Considering uncertainty in the multi-objective stochastic capacitor allocation problem using a novel self adaptive modification approach

• Using Hong's 2m PEM scheme to consider uncertainty.
• Using Pareto optimality idea to handle conflicting targets.
• Using a novel self adaptive modification approach based on HBMO.

This paper suggests a new stochastic method based on point estimate method (PEM) to consider the uncertainty effects in the optimal capacitor placement problem. The proposed stochastic method will capture the uncertainty associated with the forecast errors of active and reactive loads as well as the cost function coefficients, concurrently. The objective functions to be investigated are the (1) active power losses, (2) voltage deviation and (3) total cost. Investigating the capacitor placement problem in the proposed stochastic framework will convert it to a complex, nonlinear, discrete multi-objective optimization problem which requires a powerful optimization tool to escape from the local optimal. In this regard, a novel self adaptive modification approach based on Honey Bee Mating Optimization (HBMO) algorithm is proposed to enhance the total ability of the algorithm effectively. During the optimization process, the proposed algorithm will find a set of Pareto optimal solutions which are stored in an external memory called repository. In addition, a fuzzy based clustering technique is used to control the size of the repository in the pre-determined values. The feasibility and effectiveness of the proposed method are assessed through 2 standard IEEE test systems.