Recent progress in energy storage raises the possibility of creating large-scale storage facilities at lower costs. This may bring economic opportunities for storage operators, especially via energy arbitrage. However, storage operation in the market could have a noticeable 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 the New York state market. 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. Our computational experiments show that the robust strategies thus obtained allow to reduce significantly the loss exposure while maintaining reasonably high expected profits.