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An improved equilibrium optimizer for optimal placement of photovoltaic systems in radial distribution power networks

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Abstract

This paper proposes an improved equilibrium optimizer (IEO) for selecting the most suitable location and the most effective size of photovoltaic systems (PVSs) in radial distribution power networks (RDPNs). The objective of the study is to reduce the total active power loss on all distribution lines of RDPNs while constraints regarding node voltage limits, branch current limits and active and reactive power balance must be satisfied exactly. IEO is first developed in the paper by modifying the newly generated solution mechanism of the conventional equilibrium optimizer (EO). In addition to the proposed IEO method and EO, two previously published methods including modified equilibrium optimizer (MEO) and adaptive equilibrium optimizer (AEO) are also implemented for three study cases with one, two and three PVSs placed in the IEEE 33-node and 85-node RDPNs. Compared to the base systems, the proposed IEO can reach the loss reduction with 65.5% for the IEEE 33-node RDPN and 52.96% for the IEEE 85-node RDPN. Total loss, loss reduction and computation speed comparisons indicate that the proposed IEO outperforms EO, MEO, AEO and other previously published methods shown in the literature for approximately all study cases. As a result, it concludes that the proposed IEO is a favorable optimization algorithm applied to the problem of PVSs placement in RDPNs.

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Abbreviations

I o,n :

Current of the nth branch

R n, X n :

Resistance and reactance of the nth branch

N :

Number of branches

U o,m :

Operating voltage at the mth node

M :

Number of nodes

U ll, U ul :

Lower limit and upper limit of load node voltage

I max,n :

Maximum current of the nth branch

\(P_{PVS}^{min} ,\,P_{PVS}^{max}\) :

The lowest and highest active power generation of each photovoltaic system

D min, D max :

Lower limit and upper limit of solutions

D best1 :

The best solution

D best2, D best3, D best4 :

The second, third and fourth best solutions

D mean :

Mean solution of the first four best solutions

D oc :

Solution set with the first four best and the mean solutions

D e :

A randomly picked solution from the solution set Doc

z 1, z 2 :

Random numbers within 1 and 0

D i :

The ith solution

\(D_{i}^{new}\) :

The ith new solution

F i :

Fitness function of the ith solution

\(F_{i}^{new}\) :

Fitness function of the ith new solution

NI, NI max :

Current iteration and the maximum iteration number

x kmin , x kmax :

The minimum and maximum values of the adjustment variable xk

x ki :

The kth control variable in the ith solution

PVS:

Photovoltaic system

PVSs:

Photovoltaic systems

TRPLs:

Total reactive power losses

TAPLs:

Total active power losses

RDPNs:

Radial distribution power networks

DPNs:

Distribution power networks

RDPN:

Radial distribution power network

DPN:

Distribution power network

DPNs:

Distribution power networks

GSA:

Gravitational search algorithm

LSF:

Loss sensitivity factor-based method

GWO:

Grey wolf optimizer

BA:

Bat algorithm

SOA:

Squirrel optimization algorithm

WDA:

Wind-driven algorithm

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Acknowledgements

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 102.02-2020.07

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Authors and Affiliations

  1. Power System Optimization Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Thang Trung Nguyen

  2. Faculty of Electrical Engineering Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam

    Thuan Thanh Nguyen

  3. Department of Electrical Engineering, University of Science and Technology—The University of DaNang, 54 Nguyen Luong Bang Street, LienChieu District, DaNang City, 59000, Vietnam

    Minh Quan Duong

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Nguyen, T.T., Nguyen, T.T. & Duong, M.Q. An improved equilibrium optimizer for optimal placement of photovoltaic systems in radial distribution power networks. Neural Comput & Applic 34, 6119–6148 (2022). https://doi.org/10.1007/s00521-021-06779-w

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