| CPC G06F 30/20 (2020.01) [G06F 17/16 (2013.01); G06F 2119/06 (2020.01)] | 1 Claim |
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1. A method for real-time electromagnetic transient simulation based on a field programmable logic array (FPGA) for power system stability analysis and control research, comprising
providing a host computer and a field programmable logic array (FPGA) for real-time electromagnetic transient simulation of a circuit of a power system,
performing an initialization operation in the host computer, wherein a history current source vector Ihis1, an equivalent current source vector Isrcn, voltage coefficient matrix α, and current coefficient matrix β of a history current source expression are obtained through the following steps of (1) to (5):
(1) sequentially numbering branches and nodes in the circuit to be simulated respectively, wherein the number of a grounding node is 0;
(2) forming a correlation matrix M of the circuit to be simulated according to the following rules:
(i) if a branch p is connected to a node q and a positive current direction defined by the branch p is an outflow node q, M (q, p)=1;
(ii) if the branch p is connected to the node q and the positive current direction defined by the branch p is an inflow node q, M (q, p)=−1;
(iii) if the branch p and the node q are not connected, M (q, p)=0;
(3) forming a branch equivalent admittance vector Yeq, a node admittance matrix Yn, a voltage coefficient matrix α, and a current coefficient matrix β of a history current source expression of the circuit to be simulated according to the following substeps:
(i) respectively replacing each resistance branch, inductance branch, capacitance branch and switch branch with an companion circuit model, wherein each companion circuit respectively comprises an equivalent admittance, and a history current source connected in parallel;
(ii) an independent voltage source branch and an independent current source branch are represented by a Norton equivalent circuit, and each Norton equivalent circuit comprises an equivalent admittance, and an equivalent current source connected in parallel;
(iii) forming branch equivalent admittance column vectors Yeq according to the branch numbers by equivalent admittances of all branches, forming branch history current source column vectors Ihis according to the branch numbers by history current sources of all branches, and forming branch equivalent current source column vectors Isrc according to the branch numbers by equivalent current sources of all branches, wherein elements at corresponding positions in Isrc of resistance, inductance, capacitance and switch branches are zero; and the elements at the corresponding positions in Ihis of the independent voltage source and the independent current source branch are zero;
(iv) calculating a node admittance matrix Yn of the circuit to be simulated according to the equivalent admittance of each branch;
(v) calculating the voltage coefficient matrix α and the current coefficient matrix β of the history current source expression, wherein the formula is as follows:
Ihisn+1=αYeqVbrnn+βIbrnn
wherein, Ihisn+1 is a history current source vector at a (n+1)th simulation moment, a branch voltage vector at a nth simulation moment and a branch current vector at the nth simulation moment;
(4) forming a node voltage/branch current coefficient matrix P and a history current source coefficient matrix Q according to the correlation matrix M, the branch equivalent admittance vector Yeq and the node admittance matrix Yn of the circuit to be simulated;
 wherein, Yn−1 is an inverse matrix of the node admittance matrix, MT is a transpose matrix of the correlation matrix, I is an identity matrix with dimensions of Nbrn*Nbrn, and Nbrn is the number of branches of the circuit to be simulated; and
(5) setting the initial history current source vector Ihis1 to zero and the current simulation moment n to 1 at end of the initiation operation;
performing one or more cycles of simulation in the FPGA, wherein electric parameters at each simulation moment in each simulation cycle are obtained by a compressed matrix calculation in the FPGA through the following steps of (6) and (7):
(6) calculating a node voltage vector Vnn and a branch current vector Ibrnn at the current simulation moment according to the history current source vector Ihisn and the equivalent current source vector Isrcn at the current simulation moment, and updating the history current source vector Ihisn+1 at a next simulation moment, wherein the formula is as follows:
 wherein, the equivalent current source vector Isrcn is automatically updated along with the n magnitudes of independent voltage sources and independent current sources, diagonal elements corresponding to switch branches in diagonal arrays α and β change instantly along with switch states, and other elements remain constant; and
(7) returning to the step (6) when the next simulation moment n+1 becomes the current simulation moment, and running the steps (6) and (7) repeatedly to update the electric parameters real-time in the FPGA;
displaying real-time simulation waveforms of the electric parameters obtained by the FPGA at each simulation moment in the host computer, and conducting stability analysis and control research of the power system based on the displayed real-time simulation waveforms; and
terminating the simulation until a predetermined simulation moment is reached or an instruction of early termination is received.
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