Feasible regions (shadow area) for the maximum up reserves that storage can provide by using an LP relaxed (left) or an integer (right) model.

Feasible regions (shadow area) for the maximum up reserves that storage can provide by using an LP relaxed (left) or an integer (right) model.

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Energy storage models require binary variables to correctly model reserves and to ensure that the storage cannot charge and discharge simultaneously. This paper proposes a tight linear program (LP), i.e., convex hull, for the storage, which guarantees that there is no better LP approximation to its mixed-integer program (MIP) counterpart. Although...

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... if the storage is charging c t = 8MW, then the maximum up reserves the model guarantee is r c+ t ≤ 8MW from (5). Also, since the unit is charging δ t = 1 forces r d+ t , x d− t , d t = 0. On the other hand, in the LP relaxation, when c t = 8MW, δ t can take the value of 0.8 from (3), then r c+ t ≤ 8MW from (5), and r d+ t ≤ 4MW from (4), see Fig. 1. The total up reserves are now r + t = 12MW from (7), and even though the storage unit can be fast enough to provide them (see Section II-B), these reserves are 50% higher than what the MIP model (1)-(10) intended to be feasible. There are many possible combinations where the relaxed model can maximize the amount of reserves outside ...