Optimal capacitor allocation in power systems

Abstract

Static capacitors are installed at specific locations in large power systems for minimising power losses and to ensure quality of the supply system. It has been found that the number of units in each capacitor bank can be considerably reduced by suitable choice of transformer tap settings and generator voltage magnitudes, thereby reducing the cost of installation of capacitors. This paper presents an efficient method for finding the optimal values for the number of units in each capacitor bank and their locations for the purpose of reducing power losses and for ensuring the quality of the supply system. This is accomplished by optimal allocation of all reactive power sources in the system in a coordinated fashion by varying the number of units in each capacitor bank and generator voltage magnitudes and transformer tap setting positions. The problem is formulated as an optimisation problem with the objective function representing the revenue resulting from reduction in power losses, taking into account the cost due to interest and depreciation on the static capacitor installation and the constraints based on physical and technical limitations on the system. The problem falls in the category of Mixed Integer Linear Programming (M.I.L.P.) and is solved by decomposing the problem into two smaller subproblems viz., a pure integer programming problem in binary variables and a linear programming problem. The solutions of these subproblems are coordinated to get the solution of the original problem. Very fast convergence is obtained by preventing zigzagging of the solution about the optimal point. All these result in considerable savings in computer time and memory. The proposed model has been applied to sample systems and the results presented and discussed.