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Improved social spider optimization algorithm for optimal reactive power dispatch problem with different objectives

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Abstract

This paper proposes an improved social spider optimization (ISSO) for achieving different objectives of optimal reactive power dispatch (ORPD). The proposed ISSO method is developed by applying two modifications on new solution generation process. The proposed method uses only one modified equation for producing the first new solution generation and the second new solution generation while the standard SSO uses two equations for each process. The improvement in the proposed method is confirmed by solving benchmark optimization functions, IEEE 30-bus system and IEEE 118-bus system. Obtained results from ISSO are compared to those from other existing methods available in other studies together with other popular and state-of-the-art methods, which are implemented in the work. As compared to standard SSO for application to ORPD problem, ISSO can reduce the number of computation steps and one control parameter, and shorten simulation time. About the result comparisons with SSO and other remaining methods, ISSO can find more favorable solutions with higher quality and ISSO can stabilize solution search function with approximately all trial runs finding lower value of fitness. Furthermore, the strong search ability of ISSO is also indicated because it uses less value for control parameters. As a result, the proposed ISSO method can be a very effective optimization tool for dealing with the ORPD problem.

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Abbreviations

HI:

The highest iteration

N bus :

Number of buses in the considered power system

N c :

Number of VAR compensator buses

Nfs, Nms :

Number of females and males, respectively

N G :

Number of generator buses

N line :

Number of transmission lines

N load :

Number of load buses in the considered power system

N pop :

Population size or the sum of males and females

N t :

Number of buses with transformer

Pdi, Qdi :

Real and reactive power required by load of bus i

P m :

Movement probability of female spiders

Q ci :

Reactive power generation of VAR compensator of bus i

Qci,min, Qci,max :

Lower and upper limitations of reactive power generation of VAR compensator at bus i

QGi,min, QGi,max :

Lower and upper limitations of reactive power generation of generator at bus i, respectively

RNf :

Random number within 0 and 1 for female spider f

S l,max :

Maximum apparent power flow of line l

Ti,min, Ti,max :

Lower and upper limitations of tap changer of transformer at bus i

VGi,min, VGi,max :

Lower and upper limitations of voltage magnitude of generator at bus i, respectively

Vi, Vj :

Voltage magnitude of buses i and j

Vloadi,min, Vloadi,max :

Lower and upper limitations of voltage magnitude of the load at bus i, respectively

X fs,f :

Position of female spider f corresponding to a solution

X Gbest :

Position of the best spider corresponding to the best solution

X ms,m :

Position of male spider m corresponding to a solution

ABCA:

Artificial bee colony algorithm

ACO:

Ant colony optimization

AGA:

Adaptive genetic algorithm

ALO:

Ant lion optimizer

ASCSA:

Adaptive selective cuckoo search algorithm

BA:

Bat algorithm

BB–BCA:

Big bang–big crunch algorithm

BBDE:

Bare-bones differential evolution

BBPSO:

Bare-bones particle swarm optimization

BOFs:

Benchmark optimization functions

BRCFA:

Binary real-coded firefly algorithm

BTSA:

Backtracking search algorithm

CABC-DE:

Hybrid chaotic artificial bee colony differential evolution

CKHA:

Chaotic krill herd algorithm

CLPSO:

Comprehensive learning particle swarm optimization

COA:

Coyote optimization algorithm

CSA:

Cuckoo search algorithm

CSSA:

Charged system search algorithm

DE:

Differential evolution

DE–AS:

Differential evolution and ant system

DPM:

Dynamic programming method

DSA:

Differential search algorithm

EMA:

Exchange market algorithm

EP:

Evolution programming

FA:

Firefly algorithm

FPA:

Flower pollination algorithm

GBBWCA:

Gaussian bare-bones water cycle algorithm

GBTLBO:

Gaussian bare-bones teaching learning-based optimization

GSA:

Gravitational search algorithm

GSA-CSS:

Gravitational search algorithm with original selection

GSA-NHCM:

Gravitational search algorithm with new constraint handling method

GWO:

Gray wolf optimizer

GWPSO:

Particle swarm optimization with inertia weight

HFA-NMS:

Hybrid Nelder–Mead simplex-based firefly algorithm

HFVNS:

Hybrid stochastic fractal search and variable neighborhood search

HICTS:

Hybrid imperialist competitive algorithm and tabu search

HISGA:

Hybrid interior search algorithm and genetic algorithm

HKAGA:

Hybrid Keshtel algorithm and genetic algorithm

HKASA:

Hybrid Keshtel algorithm and simulated annealing

HLGA:

Hybrid loop genetic algorithm

HMA:

Hybrid metaheuristic algorithm

HMPSO:

Hybrid multi-agent particle swarm optimization

HPSO–ICA:

Hybrid particle swarm optimization and imperialist competitive technique method

HPSO–TS:

Hybrid particle swarm optimization and tabu search

HRDSA:

Hybrid red deer algorithm and simulated annealing

HSA:

Harmony search algorithm

HSFSA:

Hybrid stochastic fractal search and simulated annealing

HSSSA:

Hybrid salp swarm algorithm and simulated annealing

HWPSO:

Hybrid whale optimization algorithm and particle swarm optimization

HWWGA:

Hybrid water wave optimizer and genetic algorithm

ICBO:

Improved colliding bodies optimization

IDA:

Improved deterministic algorithm

IMA:

Improved metaheuristic algorithm

IPG-PSO:

Improved pseudo-gradient search-particle swarm optimization

IPM:

Interior point method

IQP:

Improved quadratic programming

ISA:

Interior search algorithm

ISSO:

Improved social spider optimization

JA:

Jaya algorithm

KA:

Keshtel algorithm

LCA:

League championship algorithm

LDGWPSO:

Particle swarm optimization with linearly decreasing inertia weight

LPM:

Linear programming approach

MDE:

Modified differential evolution

MFO:

Moth flame optimization

MLPM:

Mixed-integer linear programming

MNM:

Modified Newton method

MORDA:

Multi-objective red deer algorithm

MPSO:

Modified particle swarm optimization

MSSA:

Modified salp swarm algorithm

MSSO:

Modified social spider optimization

MTLT–DDE:

Modified teaching learning technique and double differential evolution algorithm

NMSFLA:

Shuffled frog leaping algorithm and Nelder–Mead

ORCSA:

One rank cuckoo search algorithm

PG-PSO:

Particle swarm optimization with pseudo-gradient search

PGSWT-PSO:

Particle swarm optimization with stochastic weight trade-off and pseudo-gradient search

PSO:

Particle swarm optimization

PSO-ALC:

Particle swarm optimization with an aging leader and challengers

PSO-CF:

Particle swarm optimization with constriction factor

PSO-GT:

Particle swarm optimization with graph theory

PSO-TVAC:

Particle swarm optimization with time-varying acceleration coefficients

PSO-TVIW:

Particle swarm optimization with time-varying inertia weight

QODE:

Quasi-oppositional differential evolution

QOTLBO:

Quasi-oppositional teaching learning-based optimization

RCGA:

Real-coded genetic algorithm

RDA:

Red deer algorithm

RSGA:

Genetic algorithm with rank selection technique

SARCGA:

Self-adaptive real-coded genetic algorithm

SEO:

Social engineering optimizer

SFOA:

Sunflower optimization algorithm

SFS:

Stochastic fractal search

SGA:

Specialized genetic algorithm

SPSO-TVAC:

Particle swarm optimization with time-varying acceleration coefficients

SPSO-TVAC:

Particle swarm optimization with self-organization and time-varying acceleration coefficients

SSA:

Salp swarm algorithm

SSO:

Social spider optimization

SWT-PSO:

Particle swarm optimization with stochastic weight trade-off

TVAC:

Time-varying acceleration coefficients

WOA:

Whale optimization algorithm

WWO:

Water wave optimizer

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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. Department of Power Systems, Ho Chi Minh City University of Technology, VNU-HCM, Ho Chi Minh City, Vietnam

    Dieu Ngoc Vo

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  1. Thang Trung Nguyen
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  2. Dieu Ngoc Vo
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Appendix

Appendix

See Tables 14, 15, 16 and 17.

Table 14 Optimal solutions obtained by the proposed method for Case 3
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Table 15 Optimal solution obtained by ISSO for the IEEE 118-bus power system with minimization of power loss
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Table 16 Optimal solution obtained by ISSO for the IEEE 118-bus power system with minimization of voltage deviation
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Table 17 Optimal solution obtained by ISSO for the IEEE 118-bus power system with minimization of L index
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Nguyen, T.T., Vo, D.N. Improved social spider optimization algorithm for optimal reactive power dispatch problem with different objectives. Neural Comput & Applic 32, 5919–5950 (2020). https://doi.org/10.1007/s00521-019-04073-4

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