Non-convex Economic Load Dispatch Research Articles

Economic load dispatch using population-variance harmony search algorithm

This paper presents a novel stochastic optimization approach to solve the constrained economic load dispatch (ELD) problem using the harmonic search algorithm (HS). HS is a recently developed derivative-free, meta-heuristic optimization algorithm, which draws inspiration from the musical process of searching for a perfect state of harmony. This work analyses the evolution of the population-variance over successive generations in HS and thereby draws some important conclusions regarding the explorative power of HS. The proposed methodology easily takes care of solving non-convex ELD problems along with different constraints like transmission losses, ramp rate limits of the generators and prohibited operating zones. Simulations were performed over various standard test systems with different number of generating units and a comparative study is carried out with other existing relevant approaches. The findings affirmed the robustness and proficiency of the proposed methodology over other existing techniques.

Economic Load Dispatch Using Hybrid Swarm Intelligence Based Harmony Search Algorithm

This article presents a novel stochastic optimization approach to solve the constrained economic load dispatch problem using a hybridization of the harmony search algorithm and particle swarm optimization, named hybrid harmony search based on the swarm intelligence principle. Harmony search is a recently developed derivative-free, meta-heuristic optimization algorithm, which draws inspiration from the musical process of searching for a perfect state of harmony. This work is an attempt to utilize the velocity-based particle updating process from particle swarm optimization in the improvisation process of the harmony search algorithm for a better convergence of the proposed algorithm. The proposed methodology also easily takes care of solving non-convex economic load dispatch problems along with different constraints, such as power balance, ramp rate limits of the generators, and prohibited operating zones. Simulations were performed over four various standard test systems with different numbers of generating units, and a comparative study is carried out with other existing relevant approaches. The findings affirm the robustness and proficiency of the proposed methodology over other existing techniques.

Non-convex Economic Dispatch with Heuristic Load Patterns using Harmony Search Algorithm

paper presents an attempt to explore the applicability of harmony search algorithm (HSA) to solve extremely challenging non-convex economic load dispatch (ELD) problem with transmission losses involving variations of consumer load patterns. The efficiency of the proposed approach HSA has been tested successfully on the standard 6-bus system, IEEE-14 bus system, and the IEEE-30 bus system with several heuristic load patterns. The results of this study reveals that the proposed approach is able to find appreciable economical load dispatch solutions than the improved fast evolutionary program (IFEP) and particle swarm optimization (PSO). Besides this, the transmission line losses also considerably reduced and the computation time is reasonably even in all test cases and less when compared to other methods.

Economic load dispatch solution by improved harmony search with wavelet mutation

This paper presents a new evolutionary optimisation algorithm to solve economic load dispatch (ELD) problem with operational constraints using the improved harmony search algorithm. Harmony search algorithm is a recently developed derivative-free, meta-heuristic optimisation algorithm, which draws inspiration from the musical process of searching for a perfect state of harmony. In this paper we replace the random selection process in the classical harmony search method by wavelet theory based mutation process to improve the performance of the algorithm. The proposed methodology easily takes care of solving non-convex ELD problems along with different constraints like power balance, ramp rate limits of the generators and prohibited operating zones. Simulations were performed over various standard test systems with different number of generating units and a comparative study is carried out with other existing relevant approaches. The results obtained reveal the robustness and ability of the proposed methodology over other existing techniques.

Hybrid Differential Evolution With Biogeography-Based Optimization for Solution of Economic Load Dispatch

This paper presents a hybrid technique combining differential evolution with biogeography-based optimization (DE/BBO) algorithm to solve both convex and nonconvex economic load dispatch (ELD) problems of thermal power units considering transmission losses, and constraints such as ramp rate limits, valve-point loading and prohibited operating zones. Differential evolution (DE) is one of the very fast and robust evolutionary algorithms for global optimization. Biogeography-based optimization (BBO) is a relatively new optimization. Mathematical models of biogeography describe how a species arises, migrates from one habitat (Island) to another, or gets extinct. This algorithm searches for the global optimum mainly through two steps: migration and mutation. This paper presents combination of DE and BBO (DE/BBO) to improve the quality of solution and convergence speed. DE/BBO improves the searching ability of DE utilizing BBO algorithm effectively and can generate the promising candidate solutions. The effectiveness of the proposed algorithm has been verified on four different test systems, both small and large. Considering the quality of the solution and convergence speed obtained, this method seems to be a promising alternative approach for solving the ELD problems in practical power system.

Biogeography-Based Optimization for Different Economic Load Dispatch Problems

This paper presents a biogeography-based optimization (BBO) algorithm to solve both convex and non-convex economic load dispatch (ELD) problems of thermal plants. The proposed methodology can take care of economic dispatch problems involving constraints such as transmission losses, ramp rate limits, valve point loading, multi-fuel options and prohibited operating zones. Biogeography deals with the geographical distribution of biological species. Mathematical models of biogeography describe how a species arises, migrates from one habitat to another and gets wiped out. BBO has some features that are in common with other biology-based optimization methods, like genetic algorithms (GAs) and particle swarm optimization (PSO). This algorithm searches for the global optimum mainly through two steps: migration and mutation. The effectiveness of the proposed algorithm has been verified on four different test systems, both small and large, involving varying degree of complexity. Compared with the other existing techniques, the proposed algorithm has been found to perform better in a number of cases. Considering the quality of the solution obtained, this method seems to be a promising alternative approach for solving the ELD problems in practical power system.

Solving complex economic load dispatch problems using biogeography-based optimization

This paper presents an algorithm, biogeography-based optimization (BBO) to solve both convex and non-convex economic load dispatch (ELD) problems of thermal generators of a power system. The Proposed methodology easily takes care of solving non-convex economic dispatch problems considering different constraints such as transmission losses, ramp rate limits, multi-fuel options and prohibited operating zones. Biogeography deals with the geographical distribution of biological organisms. Mathematical models of biogeography describe how species migrate from one habitat to another, how species arise, and how species become extinct. BBO has features in common with other biology-based optimization methods, like genetic algorithms (GAs) and particle swarm optimization (PSO). Here, first it will be discussed how BBO can be used to solve ELD problems. This algorithm searches the global optimum mainly through two steps: migration and mutation. To show the advantages of the proposed algorithm, it has been applied to four different test systems for solving ELD problems. First, a 6-generator system along with ramp rate limits and prohibited operating zone. Second, considers 40 generators with valve-point loading. Third, considers 20-generator systems with simple quadratic cost function considering transmission loss and operating limit constraints. Last one is addressing both valve-point effects and multiple fuels in a 10-generator system. Comparing with the other existing techniques, the current proposal is found better than, or at least comparable to them considering the quality of the solution obtained. This method is considered to be a promising alternative approach for solving the ELD problems in practical power system.

Nonconvex economic load dispatch using an efficient real-coded genetic algorithm

An efficient optimisation procedure based on real-coded genetic algorithm (RCGA) is proposed for the solution of economic load dispatch (ELD) problem with continuous and nonsmooth/nonconvex cost function and with various constraints being considered. The effectiveness of the proposed algorithm has been demonstrated on different systems considering the transmission losses and valve point loading effect in thermal units. The proposed algorithm is equipped with an effective constraint handling technique, which eliminates the need for penalty parameters. For the purpose of comparison, the same problem has also been solved using binary-coded genetic algorithm (BCGA) and three other popular RCGAs. In the proposed RCGA, simulated binary crossover and polynomial mutation are used against the single point crossover and bit-flipping mutation in BCGA. It has been observed from the test results that the proposed RCGA is more efficient in terms of thermal cost minimisation and execution time for ELD problem with continuous search space than BCGA and some other popular RCGAs.

Nonconvex Economic Dispatch with Heuristic Load Patterns Using Improved Fast Evolutionary Program

This article presents an attempt to explore the feasibility of an improved fast evolutionary program (IFEP) search technique to solve extremely challenging nonconvex economic load dispatch (ELD) problem with transmission losses involving variations of consumer load patterns. The effectiveness of the proposed approach has been tested successfully on the standard 6-bus system, IEEE 14-bus system, and the IEEE-30 bus system with several heuristic load patterns. The numerical results reveal that the proposed approach can provide better optimal dispatch solutions than those of classical lambda-iteration method (CLIM). Aside from this, the computation time is reasonable even with nonconvex fuel cost functions where the gradient based search methods are inapplicable.