Direct approach for optimal allocation of multiple capacitors in distribution systems using novel analytical closed-form expressions

In this paper, novel and efficient analytical closed-form expressions are proposed for the optimal allocation of multiple capacitors in distribution systems to maximize the total cost reduction (CR) while considering power losses. The proposed expressions are novel since they can directly solve the allocation problem without requiring iterative processes or optimization algorithms. Specifically, two analytical closed-form expressions are introduced to determine the optimal number, locations, and sizes of multiple capacitors. The first analytical expression computes directly the optimal sizes of multiple capacitors where it is employed for the optimal sizing of capacitors for all possible combinations of locations. In turn, the best combination is then assigned by using a second analytical expression which directly evaluates all the combinations in terms of their contribution in CR. Unlike the existing methods/expressions that utilize sensitivity factors or optimize each capacitor individually, the proposed analytical closed-form expressions involve a unified mathematical model for multiple capacitors. The proposed direct approach is tested using a 69-bus distribution system. The accuracy and efficacy of the proposed analytical closed-form expressions are verified by comparisons with existing methods and intensive simulations of various allocation scenarios.