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Optimal Sizing and Placement of Capacitors in Radial Distribution Systems Based on Grey Wolf, Dragonfly and Moth–Flame Optimization Algorithms

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Abstract

The applications of grey wolf (GWO), dragonfly (DFO) and moth–flame (MFA) optimization techniques for optimum sitting of capacitors in various radial distribution systems (RDSs) are presented. The loss sensitivity factor is applied to determine the most candidate buses. Then, each optimization technique is utilized to find optimum placements and sizes of capacitors for determined Buses. In this study, 33-, 69- and 118-bus RDSs are considered for validating the effectiveness and efficiency of studied algorithms. The convergence performance is evaluated for tested RDSs using MATLAB/Simulink software. The obtained results confirm that GWO, DFO and MFA offer accurate convergence to the global minimum point of the objective function with high convergence speed. The ability of the studied techniques for enhancing voltage profiles with considered distribution systems is achieved. Finally, a comparison study between each studied technique with each other and with other techniques like PSO, fuzzy-GA, heuristic, DSA, TLBO, DA-PS, FPA and CSA has been carried out. The parameters of the comparison include: efficiency, execution time, the speed of convergence, minimizing total cost and increasing net savings. The results of comparison indicated that GWO-based algorithm has accurate convergence to optimal location and size of capacitor banks. In addition, it has the best performance in comparison with other techniques.

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Abbreviations

\({\text{Cost}}\_{\text{fun}}\) :

Objective function

\(P_{\text{Loss}}^{T}\) :

Power loss

J :

Number of candidate buses

\(P_{{{\text{eff}}\left( j \right)}}\) :

Total effective active power

LSF:

Loss sensitivity factors

\({\text{PF}}_{\text{overall}}\) :

Overall power factor

\(Q_{\text{Load}}^{T}\) :

Total load reactive power

N :

Number of lines

\(K_{\text{p}}\) :

Equivalent cost/unit of power loss

\(K_{j}^{\text{c}}\) :

Annual capacitor cost in ($/kW-year)

\(Q_{j}^{\text{c}}\) :

Shunt capacitor size

\(Q_{{{\text{eff}}\left( j \right)}}\) :

Total effective reactive power

VSF:

Voltage sensitivity factor

S :

Apparent power

\(Q_{c}^{\hbox{max} }\) :

Maximum capacitor size

\(R + jX\) :

Impedance

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Authors and Affiliations

  1. College of Engineering at Wadi Addawaser, Prince Sattam Bin Abdulaziz University, Al-Kharj, Kingdom of Saudi Arabia

    Hegazy Rezk

  2. Electrical Engineering Department, Faculty of Engineering, Minia University, Minia, Egypt

    Ahmed A. Zaki Diab & Hegazy Rezk

  3. Electrical Power Systems Department, National Research University, “MPEI”, Moscow, Russian Federation

    Ahmed A. Zaki Diab

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  1. Ahmed A. Zaki Diab
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  2. Hegazy Rezk
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Correspondence to Ahmed A. Zaki Diab.

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Diab, A.A.Z., Rezk, H. Optimal Sizing and Placement of Capacitors in Radial Distribution Systems Based on Grey Wolf, Dragonfly and Moth–Flame Optimization Algorithms. Iran J Sci Technol Trans Electr Eng 43, 77–96 (2019). https://doi.org/10.1007/s40998-018-0071-7

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