A Bio-inspired Meta-heuristic Optimization approach for Economic Load Dispatch

An ɛ-dominance-based multiobjective genetic algorithm for economic emission load dispatch optimization problem

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.

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

Economic Load Dispatch (ELD) optimization is an important and difficult task in power system planning. Previously, most of the research mainly focused on proposing various evolutionary algorithms (EAs) to pursue better results of ELD problems. However, few comprehensive analysis of the effects of various constraint handling techniques (CHTs) on the performance of EA-based techniques are available so far. In this paper, we try to fill this gap by experimentally testing the algorithmic variants of combining four effective and widely used EAs with three CHTs. From the experimental results on the ELD problems with valve-point and those problems with both valve-point and multiple-fuel effect, several important conclusions can be achieved, including 1) for the low scale ELD problem with valve-point only, the selection of EAs is more important than CHTs; 2) for the large scale problems, CHTs play crucial roles; 3) the appropriate combination of EA and CHT is helpful to achieve better performance. This study is also expected to provide solid basis for further strengthening the robustness of EAs for ELD optimization. It is also interesting to observe that the experimental results obtained in this paper are much better than those of the previous effective ELD optimization algorithms.

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.

Electric power system problems are amongst the most complex and challenging problems of electric industry market. The main aim of economic load dispatch in power system operation control and planning is to satisfy the energy demand at the least cost while fulfilling all the equality and inequality constraints. This paper presents the mathematical formulation of optimal load dispatch problem by considering the sources of energy generation from conventional power plants and all the important constraints of the realistic power system. In the proposed research the memetic optimizer is developed by hybridizing slime mould algorithm with pattern search algorithm. The proposed hSMA-PS has been tested to obtain the solution of economic load dispatch problem and experimentally it has been observed that the proposed memetic optimizer is providing cost effective solution to complex economic load dispatch problem of electric power system.

A multi-objective multi-verse optimization algorithm for dynamic load dispatch problems

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.

Optimization of economic load dispatch of higher order general cost polynomials and its sensitivity using modified particle swarm optimization

This paper presents applications of Antlion optimization algorithm (ALO) for handling optimal economic load dispatch (OELD) problems. Electricity generation cost minimization by controlling power output of all available generating units is a major goal of the problem. ALO is a metaheuristic algorithm based on the hunting process of Antlions. The effect of ALO is investigated by solving a 10-unit system. Each studied case has different objective function and complex level of restraints. Three test cases are employed and arranged according to the complex level in which the first one only considers multi fuel sources while the second case is more complicated by taking valve point loading effects into account. And, the third case is the highest challenge to ALO since the valve effects together with ramp rate limits, prohibited operating zones and spinning reserve constraints are taken into consideration. The comparisons of the result obtained by ALO and other ones indicate the ALO algorithm is more potential than most methods on the solution, the stabilization, and the convergence velocity. Therefore, the ALO method is an effective and promising tool for systems with multi fuel sources and considering complicated constraints.

To overcome the challenges of conventional power systems, such as increasing power demand, requirements of stability and reliability, and increasing integration of renewable energy sources, the concept of microgrids was introduced and is currently one of the most important solutions for solving the mentioned problems. Generally, microgrids have two operating modes, namely grid-connected and islanded modes. Based on the literature and its unique characteristics, the islanded mode is more challenging than the other one. In this paper, a new self-adaptive comprehensive differential evolution (SACDE) algorithm is proposed for solving economic load dispatch (ELD) and combined economic emission dispatch (CEED) problems, achieving optimal power consumption in isolated microgrids. Initially, SACDE is employed for solving the ELD problem as a single-objective function, meaning that the operational cost is just considered as the objective function, and thereby, the resources are scheduled accordingly. Then, a multi-objective platform based on SACDE is also proposed to solve the CEED problem. It means two objective functions, including operational cost and emission, are simultaneously optimized. For evaluating the performance of the proposed method, three different scenarios under various cases are considered. According to the results, when SACDE is employed to solve the single objective function (cost minimization) problem, it has better performance than other methods. In terms of the bi-objective scheme (cost and emission minimization), SACDE is significantly superior to the price penalty factor technique which is frequently used in previous studies.

In this paper we propose an Interval based Differential Evolution (IDE) algorithm, an improved version of Differential Evolution (DE) algorithm using interval arithmetic. After estimating the global minimum roughly, the IDE algorithm constructs a mechanism which updates the upper bound of global minimum at each generation and defines an efficient termination criterion. Also at each generation it modifies the new population using the subset of current population and thus reduces the computational effort. We apply the proposed algorithm to the Combined Economic Emission Load Dispatch (CEELD) problem which obtains the optimal amount of generated power for the thermal generating units in the system by simultaneously minimising the fuel and emission costs. We find the proposed algorithm to be more efficient than the conventional DE when applied to IEEE 6 generators system. We also find that these results using the IDE algorithm are better than some recently reported evolutionary algorithms.

Economic dispatch (ED) problem exhibits highly nonlinear characteristics, such as prohibited operating zone, ramp rate limits, and non-smooth property. Due to its nonlinear characteristics, it is hard to achieve the expected solution by the classical methods. To overcome the challenging difficulty, this paper proposes an improved firefly algorithm (FA) to solve economic dispatch (ED) problem. The improved FA employs two strategies to enhance the search ability and avoid the premature usually suffered from in standard FA. The first one is based on the distance information among the fireflies, and it adjusts the light absorption coefficient adaptively. The other one is a decreasing strategy for the randomization parameter. Additionally, a crossover operation is employed to create potential solution with high diversity. The designs are able to enhance the search ability and performance of FA, which have been demonstrated on six benchmark functions. To validate the proposed algorithm, we also use three different systems to demonstrate its efficiency and feasibility in solving ED problem. The experimental results show that the proposed FA method was capable of achieving higher quality solutions in ED problems.

This paper presents a modified particle swarm optimization (MPSO) for economic load dispatch (ELD) problem. Considering multifuel operations, valve-point effects, accurate curve fitting, etc., real cost function is more complex than a conventional second order cost function in the deregulated changing market. Modified PSO consists of problem dependent variable number of promising values (in velocity vector), unit vector, error-iteration dependent step length, etc. It reliably and accurately tracks a continuously changing solution of the complex cost function and no extra concentration/effort is needed for more complex higher order cost polynomial in ELD. Constraint management is incorporated in the modified PSO. The modified PSO has balance between local and global searching abilities, and an appropriate fitness function helps to converge it quickly. To avoid the method to be frozen, stagnated/idle particles are reset. In this paper, sensitivity of higher order cost polynomial is also analyzed visually to realize the importance of higher order cost polynomial in ELD. Finally, benchmark data and methods are used to show the effectiveness of the proposed method.

The Economic Load Dispatch (ELD) is considered to minimize the only fuel cost in power system planning and operation. Due to environmental issues, the emission amount released by thermal power generation should be considered in minimizing the total cost generation as well. This make the power dispatch problem become multi-objective problem that called Economic and Emission Load Dispatch (EELD). This paper investigates the performances of Artificial Bee colony (ABC) algorithm for determining optimal solution for EELD problem. In this paper, the EELD problem is formulated as a single objective problem by taking minimization of total cost and emission level as separated objective. The cost characteristic of thermal generator considered the effect of opening and closing of the valve for practical application. The ABC algorithm has been tested on standard test systems which is 10-generating unit test system in order to validate the effectiveness of proposed ABC algorithm. The results obtained have been compared with reported result by other methods in literature. From the result, it found that ABC algorithm is better than other methods for minimizing fuel cost of thermal power generation and obtained comparative results in reducing the emission level.