Optimal capacitor placement and sizing in distorted radial distribution systems part II: Problem formulation and solution method

The capacitor placement and sizing problem is formulated as a nonlinear integer optimization problem. The discrete nature of commercially available capacitor sizes is considered. This research investigates two objectives of the optimal placement and sizing of shunt capacitors. The first objective is to minimize the system real power loss while keeping voltage profiles and total harmonic distortions within permissible limits. The second objective is to minimize the cost of real power losses and that of shunt capacitor installation while satisfying the same constraints. The constraints considered are of two types, equality constraints and inequality constraints. The equality constraints are the nonlinear power flow equations, while the inequality constraints are those associated with the bus voltages, harmonic distortion levels, and shunt capacitors. The optimal capacitor placement and sizing problem is tackled by particle swarm optimization (PSO).