A general parametric optimal power flow

The objective of an Optimal Power Flow (OPF) algorithm is to find the steady-state operation point of a generation-transmission system which minimizes a pre-specified cost function and meets a set of operational and/or security constraints. OPF algorithms are among the tools present in many Energy Management Systems and their usefulness is increasingly being recognized by power utilities.This thesis presents an algorithm which uses the parameters existing in the OPF problem to find its solution. These parameters can be in the objective function or the equality or inequality constraints. This algorithm is applied to a parameterized OPF model built according to the following criteria: (i) when all parameters present in the model are relaxed from their given levels, a solution can be trivially found for this parameterized problem and (ii) when all parameters are returned to their original values, the parameterized model is equal to the original OPF. As the initially relaxed parameters are returned to their original values, they define a sequence of OPF problems which converge to the original one. The algorithm is designed to track the optimal solutions of these intermediate problems until the optimum of the original OPF. This tracking is made in a systematic manner. By using a binary search or a linear prediction method, the algorithm finds the maximum increment of the parameters which allow only one inequality to be fixed at its limit or to be released. The parameters are then adjusted to their new values, defining a new OPF problem with known optimal active feasible set. As a consequence, the optimal solution of this new problem can be easily found by solving the first order optimality conditions by Newton's method. In this way, the optimum is tracked from one active feasible set to the next until the parameters reach their original values.The parameterization permits the solution of the OPF problem for a fixed and variable load using the same mechanism described in the previous paragraph. As a result of this systematic tracking, the method is robust and able to provide a very good insight about the behaviour of the OPF solutions. In addition, the main difficulties encountered in solving the OPF problem are easily visualized and, in particular, the approach permits the differentiation of the potential causes for the failure of the tracking process, including the identification of unsolvable cases. The sensitivities of the optimal solution as a function of the parameters are also by-products of the method; including the Bus Incremental Costs and the System Incremental Cost as functions of the loads. The approach is also flexible enough to permit the simulation of line contingencies and of Flexible AC Transmission Systems (FACTS devices). The algorithm developed was tested in numerous networks with different objective functions and initializations and the results demonstrated the potential of this technique