*6.3. Simulation*

A simulation of the full system, formed by a 2LVSI operating as central inverter grid-tied PV system, and ESS formed by a Battery ESS (BESS) and an Isolated Bidirectional Boost Converter [35], is shown in Figure 9. The control strategies previously described in Section 6.2 were applied. It must be noted that the ESS was undersized to allow its control system to be tested in all possible scenarios and display those results in a single figure; this was performed considering the dynamics of the systems and an ESS operating range of 20–80% of the SoC. Several irradiance conditions were tested in the simulations, all with PV cell temperature of 298.15 ◦K.

The PV plant parameters correspond to those presented in Table 1, while Table 4 presents the parameters of the converters and ESS. To calculate per-unit values in Figure 9, the following base values were considered: *G*base = 1000 W/m2, *P*base = 1540 kW, *i*base = 3.767 kA and *v*base = 800 V.


**Table 4.** Simulation parameters.

**Figure 9.** PV plant with ESS connected at the DC-link simulation results: (**a**) irradiance in kW/m2; (**b**) DC-link voltage and reference; (**c**) generated PV power (*P*pv), available PV power without considering clipping limitation (*P*mpp (available PV power)) and inverter power (*P*inv (inverter)); (**d**) ESS power (*P*ess); (**e**) ESS SoC (*SoC*); and (**f**) grid currents (*i*u, *i*v and *i*w) and phase u voltage (*v*u).

From 0 to 0.03 s (Case I), the system is operating at a power rating below *<sup>P</sup>*clip (1540 kW) and the ESS is at a SoC level of 20%, hence ESS power reference is zero. From 0.03 to 0.14 s (Case II), a step in solar irradiance causes the PV power (*P*pv) to reach *<sup>P</sup>*clip, since *SoC* < 80%, *P*<sup>∗</sup>ess power reference is set to *P*<sup>∗</sup>ess = *<sup>P</sup>*pre − *<sup>P</sup>*mpp (and *i*<sup>∗</sup>ess = *<sup>P</sup>*<sup>∗</sup>ess/*v*pv), which reduces power flowing through the inverter (*P*inv) enabling MPP tracking. From 0.14 to 0.20 s (Case III), a step down in solar irradiance causes the PV power (*P*pv) to be lower than *<sup>P</sup>*clip, but, since *<sup>P</sup>*pre < *<sup>P</sup>*pv < *<sup>P</sup>*clip, the ESS power reference (*P*∗ess) is set to zero. From 0.2 to 0.25 s (Case II), a second step up in irradiance generates for the PV power to surpass *<sup>P</sup>*clip, the system behaves exactly as from 0.03 to 0.14 s. Once the ESS reaches 80% of the SoC, the ESS stops drawing power and the inverter losses momentarily the capability to track the MPP (Case IV from 0.25 to 0.28 s). Note that the ESS was undersized, to show the behavior of the system

when reaching its maximum and minimum permitted SoC. From 0.28 to 42 s (Case V), a step down in solar irradiance causes the PV power to be below pre clipping level (*P*pv < *<sup>P</sup>*pre < *P*clip), and the ESS releases power towards the DC-link (*P*<sup>∗</sup>ess = *<sup>P</sup>*pre − *P*mpp) and through the inverter into the grid. From 0.42 to 0.5 s, the ESS reaches 20% of the SoC, hence power flow from ESS towards the DC-link is stopped and the system goes back to operating in Case I; in this part, grid currents show high harmonic content due the comparison of power flowing to the grid and power required to generate voltage steps to perform MPPT. In a real case, the MPPT period is longer, hence harmonic content would be lower.

Note that the instantaneous power balance is given by Equation (8), where the corresponding terms are given by Equations (9)–(11). This can also be verified in power curves shown in Figure 9c,d. Variables *<sup>v</sup>*gd, *<sup>v</sup>*gq, *i*d and *i*q in Equation (9) correspond to the grid voltage and current in rotational coordinates.

$$P\_{\rm inv}(t) \quad = \quad P\_{\rm pv}(t) + P\_{\rm ess}(t) \tag{8}$$

$$P\_{\rm inv}(t) \quad = \ \frac{3}{2} \cdot \left( v\_{\rm gd}(t) \cdot i\_{\rm d}(t) + v\_{\rm gq}(t) \cdot i\_{\rm q(t)} \right) \tag{9}$$

$$P\_{\rm PV}(t) \quad = \ i\_{\rm PV}(t) \cdot v\_{\rm PV}(t) \tag{10}$$

$$P\_{\rm ess}(t) \quad = \ i\_{\rm ess}(t) \cdot \upsilon\_{\rm pv}(t) \tag{11}$$
