懲罰函數─直接搜尋法應用於考慮環保限制之經濟調度

Environmentally-Constrained Economic Dispatch Using a Penalty Function-Direct Search Method

本研究擬提出一套簡單、有效之演算法，以解決考量環保限制之經濟調度問題。對於處理污染限制之經濟調度問題，本文乃採懲罰函數─直接搜尋演算法以改善傳統直接搜尋法容易落入局部最佳解的問題。首先，將調度週期內污染量限制的不等式限制條件，經由懲罰函數轉換將其併入目標函數；其次，改良型直接搜尋法則用以最小化此目標函數，許多不等式限制條件及非凸集之機組燃料成本曲線皆可經由直接搜尋的程序來適當地控制；最後透過懲罰參數規律性的調整以逼近全域或接近全域最佳解。實例模擬結果顯示，比起其它文獻已經發表的最佳化技巧，本文所提出的演算法能以合理的時間內求得較高品質的解。

This paper develops a simple and efficient approach for solving theenvironmentally-constrained economic dispatch (ECED). The conventionaldirect search method (DSM) makes no guarantee that the solutions are optimalor even close to the optimal solution for solving the ECED problem.This situation can be improved by the proposed approach, a penalty function–direct search method (PF-DSM). First, the total emission limit overthe scheduling horizon is constrained by adding it as the exact penalty termto the objective function to form a generalized objective function. Second,an improved direct search method is also applied to minimize the generalizedobjective function. A number of inequality and equality constraintsand nonconvex unit cost functions can be handled properly in the directsearch procedure. Finally, satisfactory solutions were obtained by regularlyadjusting the penalty parameter. The results obtained by use of the pro- posed algorithm are compared with those obtained using previously publishedmethods to illustrate the merits of this technique.