The Hydro-Thermal Optimal Power Flow Problem in Rectangular Coordinates

Abstract

This paper considers the formulation and computational solution of the optimal power flow problem in hydro-thermal electric system. The problem is formulated using the cartesian coordinate form of the power flow equations. Here the hydro generation is energy limited. As a result, a dynamic optimization problem involving the daily scheduling of the system is encountered. This dynamic optimal power flow problem requires the solution of a large scale set of non-linear simultaneous equations. In this paper, Newton's method is used to solve the problem. Due to the large scale nature of the problem, we have exploited the sparsity of the Jacobian and developed three different versions of the algorithms andhplementation of these versions have been detailed in this paper. In all cases, the algorithm has been successfully tested with six standard IEEE test systems varying in size from 5 bus to 118 bus. Computational results and the CPU times required by all of the methods are given. Results are compared with the results obtained by the earlier version using polar form for load flow constraints and it is shown that the sparse implementation using rectangular coordinates offers superior computational speed.