Document Type : Research Articles


Department of Electrical and Computer Engineering, Hakim Sabzevari University,


This paper presents a new solution method to efficiently handle non-convexity stemmed from valve points in the economic load dispatch problem. The proposed solution technique integrates both the advantage of fast solution algorithms of linear programming and powerful solution techniques of nonlinear programming to find the global solution. In the first step of the proposed solution framework, non-convex terms are replaced by some linear segments and the new linear model solved by modern fats algorithms. In the second step, a nonlinear programming algorithm as a powerful local search algorithm solves the original non-convex model to improve the solution obtained in the previous step. By exploiting the main strength of linear and nonlinear programming algorithms, the proposed solution approach can quickly converge to nearly the global solution method. By experimental results on three test cases with different sizes, we show that the presented method outperforms the other algorithms published in the literature in the quality of the solution.


Main Subjects

[1] Conejo, Antonio J., and Luis Baringo, Power system
operations, Springer, 2018.

[2] Amjady N, Sharifzadeh H. Solution of non-convex
economic dispatch problem considering valve loading
effect by a new modified differential evolution algorithm.
Int J Electr Power Energy Syst 2010; 32(8):893–903.

[3] Hindi KS, Ghani MRA. Dynamic economic dispatch for
large scale power systems: a Lagrangian relaxation
approach. Int J Elect Power Energy Syst ,1991;13(1):51–6.

[4] Dike DO, Adinfono MI, Ogu G. Economic dispatch of
generated power using modified lambda-iteration method.
IOSR J Electr Electron Eng (IOSR-JEEE)
2013;3331:49–54 e-ISSN: 2278-1676, p-ISSN: 2320.

[5] Parikh J, Chattopadhyay D. A multi-area linear
programming approach for analysis of economic operation
of the Indian power system. IEEE Trans Power Syst
1996;11(February (1)):52–8.

[6] Reid GF, Hasdorff L. Economic dispatch using quadratic
programming. IEEE Trans Power Apparat Syst 1973;

[7] Amjady N, Sharifzadeh H., Security constrained optimal
power flow considering detailed generator model by a new
robust differential evolution algorithm, Electr Power Syst
Res, 2011, 81(2), 740-749.

[8] Farzaneh J, Keypour R, Ali Karsaz A, A novel fast
maximum power point tracking for a PV system using
hybrid PSO-ANFIS algorithm under partial shading
conditions, International Journal of Industrial Electronics,
Control and Optimization (IECO), 2019, 2(1), 47-58.

[9] Barati H, Shahsavari M, Simultaneous Optimal placement
and sizing of distributed generation resources and shunt
capacitors in radial distribution systems using Crow
Search Algorithm, International Journal of Industrial
Electronics, Control and Optimization (IECO), 2018, 1(1),

[10] Bikdeli Sh, Farshad M, Allocation of Fault Current
Limiters in Power Systems Considering Fault Current, Cost,
and Lost Power Indices Using Imperialist Competitive
Algorithm, International Journal of Industrial Electronics,
Control and Optimization (IECO), 2020, 3(1), 91-102

[11] B.R.Adarsh, T.Raghunathan, T.Jayabarathi, Xin-SheYang,
Economic dispatch using chaotic bat algorithm, Energy,
2016, 96(1), 666-675.

[12] Derafshi Beigvand S, Abdia H, La Scala M, Combined heat
and power economic dispatch problem using gravitational
search algorithm, Electr Power Syst Res, 2016, 133(1),

[13] CalinSecui. D, A modified Symbiotic Organisms Search
algorithm for large scale economic dispatch problem with
valve-point effects, Energy, 2016, 113(1), 366-384.

[14] Chen G, Ding X, Optimal economic dispatch with valve
loading effect using self-adaptive firefly algorithm, Applied
Intelligence, 2015, 42(2), 276-288.

[15] Basu M, Chowdhury A, Cuckoo search algorithm for
economic dispatch, Energy, 2013, 60(1), 99-108.

[16] AghayKabolia Abdullah S. Hr, Alqallafb. K, Solving
non-convex economic load dispatch problem via artificial
cooperative search algorithm, Expert Systems with
Applications, 2019, 128r(1), 14-27

[17] Gholamghasemi.M, Akbari E, Asadpoor M.B,Ghasemi M,
A new solution to the non-convex economic load dispatch
problems using phasor particle swarm optimization,
Applied Soft Computing, 2019, 79(1), 111-124.

[18] Silva Chavez J.C., Zamora-Mendez A, Yrena Heredia J.F,
Cardenas-Javier. R, A hybrid optimization framework for
the non-convex economic dispatch problem via
meta-heuristic algorithms, Electr Power Syst Res,2019,
77(1), 1-10.

[19] Victoire, T. Aruldoss Albert, and A. Ebenezer Jeyakumar.
"Hybrid PSO–SQP for economic dispatch with valve-point
effect." Electric Power Systems Research 71.1 (2004):

[20] Alsumait, J. S., J. K. Sykulski, and A. K. Al-Othman. "A
hybrid GA–PS–SQP method to solve power system
valve-point economic dispatch problems." Applied Energy
87.5 (2010): 1773-1781.


[22] Jeroslow, R. and Lowe, J., Modelling with integer variables.
Mathematical Programming Studies, 1984, 22,167–84.

[23] N. Sinha,R.Chakrabarti,P.K.Chattopadhyay, Evolutionary
programming techniques for economic load dispatch,
IEEETrans.Evol.Comput.,2003, 7(1), 83–94.

[24] Yanga XY, Sadat Hosseini S.S, Gandomi AH, Firefly
Algorithm for solving non-convex economic dispatch
problems with valve loading effect, Applied Soft
Computing , 2012, 12(1) ,1180–1186.

[25] Alsumait JS, Al-Othman AK, Sykulski JK, Application of
PS method to power system valve-point ELD, Electr Power
Energy Syst, 2007, 29(1),720–30.

[26] Dos Santos Coelho L,*, Cocco Mariani V, An efficient
cultural self-organizing migrating strategy for economic
dispatch optimization with valve-point effect, Energy
conversion and management, 2010, 51(1), 2580–2587.

[27] Pereira-Neto A, Unsihuay C, Saavedra OR, Efficient
evolutionary strategy optimization procedure to solve the
nonconvex economic dispatch problem with generator
constraints. IEE Proc Gen Transm Distrib

[28] Niu Q, Zhang H, Wanga X, Li K, Irwin G.B, A hybrid
harmony search with arithmetic crossover operation for
economic dispatch, . Int J Electr Power Energy Syst 2014;
62(1), 237–257.

[29] Kavousi-Fard A, Khosravi A, An intelligent θ-Modified Bat
Algorithm to solve the non-convex economic dispatch
problem considering practical constraints, Int J Electr
Power Energy Syst 2016; 82(1), 189–196.