Matrix-Based Generalization for Power-Mismatch Newton-Raphson Load Flow Computations With Arbitrary Number of Phases

Abstract

The standard power-mismatch Newton method is still frequently used for computing load flow due to its simplicity and generality. In this paper, a matrix-based generalization for the usual power flow equations to an arbitrary number of phases is derived. The proposed equations enable computing power injections and the Jacobian matrix in terms of submatrices that compose the network admittance matrix. Besides the more compact representation, another advantage of the proposed generalization is execution time reduction compared to the standard scalar formulation. Simulations are carried out to demonstrate the time reduction achieved via the proposed equations.

A Modification of Newton–Raphson Power Flow for Using in LV Distribution System

“…Studies present various LF algorithms, such as the Gauss-Seidel (GS), forwardbackward sweep (FBS), and Newton-Raphson (NR) methods to handle the LF with various applications and LVDS structures [1,[3][4][5][6][7][8][9][10][11][12]. First, the GS method allows performing LF with complex variables by reducing the number of required calculations and avoiding the calculation of derivative equations.…”

“…This method has precision and quadratic convergence properties, and the calculation requires less iterations [7][8][9][10][11][12]. The power injection-based approach used in [7][8][9] corresponds to the traditional Newton-Raphson method, whereas the current injection-based approach used in [10,11] was in-Energies 2021, 14, 7600 2 of 19 vented later by [12]. The latter approach tends to perform better because of the linearity of its current injection equations.…”

“…The latter approach tends to perform better because of the linearity of its current injection equations. Overall, [7][8][9][10][11] solve LFs in unbalanced LVDSs, but [12] is used for balanced LVDSs.…”

“…The total processing time of the NR method will increase if it requires the inversion of high-dimensional matrices. Moreover, the NR method can perform poorly for ill-conditioned LVDSs [7][8][9][10][11][12].…”

“…There are some weaknesses of the aforementioned reviews [1,[4][5][6][7][8][9][10][11][12]. Determining the balanced LVDSs in [1,4,12] is inaccurate because the loading of any LVDS is inherently unbalanced due to the many unequal single-phase loads and non-symmetrical spacings between conductors.…”