Optimizing energy and demand response programs using multi-objective optimization

This paper proposes a new multi-objective day-ahead market clearing (DAMC) mechanism with demand response offers, considering realistic voltage-dependent load modeling. This paper presents several objectives such as Social Welfare Maximization including demand response offers (SWM), Load reduction Minimization (PredM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${P}_{\mathrm{red}}{M}$$\end{document}), and Load Served Error (LSE) minimization. Energy and demand-side reserves are cleared through co-optimization process. The proposed approach is particularly suitable for stressed system conditions, where demand elasticity alone cannot yield a feasible optimal solution. The feasible solution is obtained by invoking demand-response offers. Here, multi-objective Strength Pareto Evolutionary Algorithm 2+ (SPEA 2+) has been used to solve the proposed DAMC problem. This paper emphasizes the requirement for selecting judiciously, a combination of objectives best suitable for the DAMC. The effectiveness of proposed DAMC scheme is confirmed with the results obtained from IEEE 30 bus system. It is assumed that all the generators and loads participate in DAMC. Two different cases—one with constant load modeling and the other with the voltage-dependent load modeling—have been simulated at stressed loading conditions. When loads are modeled as the voltage dependent, then it is shown that SWM and PredM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${P}_{\mathrm{red}}{M}$$\end{document} are not valid single or multiple objectives with this load model, due to reduction in load served. With voltage-dependent load modeling, SWM and LSE minimization are best suited objectives to be optimized simultaneously. The obtained Pareto optimal front allows system operator to make a better decision regarding compromise between the conflicting objective functions.