Neural Computing and Applications

, Volume 31, Issue 12, pp 8787–8806 | Cite as

Single- and multi-objective optimal power flow frameworks using Jaya optimization technique

  • Salma Abd El-Sattar
  • Salah Kamel
  • Ragab A. El Sehiemy
  • Francisco JuradoEmail author
  • Juan Yu
Original Article


Solution of optimal power flow (OPF) problem is very important for power system operation, planning and energy management. OPF analysis aims to find the optimal solution of system nonlinear algebraic equations with satisfying operational constraints. In this paper, a new and efficient technique called Jaya optimizer is comprehensively applied to solve the OPF problem in power systems. Jaya optimization algorithm is characterized with the movement toward the best solution and avoiding the trapping into local optima. Different frameworks are developed for solving the single- and multi-objective (two- to five-objective functions) OPF problems. These frameworks are developed to achieve the following objective functions: fuel cost minimization, voltage deviation minimization, voltage stability enhancement, power loss minimization and emission minimization. In the developed multi-objective OPF framework, Pareto concept is combined with Jaya optimization algorithm to obtain a set of non-dominated solutions, and then the best compromise solution is extracted using fuzzy set theory. The developed OPF frameworks are validate using two standard IEEE test systems with 23 studied cases. The results prove the effectiveness and superiority of the developed OPF frameworks compared with other well-known optimization algorithms.


Optimal power flow Jaya optimizer Pareto front Single- and multi-objective functions Voltage stability enhancement Power loss minimization Voltage profile improvement 

List of symbols


Objective function


Number of objectives


Equality constraints


Number of equality constraints


Inequality constraints


Number of inequality constraints


Vector of control variables


State vector of dependent variables


Generated active and reactive powers, respectively


Generation bus voltage


Reactive power output of VAR source


Transformer tap ratio


Load bus voltage


Apparent power flow


Number of generators


Number of regulating transformers


Number of existing VAR sources


Number of load buses


Number of transmission lines


Number of buses


Active and reactive load demand, respectively

G, B

Conductance and substance of line, respectively

\(\delta_{j} , \delta_{i}\)

Voltage angles of buses i and j, respectively

\(a_{i} ,b_{i} ,c_{i}\)

Coefficients of ith generator cost coefficients

\(\gamma_{i} ,\beta_{i} ,\alpha_{i} ,\zeta_{i} ,\lambda_{i}\)

Emission coefficients of ith unit


Value of jth variable for the kth candidate solution at ith iteration


Updated value of \(X_{j,k,i}\)


The best solution of variable j


The worst solution of variable j

\(r_{1} ,r_{2}\)

Random values in interval [0, 1]

\(f_{j}^{\hbox{min} } ,f_{j}^{\hbox{max} }\)

Lower and upper bounds of ith objective function, respectively

\(\lambda_{\text{p}} ,\lambda_{\text{v}} ,\lambda_{\text{Q}} ,\lambda_{\text{s}}\)

Penalty factors


Non-dominated solutions number



The authors gratefully acknowledge the contribution of the NSFC (China)-ASRT (Egypt) Joint Research Fund, Project No. 51861145406, for providing partial research funding to the work reported in this research.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electrical Engineering, Faculty of EngineeringAswan UniversityAswânEgypt
  2. 2.State Key Laboratory of Power Transmission Equipment and System Security and New TechnologyChongqing UniversityChongqingChina
  3. 3.Department of Electrical Engineering, Faculty of EngineeringUniversity of KafrelsheikhKafrelsheikhEgypt
  4. 4.Department of Electrical Engineering, EPS LinaresUniversity of JaénJaénSpain

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