# Dynamic economic emission dispatch of combined heat and power system based on multi-objective differential evolution algorithm

## TL;DR

This paper introduces an improved multi-objective differential evolution algorithm to optimize the economic and environmental performance of combined heat and power systems.

## Contribution

The novel contribution is an enhanced multi-objective differential evolution algorithm with adaptive parameters and improved optimization performance for energy systems.

## Key findings

- The improved algorithm achieved a generational distance of 0.0513 and a hyper volume metric of 0.1301 on the Zitzler-Deb-Thiele 1 function test.
- It reduced fuel cost to $2,300,590 and pollution emissions to 200,285 kg in the IEEE 30-node system simulation.
- The algorithm outperformed other methods in hyper volume metric and inverted generational distance metrics.

## Abstract

Engineering frequently deals with multi-objective optimization problems. In the scheduling of combined heat and power systems, the competing goals of economic cost and pollutant emission are challenging for conventional single-objective algorithms to handle, necessitating the use of effective multi-objective optimization algorithms. The research design improves the multi-objective differential evolution algorithm, which is constructed by making the scaling factor and crossover probability change adaptively, adopting non-dominated sorting, combining the congestion distance calculation to deal with multi-objectives, adding elite populations and quadratic mutation links, and so on. Based on this algorithm, the dynamic economic emission dispatch model of combined heat and power system is constructed to optimize the economic and environmental benefits of the system. The results revealed that the improved multi-objective differential evolution algorithm in Zitzler-Deb-Thiele 1 function test had generational distance of 0.0513, inverted generational distance of 0.3265, and hyper volume metric of 0.1301. Its Pareto optimal frontier fitted the standard curve better and was uniformly distributed, giving better performance. It was applied to solving dynamic economic emission dispatch model for combined heat and power system and compared with time-varying multi-objective PSO algorithm and others. Based on the ieee 30-node system deployment, it contained two cogeneration units, seven generator units, and one heating unit. The improved multi-objective differential evolution algorithm optimized the fuel cost as low as $2300590 and the pollution emission as low as 200285 kg. Its Pareto optimal frontier distribution was better, and it performed better in the hyper volume metric and inverted generational distance metrics. The research demonstrates that the improved multi-objective differential evolution algorithm can effectively balance operational cost and performance, achieving reduced fuel cost and pollution emissions. Furthermore, it exhibits strong adaptability and optimization capabilities in practical engineering applications, enhancing system operation efficiency and reducing pollution.