Arithmetic optimization algorithm with three-dimensional chaotic mapping in spherical coordinate system for combined economic emission dispatch problem

Yixuan Li

doi:10.1016/j.apenergy.2024.124953

2025-02-01

PRE

DOI：10.1016/j.apenergy.2024.124953

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The objective of the Combined Economic Emissions Dispatch (CEED) problem is to reduce pollutant emissions by lowering the total cost of generating electricity while complying with all other constraints. The multiple objective functions of the CEED problem may be converted into a single objective by using a price penalty factor. Then it was solved with the Arithmetic Optimization Algorithm (AOA) with three-dimensional chaotic mapping in spherical coordinate system. Firstly, five three-dimensional chaotic mappings in Cartesian coordinate system are embedded in the Mathematical Optimization Accelerator (MOA) and the Mathematical Optimization Probability (MOP) of the original algorithm. Secondly, 15 three-dimensional chaotic mappings in spherical coordinate system are constructed from the values of 5 three-dimensional chaotic mappings in Cartesian coordinate system through the mathematical expressions of mode length, polar angle and azimuth angle in spherical coordinate system. Then through a large number of simulation experiments, five best three-dimensional chaotic mappings in the spherical coordinate system are selected to be embedded into the two parameters (MOA and MOP) of the original algorithm to better balance the algorithm's global and local searching ability. The superiority of the improved algorithm is verified by employing 12 benchmark test functions in CEC2022. Eventually, the improved optimal algorithm (IAOA-r) to solve the power system CEED problem is tested on six generating units with four different loads (150 MW, 175 MW, 200 MW and 225 MW). The results of the improved algorithm are compared and analyzed with the results of the Reptile Search Algorithm (RSA), Prairie Dog Optimization (PDO), Bat Algorithm (BAT), Whale Optimization Algorithm (WOA), Harris Hawk Optimization (HHO), Rat Swarm Optimization (RSO). The results demonstrate that the improved algorithm is capable of obtaining optimal fuel costs and smaller pollution emissions in every test case.

Keyword:

Combined economic emissions dispatch

Arithmetic optimization algorithm

Three-dimensional chaotic mapping

Spherical coordinate system