Estimating the impact of uncertainty on optimum capacitor placement in wind‐integrated radial distribution system

Abstract

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".

Parameter-Free Improved Best-Worst Optimizers and Their Application for Simultaneous Distributed Generation and Shunt Capacitors Allocation in Distribution Networks

“…To optimize the technical indicators and operational cost of the RDN with simultaneous DG/SC allocation and network reconfiguration, Tolabi et al [22] introduced a thief and police algorithm (TPA). To minimize the annual operating cost for RDNs, in [23], Das and Malakar proposed the opposition-based competitive swarm optimizer (OCSO) to optimize the placement of SCs under the uncertain load and wind power generation conditions. In another study [24], Elmitwally and Eldesouky employed the modified simulated annealing (MSA) to optimize the allocation of SCs in a windintegrated distribution system to maximize the annual cost saving.…”

Assessment of effective reactive power reserve in power system networks under uncertainty applying coronavirus herd immunity optimizer (CHIO) for operation simulation

“…Authors in [29] have used a probabilistic linear transformation-based approach to solve an uncertain load flow problem. In [30] , optimal dispatch problem considering load uncertainty is addressed using the Probability Density Function (PDF) of the output random variables.…”

“…Variations in load demand and intermittent power generation from RES are major sources of uncertainties. Literature survey reveals that the modeling of demand uncertainty is mostly performed using probabilistic or stochastic approaches [26] , [27] , [28] , [29] , [30] . The load uncertainty modeling has been done either by considering only real power demand [26] , [27] , [28] or both real and reactive power demand [ 29 , 30 ].…”

HybridGA‐MCSbased optimization for distributed generation with dynamic voltage restorer planning in distribution networks

“…Bharti and Mala 15 addressed a new graph‐theoretic method for placement of reactive power compensator in radial distribution system using the “average electrical centrality index”. Das and Malakar 16 suggested the earliest effort toward the optimal allocation of the shunt capacitors in radial distribution system under uncertain load and wind power generation. Wang and Qiu 17 elaborated a novel optimum programming‐based algorithm that embeds the stochastic multi‐objective particle swarm optimization method and the deterministic interior point method to calculate the maximum wind power penetration level.…”