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A new Pareto multi-objective sine cosine algorithm for performance enhancement of radial distribution network by optimal allocation of distributed generators

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Abstract

The integration of distributed generators (DGs) is considered to be one of the best cost-effective techniques to improve the efficiency of power distribution systems in the recent deregulation caused by continuous load demand and transmission system contingency. In this perspective, a new multi-objective sine cosine algorithm is proposed for optimal DG allocation in radial distribution systems with minimization of total active power loss, maximization of voltage stability index, minimization of annual energy loss costs as well as pollutant gas emissions without violating the system and DG operating constraints. The proposed algorithm is enhanced by incorporating exponential variation of the conversion parameter and the self-adapting levy mutation to increase its performance during different iteration phases. The contradictory relationships among the objectives motivate the authors to generate an optimal Pareto set in order to help the network operators in taking fast appropriate decisions. The proposed approach is successfully applied to 33-bus and 69-bus distribution systems under four practical load conditions and is evaluated in different two-objective and three-objective optimization cases. The effectiveness of the algorithm is confirmed by comparing the results against other well-known multi-objective algorithms, namely, strength Pareto evolutionary algorithm 2, non-dominated sorting genetic algorithm II and multi-objective particle swarm optimization. The quality of Pareto fronts from different multi-objective algorithms is compared in terms of certain performance indicators, such as generational distance, spacing metric and spread metric (\({\varDelta }\)), and its statistical significance is verified by performing Wilcoxon signed rank test.

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Abbreviations

\(R_2, R_3\), \( R_4\) :

Random numbers

TAPL :

Total active power loss

npop :

Population size

NB :

Number of branches of the distribution system

\(\mu \) :

Fuzzy membership function

\(I_m\) :

Current in the line ‘m’ connected between mth and (m+1)th node

\(\mu ^b\) :

Fuzzy membership value of the optimum solution

DG:

Distributed generator

Nb :

Total number of nodes

PSO:

Particle swarm optimization

VSI :

Voltage stability index

ODGLS:

Optimal DG location and sizing

IVSI :

Inverse voltage stability index

GA:

Genetic algorithm

EC :

Energy loss cost ($/kWh)

ORCSA:

One rank cuckoo search algorithm

T :

Study period (h)

ABC:

Artificial bee colony

NDG :

Total number of DG units

DisCo:

Distribution company

\(C_{GP}\) :

Cost of DG generated power ($/kW)

EHSA:

Enhanced harmony search algorithm

NBPY :

Net benefit per year

MOPSO:

Multi-objective PSO

\(N_{PG}\) :

Number of different category of pollutant gases

NSGA II:

Non-dominated sorting GA II

\(E_i\) :

Emission intensity of ith pollutant gas

MODE:

Multi-objective differential evolution

\(TAP_{sub}\) :

Total active power drawn from substation (kW)

CODE:

Chaotic opposition differential evolution

\(P_{DG,i}\) :

Active power output of ith DG

MOCSA:

Multi-objective cuckoo search algorithm

\(P_{load,m}\) :

Active load demand of mth node

ENSGA II:

Enhanced NSGA II

LOC :

DG location

SPEA2:

Strength Pareto evolutionary algorithm 2

itr :

Current iteration

EDCP:

Exponential decreasing conversion parameter

\(itr_{max}\) :

Maximum number of iteration

SLM:

Self-adapting levy mutation

\(R_1\) :

Conversion parameter

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Authors and Affiliations

  1. Department of Electrical Engineering, International Institute of Information Technology, Bhubaneswar, Odisha, 751003, India

    Usharani Raut

  2. Department of Electrical Engineering, Centre for Advanced Post Graduate Studies, Biju Pattnaik University of Technology, Rourkela, Odisha, India

    Sivkumar Mishra

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  1. Usharani Raut
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Raut, U., Mishra, S. A new Pareto multi-objective sine cosine algorithm for performance enhancement of radial distribution network by optimal allocation of distributed generators. Evol. Intel. 14, 1635–1656 (2021). https://doi.org/10.1007/s12065-020-00428-2

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