Binary-constrained complementarity problems: a solution approach and applications to energy market and transportation network Seminar

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Complementarity problems have become an important tool for modelling equilibria. In energy markets for example, they can be used to compute the production level of each Nash-Cournot producer and the price of energy in order to satisfy demand. Complementarity problems have also been used to model the flow pattern in a traffic network given a set of travel demands between the origin-destination pairs. Other applications of complementarity problems can be found in the literature of game theory and market equilibrium in economics. In this presentation, we will explore a study of equilibria in traffic networks and power systems with storage in the presence of logic constraints. These constraints are modelled as binary variables that are added to standard complementarity-based equilibrium models. The resulting formulations are binary-constrained linear complementarity problems (we will briefly discuss a solution algorithm). For the traffic equilibrium problem, we show how logic constraints can introduce some equity in the assignment of traffic flows when more than one equilibrium exists. For power systems with storage, we show how the presence of a storage operator in a power market may be beneficial in terms of stabilizing the price of electricity during peak demand periods. A particular novelty in the approach presented here is that the storage operator operates as a service provider rather than a competitor to the power producers.