Optimization economic dispatch with transmission losses using by firefly 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.

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

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

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.

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

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.

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.

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.

This chapter discusses the application of linear programming (LP) techniques to find the optimal solution of the economic dispatch (ED) problem without considering transmission losses. The ED problem is concerned with optimizing the power generated by several generating units. The objective is to find the optimal power produced by each unit to supply the required load at minimum total cost. The generation cost associated with each unit is usually in the form of a quadratic or cubic function of the power produced. To apply LP, these nonlinear cost functions have to be linearized. The optimal solution is then determined by LP based on the approximate linear model. Piece-wise linearization methodology is adopted in this chapter. To evaluate the performance of the linearization method, a comprehensive set of benchmark test problems is used. LP solutions of linearized ED problems are compared with several other techniques from the literature. The LP technique with piece-wise linearization shows an overall competitive advantage in terms of total cost, solution time, and load satisfaction.

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

The economic load dispatch problem is a very important practical problem in electric power systems operation, where an efficient solution can lead to cost and emissions reductions. The use of metaheuristics, as the Firefly Algorithm, for the solution of economic load dispatch problems has been shown to be a more appropriate alternative than classical optimisation methods. In this work, we have proposed a new variant for the Firefly Algorithm, considering a non-homogeneous population. This new variant was validated using ten benchmark functions, and then applied to solve a 15-units economic load dispatch problem, considering transmission line losses, power limits, ramp limits and prohibited zones for each generator, and a 13-units non-convex system with valve-point loading effect in the cost function and power generation limits. The results show that the proposed non-homogeneous variant is able to reach better solutions than the original Firefly Algorithm, using both penalty and non-penalty power balance constraint handling methods. In general, the non-penalty approach reached better results than the penalty method. Moreover, the new variant presented relatively competitive results for the economic load dispatch problems considered, when compared to the best results found in the literature.

Dynamic economic emission dispatch problems are complex optimization tasks in power systems that aim to simultaneously minimize both fuel costs and pollutant emissions while satisfying various system constraints. Traditional methods often involve solving intricate nonlinear load flow equations or employing approximate loss formulas to account for transmission losses. These methods can be computationally expensive and may not accurately represent the actual transmission losses, affecting the overall optimization results. To address these limitations, this study proposes a novel approach that integrates transmission loss prediction into the dynamic economic emission dispatch (DEED) problem. A Random Forest machine learning model was offline-trained to predict transmission losses accurately, eliminating the need for repeated calculations during each iteration of the optimization process. This significantly reduced the computational burden of the algorithm and improved its efficiency. The proposed method utilizes a powerful multi-objective stochastic paint optimizer to solve the highly constrained and complex dynamic economic emission dispatch problem integrated with random forest-based loss prediction. A fuzzy membership-based approach was employed to determine the best compromise Pareto-optimal solution. The proposed algorithm integrated with loss prediction was validated on widely used five and ten-unit power systems with B-loss coefficients. The results obtained using the proposed algorithm were compared with seventeen algorithms available in the literature, demonstrating that the multi-objective stochastic paint optimizer (MOSPO) outperforms most existing algorithms. Notably, for the Institute of Electrical and Electronics Engineers (IEEE) thirty bus system, the proposed algorithm achieves yearly fuel cost savings of USD 37,339.5 and USD 3423.7 compared to the existing group search optimizer algorithm with multiple producers (GSOMP) and multi-objective multi-verse optimization (MOMVO) algorithms.

This paper presents a new resolution approach of Economic Dispatch (ED) problem considering wind power penetration planning with specified wind farm locations. Firstly, the total fuel cost of conventional generating units is optimized with a wind power contribution. When the optimal wind power penetration for each wind farm location is specified, a planning process is performed to get the total number and the total cost of wind generators. Three levels of the total wind power penetration are examined, which are 25%, 30% and 35%. The Wind Power Planning (WPP) is effected based on the practical weather report for each wind farm location. The ED problem is solved taking in the account the valve point effects of thermal generating units and using Time Varying Acceleration Coefficients (TVAC) based Particle Swarm Optimization method (PSO) due to its effectiveness overcoming the conventional PSO. The model is applied on the well known IEEE 30 bus test system.

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.