Bilevel programming solution algorithms for optimal price-bidding of energy producers in multi-period day-ahead electricity markets with non-convexities

Abstract

We consider the problem of devising optimal price-offers (bids) for an energy producer participating in a multi-period day-ahead electricity market which exhibits non-convexities due to the discrete nature of the generation units’ commitments and quantities. The problem definition assumes perfect knowledge of the market’s technical characteristics, as well as of the bidding offers of the remaining producers. The problem is formulated as a bilevel optimization model with integer decision variables and linear constraint sets at both levels. The producer acts as the upper-level decision maker, aiming to find the optimal bidding offers that will maximize his individual profit upon clearing of the market, while an independent system operator acts as the lower-level decision maker, aiming to ensure satisfaction of the demand for energy at the minimum total bid-cost. Utilizing the theoretical properties of this problem, we develop both a heuristic as well as an exact algorithmic solution methodology for tackling it. More effective between the two naturally turns out to be the heuristic approach, which works iteratively, optimizing a single price-offer at each iteration, given that the remaining ones are kept fixed at their current values. We present experimental results demonstrating that it provides high quality solutions, while exhibiting reasonable computational requirements. We also demonstrate how the underlying theory can be utilized for the generation of valid inequalities to a suitable relaxation of the original formulation, in which the so-called bilevel feasibility of the obtained solution is not guaranteed. These inequalities are exploited within a cutting-plane framework by the exact solution approach for identifying the global optimum of the problem.