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VLCI approach for optimal capacitors allocation in distribution networks based on hybrid PSOGSA optimization algorithm

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Abstract

The use of Shunt Capacitor Banks (SCB) as a convenient compensation source of reactive power in distribution networks has an efficient role in enhancement voltage profile, correction of power factor and minimizing the network power losses. In this regard, this article investigates the enforcement of a modern robust and effective hybridization of Particle Swarm Optimization besides a Gravitational Search Algorithm (PSOGSA) as an optimization mechanism for solving the problem of optimum SCB allocation with minimizing the annual operating cost and enhancement of the system power quality. Moreover, a new Voltage-Loss-Cost Index (VLCI) has been associated with the proposed optimization technique as an efficient objective function to increase the voltage levels, minimize active power losses and the annual operating cost of the grid. Furthermore, the implemented methodology is introduced in two stages. Firstly, the most appropriate buses for locating SCB are estimated using Loss Sensitivity Factor (LSF). Then, the hybrid PSOGSA optimization algorithm is structured to detect the optimum sitings of SCB and their sizing from the elected buses based on VLCI as the main objective function. The suggested mechanism has been applied on 33-bus besides 69-bus IEEE radial distribution networks. In addition, it is applied on a practicality case study of 111-bus Moscow region radial distribution network. With a view to making certain of the validation of the suggested methodology, the acquired results have been compared with other mechanisms and techniques. The numerical results demonstrated that the suggested optimization technique has superiority with high performance to deduce the optimum decision of SCB allocation for minimizing the network power losses, enhancing the profile of voltage level, and maximizing the net savings as compared to other different techniques.

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Abbreviations

SCB :

Shunt Capacitor Banks

N :

Number of branches

P ij , Q ij :

The active and reactive power that inflow over line “N”

\(P_{Lj}\), \(Q_{Lj}\) :

Active and reactive load that connected at node “j”

ɛ t :

Epsilon tolerance “error” = 0.000001

nb :

Number of buses

i :

1: nb (no. of buses)

\(P_{TLoss}\) :

Base total active power losses

\(T_{h}\) :

The time in hour

\(K_{e}\) :

The cost per kW h

\(E_{TLoss}\) :

Base total active energy losses

\(P_{SCB,TLoss}\) :

Total active power losses with SCB

\(E_{SCB,TLoss}\) :

Total active energy losses with SCB

\(P_{lineloss(ij)}\) :

The active power losses through branches

\(\nu_{it}^{ti}\) :

The velocity of particle “it”

ti :

Number of iteration

\(M_{ak}\) :

The active gravitational mass

\(\varepsilon\) :

A small constant of gravitational force in GSA

\(R_{lk} (t)\) :

Euclidian distance between two agents’ l and k

d :

Dimension of problem space

\(M_{l}\) :

The mass of object l during time “t”

w :

Random number within [0, 1]

d :

Dimension of problem space

\(\Delta Pl_{SCB}\) :

Power loss index

\(\Delta V_{Dev}\) :

Voltage deviation index

\(V_{1}\) :

Base per unit voltage

TOC :

Total operating cost with SCB

TOC base :

Base total operating cost without SCB

\(K_{SCB}\) :

The cost per kVAr

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

The value of reactive power installation at j bus (kVAr)

\(K_{b}\) :

The number of compensated buses

\(K_{f}\) :

The cost per installation

\(\Delta OC\) :

Cost index (net operating cost)

\(\lambda_{k}\) :

\(\lambda_{1}\), \(\lambda_{2}\), \(\lambda_{3}\) Parameter considered as weight factors of the proposed objective function

\(P_{j,eff}\), \(Q_{j,eff}\) :

Total effective active and reactive power supplied beyond bus “j”

\(LSF_{(ij)}\) :

Loss sensitivity factor

VSF :

Voltage sensitivity factor

c 1 and c 2 :

Weighting factors constants

G(t):

Gravitational constant at time “t”

\(M_{pl}\) :

Passive gravitational mass

G O and α :

Initial value and descending coefficient respectively

iter :

Current iteration

maxitere :

Maximum number of iterations

\(ac_{l} (t)\) :

Acceleration of all agents at time “t”

r 1 , r 2 :

Two random numbers (variables) generated in the range [0, 1]

r k :

Random number

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Authors and Affiliations

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

    Mohamed A. Tolba, Ahmed A. Zaki Diab & Vladimir N. Tulsky

  2. Nuclear Research Center, Egyptian Atomic Energy Authority, Cairo, Egypt

    Mohamed A. Tolba

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

    Ahmed A. Zaki Diab

  4. Electrical Power and Machines Department, Faculty of Engineering, Ain Shams University, Cairo, Egypt

    Almoataz Y. Abdelaziz

Authors
  1. Mohamed A. Tolba
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  2. Ahmed A. Zaki Diab
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  3. Vladimir N. Tulsky
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  4. Almoataz Y. Abdelaziz
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Correspondence to Mohamed A. Tolba.

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Tolba, M.A., Zaki Diab, A.A., Tulsky, V.N. et al. VLCI approach for optimal capacitors allocation in distribution networks based on hybrid PSOGSA optimization algorithm. Neural Comput & Applic 31, 3833–3850 (2019). https://doi.org/10.1007/s00521-017-3327-7

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