Optimal capacitor placement and sizing in unbalanced distribution systems with harmonics consideration using PSO

The benefits of shunt capacitor installation in distribution systems include reactive power support, power factor correction, release system capacity, loss reduction, and voltage improvement. Loss reduction and voltage profile improvement are investigated in this work. Studies have indicated that approximately 13% of generated power is consumed as loss at the distribution level. A portion of this loss can be reduced by the inclusion of shunt capacitors. Voltage profiles tend to drop below permissible operating limits. Installation of shunt capacitors brings voltage profiles back within those limits. The achievement of the aforementioned benefits among other benefits of shunt capacitor installation requires optimal placement and sizing of these capacitors.;The capacitor placement and sizing problem was formulated as a constrained nonlinear integer optimization problem, with both locations and ratings of shunt capacitor being discrete. Two objective functions are adopted in this study: real power loss function and cost function. The first objective is to minimize the total real power loss while imposing operating and power quality constraints. The second objective is to minimize the cost of the total real power loss and that of shunt capacitors to be installed while keeping the same constraints within the allowable limits. The constraints considered here are of two types: equality and inequality. Equality constraints are the nonlinear power flow equations. Inequality constraints are those constraints associated with voltage profiles, harmonic distortion levels, and shunt capacitors. Voltage profiles are to be kept within ±10% of the nominal voltage, while total harmonic distortions are to be maintained within 5% of the voltage value as recommended by the IEEE standard 519-1992.;The optimal capacitor placement and sizing problem is solved using particle swarm optimization (PSO). PSO is a population-based heuristic optimization technique developed in 1995 by Kennedy and Eberhart. A discrete version of PSO was combined with a radial distribution power flow algorithm (RDPF) to form a hybrid PSO algorithm (HPSO). The former was employed as a global optimizer to find the global optimal solution, while the latter was used to calculate the objective functions (e.g. total real power loss) and to check bus voltage limits. The proposed HPSO algorithm was tested on an IEEE 13-bus radial distribution system (13-Bus-RDS). The results obtained signify the robustness and effectiveness of the developed HPSO algorithm. To include the presence of harmonics, the developed HPSO was integrated with a harmonic power flow (HPF). The proposed (HPSO-HPF) based approach was tested on the same test system. The findings clearly demonstrate the necessity of including harmonics in optimal capacitor placement and sizing to avoid any possible problems associated with harmonics.;Due to the proliferation of electronic devices, more harmonics are being injected into distribution systems. Harmonics cause equipment to overheat and to fail. The addition of shunt capacitors may lead to high distortion levels causing damage to the electric equipment of both the electric utility and customers. As a result, shunt capacitors should be optimally located and rated, taking the presence of harmonics into account.