Pranab Kumar Chattopadhyay

Evolutionary programming techniques for economic load dispatch

Evolutionary programming has emerged as a useful optimization tool for handling nonlinear programming problems. Various modifications to the basic method have been proposed with a view to enhance speed and robustness and these have been applied successfully on some benchmark mathematical problems. But few applications have been reported on real-world problems such as economic load dispatch (ELD). The performance of evolutionary programs on ELD problems is examined and presented in this paper in two parts. In Part I, modifications to the basic technique are proposed, where adaptation is based on scaled cost. In Part II, evolutionary programs are developed with adaptation based on an empirical learning rate. Absolute, as well as relative, performance of the algorithms are investigated on ELD problems of different size and complexity having nonconvex cost curves where conventional gradient-based methods are inapplicable.

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.

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.

Simulated Annealing Technique for Dynamic Economic Dispatch

Dynamic economic dispatch (DED) is one of the main functions of power system operation and control. It determines the optimal operation of units with predicted load demands over a certain period of time with an objective to minimize total production cost while the system is operating within its ramp rate limits. This paper presents DED based on a simulated annealing (SA) technique for the determination of the global or near global optimum dispatch solution. In the present case, load balance constraints, operating limits, valve point loading, ramp constraints, and network losses using loss coefficients are incorporated. Numerical results for a sample test system have been presented to demonstrate the performance and applicability of the proposed method.

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.

Fast Evolutionary Progranuning Techniques for Short-Term Hydrothermal Scheduling

Fast evolutionary programming techniques are applied for solution of short-term hydrothermal scheduling problem. Evolutionary programming (EP) based algorithms with Gaussian and other mutation techniques have been developed and tested on a multireservoir cascaded hydroelectric system having prohibited operating zones and a thermal unit with valve point loading. Numerical results show that all EP algorithms are capable of finding very nearly global solutions within a reasonable time, but an EP-algorithm with the better of the Gaussian and Cauchy mutations appears to be the best among all EPs in terms of convergence speed, solution time, and cost.

Fast evolutionary programming techniques for short-term hydrothermal scheduling

Abstract This paper presents fast evolutionary programming (FEP) techniques for solution of short-term hydro thermal scheduling problems. Evolutionary programming (EP) based algorithms with Gaussian mutation and other fast mutation techniques have been developed for hydrothermal scheduling (HS) problems. Numerical results for a test case show that all the EP-algorithms are capable of finding very nearly global solutions within a reasonable time but EP-algorithm with better of Gaussian and Cauchy mutations was the best amongst all EPs in terms of convergence rate, solution time and success rate.

Application of Biogeography-based Optimization for Solving Multi-objective Economic Emission Load Dispatch Problems

Abstract This article presents a biogeography-based optimization algorithm to solve complex economic emission load dispatch problems of thermal generators of power systems. Different emission substances, such as NOX, SOX, and COX, are considered for case studies. The methodology considers the power demand equality constraint and the operating limit constraint during the time of solving economic emission load dispatch problems. 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. Here, it will be discussed how biogeography-based optimization can be used to solve economic emission load dispatch problems. This algorithm searches the global optimum mainly through two steps: migration and mutation. To show the advantages of the proposed algorithm, this algorithm has been applied for solving multi-objective economic emission load dispatch problems in a six-generator system considering NOX emission for different loading condition; in a three-generator system with NOX and SOX emission; in a six-generator system with SOX, NOX, and COX emissions; and in a six-generator system addressing both valve-point loading and NOX emission. Compared with the other existing techniques, the current proposal is found to be better in terms of quality of the compromising and individual solution obtained.

Hybrid differential evolution with biogeography-based optimization algorithm for solution of economic emission load dispatch problems

Abstract This paper presents combination of differential evolution (DE) and biogeography-based optimization (BBO) algorithm to solve complex economic emission load dispatch (EELD) problems of thermal generators of power systems. Emission substances like NO X , SO X , CO X , Power demand equality constraint and operating limit constraint are considered here. Differential evolution (DE) is one of the very fast and robust, accurate evolutionary algorithms for global optimization and solution of EELD problems. Biogeography-based optimization (BBO) is another new biogeography inspired algorithm. Biogeography deals with the geographical distribution of different biological species. This algorithm searches for the global optimum mainly through two steps: migration and mutation. In this paper combination of DE and BBO (DE/BBO) is proposed to accelerate the convergence speed of both the algorithm and to improve solution quality. To show the advantages of the proposed algorithm, it has been applied for solving multi-objective EELD problems in a 3-generator system with NO X and SO X emission, in a 6-generators system considering NO X emission, in a 6-generator system addressing both valve-point loading and NO X emission. The current proposal is found better in terms of quality of the compromising and individual solution obtained.

Solution of Economic Power Dispatch Problems Using Oppositional Biogeography-based Optimization

Abstract This article describes a quasi-reflection oppositional biogeography-based optimization for the solution of complex economic load dispatch problems of thermal power plants. This algorithm can take care of economic load dispatch problems, considering different constraints such as transmission losses, ramp rate limits, valve-point loading, and prohibited operating zones. Biogeography deals with the geographical distribution of different biological species. Mathematical models of biogeography describe how a species arises, migrates from one habitat (island) to another, and disappears. This algorithm searches the global optimum mainly through two steps: migration and mutation. This article presents a quasi-reflection oppositional biogeography-based optimization to accelerate the convergence of biogeography-based optimization and to improve solution quality. The proposed method employs opposition-based learning along with a biogeography-based optimization algorithm. Instead of opposite numbers, here, quasi-reflected numbers are used for population initialization and also for generation jumping. The effectiveness of the proposed algorithm has been verified on four different test systems. 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 and convergence speed obtained, this method seems to be a promising alternative approach for solving the economic load dispatch problems.