| This thesis is the result of an investigation to assess the potential of the continuation method to solve the minimum cost optimal power flow problem. For this purpose, a restart homotopy continuation method algorithm is developed, which contains in essence two phases.;The solution in step (3) is used as an initial starting point in a continuation process, designed to track this solution to the optimal solution of the sub-problem defined in step (1). The tracking is accomplished via a predictor-corrector path following algorithm embodying certain special features, such that the solution accuracy can be improved to any desired degree through a flexible restart feature developed in this study. Within the tracking process only a subset (identified in step 2 above) of the whole set of controls require specific monitoring for break-points. This feature greatly reduces the computational burden. Termination of the first phase marks an operating point in which all controls are strictly feasible.;If, following the termination of the first phase, functional variables previously ignored prove to be within their respective bounds, the solution to the sub-problem becomes the solution to the complete optimal power flow problem. However, should functional variables violate their bounds the second phase of the algorithm is invoked, which in essence creates a new sub-problem by changing the roles of the control and violated dependent variables, such that the newly modified sub-problem maintains the same basic structure as its predecessor.;Phase I is invoked again at this juncture to solve the modified sub-problem. This process is repeated in cycles until the Kuhn-Tucker optimality conditions are satisfied. Simulations suggest that convergence is usually achieved within two or three Phase I/II cycles.;The pertinent steps of the first phase are as follows: (1) Create a sub-problem of the complete optimal power flow problem by relaxing boundary limits on all functional variables, namely voltages at load buses, line flows and reactive generations. (2) Parameterize a subset of the whole set of controls which comprises initially of tap-changers, phase-shifters, shunt controllers, and the voltages at generation buses. (3) Optimize the resulting problem.;This being a method unique to the minimum cost optimal power flow problem, numerous examples (up to 118 buses) have been tested and compared against the commercial code MINOS. The newly proposed algorithm appears to be faster and more reliable. |
