Liberalization of electricity markets and dissemination of renewable energy sources leads to the variability of electricity prices, intermittency of generation and thus the necessity to develop new electrical energy storage systems for integration of renewables. Due to the high volatilities, stochastic optimization methods need to be applied for operational and investment planning of power plants. This paper presents a stochastic approach to solving a combined optimization problem for short-term scheduling and long-term investment planning of storage power plants for 30-year long planning horizon. The proposed methodology is applied to cost-benefit analysis of stand-alone storage plants operating under market conditions through price arbitrage: pumped hydropower plant and hydrogen storage plant. The results show that the pumped hydropower plant is profitable, whereas the hydrogen storage plant project is not economically viable without additional support. Possible economic incentives resulting in a profitable hydrogen storage plant are examined.