A hybrid genetic algorithm approach based on differential evolution for economic dispatch with valve-point effect

The differential evolution (DE) is an improved version of evolution strategies and Nelder-Mead simplex methods. DE has been successfully applied in various fields, such as optimization nonlinear functions, multi sensor fusion, control system, and system identification. The potentialities of DE are its simple structure, easy use, convergency speed and robustness. This paper proposes a new hybrid methodology for solving the economic load dispatch problem with valvepoint effect. The proposed hybrid method combinates the DE and sequential quadratic programming (SQP) technique. The DE is used to produce good potential solutions, and the SQP is used to fine-tune the DE run. The hybrid methodology and its variants are validated for a test system consisting of 40 thermal units whose incremental fuel cost function takes into account the valvepoint loading effects. The proposed hybrid method outperforms other state-of-theart algorithms in solving load dispatch problems with the valve-point effect.Keywordsdifferential evolutioneconomic dispatchoptimizationpower generation operation and control

A novel and effective method for solving economic load dispatch (ELD) problem is presented in this work by integrating the ? constrained method with differential evolution (DE) algorithm. The ? constrained method sets us free from selecting the appropriate value for the penalty coefficient in the objective function, which is difficult and often chosen empirically. Differential evolution with ? constrained method (?DE) has proven to be effective in solving non-linear constrained optimisation problems. Here, the effectiveness of ?DE, in solving ELD problems is investigated by using three different ELD problems that take the valve-point loading effect into consideration. The proposed approach provides very high quality solutions which are very competitive to other existing techniques to ELD considering the valve-point effect.

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.

This article applies the horse herd optimization (HHO) algorithm to convoluted economic dispatch (ED) problems. HHO mimics the social behaviour of horses of different ages using six significant traits: grazing, hierarchy, sociability, imitation, defence mechanism and roam. The efficacy of the HHO method is demonstrated on five different ED problems, namely, valve-point effects, prohibited feasible area, ramp rate limits and multiple fuels. The simulated outcomes of the recommended method are comparable to those obtained by established artificial intelligence methods. Comparative and statistical analyses demonstrate that the proposed HHO algorithm performs well and can produce superior results to some other well-known and established algorithms, namely, differential evolution (DE), success-history based adaptive differential evolution with linear population size reduction (L-SHADE) and covariance matrix adaptation–evolution strategy (CMA-ES).

This paper proposes a new differential evolution optimization (DE) strategy namely, Self-Realized Differential Evolution (SRDE) for solving the economic dispatch (ED) problem with non-smooth cost functions in power systems. The proposed SRDE is in the structure of differential evolution owning new mutation operation and selection mechanism. An effective constraint handling method is presented in the suggested stochastic search technique. The proposed approach has been examined and tested with the numerical results of ED problems with forty-generation units including ramp rate limits, prohibited operating zones and valve-point loading effects also ten-generation units with multiple fuel options. The results of the proposed technique are compared with that of other techniques reported in the literature. For both the cases, the proposed algorithm outperforms the solution reported for the existing algorithms. In addition, the promising results show the robustness, fast convergence and efficiency of the proposed technique.

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.

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.

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.

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

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

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.

Increasing environmental concerns have led to a push for renewable energy sources to be extensively used to reduce emissions. In this paper, we investigate a hybrid dynamic economic emission dispatch (HDEED) problem involving thermal, wind, and photovoltaic (PV) generation systems. Our formulation considers the stochastic nature of both wind and PV generated power, and differences because of mismatches between the actual and allocated wind and PV power. A hybrid backtracking search algorithm with sequential quadratic programming was used to minimize the total operational costs and emissions, while dispatching power to the committed generation units subject to all operational constraints. To verify the efficacy, we applied the proposed technique to solve the dynamic economic emission dispatch problem on five and ten unit test systems. The proposed technique was also used to solve the HDEED problem on IEEE 30 bus, 6-unit and IEEE 57 bus, 7-unit test systems, with and without renewable generation. The results of our numerical simulations show the efficiency of the proposed technique with respect to reducing operational costs and emissions. Moreover, our results show that by incorporating renewable energy into existing power systems, we can reduce operational costs and emissions.

Hybridization of bee colony optimization and sequential quadratic programming for dynamic 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.

A novel space contraction based on evolutionary strategy for economic dispatch