Recent progress in energy storage have contributed to create large-scale storage facilities and to decrease their costs. This may bring economic opportunities for storage operators, especially via energy arbitrage. However, storage operation in the market could have significant impact on electricity prices. This work aims at evaluating jointly the potential operating profit for a price-maker storage facility and its impact on the electricity prices in New-York state. Based on historical data, lower and upper bounds on the supply curve of the market are constructed. These bounds are used as an input for the robust self-scheduling problem of a price-maker storage facility.