Tight Unit Commitment models with Optimal Transmission Switching: Connecting the dots with perturbed objective function

In this paper we address the issue of solving a Unit Commitment (UC) problem including the transmission network with Active Switching (AS). The switching operation consists in a dynamic reconfiguration of the network, i.e. a tripping of some lines; this paradigm is named UC with Optimal Transmission Switching (UCOTS). The UCOTS is a novel way to leverage grid controllability, that may re-route the electrical energy in the network to resolve some line congestion and reduce the overall production cost, e.g. by allowing to increase the power output of cheaper units. The UCOTS can also aim at improving other system performances such as stability. This work provides a tight Mixed Integer Linear Programming (MILP) formulation of the UCOTS. It proposes to approximate the quadratic thermal cost objective function by means of a perspective cuts (PC) piece-wise-linear function and to perturb it in a special way, in order to break some of the symmetries deriving from the OTS variables. We show that, combining these two ingredients and using recent tight UC constraints formulations, optimal and near-optimal solutions can be obtained in reasonable computing time for a custom 81 units-IEEE 118 bus test case without resorting to any kind of heuristic.