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Description: We consider the problem of a price-taker generating company that wants to select energy offering strategies for its generation units, to maximize the profit while considering the uncertainty of market price. First, we review central references available in literature about the use of Robust Optimization (RO) for price-uncertain energy offering, pointing out how they can expose to the risk of suboptimal and even infeasible offering. We then propose a new RO method for energy offering that overcomes all the limits of other RO methods. We show the effectiveness of the new method on realistic instances provided by our industrial partners, getting very high increases in profit. Our method is based on Multiband Robustness (MR - Büsing, D'Andreagiovanni, 2012), an RO model that refines the classical RO model by Bertsimas and Sim, while maintaining its computational tractability and accessibility. MR is essentially based on the use of histogram-like uncertainty sets, which result particularly suitable to represent empirical distributions commonly available in uncertain real-world optimization problems.

Description: The classical Unit Commitment Problem (UC) consists in determining the production of a set of thermal and hydro power generation units over a given time horizon, in order to meet a forecast energy demand and minimize a cost function. In the last years, in connection with the UC, increasingly attention has been given to active switching, namely the possibility of changing the topology of the transmission network by tripping some of the lines. Active switching has been indeed recognized as an important way to improve capacity and reliability of the network. Modifying the network topology is also very useful in modern electricity systems, where the penetration of on-programmable renewable energy sources is high and tends to be very concentrated in some zones of the network. As a consequence, the interest for automatic and optimized switching procedures is currently spreading. In this paper, we address the UC when complemented by active switching, thus leading to so-called Unit Commitment with Optimal Transmission Switching (UCOTS). We formulate the UCOTS as a mixed integer linear program, where we unify tight formulations recently proposed in literature for relevant subfamilies of constraints of the problem. Concerning the cost function, in our formulation we approximate the quadratic thermal cost objective function by a piecewise linear function based on perspective cuts and we propose a new simple and effective way to perturb it, with the aim of breaking symmetries induced by optimal transmission switching decision variables. Our original solution approach also exploits specialized branching priorities. Computational experiments on realistic UCOTS instances highlight that our new framework is able to find optimal and near-optimal solutions in reasonable amount of time by direct use of a state-of-the-art commercial MIP solver.

Description: We propose a new Robust Optimization method for the energy offering problem of a price-taker generating company that wants to build offering curves for its generation units, in order to maximize its profit while taking into account the uncertainty of market price. Our investigations have been motivated by a critique to another Robust Optimization method, which entails the solution of a sequence of robust optimization problems imposing full protection and defined over a sequence of nested subintervals of market prices: this method presents a number of issues that may severely limit its application and computational efficiency in practice and that may expose a company to the risk of presenting offering curves resulting into suboptimal or even infeasible accepted offers. To tackle all such issues, our method provides for solving one single robust counterpart, considering an intermediate level of protection between null and full protection, and to make energy offers at zero price, practically eliminating the risk of non-acceptance. Computational results on instances provided by our industrial partners show that our new method is able to grant a great improvement in profit.