Optimal power-flow solutions for power system planning

Since the development of sparsity techniques by Tinney, the power-flow program has become an extremely effective and often used tool for planning electric power networks. This program solves for the unknowns--voltages, phase angles, etc.--of a set of simultaneous nonlinear algebraic equations, the ac power-flow equations. The optimum power flow is likely to replace, in due time, the normal power flow in many important planning functions discussed in this paper. A number of mathematical programming techniques have recently been studied to solve the optimum power flow and several small-to-medium sized experimental programs have been written. The generalized reduced gradient (GRG), one of the most elegant nonlinear-programming techniques, is described and it is shown how it can be extended to solve optimum power flows of very high dimension (of the order of several thousand nodes). This extension consists mainly of using sparsity techniques in several of the solution steps of the GRG.