In recent years, with increasing renewable supply variability, thermal power plants have started up and shut down more frequently. These discrete commitment decisions, optimized in the unit commitment (UC) problem, have an impact on system operations as well as generation expansion planning (GEP). The non-convex costs associated with the commitment decisions may also lead to generators' incentive to deviate from the optimal dispatch under locational marginal prices. In this dissertation, we

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... t propose a convex relaxation of UC based on a primal formulation of the Lagrangian dual problem. This convex relaxation is used (i) to solve the convex hull pricing problem in polynomial time, providing prices with better incentives in non-convex electricity markets, and (ii) to construct a computationally efficient GEP model that represents operational flexibility limits. Next, we present a tight formulation for the commitment of combined-cycle units with representation of their transition ramping. Finally, we propose a pricing method that reduces out-of-market payments in multi-interval real-time markets.