A new analytical index for solving capacitor placement problem of distribution networks in bi‐level framework: Total loss index

Abstract

Capacitor allocation of distribution network is a complex and highdimensional optimization problem. As a result, most often, optimization techniques are entangled in local optima. To overcome this problem, this article presents a new bi-level framework for capacitor allocation: (a) at the first level, a new analytical index, named total loss index (TLI), has been proposed to identify high potential buses; and (b), at the second level, a metaheuristic optimization, crow search algorithm (CSA), has been applied for finding the best solution among the candidate solutions. TLI, which depends on the network topology, considers the sensitivity of the network losses to reactive power injection. The proposed framework (TLI + CSA) has been tested on 33-bus and 69-bus radial distribution networks. It is observed that reduction of search space will increase the probability of finding global solution so that (a) on 33-bus network, when three high potential buses are identified at the first level, the optimizer can find the global solution at the second level and (b) on 69-bus network, when six high potential buses are identified by TLI, CSA can find the global solution. It can be drawn that using the proposed TLI + CSA leads to finding more accurate results than the other methodologies. K E Y W O R D S bi-level optimization, capacitor placement, crow search algorithm, radial distribution network, total loss index 1 | INTRODUCTION Capacitor placement problem (CPP) is one of the most important issues for distribution network planners. CPP is defined as the optimal determination of location, type and size of shunt capacitors to reach different goals such as minimization of power losses, improvement of voltage profile and correction of power factor. These objectives are considered with respect to List of symbols and abbreviations: C c , Capacitor cost; C cI , Installation cost; C e , Average cost per unit of power loss ($/kWh); F, Objective function; I k , Current of branch k; LR i , Value of bus reduction at bus i; N B , Number of candidate buses; N L , Number of load buses; P i , Total effective active power supplied to bus i; P Loss , Total network active power loss; PF min , Lower limit of power factor; PF overall , Power factor; Q i , Capacitor bank rating at bus i; Q min Ci , Lower reactive power limit of compensated bus i; Q max Ci , Upper reactive power limit of compensated bus i; Q Ci , Reactive power injected to bus i; Q d, i , Reactive power demand at load bus i; R ij , Resistance between buses i and j; S Li , Actual line flow; S rated Li , Rated line capacity; T, Time period; jV i j, Voltage magnitude at bus i.