The solution of the economic dispatch problem via an efficient Teaching-Learning-Based Optimization method

Solving non-convex economic load dispatch problem via artificial cooperative search algorithm

Economical dispatch of power is a significant real time optimization problem in the operation of power system, which allocates the loads on the committed generating units to reduce the generation cost, while meeting all the inequality and equality constraints. Traditionally, economic load dispatch problems have been formulated as convex optimization problem and various classical methods such as gradient methods, base-point participation factor method, etc. have been used for solving them. The traditional formulation is a quadratic input-output curve or piece wise linear cost curve, which are continuous and convex, however, real generating units have valve loading effects, which make the cost curve discontinuous and non-convex and hence the economic dispatch problem is no longer simple to handle. Thus, the classical methods cannot be employed for non-convex problems. The non-convex, non-linear and discontinuous economic dispatch (ED) problem can be better solved by metaheuristic approaches. Such approaches often require tuning of their respective evolutionary parameters. Although, solution to such type of problem have already been solved by different metaheuristic optimization techniques in previous studies as well, however, the algorithm employed in this paper to solve Power Economic Load Dispatch (PELD) problem is adaptive real coded quantum-inspired evolutionary algorithm, which does not require tuning of evolutionary parameters and performs better than some of the existing techniques on standard 6-bus 3 machine system and IEEE 14 bus 5 unit system.

This paper presents survey of optimization techniques used to solve the problem of economic load dispatch in power stations. Since there is no single method available for solving all economic dispatch problems efficiently, thus a number of different optimization methods have been developed to solve this problem. These techniques were divided into three types depending on the efficiency of the solution: stochastic process techniques, statistical methods, and mathematical programming techniques which divided to local optimization, and global optimization. It is found that is better to use hybrid techniques to overcome load dispatch problems so as to achieve significant improvements in computation time, convergence properties, solution quality, or parameter robustness.

The major issue in power system is economic dispatch (ED) problem. The Economic dispatch problem is aim to distribute electrical power generators in some active electrical system to minimize the total of cost of generators. Here, the purpose of this paper is to achieve the combination of power output, maximum total of demand with the transmission losses, minimum the total cost of generating unit and design web based application to simplify the calculation of economic dispatch problem for user at PT. Indonesia Power. This paper introduces a solution to ED problem using Dr. Xin She Yang developed firefly algorithm. The result obtained by the proposed algorithm have been compared with the result from the data source and that results is more optimal using firefly algorithm than the results of the data source. Based on the result, it can be concluded that this web based application is very useful to user in calculating the economic dispatch problem with transmission losses at PT. Indonesia Power.

Solving non-convex economic dispatch problem with valve point effects using modified group search optimizer method

In India Electrical Energy is generated mainly Coal based Thermal Power stations and hydro Electric Power Stations. The main aim of power generating company is to provide good quality and reliable power to consumers at minimum cost. The problem of Combined Economic and Emission Dispatch deals with the minimization of both fuel cost and emission of pollutants such as oxides of Nitrogen and Oxides of Sulphur. In our power system the emission is major problem created that’s why in now a days we move from green energy source or renewable energy such as Sunlight, Wind, Tides, Wave, and Geothermal Heat Energy. The Emission constrained Economic Dispatch problem treats the emission limit as an additional constraint and optimizes the fuel cost. In this paper we optimizes the Combined Economic and Emission Dispatch problem by using two different optimization method such as Artificial Bee Colony (ABC) and Genetic Algorithm (GA).The proposed ABC Algorithm has been successfully implemented is to IEEE 30 bus and Indian Utility sixty two Bus System The simulation result are compare and found the effective algorithm for Combined Economic and Emission Dispatch problem.

In this paper, a Q learning quantum-behaved particle swarm optimization (QPSO) method is proposed to solve the economic dispatch (ED) problem in power systems, whose objective is to simultaneously minimize the generation cost rate while satisfying various equality and inequality constraints. The proposed method enhance the global search ability of the algorithm. The feasibility of the QlQPSO method is demonstrated by three different power systems, compared with the GIQPSO, the MeQPSO, and the SlQPSO in terms of the solution quality, robustness and convergence property. The simulation results show that the proposed QlQPSO method is able to obtain higher quality solutions stably and efficiently in the ED problem than other tested optimization algorithm.

A social spider algorithm for solving the non-convex economic load dispatch problem

<p>Multi-area Combined Economic Emission Dispatch (MACEED) problem is an optimization task in power system operation for allocating the amount of generation to the committed units within the system areas. Its objective is to minimize the fuel cost and the quantity of emissions subject to the power balance, generator limits, transmission line and tie-line constraints. The solutions of the MACEED problem in the conditions of deregulation are difficult, due to the model size, nonlinearities, and the big number of interconnections, and require intensive computations in real-time. High-Performance Computing (HPC) gives possibilities for the reduction of the problem complexity and the time for calculation by the use of parallel processing techniques for running advanced application programs efficiently, reliably and quickly. These applications are considered as very new in the power system control centers because there are not available optimization methods and software based on them that can solve the MACEED problem in parallel, paying attention to the existence of the power system areas and the tie-lines between them. A decomposition-coordinating method based on Lagrange’s function is developed in this paper. Investigations of the performance of the method are done using IEEE benchmark power system models.</p>

Double weighted particle swarm optimization to non-convex wind penetrated emission/economic dispatch and multiple fuel option systems

Economic load dispatch is one of the vital purposes in electrical power system operation, management and planning. Economic dispatch problem is one of the most important problems in electric power system operation. In large scale system, the problem is more complex and difficult to find out optimal solution because it is nonlinear function and it contains number of local optimal. Combined economic emission dispatch (CEED) problem is to schedule the committed generating units outputs to meet the required load demand at minimum operating cost with minimum emission simultaneously. The main aim of economic load dispatch is to reduce the total production cost of the generating system and at the same time the necessary equality and inequality constraints should also be fulfilled. This leads to the development of CEED techniques. There are various techniques proposed by several researchers to solve CEED problem based on optimization techniques. But still some problems such as slower convergence and higher computational complexity exist in using the optimization techniques such as GA for solving CEED problem. This paper proposes an efficient and reliable technique for combined fuel cost economic optimization and emission dispatch using the Modified Ant Colony Optimization algorithm (MACO) to produce better optimal solution. The simulation results reveal the significant performance of the proposed MACO approach.

A hybrid optimization framework for the non-convex economic dispatch problem via meta-heuristic algorithms

Optimizing multiple objectives is a common challenge in complex decision-making scenarios, where improving one objective often comes at the expense of another. In power system generation, two critical objectives must be simultaneously minimized: the total generation cost and the total emissions released. This study introduces a multi-objective optimization method developed to address these dual objectives. The proposed approach aims to identify the optimal solution to the economic dispatch problem, balancing the trade-off between minimizing generation costs and reducing environmental impact by lowering total emissions. Heuristic optimization is used to solve this multi-objective combined economic and emission dispatch (MOCEED) problems through the implementation of Multi-Objective Evolutionary Programming (MOEP). In this study, the Weighted Sum Method (WSM) is combined with the Evolutionary Programming (EP) technique to minimize both objectives. The developed approach is validated on the IEEE 30-Bus RTS, which consists of six generators. The effectiveness of the developed technique is evaluated and compared the results against scenarios without optimization. Simulations are performed using MATLAB software, and the results demonstrate that the proposed Multi-Objective Evolutionary Programming (MOEP) successfully identifies the optimal generator outputs, achieving significant reductions in both total generation cost and emissions. These results highlight the method's capability to provide superior solutions for multi-objective economic dispatch problems.

Due to the frequent opening and shutting of turbine valves in the power system, valve point effect (VPE) that makes the economic dispatching (ED) problem non-linear, non-smooth and non-convex may be generated. Moreover, various constraints appear in the operation process, such as network transmission loss, and power balance during unit operation, which make it more difficult to find the global optimum through traditional mathematical methods. Nowadays, intelligent algorithms have successfully become a useful optimization tool to deal with nonlinear problems. In this paper, an improved bat algorithm (IBA), into which random black hole strategy and Gaussian mutation are introduced, is proposed to solve the ED problem. Furthermore, the random black hole strategy can enhance the diversity of the population and improve the convergence speed of IBA. Gaussian mutation is adopted to help jumping out of the local optimum. IBA is tested in 50 and 100 dimensions on 10 sets of well-known benchmark functions respectively, and compared with the methods in literature to verify its feasibility. Then, three different scales economic dispatching problems (3 units, 13 units, 40 units) are solved by this method, which further proves its effectiveness. The results show that IBA has obvious advantages and practical application value compared with other optimization methods.

Firefly Algorithm for solving non-convex economic dispatch problems with valve loading effect