present invention, K.sub.pi=0.05, and K.sub.i1=3,223.

[0129] Step 3.9: Obtain control signals u.sub.d, u.sub.q through a current loop control equation according to the reference signals i.sub.gdref, i.sub.gqref for the output grid-connected currents in Step 3.8 and the dq-axis components i.sub.gd, i.sub.gq for the output grid-connected currents in Step 3.6.

[0130] The current loop control equation is:

[00029]$u_d=\left(K_{p2}+\frac{K_{i2}}{s}\right).Math.\left(i_{gdref}-i_{gd}\right)$$u_q=\left(K_{p2}+\frac{K_{i2}}{s}\right).Math.\left(i_{gqref}-i_{gq}\right)$

[0131] where, K.sub.p2 is a proportional coefficient of a PI controller in the current loop control equation, and K.sub.i2 is an integral coefficient of the PI controller in the current loop control equation. In the embodiment of the present invention, K.sub.p2=200, and K.sub.i2=0.

[0132] Step 3.10: Transform, according to the output phase angle θ.sub.0 of the GCI in Step 3.4, the control signals u.sub.d, u.sub.q in Step 3.9 into components u.sub.a, u.sub.b, u.sub.c for the control signals in the three-phase static coordinate system through a transformation equation from the two-phase rotating coordinate system to the three-phase static coordinate system.

[0133] A transformation equation for transforming the control signals from the two-phase rotating coordinate system to the three-phase static coordinate system is:

[00030]$u_a=u_d\cos {\theta }_0-u_q\sin {\theta }_0$$u_b=u_d\cos \left({\theta }_0-\frac{2\pi }{3}\right)-u_q\sin \left({\theta }_0-\frac{2\pi }{3}\right)$$u_c=u_d\cos \left({\theta }_0+\frac{2\pi }{3}\right)-u_q\sin \left({\theta }_0+\frac{2\pi }{3}\right)$

[0134] Step 3.11: Add the components u.sub.a, u.sub.b, u.sub.c in the three-phase static coordinate system in Step 3.10 and the PCC voltages u.sub.pcca, u.sub.pccb, u.sub.pccc in Step 3.1 to obtain bridge arm voltage control signals u.sub.a+u.sub.pcca, u.sub.b+u.sub.pccb, u.sub.c+u.sub.pccc of the three-phase full-bridge GCI, generate switching signals for a power device of the GCI through the SVPWM, and control the opening and closing of the power device of the three-phase full-bridge GCI through a driving circuit.

[0135] FIG. 6 is a block diagram of a grid impedance identification algorithm based on uncharacteristic harmonic injection according to the present invention. As shown in FIG. 6, the grid impedance identification algorithm in Step 1 includes the following steps:

[0136] Step 1.1: Inject an uncharacteristic harmonic current having a 75 Hz frequency at the PCC. In the embodiment of the present invention, the amplitude of the injected uncharacteristic harmonic current having the 75 Hz frequency is 8 A.

[0137] Step 1.2: Sample a harmonic response voltage u.sub.pcch and a harmonic response current i.sub.gh at the PCC.

[0138] Step 1.3: Analyze a spectrum of each of the harmonic response voltage u.sub.pcch and a harmonic response current i.sub.gh through a fast Fourier transform (FFT) to obtain an amplitude |U.sub.pcch_75Hz| of a harmonic response voltage component at the 75 Hz frequency, a phase ∠U.sub.pcch_75Hz of the harmonic response voltage component at the 75 Hz frequency, an amplitude |I.sub.pcch_75Hz| of a harmonic response current component at the 75 Hz frequency, and a phase ∠I.sub.pcch_75Hz of the harmonic response current component at the 75 Hz frequency; and obtain an amplitude |Z.sub.g| of a grid impedance at the 75 Hz frequency and a phase ∠Z.sub.g of the grid impedance at the 75 Hz frequency according to the following equation:

[00031]$.Math.Z_g.Math.=\frac{\left|U_{pcc{h}_{-}75Hz}\right|}{\left|I_{pcc{h}_{-}75Hz}\right|}$$\angle Z_g=\angle U_{pcc{h}_{-}75Hz}-\angle I_{pcc{h}_{-}75Hz}.$

[0139] Step 1.4: Calculate the reference equivalent grid impedance Z.sub.g_est according to the following equation according to the amplitude |Z.sub.g| of the grid impedance at the 75 Hz frequency and the phase ∠Z.sub.g of the grid impedance at the 75 Hz frequency in Step 1.3:

[00032]$Z_{g_{-}est}=\frac{\left|Z_g\right|.Math.\sin \angle Z_g}{2\pi .Math.75}$

[0140] In the embodiment of the present invention, FIG. 7 illustrates an experimental waveform of a dual-mode combined control strategy for a multi-inverter system based on a double split transformer. The experimental process is described as follows:

[0141] Time period t.sub.1-t.sub.2: the 0.2 mH inductor is connected to the system at the time t.sub.1 to simulate the strong grid. According to the flow chart for implementation in FIG. 3, both the 1 # GCI and the 2 # GCI operate in the current source mode because of Z.sub.g_est≤λ.sub.1=0.98 mH. FIG. 8 illustrates an enlarged experimental waveform of the time period t.sub.1-t.sub.2 in FIG. 7. It can be seen that the grid current i.sub.ga and the capacitor voltage u.sub.Cab are stable, with the 75 Hz harmonics (which is the response obtained by injecting 75 Hz harmonics into the GCI using the grid impedance identification algorithm). In addition, the output of the grid impedance identification is 0.2 mH, and the flag of control modes of the 1 # GCI and the 2 # GCI are 0, indicating that the system operates in the full current source mode.

[0142] Time period t.sub.2-t.sub.3: the 1 mH inductor is continuously put into the system at the time t.sub.2 to simulate the weak grid. According to the flow chart for implementation in FIG. 3, the 2 # GCI operates in the voltage source mode, and the 1 # GCI still operates in the current source mode because of λ.sub.1=0.98 mH<Z.sub.g_est≤λ.sub.2=2 mH. FIG. 9 illustrates an enlarged experimental waveform of the time period t.sub.2-t.sub.3 in FIG. 7. The grid current i.sub.ga and the capacitor voltage u.sub.Cab are still stable; and because of the grid impedance identification algorithm, there are 75 Hz harmonics in the voltage waveform and the current waveform. In addition, the output of the grid impedance identification is 1.2 mH, and the change of the grid impedance can be tracked in real time. The flag of control modes of the 1 # GCI and the 2 # GCI are 0 and 1 respectively, indicating that the system operates in the hybrid mode.

[0143] Time period t.sub.3-t.sub.4: the 1.6 mH inductor is continuously put into the system at the time t.sub.3 to simulate the extremely-weak grid. According to the flow chart for implementation in FIG. 3, both the 1 # GCI and the 2 # GCI operate in the voltage source mode because of Z.sub.g_est>λ.sub.2=2 mH. FIG. 10 illustrates an enlarged experimental waveform of the time period t.sub.3-t.sub.4 in FIG. 7. The grid current i.sub.ga and the capacitor voltage u.sub.Cab are still stable; and because of the grid impedance identification algorithm, there are 75 Hz harmonics in the voltage waveform and the current waveform. In addition, the output of the grid impedance identification is 2.8 mH, and the change of the grid impedance can be tracked in real time. The flag of control modes of the 1 # GCI and the 2 # GCI are 1, indicating that the system operates in the full voltage source mode.

[0144] Time period t.sub.4-t.sub.5: the 1.6 mH inductor is continuously put into the system at the time t.sub.4. Both the control strategy and the experimental waveform are the same as those in the time period t.sub.2-t.sub.3.

[0145] Time period 646: the 1 mH inductor is continuously put into the system at the time t.sub.5. Both the control strategy and the experimental waveform are the same as those in the time period t.sub.1-t.sub.2.

[0146] In conclusion, the experimental waveform in FIG. 7 is in good agreement with the flow chart for implementation in FIG. 3. The present invention is implemented simply, and greatly increases the stability margin of the multi-inverter system based on the double split transformer during the drastic fluctuation of the grid impedance; and particularly, the present invention ensures that the system can still operate stably in the extremely-weak grid, and makes the system more adaptable to the power grid.