Mathematical modelling of the optimal power dispatch problem
This thesis is concerned with the optimum operating conditions in a power system. The various aspects of the problem are modelled and solved as a number of optimization problems applying linear programming techniques. A generalized linear mathematical model has been developed for this purpose. A two-stage formulation is adopted to represent the various problems considered. In each case one power system quantity is chosen as an objective function to be optimized under a number of constraints and operating limits relating to the power system relationships and upper and lower bounds on the variables. These include constraints derived from the power flow equations and transmission network capacity. Limits are also imposed on bus voltage magnitudes and generator outputs. With the appropriate selection of the combination of objective function and constraints, the model can be used to minimize the overall generation cost, the total system losses or the total reactive power generation. The two-stage modelling of the problem also allows optimizing two different objective functions at the same time. Two such combinations are possible. In one case the total system losses can be minimized in the first stage and the generation cost minimized in the second stage. The other combination minimizes the total system reactive power output and the active power generation cost. Using the same model, the problem is then solved using decomposition techniques. These imply breaking up the original problem into a number of smaller problems that can be solved almost independently. The mathematical model has been developed in general terms and the associated computer program is written for a general power system. A sample system of medium size has been used to test the validity of the various aspects of the suggested model and produce numerical results.