3.2.3. Energy Storages

The adopted model of energy storage allows for the implementation of any type of ESS by defining appropriate parameters. Equation (3) reflects capacity limits.

$$\forall \mathbf{s} \in S\_{\prime} \; \forall \mathbf{t} \in T: E\_{\text{mins}} \le E\_{\mathbf{s}}^{\prime} \le E\_{\text{max}} \tag{3}$$

A given ESS charges and discharges taking into account actual capacity and storage efficiency—Equation (4).

$$\forall \mathbf{s} \in \mathbb{S}, \ \forall \mathbf{t} \in \mathbf{2}, \ \dots, \ \mathbf{96}: E^t\_{\mathbf{s}} = E^{t-1}\_{\mathbf{s}} + E^t\_{\text{imps}} \cdot \eta\_{\mathbf{s}} - \frac{E^t\_{\text{expps}}}{\eta\_{\mathbf{s}}} \tag{4}$$

Operational constraints given by Equations (5)–(7) contain binary variables to ensure switching between charging, discharging and idle mode of a given ESS.

$$\forall \mathbf{s} \in S\_{\prime} \; \forall t \in T: P\_{imp\,\,\,s}^{t} \le s\_{imp\,\,s}^{t} \cdot P\_{\text{maxs}} \tag{5}$$

$$\forall s \in S, \ \forall t \in T: P\_{\exp s}^t \le s\_{\exp s}^t \cdot P\_{\max s} \tag{6}$$

$$
\forall s \in S, \ \forall t \in T: \ s\_{imp\ s}^t + s\_{exp\ s}^t \le 1 \tag{7}
$$
