*A.1.3. Li-Ion BESS*

The charging and discharging rate of the Li-ion BESS is limited by either the C-rate or the state of charge (SOC) as shown by Equations (A5) and (A6). In these equations, *SLi* is the rated size of the Li-ion BESS installation, *C* is the C-rate, and the min# *x*, *y* \$ function returns whichever is smaller among *x* or *y*. The negative sign indicates charging, as this will be relevant in the later equations. In Equation (A6), a maximum depth of discharge (DODmax) of 0.8 is implemented as too much discharge that will damage the BESS:

$$P\_c^{\text{max}}(t) = -\min \left\{ \begin{array}{ll} \text{S}\_{Li}\text{C}\_t & \text{S}\_{Li}(1 - \text{SOC}(t)) \end{array} \right\} \tag{A5}$$

$$P\_{dc}^{\text{max}}(t) = \min \left\{ \ S\_{Li} \mathbb{C}\_{\prime} \quad \mathcal{S}\_{Li}(\text{SOC} - (1 - \text{DOD}\_{\text{max}})) \right\} \tag{A6}$$

Next, the power entering one battery module *P*(*t*) is determined as shown in Equations (A7) and (A8) for charging and discharging, respectively. A charge *<sup>c</sup>* and discharge *dc* efficiency of 0.95 is applied, which results in a roundtrip efficiency of 0.90 when combined. *Snom* is the nominal size of one battery module (4.8 kWh).

$$P(t) = \frac{P\_{\varepsilon}(t)\varepsilon\_{\varepsilon}}{S\_{st}/S\_{\text{nom}}},\tag{A7}$$

$$P(t) = \frac{P\_{\rm dc}(t) / \varepsilon\_{\rm dc}}{S\_{\rm st} / S\_{\rm nonn}},\tag{A8}$$

The Li-ion battery chemistry is modeled using the Thevenin equivalent circuit as shown in Figure A1. *P*(*t*) represents the power at the terminals. *R*<sup>1</sup> (1.4 Ω) is the resistance due to the electrolyte, while *R*<sup>2</sup> (0.5 Ω) and *C* (52 F) are resistances at the electrode interface [66].

**Figure A1.** Thevenin equivalent circuit for modelling Li-ion battery chemistry.

The current through the EMF element is determined and the SOC for the next timestep is given by Equation (A9). *V*0(*t*) is the open circuit voltage (OCV) of the battery module.

$$\text{SOC}(t+1) = \text{SOC}(t) - \frac{I(t)V\_0(t)}{S\_{\text{mm}}},\tag{A9}$$

The module OCV is given as a function of SOC by Figure A2.

**Figure A2.** Open circuit voltage (OCV) as a function of SOC for a 48 V Li-ion battery module.
