Self-Adaptive Differential Evolution Based Power Economic Dispatch of Generators with Valve-Point Effects and Multiple Fuel Options
This paper presents the solution of power economic dispatch (PED) problem of generating units with valve point effects and multiple fuel options using Self-Adaptive Differential Evolution (SDE) algorithm. The global optimal solution by mathematical approaches becomes difficult for the realistic PED problem in power systems. The Differential Evolution (DE) algorithm is found to be a powerful evolutionary algorithm for global optimization in many real problems. In this paper the key parameters of control in DE algorithm such as the crossover constant CR and weight applied to random differential F are self-adapted. The PED problem formulation takes into consideration of nonsmooth fuel cost function due to valve point effects and multi fuel options of generator. The proposed approach has been examined and tested with the numerical results of PED problems with thirteen-generation units including valve-point effects, ten-generation units with multiple fuel options neglecting valve-point effects and ten-generation units including valve-point effects and multiple fuel options. The test results are promising and show the effectiveness of proposed approach for solving PED problems.
[1] D.C.Walters, G.B.Sheble, "Genetic algorithm solution of economic
dispatch with valve-point loadings," IEEE Trans. Power Systems, vol. 8,
no. 3, 1993, pp.1325-1331.
[2] N.Sinha, R.chakrabarti, P.K.Chattopadhyay "Evolutionary programming
techniques for economic load dispatch," IEEE Trans. on Evolutionary
Computation, vol. 7, no. 1, 2003, pp. 83-94.
[3] H.T.Yang, P.C.Yang, C.L.Huang "Evolutionary programming based
economic dispatch for units with non-smooth incremental fuel cost
function,". IEEE Trans. on Power Systems vol.11, no.1, 1996, pp.112- 118.
[4] K.P.Wong, Y.W.Wong "Genetic and genetic/simulated-annealing
approaches to economic dispatch," IEE proceedings Generation,
Transmission and Distribution, vol. 141, no. 5, 1994, pp. 507-513.
[5] Zwe-Lee Gaing "Particle swarm optimization to solving the economic
dispatch considering the generator constraints," IEEE Trans. on Power
Systems, vol. 18, no. 3, 2003, pp. 1187-1195.
[6] T.A.A.Victoire, A.E.Jeyakumar "Discussion of Particle swarm
optimization to solving the economic dispatch considering the generator
constraints," IEEE Trans. on Power Systems, vol.19, no. 4, 2004, pp.
2121-2123.
[7] D.Bhagwan Das, C.Patvardhan, "Solution of economic load dispatch
using real coded hybrid stochastic search," Electrical Power Energy
System, vol. 21, 1999, pp. 165-170.
[8] S.Khamsawang, C.Booseng, S.Pothiya "Solving the economic dispatch
problem with Tabu search algorithm," IEEE Int. Conf. on Ind.
Technology vol. 1, 2002, pp. 108-112.
[9] D.B.Fogel "Evolutionary computation: Toward a new philosophy of
machine intelligence," 2nd ed. Piscataway, NJ: IEEE Press, 2000.
[10] D.Bhagwan Das, C.Patvardhan "Solution of economic load dispatch
using real coded Hybrid stochastic search," Electrical Power Energy
System, vol. 22, 1999, pp. 165-170.
[11] P.Attaviriyanupap, H.Kita, E.Tanaka, J.Hasegawa "A hybrid EP and
SQP for dynamic economic dispatch with nonsmooth incremental fuel
cost function," IEEE Trans. Power Systems, vol. 17, no. 2, 2002, pp.
411-416.
[12] W.M.Lin, F.S.Cheng, M.T.Tsay "Nonconvex economic dispatch by
integrated artificial intelligence," IEEE Trans. Power Systems, vol. 16,
no. 2, 2001, pp. 167-177.
[13] T.Aruldoss Albert Victoria, A.Ebenezer Jeyakumar "Hybrid PSO-SQP
for economic dispatch with valve-point effect," Electric Power System
Research, vol. 71, 2004, pp. 51-59.
[14] C.E.Lin and G.L.Vivani "Hierarchical economic dispatch for piecewise
quadratic cost function," IEEE Trans. on Power App. Syst. Vol. 103, no.
6, 1984, pp. 1170-1175.
[15] J.H.Park, Y.S.Kim, I.K.Ecom, K.Y.Lee "Economic load dispatch for
piecewise quadratic cost function using Hopfield neural network," IEEE
Trans. on Power Systems, vol. 8, no.3, 1993, pp. 1030-1038.
[16] K.Y.Lee, A.Sode-Yome, and J.H.Park "Adaptive Hopfield neural
network for Economic load dispatch," IEEE Trans. on Power Systems,
vol.13, no. 2, 1998, pp. 519-526.
[17] S.Baskar, P.Subbaraj, and M.V.C.Rao "Hybrid real coded genetic
algorithm solution to economic dispatch problem," Paragmon,
Computers and Electrical Engineering, vol. 29, 2003, pp. 407-419.
[18] Chao-Lung Chiang "Improved genetic algorithm for power economic
dispatch of units with valve-point effects and multiple fuels," IEEE
Trans. Power Systems, vol.20, no. 4, 2005, pp.1690-1699.
[19] R.Storn, K.Price, Differential evolution - A simple and efficient heuristic
for global optimization over continuous space. Journal of Global
Optimization, vol. 11, 1997, pp. 341-359.
[20] Wood AJ, Woollenberg BF. Power Generation Operation and Control.
2nd ed. New York; Wiley; 199
[1] D.C.Walters, G.B.Sheble, "Genetic algorithm solution of economic
dispatch with valve-point loadings," IEEE Trans. Power Systems, vol. 8,
no. 3, 1993, pp.1325-1331.
[2] N.Sinha, R.chakrabarti, P.K.Chattopadhyay "Evolutionary programming
techniques for economic load dispatch," IEEE Trans. on Evolutionary
Computation, vol. 7, no. 1, 2003, pp. 83-94.
[3] H.T.Yang, P.C.Yang, C.L.Huang "Evolutionary programming based
economic dispatch for units with non-smooth incremental fuel cost
function,". IEEE Trans. on Power Systems vol.11, no.1, 1996, pp.112- 118.
[4] K.P.Wong, Y.W.Wong "Genetic and genetic/simulated-annealing
approaches to economic dispatch," IEE proceedings Generation,
Transmission and Distribution, vol. 141, no. 5, 1994, pp. 507-513.
[5] Zwe-Lee Gaing "Particle swarm optimization to solving the economic
dispatch considering the generator constraints," IEEE Trans. on Power
Systems, vol. 18, no. 3, 2003, pp. 1187-1195.
[6] T.A.A.Victoire, A.E.Jeyakumar "Discussion of Particle swarm
optimization to solving the economic dispatch considering the generator
constraints," IEEE Trans. on Power Systems, vol.19, no. 4, 2004, pp.
2121-2123.
[7] D.Bhagwan Das, C.Patvardhan, "Solution of economic load dispatch
using real coded hybrid stochastic search," Electrical Power Energy
System, vol. 21, 1999, pp. 165-170.
[8] S.Khamsawang, C.Booseng, S.Pothiya "Solving the economic dispatch
problem with Tabu search algorithm," IEEE Int. Conf. on Ind.
Technology vol. 1, 2002, pp. 108-112.
[9] D.B.Fogel "Evolutionary computation: Toward a new philosophy of
machine intelligence," 2nd ed. Piscataway, NJ: IEEE Press, 2000.
[10] D.Bhagwan Das, C.Patvardhan "Solution of economic load dispatch
using real coded Hybrid stochastic search," Electrical Power Energy
System, vol. 22, 1999, pp. 165-170.
[11] P.Attaviriyanupap, H.Kita, E.Tanaka, J.Hasegawa "A hybrid EP and
SQP for dynamic economic dispatch with nonsmooth incremental fuel
cost function," IEEE Trans. Power Systems, vol. 17, no. 2, 2002, pp.
411-416.
[12] W.M.Lin, F.S.Cheng, M.T.Tsay "Nonconvex economic dispatch by
integrated artificial intelligence," IEEE Trans. Power Systems, vol. 16,
no. 2, 2001, pp. 167-177.
[13] T.Aruldoss Albert Victoria, A.Ebenezer Jeyakumar "Hybrid PSO-SQP
for economic dispatch with valve-point effect," Electric Power System
Research, vol. 71, 2004, pp. 51-59.
[14] C.E.Lin and G.L.Vivani "Hierarchical economic dispatch for piecewise
quadratic cost function," IEEE Trans. on Power App. Syst. Vol. 103, no.
6, 1984, pp. 1170-1175.
[15] J.H.Park, Y.S.Kim, I.K.Ecom, K.Y.Lee "Economic load dispatch for
piecewise quadratic cost function using Hopfield neural network," IEEE
Trans. on Power Systems, vol. 8, no.3, 1993, pp. 1030-1038.
[16] K.Y.Lee, A.Sode-Yome, and J.H.Park "Adaptive Hopfield neural
network for Economic load dispatch," IEEE Trans. on Power Systems,
vol.13, no. 2, 1998, pp. 519-526.
[17] S.Baskar, P.Subbaraj, and M.V.C.Rao "Hybrid real coded genetic
algorithm solution to economic dispatch problem," Paragmon,
Computers and Electrical Engineering, vol. 29, 2003, pp. 407-419.
[18] Chao-Lung Chiang "Improved genetic algorithm for power economic
dispatch of units with valve-point effects and multiple fuels," IEEE
Trans. Power Systems, vol.20, no. 4, 2005, pp.1690-1699.
[19] R.Storn, K.Price, Differential evolution - A simple and efficient heuristic
for global optimization over continuous space. Journal of Global
Optimization, vol. 11, 1997, pp. 341-359.
[20] Wood AJ, Woollenberg BF. Power Generation Operation and Control.
2nd ed. New York; Wiley; 199
@article{"International Journal of Electrical, Electronic and Communication Sciences:59101", author = "R.Balamurugan and S.Subramanian", title = "Self-Adaptive Differential Evolution Based Power Economic Dispatch of Generators with Valve-Point Effects and Multiple Fuel Options ", abstract = "This paper presents the solution of power economic dispatch (PED) problem of generating units with valve point effects and multiple fuel options using Self-Adaptive Differential Evolution (SDE) algorithm. The global optimal solution by mathematical approaches becomes difficult for the realistic PED problem in power systems. The Differential Evolution (DE) algorithm is found to be a powerful evolutionary algorithm for global optimization in many real problems. In this paper the key parameters of control in DE algorithm such as the crossover constant CR and weight applied to random differential F are self-adapted. The PED problem formulation takes into consideration of nonsmooth fuel cost function due to valve point effects and multi fuel options of generator. The proposed approach has been examined and tested with the numerical results of PED problems with thirteen-generation units including valve-point effects, ten-generation units with multiple fuel options neglecting valve-point effects and ten-generation units including valve-point effects and multiple fuel options. The test results are promising and show the effectiveness of proposed approach for solving PED problems. ", keywords = "Multiple fuels, power economic dispatch, selfadaptivedifferential evolution and valve-point effects.", volume = "1", number = "3", pages = "496-8", }
