Exercise of Market Power on Ramp Rate in Wind-Integrated Power Systems

With an increasing penetration of wind power, there is likely to be an increasing need for fast-ramping generating units. These generators ensure that no load is lost if supply drops due to the uncertainties in wind power generation. However, it is observed in practice that, in a presence of network constraints, fast-ramping generating units are prone to act strategically and exercise market power by withholding their ramp rates. In this paper we model this gaming behavior on ramp rates. We assume a market operator who collects bids in form of marginal costs, quantities, and ramp rates. He runs a ramp-constrained economic dispatch given the generators' bids, forecasted demand, and contingencies. Following the game-theoretic concepts, we set up a multi-level optimization problem. The lower-level problem is the ramp-constrained economic dispatch and the higher-level represents the profit maximization problems solved by strategic generators. The whole problem is formulated as an equilibrium problem with equilibrium constraints (EPEC). The outcome of the EPEC problem is a set of Nash equilibria. To tackle the multiple Nash equilibria problem, the concept of the extremal-Nash equilibria is defined and formulated. We model the concept of extremal-Nash equilibria as a single-stage mixed-integer linear programming problem (MILP) and demonstrate the application of this mathematical framework on an illustrative case and on a more realistic case study with tractable results.