Solving realistic large‐scale ill‐conditioned power flow cases based on combination of numerical solvers

Abstract

With the increasing electricity consumption and difficulty in upgrading existing infrastructures, ill-conditioned power flow (PF) cases are becoming more frequent nowadays. In this context, classical robust solvers may be unsuitable for realistic networks, which typically encompass thousands of buses, because of their high computational burden or low convergence rate. This article tackles this issue by proposing a novel PF solver, which presents acceptable robustness and efficiency in solving large-scale ill-conditioned systems. The proposed algorithm collects the advantage of various numerical solvers, which by separate present different weaknesses, but actuating in coordination their strengths can be jointly exploited. More precisely, the robust Forward-Euler and Trapezoidal rules are combined with the efficient Darvishi cubic technique. Thereby, an original predictor-corrector algorithm is developed to effectively coordinate the different numerical algorithms involved, obtaining a robust but efficient yet solution procedure. Various large-scale illconditioned benchmark systems are studied under different stressing conditions. The results obtained with the developed technique are promising, outperforming other robust and standard PF solvers. K E Y W O R D S computational efficiency, ill-conditioned cases, large-scale systems, power flowList of Symbols and Abbreviations: t, time instant; (.) sch , scheduled value; i, denotes the ith bus of the system; k, Denotes the kth iteration of an iterative algorithm; n l , total number of PQ buses; n g , total number of PV buses; n, size of the power flow state vector (n = 2n l + n g in polar coordinates); N, number of iterative loops; ω, state vector of a dynamic system; Δt, time step; P, nodal active power injection; Q, nodal reactive power injection; V∠δ, nodal voltage; Y∠θ, element of the admittance matrix; h, step size; ε, convergence tolerance; k max , maximum number of iterations allowed; g, power flow equations; [Á] T , transpose operator; [Á] À1 , inverse operator; kÁk ∞ , infinity norm; r x , vector/matrix gradient (first derivative) with respect to x; max{a,b}, returns b if b > a and a otherwise; min{a,b}, returns b if b < a and a otherwise; x, y, z, power flow state vector; δ PV , voltage angles at PV buses; δ PQ , voltage angles at PQ buses; V PQ , voltage magnitudes at PQ buses; g x , Jacobian matrix formed by the first partial derivatives of g with respect x; I, identity matrix; BEM, Backward-Euler method; HKW, Heun-King Werner approach; HOLM, high order Levenberg-Marquardt solver; LU, lower-upper; NR, Newton-Raphson technique; OMP, optimal multiplier method in polar coordinates; PF, power flow; TR, trapezoidal rule applied to PF analysis; 3OD, darvishi's cubic method applied to PF analysis.