Economic Load Dispatch With Multiple Fuel Options and Valve Point Effect Using Cuckoo Search Algorithm With Different Distributions

Economic Load Dispatch With Multiple Fuel Options and Valve Point Effect Using Cuckoo Search Algorithm With Different Distributions

Cuong Dinh Tran (Ton Duc Thang University, Vietnam), Tam Thanh Dao (Ho Chi Minh City Industry and Trade College, Vietnam), and Ve Song Vo (Ho Chi Minh City University of Food Industry, Vietnam)
Copyright: © 2020 |Pages: 15
DOI: 10.4018/IJEOE.2020070102
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The cuckoo search algorithm (CSA), a new meta-heuristic algorithm based on natural phenomenon of the cuckoo species and Lévy flights random walk has been widely and successfully applied to several optimization problems so far. In the article, two modified versions of CSA, where new solutions are generated using two distributions including Gaussian and Cauchy distributions in addition to imposing bound by best solutions mechanisms are proposed for solving economic load dispatch (ELD) problems with multiple fuel options. The advantages of CSA with Gaussian distribution (CSA-Gauss) and CSA with Cauchy distribution (CSA-Cauchy) over CSA with Lévy distribution and other meta-heuristic are fewer parameters. The proposed CSA methods are tested on two systems with several load cases and obtained results are compared to other methods. The result comparisons have shown that the proposed methods are highly effective for solving ELD problem with multiple fuel options and/nor valve point effect.
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  • aij, bij, cij fuel cost coefficients for fuel type j of unit i

  • eij, fij fuel cost coefficients for fuel type j of unit i reflecting valve-point effects

  • N total number of generating units

  • mi number of fuel types of unit i

  • Pi power output of unit i

  • Pi,max maximum power output of unit i

  • Pi,min minimum power output of unit i

  • Pij,min minimum power output for fuel j of unit i

  • PD total system load demand

  • PL total transmission loss



The objective of economic load dispatch (ELD) is to minimize total fuel cost of thermal units while satisfying both equality and inequality constraints including load balance constraint, upper and lower generation limit on thermal units (Lee & Kim, 2002). Traditionally, the fuel cost function of thermal unit is approximately represented as one single quadratic curve because each generating unit used only one fossil fuel to produces electricity. However, it is more realistic to represent the fuel function as a segmented piece-wise quadratic functions because several fuels are burned (Dieu et al., 2013).

Several methods have been applied for solving ELD problem with multiple fuel options so far. The lamda-iteration has been valued as a simple and effective one (Thang 2011). However, the disadvantages of the method are that the values of lamda and updated step size are randomly chosen initially. This can lead to a non-optimal solution or non-convergence. The best solution has been found after the method has been performed 93 independent runs with various values of lamda and fuel type. The computational time for each trial is short but total time for whole is long. Enhanced Augmented Lagrange Hopfield Network (ALHN) (Dieu & Ongsakul, 2008) solves ELD problem in two phases and gains good solutions and short simulation time. However, the gained simulation results depend on setting a large number of parameters. The Differential Evolution (DE) (Nasimul & Hitoshi, 2008) algorithm is found to be a powerful evolutionary algorithm for global optimization in many real problems. Self-Adaptive Differential Evolution (SDE) (Balamurugan & Subramanian, 2007) is a good method to solve ELD problem with valve point effects. The application of Hopfield neural network (HNN) (Park et al., 1993) with merit of simplicity created difficulties in handling some kinds of inequality constraints. For solving the problem by the enhanced Lagrangian neural network (ELANN) (Lee & Kim, 2002) method, the dynamics of Lagrange multipliers including equality and inequality constraints were improved to guarantee its convergence to the optimal solutions, and the momentum technique was also employed in its learning algorithm to achieve fast computational time. Both HNN (Park et al., 1993) and ELANN (Lee & Kim, 2002) were involved a large number of iterations for convergence.

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