Power Flow Solution by Newton's Method

TLDR

Newton’s method efficiently solves the AC power flow problem, with memory and time scaling linearly with system size, and has become practical since 1961 through optimally ordered Gaussian elimination and specialized programming. The paper presents the equations, programming details, and large‑scale solution examples that implement Newton’s method. The method converges in only five iterations—roughly seven times faster than Gauss‑Seidel—and can solve 500–1000 node systems on 32 K‑byte core memory machines.

Abstract

The ac power flow problem can be solved efficiently by Newton's method. Only five iterations, each equivalent to about seven of the widely used Gauss-Seidel method, are required for an exact solution. Problem dependent memory and time requirements vary approximately in direct proportion to problem size. Problems of 500 to 1000 nodes can be solved on computers with 32K core memory. The method, introduced in 1961, has been made practical by optimally ordered Gaussian elimination and special programming techniques. Equations, programming details, and examples of solutions of large problems are given.