**4. ESS Sizing**

ESS are composed by a bidirectional power converter and an EST, such as batteries, super capacitors, flywheels, CAES, HPS, among others [23]. Energy restrictions are imposed by EST, while charging and discharging power ratings depend on both EST and the bidirectional converter. Some ESTs, such as batteries, usually present different charge vs discharge power ratings. In this application, ESS charge power rating is limited by the clipped power.

PV power generation is strongly dependant on solar irradiance and the module temperature. The PV module temperature behaves as a low pass filter of the incident irradiance, with an equivalent time constant of a few minutes depending on the wind speed [24]. In addition, according to Vernica et al. [25], the PV plant output power can be modeled as a low-pass filtered version of the solar irradiance, where the cut-off frequency of the equivalent filter is determined by the area of the PV plant. Specifically, for the PV plant being analyzed in this work, the cut-off frequency of the equivalent filter is 0.01 Hz. Additionally, most grid code requirements related to power fluctuation (maximum power Ramp Rate) regulate power fluctuations per minute [26]. Moreover, standard PV plant available data range in sampling times between 1 and 30 min. Therefore, a data sampling rate of 1 min was selected to calculate the clipped energy and the ESS sizing strategy presented in this work.

Clipped power ( *P*clipped) is calculated according to Equation (6), where *<sup>P</sup>*mpp and *<sup>P</sup>*pv are, respectively, the predicted PV power generation from Equation (1) and measured PV power, both in kW. The clipped energy in kWh is estimated according to Equation (7), where *dt* corresponds to the sampling time in min (1 min).

$$P\_{\text{clipped}} = \begin{cases} P\_{\text{mpp}} - P\_{\text{pv}} & \text{ $\prime$ } \quad P\_{\text{pv}} > P\_{\text{clip}} \\\\ 0 & \text{ $\prime$ } \quad \text{otherwise} \end{cases} \tag{6}$$

$$E\_{\text{clipped}} = P\_{\text{clipped}} \cdot \frac{dt}{60} \tag{7}$$

ESS for clipping in PV plants are designed for a daily use cycle (dawn to dusk), which means there is no need to store energy for more than one day, and therefore the stored energy is completely depleted before a new day cycle.

The following efficiencies were considered in the sizing of the ESS: a single stage DC-DC converter with 97% efficiency [27] (94.09% round-trip efficiency), new commercially available batteries present a round-trip efficiency of 95% [28,29] and DC/AC inverter has a nominal efficiency of 97%. Therefore, the energy passing through the ESS (PV to ESS and ESS to Grid) would experience an efficiency of 86.70%.

Figure 4a shows a histogram of the maximum recoverable daily-energy-loss (*E*ˆdel) due to clipping per amount of days of occurrence during a year, and two overlapped curves showing the accumulated annual energy loss (due to clipping) and the total recoverable annual energy (including efficiency of the PV-ESS-grid system of 86.7%). Both curves are function of the maximum recoverable daily-energy-loss and were normalized respect to the annual energy loss (33 MWh).

The power rating analysis is shown in Figure 4b, for the case where four ESS power rating design criteria are depicted as a function of the recoverable-daily-energy-loss. All criteria include a 97% efficiency of the DC/DC power converter. The criteria *C*1 to *C*4 correspond respectively to maximum recoverable-daily-energy-loss in MWh (*E*ˆdel), average recoverable daily-energy-loss in MWh (*E*del), mean plus standard deviation of recoverable daily-energy-loss in MWh (*E*del + *σ*Edel) and mean plus two times the standard deviation of recoverable daily-energy-loss in MWh (*E*del + 2 · *σ*Edel).

**Figure 4.** PV plant ESS energy and power sizing analysis: (**a**) daily-energy-loss histogram, accumulated annual energy loss and total recoverable annual energy (considering the efficiency of the PV-ESS-grid system); and (**b**) power-limited recoverable daily energy considering the efficiency of the DC/DC power converter.

As an example, to recover 80% of the annual energy lost due to clipping, an ESS of 600 kWh is required to store the maximum daily-energy-loss of (Figure 4a), which considering criteria C1 (from Figure 4b) leads to a power rating of 200 kW.

## **5. Energy Storage Technology Selection**

ESS are formed by an EST and its power converter. This section focuses on selecting a suitable EST alternative to store clipped energy. According to the type of energy conversion and the nature of the stored energy, ESTs may be classified as electric, chemical, mechanical and thermal [30], as shown in Figure 5. The main characteristics of ESTs, relevant for clipping, are summarized in Table 3 [31–33]. For a detailws description of each ESTs from Figure 5, please refer to [33,34].

**Figure 5.** Energy storage technologies classification.

Based on round-trip efficiency and maturity level, the best EST alternatives for handling clipped power are SC, LiIon batteries and FES. Nonetheless, energy cost of FES doubles the energy cost of SC and LiIon batteries. Moreover, installation costs are not included in the table, although they depend on the weight of the equipment that needs to be transported. In addition, considering energy density, we have have concluded that LiIon batteries are an adequate EST technology to be applied to handle clipped power. The following section shows a simulation of a LiIon BESS applied to a PV system, for validation of the sizing methodology.


**Table 3.** Energy storage technologies specifications [31–33].

1 Conventional battery; 2 flow battery; 3 fuel cell; 4 molten salts batteries; 5 TES.
