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This paper presents linear programming (LP) formulations for short-term energy time-shift operational scheduling with energy storage systems (ESSs) in power grids. In particular, it is shown that the conventional nonlinear formulations for electric bill minimization, peak shaving, and load leveling can be formulated in the LP framework. New variables for the peak and off-peak values are introduced in peak shaving and load leveling model, and the historical peak value for demand charge are considered in the electric bill minimization model. The LP formulations simplify computation while maintaining the accuracy for including linear technical constraints of ESSs, such as the state-of-charge, charging/discharging efficiency, output power range, and energy limit considering the life cycle of ESS. Proposed LP formulations have been implemented and verified in practical power systems and a large-scale industrial customer using historical data

Linear Formulation for Short-Term Operational Scheduling of Energy Storage Systems in Power Grids