INTRODUCTION

The load-flow problem models the nonlinear relationships among bus power injections, power demands, and bus voltages and angles, with the network constants providing the circuit parameters. It is the heart of most system-planning studies and also the starting point for transient and dynamic stability studies. This section provides a formulation of the load-flow problem and its associated solution strategies. An understanding of the fundamentals of three-phase systems is assumed, including per-unit calculations, complex power relationships, and circuit-analysis techniques.

There are two popular numerical methods for solving the power-flow equations. These are the Gauss-Seidel (G-S) and the Newton-Raphson (N-R) Methods (Grainger and Stevenson, 1994; Elgerd, 1982; Glover and Sharma, 1994). The N-R method is superior to the G-S method because it exhibits a faster convergence characteristic. However, the N-R method suffers from the disadvantage that a flat start is not always possible since the solution at the beginning can oscillate without converging toward the solution. In order to avoid this problem, the load-flow solution is often started with a G-S algorithm followed by the N-R algorithm after a few iterations.

There is also an approximate but faster method for the load-flow solution. It is a variation of the N-R method, called the fast-decoupled method, which was introduced by Stott and Alsac (1974). We will not be covering this method in this section.

NOMENCLATURE