Optimal bilevel scheduling of pumped hydro storage in day-ahead energy market

Energy storage as a special market player has different characteristics compared with other market players like generators and load in the electricity market. In this paper, we built a bilevel scheduling model, the upper-level model aims for maximum profit of pumped hydro storage (PHS) and the lower-level model is the market clearing process. We use the KKT conditions to transform the bilevel model into a single-level model. Then, the objective function is linearized by the strong duality condition, and the equations of the KKT conditions are linearized by the big M method. The original bilevel model is finally transformed into a single-level mixed integer linear problem and can be solved by commercial solver such as CPLEX. The results show that the PHS would get the maximum profit when it bids at the locational marginal price (LMP) for both charging and discharging.