3.2.2. Voltage Balancing System Power Losses

As mentioned above, the ESS was made up of a series connection of cells, whose maximum voltage was 2.65 V, in order to achieve voltage levels more typical of industrial applications. Due to manufacturing tolerances, not every cell has the same capacitance or ESR, which means that the distribution of the total voltage between the different cells is not exactly the same. Therefore, there is a voltage supervisor hardware that prevents any cell from exceeding the voltage limit value (2.7 V) and facilitates the equitable distribution of voltage [45–47]. This system is based on the dissipation of the power in a resistance when the voltage in any of the cells exceeds a predetermined threshold value (approximately 2.6 V). Below this value the protection system does not work. The current and resistance where that current is dissipated is known, so the power losses can be derived from voltage measured in the SCs as follows:

$$P\_{V\\_Balancing} = R\_{DIS} \cdot I\_{DIS}^2(\mathcal{U}) \tag{8}$$

*PV*\_*Balancing*: Voltage balancing system power losses;

*RDIS*: Power dissipation resistance;

*I*2 *DIS*(*U*): Current dissipation as a function of the measured voltage.

Figure 5 shows the power losses map of the voltage balancing system as a function of the current flowing through the ESS and its voltage. Compared to the power losses calculated in the ESR, these losses can be considered negligible.

#### 3.2.3. Cooling System and Electrical Connection Plates Power Losses

Each SCs cabinet has an extractor cooling turbine on top because a natural cooling system is not sufficient for these power requirements. It is a variable speed turbine whose control depends on the temperature measured in the SC cells. The higher the temperature in the cells, the higher the rotation speed. The objective of this refrigeration system is to keep the temperature of the SCs below 40 ◦C. It is known that SCs age faster the higher the stress to which they are subjected and the higher their temperature [45]. Ageing in this ESS type causes a decrease in C and an increase in ESR. This results in a loss of available energy in the ESS with respect to its initial value and a loss of efficiency. On the other hand, uneven aging between cells causes an imbalance in the distribution of the total voltage and a limitation in the use of available useful energy. To calculate the losses at the refrigeration system, an equivalent electrical circuit has been implemented using MATLAB-Simulink [48] that models the refrigeration flow. Additionally, a turbine regulation curve has been established to improve its efficiency. Figure 6a shows the map of cooling system losses as a function of current and voltage between terminals. It can be seen that the higher the current, the higher the losses in the cooling system and in the connection bars. As in the previous case, the losses are low compared to the losses in the ESR.

**Figure 5.** (**a**) Power loss map in the voltage balancing system as a function of current and voltage and (**b**) detail of the connection plates between the cells and of the voltage balancing system.

**Figure 6.** (**a**) Power losses map of the cooling system as a function of voltage and current and (**b**) power losses map in the connection bars between cells as a function of current and voltage.

Regarding the losses in the connection plates between cells [49], it must be said that they have a certain resistance and consequently a power loss depending on the current flowing through them. These are 3 mm thick aluminum plates supplied by the manufacturer. The resistance value of each connection plate is given by:

$$R\_{CONNEC\\_PLATES} = \frac{\rho \cdot l}{\mathcal{S}} \tag{9}$$

*RCONNEC*\_*PLATE*: Resistance of connection bars;

*ρ*: Aluminum resistivity;

*l*: Connection plate length;

*S*: Connection plate section.

Therefore, the power losses in the plates (*PCONNEC*\_*PLATES*) are calculated as:

$$P\_{\text{CONNEC\\_PLATES}} = I\_{\text{SIIPERCAP}}^2 \cdot R\_{\text{CONNEC\\_PLATES}} \cdot No\_{\text{SIIPERCAP}} \tag{10}$$

*I*2 *SUPERCAP*: Current through the SCs; *NSUPERCAP*: Number of SCs connected in series.

### 3.2.4. Power Converter and Total Losses

Each SC cabinet was connected to a DC bus regulated at a voltage of 950 V through a DC/DC converter that regulated the charge/discharge current of the ESS. This current command was the consequence of the reference power value to supply/consume assigned to the SCESS. The generation of this power command and the control of the complete system will be explained in the next point. A 3-branch interleaved DC/DC converter was used to exchange power between the ESS and the mentioned DC bus. This converter was bidirectional in the current to allow both charging and discharging of ESS. Figure 7 shows the topology and the input and output voltage levels of the converter [50,51].

The DC/DC power converter is a voltage source converter that regulates the charge/discharge current of the ESS. The control strategy was designed to operate in the discontinuous driving mode to improve its efficiency. The total current that passes through the SCs was distributed among the three output branches of the converter. The converter was modeled in MATLAB-Simulink to size the power components (filters, semiconductors, cooling system, etc.) and to verify the operation of the converter with the designed control strategy. On the other hand, the model implemented in MATLAB-Simulink allowed calculating the converter losses to obtain, as in the previous cases, the power converter losses as a function of the voltage and current through the SCs. The performance of the converter was calculated according to Equation (11):

$$
\eta\_{power\\_counter} = \frac{\mathcal{U}\_{SC} \cdot I}{\mathcal{U}\_{SC} \cdot I + P\_{counter\\_losses}} \tag{11}
$$

*USC*: Voltage of the SCs system; *I*: Current through the SCs; *Pconverter*\_*losses*: Power converter losses.

**Figure 7.** Electrical diagram with the voltage levels at the input and output of the DC/DC converter used.

Figure 8a shows the power converter losses as a function of the voltage and current through the SCs. Figure 8b shows the total efficiency of the power converter. The total losses of the power converter were higher with higher currents. However, the relative efficiency of the converter (with respect to the total power) was higher the higher the current through the SCs.

Figure 9a shows the total power losses of the SC cabinet as a sum of the previously calculated map (ESR, balancing and cooling system, bus bars, and power converter losses). Likewise, Figure 9b shows the total efficiency map of each cabinet as a function of the current and voltage.

**Figure 8.** (**a**) Power losses map in the DC/DC converter as a function of the current and voltage in the SCESS module and (**b**) efficiency map in the DC/DC converter as a function of the current and voltage in the SCESS module.

**Figure 9.** (**a**) Total losses map in the energy storage system (ESS) (sum of all commented power losses) as a function of current and voltage and (**b**) total efficiency map of the SC cabinet as a function of current and voltage.
