Combining Newton-Raphson and Preconditioned Conjugate Gradient for Power Flow Analysis of Hybrid AC/DC Power Systems

Abstract

A method for performing power flow analysis in a hybrid AC/DC power system includes linearizing nonlinear power flow equations of the hybrid AC/DC power system using a Newton-Raphson (NR) method to generate a sparse Jacobian matrix, a mismatch vector and a set of initial state variables. The method also includes iteratively solving the linearized equations using a Preconditioned Conjugate Gradient (PCG) method with trust region constraint. The PCG method leverages the sparsity of the Jacobian matrix to efficiently compute updates to state variables. Also, a preconditioner is applied to improve the numerical stability and convergence of the PCG method. The method further includes refining the solution iteratively by feeding the updated state variables back into the NR method until convergence criteria are met to produce a result of the power flow analysis. Moreover, the method includes controlling the power system based on the result of the power flow analysis.

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