Multi-area Economic Dispatch Research Articles

The Auxiliary Problem Principle with Self-Adaptive Penalty Parameter for Multi-Area Economic Dispatch Problem

The auxiliary problem principle is a powerful tool for solving multi-area economic dispatch problem. One of the main drawbacks of the auxiliary problem principle method is that the convergence performance depends on the selection of penalty parameter. In this paper, we propose a self-adaptive strategy to adjust penalty parameter based on the iterative information, the proposed approach is verified by two given test systems. The corresponding simulation results demonstrate that the proposed self-adaptive auxiliary problem principle iterative scheme is robust in terms of the selection of penalty parameter and has better convergence rate compared with the traditional auxiliary problem principle method.

The Engineering Application of Improved Alternating Direction Method for Solving Power Systems Multi-Area Dispatch Problem

The alternating direction method has been widespread used to solve multi-area economic dispatch problem. Compared with traditional centered economic dispatch, alternating direction method divides centered optimal problem into completely independent sub-problems while the corresponding equality and inequality constraints are satisfied. However, plenty of applications show that the choice of penalty parameter for the consistency constraint has an important influence on the convergence performance of alternating direction method. In this paper, we proposed a novel improved alternating direction method. To be more exact, the key is to adjust penalty parameter based on iterative information of alternating direction method. Numerical results illustrate the proposed method has better stability in convergence.

Improved Particle Swarm Optimization for Multi-area Economic Dispatch with Reserve Sharing Scheme

This paper presents an improved particle swarm optimization (IPSO) to solve Multi-area Economic Dispatch (MAED) problem. The objective of MAED problem is to determine the optimal generating schedule of thermal units and inter-area power transactions in such a way that total fuel cost is optimized while satisfying tie-line, spinning reserve and other operational constraints. The spinning reserve requirements for reserve sharing provisions are investigated by considering contingency and pooling spinning reserves. The control equation of IPSO is modified by suggesting improved cognitive component of the particle’s velocity by suggesting preceding experience. The operators of IPSO are also modified to maintain a proper balance between cognitive and social behavior of the swarm. The effectiveness of the proposed method has been tested on four areas, 16 generators and 40 generators test systems. The application results show that IPSO is very promising to solve MAED problem.

Modification of multi‐area economic dispatch with multiple fuel options, considering the fuelling limitations

Nowadays, using the units with multiple fuel options is one of the ways to reduce the generation costs and increase the reliability in modern power plants. In such power plants, the minimum generation cost is achieved via selecting the optimal fuel types. Here, the fuelling conditions and limitations of different fuel types indeed have determinative roles, because they not only can significantly influence the system operation point and optimal generation dispatch, but also they certainly affect the fuel consumption cost and the electricity price, as well. This study aims to develop and solve a novel type of multi-area economic dispatch with multiple fuel options, which also considers the mathematical model of the fuelling constraints. Thus, the system operating conditions are modelled in a more realistic way in which all the models of the power plants as well as their fuelling systems are well regarded. This consequently yields a more accurate generation dispatch that can indeed reduce the generation costs, increase the fuelling reliability and subsequently increase the entire system reliability in the actual power systems in which the fuelling constraints are essential and determinative.

Teaching–learning-based optimization algorithm for multi-area economic dispatch

This paper presents teaching–learning-based optimization algorithm for solving MAED (multi-area economic dispatch) problem with tie line constraints considering transmission losses, multiple fuels, valve-point loading and prohibited operating zones. TLBO (teaching–learning-based optimization) is one of the recently proposed population based algorithms which simulates the teaching–learning process of the class room. It is a very simple and robust global optimization technique. The effectiveness of the proposed algorithm has been verified on three different test systems, both small and large, involving varying degree of complexity. Compared with differential evolution, evolutionary programming and real coded genetic algorithm, considering the quality of the solution obtained, the proposed algorithm seems to be a promising alternative approach for solving the MAED problems in practical power system.

Multi Area Economic Dispatch using Secant method and Tie line matrix

Multi Area Economic Dispatch using Secant method and Tie line matrix

Parameter evaluation of auxiliary problem principle for large-scale multi-area economic dispatch

Summary In this paper, a novel with respect to economic dispatch of large-scale multi-area power systems is formulated and studied based on decomposition and coordination algorithm. More precisely, auxiliary problem principle (APP) is applied to overcome the defects of augmented Lagrangian relaxation technology with nonlinear inseparable quadratic terms. The main purpose of this paper is to investigate the intrinsic relationship between APP control parameters and convergence speed, and develop a general criterion that ensures that a suitable control parameter set referring to the implemented APP can be effectively estimated. Theoretical and experimental results of this paper are consistent with each other based on the verification of proposed numerical results. Copyright © 2013 John Wiley & Sons, Ltd.

Artificial Immune System for Multi-Area Economic Dispatch

Abstract This article presents artificial immune system for solving multi-area economic dispatch (MAED) problem with tie line constraints considering transmission losses, multiple fuels, valve-point loading and prohibited operating zones. Artificial immune system is based on the clonal selection principle which implements adaptive cloning, hyper mutation, aging operator and tournament selection. The effectiveness of the proposed algorithm has been verified on three different test systems, both small and large, involving varying degree of complexity. Compared with differential evolution, evolutionary programming and real-coded genetic algorithm, considering the quality of the solution obtained, the proposed algorithm seems to be a promising alternative approach for solving the MAED problems in practical power system.

Multi Area Economic Dispatch using Secant Method

In this paper, Secant method is proposed to solve multi area economic dispatch (MAED) problem. Generator limits of all generators in each area are calculated at given area power demands plus export (or import) using secant method and the generator limits of all generators are modified as modified generator limits. Central economic dispatch (CED) problem is used to determine the output powers of all generators. Here, Secant method is applied to solve the CED problem. The proposed approach has been tested on two-area (two generators in each area) system and four-area (four generators in each area) system. It is observed from various cases that the proposed approach provides optimally best solution in terms of cost with tie line loss with less computational burden.

Hybrid Particle Swarm Optimization for Solving Multi-Area Economic Dispatch Problem

Hybrid Particle Swarm Optimization for Solving Multi-Area Economic Dispatch Problem

Hybrid Particle Swarm Optimization for Solving Multi-Area Economic Dispatch Problem

We consider the Multi-Area Economic Dispatch problem (MAEDP) in deregulated power system environment for practical multi-area cases with tie line constraints. Our objective is to generate allocation to the power generators in such a manner that the total fuel cost is minimized while all operating constraints are satisfied. This problem is NP-hard. In this paper, we propose Hybrid Particle Swarm Optimization (HGAPSO) to solve MAEDP. The experimental results are reported to show the efficiency of proposed algorithms compared to Particle Swarm Optimization with Time-Varying Acceleration Coefficients (PSO-TVAC) and RCGA.

Artificial bee colony optimization for multi-area economic dispatch

This paper presents artificial bee colony optimization for solving multi-area economic dispatch (MAED) problem with tie line constraints considering transmission losses, multiple fuels, valve-point loading and prohibited operating zones. Artificial bee colony optimization is a swarm-based algorithm inspired by the food foraging behavior of honey bees. The effectiveness of the proposed algorithm has been verified on three different test systems, both small and large, involving varying degree of complexity. Compared with differential evolution, evolutionary programming and real coded genetic algorithm, considering the quality of the solution obtained, the proposed algorithm seems to be a promising alternative approach for solving the MAED problems in practical power system.

Discussion of “A novel meta-heuristic optimization methodology for solving various types of economic dispatch problem” Fesanghary et al. “Energy” 34 (2009) 757–766

This paper presents a discussion of “A novel meta-heuristic optimization methodology for solving various types of economic dispatch problem” Fesanghary et al. “Energy” 34 (2009) 757–766. The discussed paper presented economic dispatch problem by experimenting with six case studies considering 38, 13, 15, 6, and 10-unit test systems along with multi area economic dispatch (MAED) problem. However, in the reported results of case study 3 and 6, the total fuel cost calculations are different for the given generation schedule. In this discussion, clarification regarding cost calculation is presented.

Discussion of “Reserve constrained multi-area economic dispatch employing differential evolution with time-varying mutation” by Manisha Sharma et al. “International Journal of Electrical Power and Energy Systems”, 33 March (2011) 753–766

This short communication presents a discussion of “Reserve constrained multi-area economic dispatch employing differential evolution with time-varying mutation” by Manisha Sharma et al. “International Journal of Electrical Power and Energy Systems”, 33 March (2011) 753–766. The discussed paper presented a multi-area economic dispatch solution for a large 40-unit system having complexities like valve point loading effects, ramp rate constraints, prohibited operating zones and transmission constraints for a large 40-unit system. Multi-area economic dispatch for such a large and complex system was not reported before in available literature. However in the reported results one unit is violating the constraints. In this communication, corrected results with lesser costs than reported in the discussed paper are presented.

Fuzzified Particle Swarm Optimization Algorithm for Multi-area Security Constrained Economic Dispatch

This article presents a new computationally efficient fuzzified particle swarm optimization algorithm for solving the security-constrained multi-area economic dispatch of an interconnected power system. The core objective of the security-constrained multi-area economic dispatch is to determine the generation allocation of each committed unit in the system and the power exchange between areas so as to minimize the total generation cost without violating the tie-line constraint. The proposed fuzzified particle swarm optimization algorithm is based on the combined application of fuzzy logic strategy incorporated in the particle swarm optimization algorithm. The proposed method was tested on a system of three interconnected areas. The investigation reveals that the proposed method can provide an accurate solution with fast convergence and has the potential to be applied to other power system optimization problems.

Reserve constrained multi-area economic dispatch employing differential evolution with time-varying mutation

For a power pool that involves several generation areas interconnected by tie-lines, the objective of economic dispatch (ED) is to determine the most economical generation dispatch strategy that could supply the area load demands without violating the tie-line capacity constraints. The objective of multi-area economic dispatch (MAED) is to determine the generation levels and the interchange power between areas which would minimize total fuel cost while satisfying power balance constraint, upper/lower generation limits, ramp rate limits, transmission constraints and other practical constraints. In reserve constrained MAED (RCMAED) problem inter-area reserve sharing can help in reducing the operational cost while ensuring that spinning reserve requirements in each area are satisfied. The tie-line limits too play a pivotal role in optimizing the cost of operation. The cost curves of modern generating units are discontinuous and non-convex which necessitates the use of powerful heuristic search based methods that are capable of locating global solutions effectively, with ease. This paper explores and compares the performance of various differential evolution (DE) strategies enhanced with time-varying mutation to solve the reserve constrained MAED (RCMAED) problem. The performance is tested on (i) two-area, four generating unit system, (ii) four area, 16-unit system and (iii) two-area, 40-unit system. The results are found to be superior compared to some recently published results.

Multi-area economic dispatch with tie-line constraints employing evolutionary approach

Economic dispatch (ED) has the objective of generation allocation to the power generators in such a manner that the total fuel cost is minimized while all operating constraints are satisfied. For the sake of simplicity, ED is generally solved without accounting for transmission constraints. However, in deregulated power system environment it is essential to model the ED problem for practical multi-area cases with tie line constraints. Most of the conventional gradient based methods are time consuming, suffer from dimensionality problem and assume the fuel cost curves of generating units to be piecewise linear, monotonically increasing in nature. The resulting dispatch solutions are therefore inaccurate; sometimes producing infeasible solutions for modern generating units having non convex cost curves. On the other hand evolutionary methods do not suffer from convexity assumptions and achieve fast solutions even for complex non-linear, non-convex, multi-modal optimization problems. This paper reviews and compares some evolutionary techniques for multi-area economic dispatch (MAED). The paper presents an extensive comparison of the search capability and convergence behavior of i) Classical differential evolution (DE) and its various strategies ii) Classical particle swarm optimization (PSO) and iii) An improved PSO with a parameter automation strategy having time varying acceleration coefficients (PSO_TVAC) for solving MAED problems for two area and three area test power systems with 4, 10 and 40- generating units. The results are found to be superior compared to some recently published results. Keywords: Differential evolution, Multi-area economic dispatch, multiple fuel options, particle swarm optimization, transmission capacity constraints. Time varying acceleration coefficients (TVAC), Valve point loading effects.

Reserve Constrained Multi-Area Economic Dispatch Employing Evolutionary Approach

The objective of Multi-area economic dispatch (MAED) is to determine the generation levels and the interchange power between areas that minimize fuel costs, while satisfying power balance and generating limit and transmission constraints. If an area with excess power is not adjacent to a power deficient area, or the tie-line between the two areas is at transmission limit, it is necessary to find an alternative path between these two areas to transmit additional power. When a MAED problem is solved with spinning reserve constraints, the problem becomes further complicated. The power allocation to each unit is done in such a manner that after supplying the total load, some specified reserve is left behind. In this paper, the authors compare classic PSO and DE strategies and their variants for reserve constrained MAED. The superior constraint handling capability of these techniques enables them to produce high quality solutions. The performance is tested on a 2-area system having 4 generating units and a 4-area, 16-unit system.

Sequential Approach with Matrix Framework for Various Types of Economic Thermal Power Dispatch Problems

This paper presents a sequential approach with matrix framework for solving various kinds of economic dispatch problems. The objective of the economic dispatch problems of electrical power generation is to schedule the committed generating units output so as to meet the required load demand while satisfying the system equality and inequality constraints. This is a maiden approach developed to obtain the optimal dispatches of generating units for all possible load demands of power system in a single execution. The feasibility of the proposed method is demonstrated by solving economic load dispatch problem, combined economic and emission dispatch problem, multiarea economic dispatch problem and economic dispatch problem with multiple fuel options. The proposed methodology is tested with different scale of power systems. The generating unit operational constraints are also considered. The simulation results obtained by proposed methodology for various economic dispatch problems are compared with previous literatures in terms of solution quality. Numerical simulation results indicate an improvement in total cost saving and hence the superiority of the proposed method is also revealed for economic dispatch problems.

Evolutionary algorithm solution and KKT based optimality verification to multi-area economic dispatch

This paper is aimed at exploring the performance of the various evolutionary algorithms on multi-area economic dispatch (MAED) problems. The evolutionary algorithms such as the Real-coded Genetic Algorithm (RGA), Particle Swarm Optimization (PSO), Differential Evolution (DE) and Covariance Matrix Adapted Evolution Strategy (CMAES) are considered. To determine the efficiency and effectiveness of various EAs, they are applied to three test systems; including 4, 10 and 120 unit power systems are considered. The optimal results obtained using various EAs are compared with Nelder–Mead simplex (NMS) method and other relevant methods reported in the literature. To compare the performances of various EAs, statistical measures like best, mean, worst, standard deviation and mean computation time over 20 independent runs are taken. The simulation experiments reveal that CMAES algorithm performs better in terms of solution quality and consistency. Karush–Kuhn–Tucker (KKT) conditions are applied to the solutions obtained using EAs to verify optimality. It is found that the obtained results are satisfying the KKT conditions and confirm the optimality. Also, the effectiveness of KKT error based stopping criterion is demonstrated.