SINGLE VECTOR-BASED FINITE CONTROL SET MODEL PREDICTIVE CONTROL METHOD OF TWO PARALLEL POWER CONVERTERS

Abstract

This invention proposes a single-vector-based finite control set model predictive control for two parallel power converters, which adopts a centralized control structure to achieve accurate control of overall performance. It establishes predictive models for line currents and three phase-circulating currents and constructs a novel cost function that uses these currents as performance indices to implement the predictive control algorithm based on the proposed predictive models. The invention proposes dynamic weighting coefficients and adjustment principles to improve system control performance. A finite set output signal matrix containing important characteristic information of all alternative vectors is constructed to avoid redundant calculations in each control horizon, reducing computation time during practical implementation. This invention addresses the limitations of existing one-vector-based FCS-MPC for two paralleled power converters, which controls each sub-converter individually with a set of available eight control actions and cannot effectively regulate the overall performance of the two paralleled power converters.

Claims

1. A single vector-based finite control set model predictive control method of two parallel power converters, comprising: establishing mathematical models of line currents and three phase-circulating currents for the two parallel power converters respectively, and obtaining discrete predictive models by discretization; establishing relationships between switching states and equivalent output terminal voltage differences of the two parallel power converters, generating a complete set of 64 alternative vector combinations available with the two parallel power converters, and creating a finite set output signal matrix that comprises characteristic information covering switching states, equivalent output voltages, and terminal voltage differences; sampling a DC bus voltage, load voltages, and three-phase currents of each converter at an instant k, determining the line currents and the three phase-circulating currents according to the three-phase currents of the two parallel power converters, and calculating reference values of the line currents at an instant k+2, while setting the reference values of the three phase-circulating currents to zero; adding delay compensation, using a two-step prediction approach, classifying the 64 alternative vector combinations of the two parallel power converters, substituting the equivalent output voltages and the terminal voltage differences in the finite set output signal matrix into the discrete predictive models by category, and generating predictive values of the line currents and the three phase-circulating currents at the instant k+2; creating a cost function using the line currents and the three phase-circulating currents as performance indices, substituting the reference values of the line currents and the predictive values of the line currents and the three phase-circulating currents of the alternative vector combinations at the instant k+2 to obtain a cost function value and obtaining an optimal vector combination that minimizes the cost function through comparison; generating switching control signals of corresponding legs of the two parallel power converters through a comparator using switching states of the optimal vector combination and amplifying the switching control signals to control power switching devices of the two parallel power converters.

2. The single vector-based finite control set model predictive control method of two parallel power converters according to claim 1, wherein, the discrete predictive models of the line currents are: $\{\begin{array}{c}{i}_a\left(k+1\right)=\frac{T_s}{L_e}\left[u_a\left(k\right)-e_a\left(k\right)-R_e{i}_a\left(k\right)\right]+i_a\left(k\right)\\ i_b\left(k+1\right)=\frac{T_s}{L_e}\left[u_b\left(k\right)-e_b\left(k\right)-R_e{i}_b\left(k\right)\right]+i_b\left(k\right),\\ i_c\left(k+1\right)=\frac{T_s}{L_e}\left[u_c\left(k\right)-e_c\left(k\right)-R_e{i}_c\left(k\right)\right]+i_c\left(k\right)\end{array}$ where T.sub.s is a switching period; Le and Re represent an equivalent inductance and its parasitic resistance respectively; L.sub.e is calculated as L.sub.e=L+L.sub.1/2 and R.sub.e is calculated as R.sub.e=R+R.sub.1/2; i.sub.a(k), i.sub.b(k) and i.sub.c(k) are the line currents calculated at the instant k; i.sub.a(k+1), i.sub.b(k+1) and i.sub.c(k+1) are the predictive line currents at an instant k+1; u.sub.a(k), u.sub.b(k) and u.sub.c(k) are the equivalent output voltages at the instant k; e.sub.a(k), e.sub.b(k) and e.sub.c(k) are grid voltages at the instant k; the discrete predictive models of the three phase-circulating currents are: $\{\begin{array}{c}{i}_{\mathrm{cira}}\left(k+1\right)=\frac{T_s}{L_1}\left[\Delta u_a\left(k\right)-R_1{i}_{\mathrm{cira}}\left(k\right)\right]+i_{\mathrm{cira}}\left(k\right)\\ i_{\mathrm{cirb}}\left(k+1\right)=\frac{T_s}{L_1}\left[\Delta u_b\left(k\right)-R_1{i}_{\mathrm{cirb}}\left(k\right)\right]+i_{\mathrm{cirb}}\left(k\right),\\ i_{\mathrm{circ}}\left(k+1\right)=\frac{T_s}{L_1}\left[\Delta u_c\left(k\right)-R_1{i}_{\mathrm{circ}}\left(k\right)\right]+i_{\mathrm{circ}}\left(k\right)\end{array}$ where i.sub.cira(k) i.sub.cirb(k) and i.sub.circ(k) are the three phase-circulating currents calculated at the instant k, i.sub.cira(k+1), i.sub.cirb(k+1) and i.sub.circ(k+1) are predictive three phase-circulating currents at the instant k+1, and Δu.sub.a(k), Δu.sub.b(k) and Δu.sub.c(k) represent the terminal voltage differences between parallel legs at the instant k, respectively.

3. The single vector-based finite control set model predictive control method of two parallel power converters according to claim 1, wherein, the relationships between the switching states and the equivalent output voltages of the two parallel power converters are: $\{\begin{array}{c}{u}_a=\frac{2\left(S_{a1}+S_{a2}\right)-\left(S_{b1}+S_{b2}\right)-\left(S_{c1}+S_{c2}\right)}{6}{V}_{DC}\\ u_b=\frac{2\left(S_{b1}+S_{b2}\right)-\left(S_{a1}+S_{a2}\right)-\left(S_{c1}+S_{c2}\right)}{6}{V}_{DC},\\ u_c=\frac{2\left(S_{c1}+S_{c2}\right)-\left(S_{a1}+S_{a2}\right)-\left(S_{b1}+S_{b2}\right)}{6}{V}_{DC}\end{array}$ where S.sub.a1, S.sub.b1, and S.sub.c1 represent ON/OFF status of IGBTs of a first power converter, and S.sub.a2, S.sub.b2, and S.sub.c2 represent ON/OFF status of IGBTs of a second power converter; all switching states only take a value of 1 or 0, taking 1 means that an upper IGBT is on and a lower IGBT is off, taking 0 means that the upper IGBT is off and the lower IGBT is on, and V.sub.DC is the DC bus voltage; the relationships between the switching states and the terminal voltage differences of the two parallel power converters are: $\{\begin{array}{c}\Delta u_a=\left(S_{a1}-S_{a2}\right)V_{DC}\\ \Delta u_b=\left(S_{b1}-S_{b2}\right)V_{DC}\\ \Delta u_c=\left(S_{c1}-S_{c2}\right)V_{DC}\end{array}$ the finite set output signal matrix is 64 rows×12 columns, whose rows are expressed as [S.sub.a1S.sub.b1S.sub.c1S.sub.a2S.sub.b2S.sub.c2u.sub.au.sub.bu.sub.cΔu.sub.aΔu.sub.bΔu.sub.c].

4. The single vector-based finite control set model predictive control method of two parallel power converters according to claim 1, wherein, the line currents and the three phase-circulating currents are determined according to the three-phase currents of the two parallel power converters as follows: $\{\begin{array}{c}{i}_a\left(k\right)=i_{a1}\left(k\right)+i_{a2}\left(k\right)\\ i_b\left(k\right)=i_{b1}\left(k\right)+i_{b2}\left(k\right)\\ i_c\left(k\right)=i_{c1}\left(k\right)+i_{c2}\left(k\right)\end{array},\mathrm{and}\{\begin{array}{c}{i}_{\mathrm{cira}}\left(k\right)=i_{a1}\left(k\right)-i_{a2}\left(k\right)\\ i_{\mathrm{cirb}}\left(k\right)=i_{b1}\left(k\right)-i_{b2}\left(k\right),\\ i_{\mathrm{circ}}\left(k\right)=i_{c1}\left(k\right)-i_{c2}\left(k\right)\end{array}$ where i.sub.a1(k), i.sub.b1(k), i.sub.c1(k), i.sub.a2(k), i.sub.b2(k) and i.sub.c2(k) are respectively the three-phase currents of the two parallel power converters at the instant k, i.sub.cira(k), i.sub.cirb(k) and i.sub.circ(k) are the three phase-circulating currents calculated at the instant k, and i.sub.a(k), i.sub.b(k) and i.sub.c(k) are the line currents calculated at the instant k.

5. The single vector-based finite control set model predictive control method of two parallel power converters according to claim 1, wherein, the reference values of the line currents at the instant k+2 are: $\{\begin{array}{c}{i}_{\mathrm{ra}}\left(k+2\right)=3i_{\mathrm{ra}}\left(k+1\right)-3i_{\mathrm{ra}}\left(k\right)+i_{\mathrm{ra}}\left(k-1\right)\\ i_{\mathrm{rb}}\left(k+2\right)=3i_{\mathrm{rb}}\left(k+1\right)-3i_{\mathrm{rb}}\left(k\right)+i_{\mathrm{rb}}\left(k-1\right),\\ i_{\mathrm{rc}}\left(k+2\right)=3i_{\mathrm{rc}}\left(k+1\right)-3i_{rc}\left(k\right)+i_{rc}\left(k-1\right)\end{array}$ where i.sub.ra(k+2), i.sub.rb(k+2) and i.sub.rc(k+2) are the reference values of the line currents at the instant k+2.

6. The single vector-based finite control set model predictive control method of two parallel power converters according to claim 1, wherein, adding delay compensation, using a two-step prediction approach, classifying the 64 alternative vector combinations of the two parallel power converters comprises: substituting the load voltages, the line currents, and the three phase-circulating currents at the instant k, along with the equivalent output voltages and the terminal voltage differences determined by a preselection vector at an instant k−1, into the discrete predictive models to obtain the predictive values of the line currents and the three phase-circulating currents at an instant k+1; classifying the 64 alternative vector combinations: classifying different vector combinations with the same equivalent output terminal voltage differences into one group, wherein the vector combinations of a same group require only one predictive calculation, classifying the 64 alternative vector combinations into 5 groups according to different values of an a-phase equivalent output voltage u.sub.a, wherein, 5 different values of u.sub.a are 2 V.sub.DC/3, V.sub.DC/3, 0, −V.sub.DC/3 and −2 V.sub.DC/3 respectively; according to different values of an a-terminal voltage difference Δu.sub.a of the two parallel power converters, classifying the 64 alternative vector combinations into 3 groups, wherein, 3 different values of Δu.sub.a are V.sub.DC, 0 and −V.sub.DC respectively, and V.sub.DC is the DC bus voltage; obtaining the predictive values of the line currents and the three phase-circulating currents at the instant k+2 corresponding to all alternative vectors based on classification.

7. The single vector-based finite control set model predictive control method of two parallel power converters according to claim 1, wherein, the cost function is: $g=\underset{x=a,b,c}{.Math.}{\left(i_{\mathrm{cirx}}\left(k+2\right)\right)}^2+\frac{1}{{\lambda }^2}\frac{\gamma }{1-\gamma }{\left(\frac{L_e}{L_1}\right)}^2\underset{x=a,b,c}{.Math.}{\left(i_x\left(k+2\right)-i_{rx}\left(k+2\right)\right)}^2,$ wherein, λ is a distribution coefficient determined based on a fluctuation amplitude analysis of the three phase-circulating currents and parallel current ripples; V.sub.DC is the DC bus voltage; i.sub.cirx(k+2) is an x-phase circulating current at the instant k+2, i.sub.x(k+2) is an x-phase parallel current at the instant k+2, i.sub.rx(k+2) is an x-phase reference current at the instant k+2; L.sub.e represents an equivalent inductance; L.sub.1 represents a filter inductance of each converter; γ∈[0,1] is a dynamic weight coefficient, in a case where distribution coefficient of two control objectives is determined by λ, γ=0.5 denotes that the three-phase circulating currents and the parallel current ripples have balanced control effect, to prioritize line current quality performance, increase γ; to prioritize circulating current performance, decrease γ.

8. The single vector-based finite control set model predictive control method of two parallel power converters according to claim 7, wherein, the distribution coefficient $\lambda =\max \left(M,\frac{4}{3}-M\right),$ M=2U.sub.m/V.sub.DC is a modulation index and U.sub.m is an amplitude of the reference voltage.

9. An electronic device, comprising a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein, the processor implements the single vector-based finite control set model predictive control method of two parallel power converters according to claim 1 when executing the computer program.

10. A computer-readable storage medium, on which a computer program is stored, wherein, the computer program implements the single vector-based finite control set model predictive control method of two parallel power converters according to claim 1 when executed by the processor.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0043] FIG. 1 is a topology diagram of two parallel power converters.

[0044] FIG. 2 is a flow chart of a single vector-based finite control set model predictive control method provided by the application.

[0045] FIG. 3 is a space vector diagram of two parallel power converters.

[0046] FIG. 4 (a) is a vector distribution diagram with maximum voltage error in the first sector.

[0047] FIG. 4 (b) is an absolute value distribution diagram of the maximum voltage vector error in the first sector.

[0048] FIG. 5 is an operation duration diagram of the model predictive control algorithm by the application.

[0049] FIG. 6 (a) shows the experimental results of the line current at γ=0.2.

[0050] FIG. 6 (b) shows the experimental results of the three phase-circulating current at γ=0.2.

[0051] FIG. 7 (a) shows the experimental results of the line current at γ=0.5.

[0052] FIG. 7 (b) shows the experimental results of the three phase-circulating current at γ=0.5.

[0053] FIG. 8 (a) shows the experimental results of the line current at γ=0.8.

[0054] FIG. 8 (b) shows the experimental results of the three phase-circulating current at γ=0.8.

DETAILED DESCRIPTION

[0055] The specific embodiments of the present application are described in detail below in combination with the drawings.

[0056] FIG. 1 depicts the configuration of two parallel power converters, where CNV1 and CNV2 are two-level converters with paralleled DC links and AC terminals connected via filter inductors. The three-phase currents of the first converter are represented by i.sub.a1, i.sub.b1 and i.sub.c1, while i.sub.a2, i.sub.b2 and i.sub.c2 denote those of the second converter. The line currents are represented by i.sub.a, i.sub.b and i.sub.c, while the three phase-circulating currents are denoted by i.sub.cira, i.sub.cirb and i.sub.circ. AC side powers/load voltages are represented by e.sub.a, e.sub.b and e.sub.c, DC bus voltage is represented by V.sub.DC, and AC side inductance and its parasitic resistance are represented by L and R, respectively. Similarly, L.sub.1 and R.sub.1 represent the filter inductance and its parasitic resistance, respectively, while S.sub.11 to S.sub.26 represent all the power switching devices of the two converters. The line currents of two parallel converters and the three-phase-circulating currents are obtained as per Kirchhoff s current law.

[00011]$\begin{array}{cc}\begin{array}{cc}\{\begin{array}{c}{i}_a=i_{a1}+i_{a2}\\ i_b=i_{b1}+i_{b2}\\ i_c=i_{c1}+i_{c2}\end{array},& \{\begin{array}{c}{i}_{\mathrm{cira}}=1_{a1}-i_{a2}\\ i_{\mathrm{cirb}}=1_{b1}-i_{b2}\\ i_{\mathrm{circ}}=1_{c1}-i_{c2}\end{array}\end{array}& \left(1\right)\end{array}$

[0057] As shown in FIG. 2, the specific implementation steps of a single vector-based finite control set model predictive control method are as follows:

[0058] Step (1): establishing mathematical models of line currents and three phase-circulating currents for the two parallel power converters respectively, and obtaining discrete predictive models by discretization.

[0059] According to Kirchhoff's laws, the mathematical model of the line currents is derived:

[00012]$\begin{array}{cc}\{\begin{array}{c}{L}_e\frac{d{i}_a}{dt}=u_a-e_a-R_e{i}_a\\ L_e\frac{d{i}_b}{dt}=u_b-e_b-R_e{i}_b\\ L_e\frac{d{i}_c}{dt}=u_c-e_c-R_e{i}_c\end{array}& \left(2\right)\end{array}$

[0060] In Equation (2), the equivalent inductance and its parasitic resistance are represented by L.sub.e and R.sub.e, respectively, where Le is calculated as L+L.sub.1/2 and R.sub.e is calculated as R+R.sub.1/2. The discrete predictive model of the line currents is obtained as:

[00013]$\begin{array}{cc}\{\begin{array}{c}{i}_a\left(k+1\right)=\frac{T_s}{L_e}\left[u_a\left(k\right)-e_a\left(k\right)-R_e{i}_a\left(k\right)\right]+i_a\left(k\right)\\ i_b\left(k+1\right)=\frac{T_s}{L_e}\left[u_b\left(k\right)-e_b\left(k\right)-R_e{i}_b\left(k\right)\right]+i_b\left(k\right)\\ i_c\left(k+1\right)=\frac{T_s}{L_e}\left[u_c\left(k\right)-e_c\left(k\right)-R_e{i}_c\left(k\right)\right]+i_c\left(k\right)\end{array}& \left(3\right)\end{array}$

[0061] The mathematical model of the three phase-circulating currents is derived as:

[00014]$\begin{array}{cc}\{\begin{array}{c}{L}_1\frac{d{i}_{\mathrm{cira}}}{dt}+R_1{i}_{\mathrm{cira}}=u_{a1o}-u_{a20}=\Delta u_a\\ L_1\frac{d{i}_{\mathrm{cir}b}}{dt}+R_1{i}_{\mathrm{cirb}}=u_{b1o}-u_{b20}=\Delta u_b\\ L_1\frac{d{i}_{circ}}{dt}+R_1{i}_{circ}=u_{c1o}-u_{c2o}=\Delta u_c\end{array}& \left(4\right)\end{array}$

[0062] where u.sub.a1o, u.sub.b1o, u.sub.c1o, u.sub.a2o, u.sub.b2o, and u.sub.c2o represent the voltage from the midpoint of each leg to the virtual midpoint of the DC bus, while Δu.sub.a, Δu.sub.b, Δu.sub.c indicate the terminal voltage differences between the parallel legs. The discrete predictive model of the line currents is obtained as:

[00015]$\begin{array}{cc}\{\begin{array}{c}{i}_{\mathrm{cira}}\left(k+1\right)=\frac{T_s}{L_1}\left[\Delta u_a\left(k\right)-R_1{i}_{\mathrm{cira}}\left(k\right)\right]+i_{\mathrm{cira}}\left(k\right)\\ i_{\mathrm{cirb}}\left(k+1\right)=\frac{T_s}{L_1}\left[\Delta u_b\left(k\right)-R_1{i}_{\mathrm{cirb}}\left(k\right)\right]+i_{\mathrm{cirb}}\left(k\right)\\ i_{\mathrm{circ}}\left(k+1\right)=\frac{T_s}{L_1}\left[\Delta u_c\left(k+1\right)-R_1{i}_{\mathrm{circ}}\left(k\right)\right]+i_{\mathrm{circ}}\left(k\right)\end{array}& \left(5\right)\end{array}$

[0063] Step (2): establishing relationships between switching states and equivalent output voltages/terminal voltage differences of the two parallel power converters, generating a complete set of 64 alternative vector combinations available with the two parallel converters, and creating a 64×12 finite output signal matrix that comprises characteristic information covering switching states, equivalent output voltages, and terminal voltage differences.

[0064] Firstly, the expression of the equivalent output voltages of two parallel converters is derived as:

[00016]$\begin{array}{cc}\{\begin{array}{c}{u}_a=\frac{2\left(S_{a1}+S_{a2}\right)-\left(S_{b1}+S_{b2}\right)-\left(S_{c1}+S_{c2}\right)}{6}{V}_{DC}\\ u_b=\frac{2\left(S_{b1}+S_{b2}\right)-\left(S_{a1}+S_{a2}\right)-\left(S_{c1}+S_{c2}\right)}{6}{V}_{DC}\\ u_c=\frac{2\left(S_{c1}+S_{c2}\right)-\left(S_{a1}+S_{a2}\right)-\left(S_{b1}+S_{b2}\right)}{6}{V}_{DC}\end{array}& \left(6\right)\end{array}$

[0065] In Equation (6), the state function values S.sub.a1, S.sub.b1, S.sub.c1, S.sub.a2, S.sub.b2, and S.sub.c2 represent the ON/OFF status of the IGBTs of the two parallel power converters, with a value of 1 indicating that the upper IGBT is on and the lower IGBT is off, and vice versa.

[0066] Secondly, the expression of the terminal voltage differences of two parallel power converters is derived as:

[00017]$\begin{array}{cc}\{\begin{array}{c}\Delta u_a=\left(S_{a1}-S_{a2}\right)V_{DC}\\ \Delta u_b=\left(S_{b1}-S_{b2}\right)V_{DC}\\ \Delta u_c=\left(S_{c1}-S_{c2}\right)V_{DC}\end{array}& \left(7\right)\end{array}$

[0067] An output signal matrix for two parallel power converters is established based on equations (6) and (7), with each row consisting of switching states, equivalent output voltages, and terminal voltage differences, represented by [S.sub.a1S.sub.b1S.sub.c1S.sub.a2S.sub.b2S.sub.c2u.sub.au.sub.bu.sub.cΔu.sub.aΔu.sub.bΔu.sub.c].

[0068] With 64 available switching states combinations, the matrix has 64 rows×12 columns, and subsequent predictive processes will reference this matrix for corresponding feature information.

[0069] Step (3): sampling a DC bus voltage V.sub.DC(k), load voltages e.sub.a(k), e.sub.b(k) and e.sub.c(k), three-phase currents of the first converter i.sub.a1(k), i.sub.b1(k) and i.sub.c1(k) and three-phase currents of the second converter i.sub.a2(k), i.sub.b2(k) and i.sub.c2(k) at an instant k, determining the line currents i.sub.a(k), i.sub.b(k) and i.sub.c(k) and the three phase-circulating currents i.sub.cira(k), i.sub.cirb(k) and i.sub.circ(k) according to the three-phase currents of the two parallel power converters, and calculating reference values of the line currents i.sub.ra(k+2), i.sub.rb(k+2) and i.sub.rc(k+2) at an instant k+2, while setting the reference values of the three phase-circulating currents to zero.

[0070] According to equation (1), the sampling values of the line currents and the three phase-circulating currents can be obtained as:

[00018]$\begin{array}{cc}\begin{array}{cc}\{\begin{array}{c}{i}_a\left(k\right)=i_{a1}\left(k\right)+i_{a2}\left(k\right)\\ i_b\left(k\right)=i_{b1}\left(k\right)+i_{b2}\left(k\right)\\ i_c\left(k\right)=i_{c1}\left(k\right)+i_{c2}\left(k\right)\end{array},& \{\begin{array}{c}{i}_{cira}\left(k\right)=i_{a1}\left(k\right)-i_{a2}\left(k\right)\\ i_{cirb}\left(k\right)=i_{b1}\left(k\right)-i_{b2}\left(k\right)\\ i_{circ}\left(k\right)=i_{c1}\left(k\right)-i_{c2}\left(k\right)\end{array}\end{array}& \left(8\right)\end{array}$

[0071] Step (4): adding delay compensation, using a two-step prediction approach, classifying the 64 alternative vector combinations of the two parallel power converters, substituting the equivalent output voltages and the terminal voltage differences in the finite set output signal matrix into the discrete predictive models by category, and generating predictive values of the line currents and the three phase-circulating currents at the instant k+2.

[0072] To account for the time delay in the microprocessor, a two-step prediction is implemented in the proposed single vector-based finite control set model predictive control method. Firstly, predictive values for line currents [i.sub.a(k+1), i.sub.b(k+1) and i.sub.c(k+1)] and three phase-circulating currents [i.sub.cira(k+1), i.sub.cirb(k+1) and i.sub.circ(k+1)] at the instant k+1 are calculated by inputting the preselection vector from the instant k−1 into equations (3) and (5). Next, predictive values for line currents [i.sub.a(k+2), i.sub.b(k+2) and i.sub.c(k+2)] and three phase-circulating currents [i.sub.cira(k+2), i.sub.cirb(k+2) and i.sub.circ(k+2)] at the instant k+2 are calculated by substituting the 64 alternative vector combinations into equation (3) and (5). This eliminates the time delay between selecting a vector combination at instant k and the corresponding action at instant k+1.

[00019]$\begin{array}{cc}\{\begin{array}{c}{i}_a\left(k+2\right)=\frac{T_s}{L_e}\left[u_a\left(k+1\right)-e_a\left(k+1\right)-R_e{i}_a\left(k+1\right)\right]+i_a\left(k+1\right)\\ i_b\left(k+2\right)=\frac{T_s}{L_e}\left[u_b\left(k+1\right)-e_b\left(k+1\right)-R_e{i}_b\left(k+1\right)\right]+i_b\left(k+1\right)\\ i_c\left(k+2\right)=\frac{T_s}{L_e}\left[u_c\left(k+1\right)-e_c\left(k+1\right)-R_e{i}_c\left(k+1\right)\right]+i_c\left(k+1\right)\end{array}& \left(9\right)\end{array}$$\begin{array}{cc}\{\begin{array}{c}{i}_{\mathrm{cira}}\left(k+2\right)=\frac{T_s}{L_1}\left[\Delta u_a\left(k+1\right)-R_1{i}_{\mathrm{cira}}\left(k+1\right)\right]+i_{\mathrm{cira}}\left(k+1\right)\\ i_{\mathrm{cirb}}\left(k+2\right)=\frac{T_s}{L_1}\left[\Delta u_b\left(k+1\right)-R_1{i}_{cirb}\left(k+1\right)\right]+i_{\mathrm{cirb}}\left(k+1\right)\\ i_{circ}\left(k+2\right)=\frac{T_s}{L_1}\left[\Delta u_c\left(k+1\right)-R_1{i}_{circ}\left(k+1\right)\right]+i_{circ}\left(k+1\right)\end{array}& \left(10\right)\end{array}$

[0073] In order to ensure control performance and system stability, the computation time should be minimized to prevent exceeding the control cycle. In the 64 alternative vector combinations of the two parallel power converters, vector combinations with equivalent output voltages or terminal voltage differences are grouped together to reduce computation time. The same group of vector combinations is calculated only once to reduce computation time. For instance, the vector combinations (100, 000) and (110, 101) with the same output voltage are classified into one group, reducing the computation time of the predictive line currents. Similarly, the vector combinations (100, 000) and (110, 010) with the same terminal voltage difference are also classified into one group, reducing the computation time of the predictive circulating currents. Besides, each phase output voltage is classified into five groups: 2V.sub.DC/3, V.sub.DC/3, 0, −V.sub.DC/3, and −2V.sub.DC/3, thereby reducing the computation time of the predictive line current from 64 to 5 groups. Likewise, the terminal voltage differences are classified into three groups: V.sub.DC, 0, and −V.sub.DC, thus reducing the computation time of the predictive circulating current from 64 to 3 groups.

[0074] Step (5): creating a cost function using the line currents and the three phase-circulating currents as performance indices, substituting the reference values of the line currents and the predictive values of the line currents and the three phase-circulating currents of the alternative vector combinations at the instant k+2 to obtain a cost function value and obtaining an optimal vector combination that minimizes the cost function through comparison.

[0075] FIG. 3 depicts that 19 basic vectors are formed using 64 vector combinations, including 1 zero vector (V.sub.0), 6 long vectors (V.sub.1˜V.sub.6), 6 medium vectors (V.sub.7˜V.sub.12), and 6 short vectors (V.sub.13˜V.sub.18). The traditional two-stage FCS-MPC ignores the complete set of 64 switching states available with two parallel converters, limiting the optimization options. As a result, existing methods cannot effectively control both line and circulating currents. This invention aims to comprehensively optimize the phase-circulating current, line current, and zero-sequence circulating current. It builds finite control set models for the line current and phase-circulating current of the two parallel power converters and establishes a mapping relationship between the key indicators and switch combinations (single vectors). Besides, to ensure the capability of adjusting the single-phase circulating currents, it is necessary to enable the asynchronous switching states of the two parallel power converters. Given it, the maximum single-phase circulating current I.sub.cirmax is:

[00020]$\begin{array}{cc}{I}_{\mathrm{cirmax}}=\frac{V_{DC}{T}_s}{2L_1}& \left(11\right)\end{array}$

[0076] The voltage vector errors are the main factor in determining the three-phase current ripples of two parallel power converters.

[00021]$\begin{array}{cc}\{\begin{array}{c}{i}_{\mathrm{ripa}}=i_a-i_{ra}=\frac{u_a-u_n}{L_e}{T}_s\\ i_{\mathrm{ripb}}=i_b-i_{rb}=\frac{u_b-u_{\mathrm{rb}}}{L_e}{T}_s\\ i_{\mathrm{ripc}}=i_c-i_{rc}=\frac{u_c-u_{rc}}{L_e}{T}_s\end{array}& \left(12\right)\end{array}$

[0077] The maximum current ripple I.sub.ripmax is:

[00022]$\begin{array}{cc}{I}_{\mathrm{ripmax}}=\frac{T_s}{L_e}\times \max \left(u_a-u_{ra},u_b-u_{\mathrm{rb}},u_c-u_{rc}\right)& \left(13\right)\end{array}$

[0078] The use of interleaved carriers results in varying maximum voltage vector errors depending on the modulation index. In the first sector (0˜60°), FIG. 4(a) shows the maximum voltage error vector in different areas, and FIG. 4(b) shows the distribution of the absolute value of the maximum voltage vector error. The modulation index M is defined as M=2 U.sub.m/V.sub.DC, where U.sub.m is the reference voltage amplitude. When M is less than ⅔, the maximum voltage vector error decreases gradually as M increases; otherwise, the maximum voltage vector error increases with increasing M.

[0079] According to FIG. 4, the maximum value of the line current ripples is:

[00023]$\begin{array}{cc}{I}_{\mathrm{ripmax}}=\{\begin{array}{cc}\frac{V_{DC}{T}_s}{2L_e}\left(\frac{4}{3}-M\right)& M\in [0,\frac{2}{3})\\ \frac{V_{DC}{T}_s}{2L_e}M& M\in \left[\frac{2}{3},\frac{4}{3}\right]\end{array}& \left(14\right)\end{array}$

[0080] where

[00024]$\lambda =\max \left(M,\frac{4}{3}-M\right),$

equation (14) be simplified as:

[00025]$\begin{array}{cc}{I}_{\mathrm{ripmax}}=\frac{\lambda V_{DC}{T}_s}{2L_e}& \left(15\right)\end{array}$

[0081] The cost function is defined as the optimization of three phase-circulating currents and line current ripples, based on equations (11) and (15).

[00026]$\begin{array}{cc}g=\underset{x=a,b,c}{.Math.}{\left(i_{\mathrm{cirx}}\left(k+2\right)\right)}^2+\frac{1}{{\lambda }^2}{\left(\frac{L_e}{L_1}\right)}^2\underset{x=a,b,c}{.Math.}{\left(i_x\left(k+2\right)-i_{\mathrm{rx}}\left(k+2\right)\right)}^2& \left(16\right)\end{array}$

[0082] where λ represents a distribution coefficient that adjusts the proportion of the two control objectives, three phase-circulating currents and line currents, in the cost function under different modulation indices to ensure control performance.

[0083] The cost function is modified to meet the requirements of different application scenarios:

[00027]$\begin{array}{cc}g=\underset{x=a,b,c}{.Math.}{\left(i_{\mathrm{cirx}}\left(k+2\right)\right)}^2+\frac{1}{{\lambda }^2}\frac{\gamma }{1-\gamma }{\left(\frac{L_e}{L_1}\right)}^2\underset{x=a,b,c}{.Math.}{\left(i_x\left(k+2\right)-i_{\mathrm{rx}}\left(k+2\right)\right)}^2& \left(17\right)\end{array}$

[0084] where γ∈[0, 1] is a variable parameter for further improving the control performance. A value of γ=0.5 balances the output performance of the three phase-circulating currents and the line current ripples. For applications that prioritize line current quality, γ can be increased; for those that prioritize circulating current, γ can be decreased.

[0085] The optimal vector combination is determined by calculating and comparing the cost function values of 64 alternative vector combinations, with the one having the lowest value being selected. The gate signals of power switching devices of two parallel converters are then generated based on this optimal vector combination.

[0086] Step (6): generating switching control signals of corresponding legs of the two parallel power converters (CNV1 and CNV2) through a comparator using switching states of the optimal vector combination and amplifying the switching control signals to control power switching devices of the two parallel power converters. It should be noted that due to time delay, the switching control signals will take effect at the instant k+1.

[0087] An experimental prototype was built to test the proposed method, with a DC voltage of 200V, an AC-side resistance load of 9Ω, a filter inductance of 14.4 mH, a switching frequency of 10 kHz, a fundamental frequency of 50 Hz, and a modulation index of 0.8. According to FIG. 5, the operation time of the proposed model predictive control algorithm is less than 0.1 ms, which is the same as the switching period.

[0088] FIG. 6(a) and FIG. 6(b) demonstrate experimental results of line currents and three phase-circulating currents at γ=0.2, respectively, FIG. 7(a) and FIG. 7(b) illustrate experimental results of line currents and three phase-circulating currents at γ=0.5, respectively, and FIG. 8(a) and FIG. 8(b) depict the experimental results of line currents and three phase-circulating currents at γ=0.8, respectively. The figures indicate that all three experimental results achieved stable control of line currents and three phase-circulating currents with no instability of single-phase circulating currents. Additionally, the figures show that line current quality and circulating current have good performance at γ=0.5; when γ=0.8, line current performance improves at the cost of sacrificing circulating current performance; and when γ=0.2, circulating current performance improves at the cost of sacrificing line current performance.

[0089] This application uses centralized control to achieve precise control of two parallel power converters' overall performance. It establishes predictive models and a cost function to comprehensively control line currents and three phase-circulating currents. It proposes dynamic weight coefficients and adjustment principles to enhance comprehensive control performance. An output signal matrix with important characteristic information of all alternative vectors is constructed to reduce computation time. Delay compensation is considered to improve the system's control effects.

[0090] The above description of embodiments is a preferred embodiment of the application, but the embodiments of the application are not limited by the above embodiments. On the basis of the ideological principle and technical scheme of the application, various modifications or variants that can be made by those skilled in the art without creative work are still within the protection scope of the application.