Robust bi-level risk-based optimal scheduling of microgrid operation against uncertainty

¹ Department of Industrial Engineering, Sanandaj Branch, Islamic Azad University, Sanandaj, Iran
² Department of Electrical Engineering, Sanandaj Branch, Islamic Azad University, Sanandaj, Iran
³ School of Economics and Management, Tsinghua University, Beijing, PR China
⁴ School of Economics and Management, Chang’an University, 710064 Xi’an Shaanxi, PR China

^* Corresponding author: herishgolpira@gmail.com

Received: 4 September 2018
Accepted: 20 April 2019

Abstract

The model introduced in this paper is the first to propose a decentralized robust optimal scheduling of MG operation under uncertainty and risk. The power trading of the MG with the main grid is the first stage variable and power generation of DGs and power charging/discharging of the battery are the second stage variables. The uncertain term of the initial objective function is transformed into a constraint using robust optimization approach. Addressing the Decision Maker’s (DMs) risk aversion level through Conditional Value at Risk (CVaR) leads to a bi-level programming problem using a data-driven approach. The model is then transformed into a robust single-level using Karush–Kahn–Tucker (KKT) conditions. To investigate the effectiveness of the model and its solution methodology, it is applied on a MG. The results clearly demonstrate the robustness of the model and indicate a strong almost linear relationship between cost and the DMs various levels of risk aversion. The analysis also outlines original characterization of the cost and the MGs behavior using three well-known goodness-of-fit tests on various Probability Distribution Functions (PDFs), Beta, Gumbel Max, Normal, Weibull, and Cauchy. The Gumbel Max and Normal PDFs, respectively, exhibit the most promising goodness-of-fit for the cost, while the power purchased from the grid are well fitted by Weibull, Beta, and Normal PDFs, respectively. At the same time, the power sold to the grid is well fitted by the Cauchy PDF.