A comprehensive study of practical economic dispatch problems by a new hybrid evolutionary algorithm

The Economic Dispatch (ED) is one of the most important optimization problems in power systems the ultimate goal of the ED is to minimize the cost of operations in a power generation. In this paper, the Woodpecker Mating Algorithm (WMA) is used to solve the ED problem considering the nonlinear properties of generators such as valve point effects (VPE), prohibited operating zones (POZ), ramp rate limits, multiple fuel options, and transmission loss. The WMA algorithm is a novel metaheuristic algorithm inspired by the mating behavior of woodpeckers and sound intensity (a physical quantity). The WMA is implemented on six test systems of different operational dimensions and characteristics to show its capacity for solving the ED problem. The results are compared with the latest and most efficient methods introduced in the literature. Proving the efficiency of the WMA to solve the ED problem, simulation results are promising and offer the optimal fuel cost of production.

Scarcity of energy resources, increasing power generation cost and ever-growing demand for electric energy necessitates optimal economic dispatch in today’s power systems. The main objective of economic dispatch is to reduce the total power generation cost, while satisfying various equality and inequality constraints. Traditionally in economic dispatch problems, the cost function for generating units has been approximated as a quadratic function which doesn’t provide accurate results. Moreover, to obtain accurate fuel cost, valve-point effect in thermal power plant has to be taken into account. The inclusion of valve-point effect makes the modeling of the fuel cost functions of generating units more practical. In this paper a new evolutionary algorithm called Pattern Search Technique, has been employed to solve economic dispatch problem with the valve-point effect. Using this technique the non-linear cost function is solved for three unit system and the results are compared with the traditional PSO and GA method. These results prove that Pattern Search method is capable of getting higher quality solution including mathematical simplicity, fast convergence, and robustness to solve hard optimization problems.

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 article presents a new optimization approach called the Wild Horse Optimizer (WHO). It is designed to be user-friendly, effective, and to converge rapidly when addressing economic dispatch (ED). Given that ED is a nonlinear and complex optimization problem, the primary goal of the WHO is to minimize overall generation costs while adhering to the system's equality and inequality constraints. The Combined Economic Emission Dispatch (CEED) problem is also considered, which considers the environmental impacts stemming from the emissions of gaseous pollutants produced by fossil-fueled power plants. To demonstrate the capabilities of the WHO, various networks with 3, 6, 10, 13, 15, and 40 stations have been tested and applied to resolve multiple ED scenarios, including factors such as valve point effects, losses, and prohibited operating zones. The simulation results indicate that the WHO's approach is significantly more effective than the methods found in current academic literature. This analysis highlights the strengths of the WHO's strategies compared to alternatives, suggesting they may offer better solutions to the challenges identified in previous studies.

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

Economic dispatch (ED) is one of the optimization problems in power system operation and planning. The practical ED problems have non-smooth cost functions with equality and inequality constraints. It becomes more complicated problem when valve point effects of generator are considered and results multiple local minima. This makes the ED problems are difficult to find global optimum solution when using any mathematical approach due to non-convex cost function. The Classical particle swarm optimization (PSO) has ability to reach near global optimum solution by tuning some parameters but always stuck at local minima. In this paper, an iteration particle swarm optimization (IPSO) is proposed to solve ED problems with valve point effects. The proposed algorithm is introduced a new parameter in the original velocity equation of PSO in order to enrich searching behaviour, solution quality and avoid being trapped at local minima. The proposed IPSO algorithm has been implemented on two test power systems (consisting 3 and 13 generating units) to validate its effectiveness. The simulation results confirmed that IPSO algorithm has better convergence characteristic and more robust compared to PSO and some published results.

99/03213 Economic emission dispatch: a case study of Myanmar

The objective of the economic dispatch problem of electrical power generation is to schedule the committed generating unit's output so as to meet the required load demand while satisfying the system equality and inequality constraints. This paper solves the combined economic emission dispatch problem by Min-Max and Max-Max price penalty factor approaches using Lagrange's method. The price penalty factor for the combined economic emission dispatch (CEED) is the ratio of fuel cost to emission value. The literature papers reported that most of them use Max-Max Price penalty factor for the CEED problem. This paper analyses Min-Max and Max-Max price penalty factors for CEED problem. This problem is solved for a five generator system by considering the valve point effect for both fuel cost and emission function. The total fuel cost by considering valve point effect of the combined economic emission dispatch problem is less when using Min-Max price penalty factor approach in comparison to Max-Max price penalty factor.

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

This paper presents a particle swarm optimization (PSO) to solve hard combinatorial constrained optimization problems such as nonconvex and discontinuous economic dispatch (ED) problem of large thermal power plants. Several measures have been suggested in the control equation of the classical PSO by modifying its operators for better exploration and exploitation. The inertia operator of the PSO is modulated by introducing a new truncated sinusoidal function. The cognitive and social behaviors are dynamically controlled by suggesting new exponential constriction functions. The overall methodology effectively regulates the velocity of particles during their flight and results in substantial improvement in the classical PSO. The effectiveness of the proposed method has been tested for economic load dispatch of three standard test systems considering various operational constraints like valve-point loading effect, prohibited operating zones (POZs), network power loss, and so forth. The application results show that the proposed PSO method is very promising.

A new honey bee mating optimization algorithm for non-smooth economic dispatch

In this paper, an effective and reliable variant of particle swarm optimization with time-varying acceleration coefficients (PSO-TVAC) technique is proposed for the economic load dispatch problem considering valve-point loading effect. Main objective of the economic load dispatch (ELD) problem is to minimize the fuel cost by allocating the generation of the committed units subjected to the equality and inequality constraints. Equation of the economic dispatch objective function gets modified with the addition of a new parameter which represents the effect of valve-point loading. While exploring the use of PSO and its other variants to the economic dispatch problem, a number of research works have not considered the transmission losses properly. This paper represents the usefulness of the proposed PSO-TVAC algorithm to significantly reduce the fuel cost while taking into account the effect of transmission losses along with the non-convex characteristic due to valve loading. The results have been demonstrated for three-generator and ten-generator test systems.

Single period economic dispatch cannot handle the intertemporal constraints in multi-period environment. To cope with this issue, the extension of economic dispatch over multiple time intervals (i.e., dynamic economic dispatch) has been introduced that considers the intertemporal constraints between different time intervals. Another issue is determining the most economical generation dispatch that could supply the area demand without violating the tie-line capacity, which cannot be solved by conventional economic dispatch problems. However, this study shows that the most economic schedule of power generation cannot satisfy echo-system expectation; therefore, making a compromise between fuel cost and environmental issues, a hot-button subject in industrialized nations, seems to be crucial. To reach the goals a bi-objective multi-area dynamic economic dispatch approach, which can handle intertemporal and multi-area constraints concurrently, is proposed to assist power system operators more and more. Finally, a hybrid algorithm, namely gray wolf optimizer-particle swarm optimization is introduced to solve the proposed problem and also a set of benchmark problems. By implementing the proposed approach on two small (10-unit, three areas) and large (40-unit, four areas) scale test systems, about 3.1% and 3.3% improvement in generation cost is obtained, respectively compare to the best reported results in the literature.

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.

Hybrid artificial algae algorithm for economic load dispatch