A solution based on fuzzy max-min approach to the bi-level programming model of energy and exiramp procurement in day-ahead market

Document Type: Article


1 Faculty of Industrial and Systems Engineering, Tarbiat Modares University, Tehran, Iran.

2 Faculty of Electrical & Computer Engineering, Tarbiat Modares University, Tehran, Iran.


In this paper, we focus on solving the integrated energy and flexiramp procurement problem in the day-ahead market. The problem of energy and ramp procurement could be perfectly analyzed through Stackelberg concept, because of its hierarchical nature of the decision-making process. Such a circumstance is modeled via a bi-level programming, in which suppliers act as leaders and the ISO appear as the follower. The ISO intends to minimize the energy and spinning reserve procurement cost, and the suppliers aim to maximize their profit. To solve the proposed model, a fuzzy max-min approach is applied to maximize the players’ utilities. The objectives and suppliers’ dynamic offers, determined regarding the market clearing prices, are reformulated through fuzzy utility functions. The proposed approach is an effective and simple alternative to the KKT method, especially for problems with non-convex lower-level.


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