The minimum cost optimal power flow problem solved via the restart homotopy continuation method

The potential of the continuation method to solve the minimum-cost optimal power flow (OPF) problem is assessed. Initially, the complete OPF problem is simplified by creating a subproblem in which limits on functional variables are ignored. A restart homotopy continuation algorithm is developed that solves the sub-problem by manipulating the control variables to satisfy the optimality conditions of a family of relaxed subproblems which converge to the desired solution. Particular features of this minimum-cost problem are exploited to make the algorithm very efficient. Numerous examples are tested using the algorithm on systems up to 118 buses, 179 transmission lines, 68 controls, and 62 generation units. The commercial code MINOS (Version 4.0) is used to evaluate the performance of the algorithm and verify the results. The algorithm appears to be faster and more reliable