The unpredictable load variations and raising presence of wind farms have caused modern-day distribution system operation and planning extremely complex. This paper puts an earliest effort toward the optimal allocation of the shunt capacitors in radial distribution system (RDS) under uncertain load and wind power generation. The authors aim to minimize the annual operating cost (AOC) for RDS by deciding the optimum placements of shunt capacitors. Here, three-point estimate method is applied to estimate the uncertainties in the load demand and power output from the wind generator. The stochastic behavior of wind generators and load demands are modeled by using Weibull and normal distribution functions, respectively. An opposition-based competitive swarm optimizer (OCSO) algorithm is applied to minimize the AOC, and the optimization problem is solved for both probabilistic and deterministic approach. The Cornish-Fisher expansion is used in this work to provide more accurate probability distribution functions of AOC. Furthermore, the impact of VAr injection on AOC values and power losses are also studied in this work. Moreover, the results obtained from the OCSO algorithm are compared with the original competitive swarm optimizer results. The proposed problem is tested on 69 bus RDS with different loading conditions, and results are analyzed for each scenario.competitive swarm optimizer, load uncertainty, optimum capacitor allocation, point estimate method, wind generation uncertainty
| INTRODUCTIONShunt capacitors (SC) are being used in power distribution system (DS) conventionally to reduce power loss, improve the system voltage, and power factor. The power loss in DS is higher than that of the transmission system because of its List of Symbols and Abbreviations: V W , wind speed; P WT , power output of WGS; Pr, rated power output of WGS; Vr, rated wind speed; Vci, cut-in wind speed; Vco, cut-out wind speed;V w , mean of the wind speed; σ w , SD of the wind speed; P Li , real power demand at the bus "i"; Q Li , reactive power demand at the bus "i"; μ PLi , mean of real power demand; μ QLi , mean of reactive power demand; σ PLi , SD of real power demand; σ QLi , SD of reactive power demand; P μ loss , mean active power loss; Q μ ci, , mean VAr supply cost; nl, number of branches; cb, number of candidate bus; nb, number of load bus; P ss , real power of the substation bus; Q ss , reactive power of the substation bus; P μ w , mean power output from WGS; Q μ ci , mean VAr injection at bus "i"; P μ di , mean demands for real power at bus "i"; Q μ di , mean demands for reactive power at bus "i"; P μ lossj , mean real power loss at branch "j"; Q μ lossj , mean reactive power loss at branch "j"; Q cn , VAr injection at bus "n"; Q cn min , minimum values of Q cn ; Q cn max , maximum values of Q cn ; S li , complex power flow through line "i"; S li max , maximum line limit through line "i".