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Strategic bidding problems in electricity markets are complex bi-level optimization problems that are hard to solve. The state-of-the-art approach to solve such problems is to reformulate them as mixed-integer linear programs (MILPs). However, the computational time of such MILP reformulations grows dramatically, once the network size increases, scheduling horizon increases, or randomness is taken into consideration. We propose effective and customized convex programming tools to solve the strategic bidding problem in nodal electricity markets. Our approach is inspired by the Schmüdgen's Positivstellensatz Theorem in semi-algebraic geometry; and results in obtaining close to optimal bidding solutions, besides having a huge advantage on reducing computation time. While the computation time of the state-of-the-art MILP approach grows exponentially when we increase the scheduling horizon or the number of random scenarios, the computation time of our approach increases rather linearly.

Note this talk has been rescheduled to Monday Nov 14.