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This paper explores a modeling framework necessary for analyzing the impact of energy storage on power system operations. We first develop a unifying definition of energy storage as an abstraction of many heterogeneous energy storage options, including flexible demand response. Then we develop, a multi-time-scale model of energy storage tailored for temporal hierarchies of power systems. Based on this model, the impact of energy storage in primary control, secondary frequency regulation, and economic dispatch can be pinpointed and analyzed explicitly. We then propose a simple scalar performance index for quantifying the value of energy storage over different horizons in competitive electricity markets. This performance index provides a value-based criteria for operating energy storage over different time horizons. Numerical case studies are conducted in a modified IEEE 14-bus system, which includes flywheel and battery energy storage.