*3.5. BESS Equivalent Circuit*

The presented battery equivalent circuit contains polarization capacitor Cpl, polarization resistor Rpl, and ohmic internal resistor R, where the battery transient feedback is simulated using Rpl and Cpl in both charging and draining modes. In that, V (h(t)) represents the nonlinear function of the SoC for h(t)'s. The terminal voltage is taken as the calculated output, and the current is considered as a control input. Figure 6 depicts a lithium-ion battery, and MATLAB/Simulink software is used to perform the simulation. Figure 7 shows the input characteristics of the battery energy storage system where E0 is constant voltage (V), K is polarization constant in (Ah<sup>−</sup>1), A is exponential voltage (V), and B is the exponential capacity (Ah<sup>−</sup>1).

**Figure 6.** BESS equivalent circuit.

**Figure 7.** Input characteristics of battery energy storage system.

To build the 440 V/30 Ah and a 100% SoC, interconnected modules are used to actualize the battery. The circuit dynamics is expressed by applying Kirchhoff's law:

$$V\_b(t) = V(h(t)) - R \ast i(t) - V\_{ca}(t) \tag{7}$$

$$\frac{dV\_{ca}(t)}{dt} = -\frac{1}{c\_{pi}R\_{pi}}V\_{ca}(t) + i(t) \tag{8}$$

Here, *Vb*(*t*) = terminal voltage, *i*(*t*) = terminal current, and *Vca*(*t*) = voltage across RC, which cannot be directly computed.
