Improved Arithmetic Optimization Algorithm To Solve Economic Dispatch Problem In Power System

The economic dispatching problem of power system is very important in power production.The economic load dispatch(ELD)problem is to minimize the power generation fuel cost under the condition of meeting the power supply demand and operation constraints.Due to the large amount of pollutants emitted in the process of thermal power generation,the combined economic emission dispatch(CEED)problem should consider both fuel cost and pollutant emissions to minimize them.At present,intelligent optimization algorithms are the effective ways to solve the economic scheduling problem in power system.In this thesis,the arithmetic optimization algorithm(AOA)was used to solve this kind of problems,and the improved AOA was proposed to enhance its performance.At the same time,a new punish strategy was proposed for the constraint problems.The main research contents are described as follows.(1)An arithmetic optimization algorithm(AOA)based on elementary function perturbation is proposed to solve the ELD problem.AOA based on elementary function perturbation introduces six elementary functions,which are sine function,tangent function,hyperbolic secant function,power function,hyperbolic cosecant function and inverse cosine function.Math optimizer accelerated(MOA)and math optimizer probability(MOP)of AOA were added with the disturbance generated by the elementary functions to the original variation trend respectively so as to improve and balance its exploration and exploitation ability,enhance its global search ability,and avoid it falling into the local optimal.At the same time,the convergence speed of the algorithm is improved.Using 23 benchmark functions,it is proved that the AOA based on elementary function perturbation is more effective than the original AOA.At the same time,three ELD cases with different scales were selected for simulation experiments.The simulation results show that the improved method is better than other optimization algorithms in solving ELD problem,and the cost can be reduced.(2)A probability distribution AOA based on variable order penalty functions was proposed to solve CEED problem.By using the maximum/maximum price penalty factor,the multi-objective optimization problem of CEED is transformed into the single objective optimization problem.The energy attenuation is used to replace the variation trend of parameter MOA in the original AOA to control the algorithm to select search mode,which better balances the exploration and exploitation of the algorithm.Five probability distribution functions,namely exponential distribution,uniform distribution,normal distribution,beta distribution and gamma distribution,were used to replace the fixed value parameters of controlling position update in AOA,in order to enhance its search ability and improve its convergence speed.The CEC-2017 benchmark functions were used to test the effectiveness of the improved method.The original AOA was compared with five improved AOAs,and the best improvement strategy was selected.The simulation was compared with the intelligent optimization algorithm with better performance of the CEC-2017 benchmark functions to verify its effectiveness.When dealing with the constraints of CEED problem,five penalty functions with varying order are proposed,which are sine function,hyperbolic tangent function,arctangent function,V-type function and hyperbolic secant function,respectively to replace the traditional fixed penalty function.The CEED problem cases with 6 units were selected to be solved under the total demand of 150 MW,175MW,200 MW and 225 MW respectively.The experimental results show that the optimization algorithm based on probability distribution is better than other optimization algorithms in solving CEED problems,and the variable order penalty strategy has higher solution quality and convergence speed than the fixed penalty strategy.(3)A multi-objective AOA based on random search strategies was proposed to solve CEED problem.The parameter MOA in AOA is an important parameter to control the selection of search mode.Adding hyperbolic tangent fluctuation to the changing trend of MOA improves the exploration ability of the algorithm.At the same time,MOP in AOA were replaced by four random search strategies,namely tangent flight,Lévy flight,Brownian motion and Lognormal flight,which enhanced the global search ability of the algorithm and avoided it falling into local optimum.In order to achieve multiobjective AOA and obtain the Pareto optimal solution with high coverage,the repository is first used to store the non-dominant Pareto optimal solutions obtained so far,then a roulette mechanism is used to select a leader from the repository for position update,and finally the Pareto optimal solution set is obtained.In order to verify the effectiveness of the proposed multi-objective AOA,20 multi-objective benchmark test functions were used for simulation,and the improvement strategy with the best effect among the four improvement methods was selected and compared with other multiobjective optimization algorithms.Next,three CEED cases with different sizes were used for simulation experiments,and two targets of fuel cost and pollutant emission were compared with the methods in other literature.Experimental results show that the proposed algorithm is better than other algorithms in solving CEED problems,has better optimization accuracy,and can obtain the Pareto optimal solution set with uniform distribution.