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

What is it about?

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 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 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.

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Why is it important?

The key contributions of the paper are summarized as follows: a) Modeling an original decentralized grid-connected MG operation scheduling problem considering PHEVs’ demand uncertainty using BLP approach with respect to DMs risk aversion level is the main contribution of the paper. Uncertainty handling in a bi-level framework is still a key point for the operation of MGs. b) Literature reveals that it is still a challenging issue to cover uncertainties caused by random loads while optimizing bi-level problems in economy. It is noticable that, in contrast to the relative literature, in this paper the final bi-level programming problem is directly formulated through the CVaR approach and, therefore, rely on a stronger mathematical theory. c) Addressing the DMs attitude toward risk using CVaR approach through a non-cooperative game in a robust manner is the other key contribution of the paper. Accordingly, the model is fully interactive and provides full control of the system operation elements with respect to different viewpoints of DMs. d) The model leads to a strong almost linear relationship between the system total cost and the DMs risk aversion level. e) Using the Kolmogrove-Smirnov (KS), Chi-Square (CS), and Anderson-Darling (AD) tests, extensive goodness-of-fit analysis is carried out to test which probability distribution fits, satisfactorily, the empirical distribution of the economic costs and power exchange between the MG and upstream network as the key variables of the problem.