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This article investigates customer-side energy storage system operations to minimize the electricity bill under a peak load limitation constraint and uncertain environments. Specifically, it is discussed how the demand and price uncertainties impact the system performance. It is shown that the energy storage system operation based on the Markov decision process with stochastic information has near-optimum performance, which is achieved by an iterative method with perfect information when the electricity price and demand are slightly varied. To address a problem, such as the failure of peak load reduction due to high uncertainties, two heuristic methodologies are suggested by modifying the peak load threshold and the charge/discharge reservation quantity. It is demonstrated that the proposed approach can effectively manage the uncertainties with marginal performance degradation.