**6. Experimental Validation**

To validate the power loss minimization method presented in section V, the experimental setup of Figure 5 was used.

**Figure 5.** Experimental setup: (**a**) Photograph and (**b**) schematic.

Each arm in Figure 5 comprises twelve modules connected in series. Each module includes a 20 Ah lithium titanate cell that is individually controlled by an H-bridge converter (a detailed description of the control architecture of the experimental hardware is

presented in [16]). In these experiments, each H-bridge is operated as a half-bridge, only allowing for a positive or zero voltage output.

Detailed characteristics of the setup and experiments are presented in Table 1. According to the cell loss minimization techniques explained in the previous section and, in particular, by changing the settings of the variables *ξDC* and *<sup>v</sup>*<sup>∗</sup>*a*,0,*AC*, four different tests were performed.


**Table 1.** Details of the performed tests and results.

Test 1 refers to the conventional method: *<sup>v</sup>*<sup>∗</sup>0,*AC*= 0 and *ξDC* = 1.

In Test 2, no AC voltage injection was used, but *ξDC* was set to a lower value (*ξDC* = 2/3 instead of *ξDC* = 1).

In Test 3, a third harmonic AC voltage injection was added and *ξDC* was further decreased to 1/√3.

Test 4 refers to the optimum proposed method with *<sup>v</sup>*<sup>∗</sup>0,*AC* = *<sup>v</sup>*0,*AC*,*OPT* and *ξDC* = <sup>3</sup>√3*ξ*/2*<sup>π</sup>*.

For each test, the current and voltage of one arm were sampled through the oscilloscope at a frequency of 25 MHz (500 k samples per 50 Hz period). Each cell current was calculated as follows:

$$i\_{cell,n}(k) = \mathbb{g}\_n(k) \; i\_a(k),\tag{28}$$

where *icell*,*<sup>n</sup>*(*k*) is the current of the *n*-th cell at the sampling time *k*, *ia*(*k*) is the arm current measured at the sample point *k*, and *gn*(*k*) is the switching signal:

$$\mathbf{g}\_{\boldsymbol{n}}(k) = \begin{cases} \begin{array}{c} 0, \text{ if } v\_{d1}(k) < nV\_{cell} \left( n - \text{cell bypassed} \right) \\ 1, \text{ if } v\_{d1}(k) \ge nV\_{cell} \left( n - \text{cell rolline} \right) \end{array} . \end{cases} . \tag{29}$$

For each test, the total cell loss of the considered arm is calculated by

$$P'\_I = \frac{R\_{cell}}{N\_s} \sum\_{k=1}^{N\_s} \sum\_{n=1}^{12} g\_n(k) \ \ i\_a^2(k),\tag{30}$$

where *Ns* is the total number of samples per cycle.

Table 1 reports these results, together with the theoretical calculation of *PJ*. All the tests were carried out in correspondence with the same modulation index value, such that the arm output power *Parm* was fixed. The error between the experimental and theoretical results, which is also shown, is less than 2.5% for all cases (within the experimental error, e.g., due to arm current measurements).

As can be noted from the Test 1 results (Figure 6a,e), the arm voltage is centered around 15 V (*NVcell*/2) and its waveform corresponds to a quantized sine wave. The theoretical calculated cell losses (see Table 1) are substantially equal to the experimental ones.

**Figure 6.** Experimental results: total voltage and current during: (**a**) Test 1, (**b**) Test 2, (**c**) Test 3, (**d**) Test 4; cells currents waveform during: (**e**) Test 1, (**f**) Test 2, (**g**) Test 3, (**h**) Test 4.

As per the theoretical considerations, the Test 2 results testify that the cell losses are dependent on *<sup>v</sup>*<sup>∗</sup>0,*DC*. Indeed, in comparison with Test 1, the losses are lower, proportional to the decrease of *ξDC*. From Figure 6b, it can be noted that the arm voltage reaches the zero value. In fact, the *ξDC* setting of Test 2 corresponds to the minimum *ξDC* value, considering that no AC common mode voltage has been injected.

Test 3 clarifies that even if *PJ* does not directly depend on *<sup>v</sup>*<sup>∗</sup>0,*AC*, an AC injection can affect the minimum settable value of *ξDC*. In this case, indeed, it was possible to set *ξDC* = 1/√3, without violating 0 ≤ *v*∗*k* ≤ *NVcell*. The third injected harmonic can be recognized from the altered waveform of the arm voltage (Figure 6c), which shows a wider constant value in correspondence with the maximum and minimum point.

Finally, the optimum AC common mode voltage injection of Test 4, which displays visible notches in the arm voltage (Figure 6d), guarantees the minimum settable value of *ξDC*, leading to the minimization of cell losses. The decrease of the cell losses is associated with a decrease of the total *rms* current value in the 12 cells, which can be easily noted when compared to Figure 6e,h. In comparison with the conventional method of Test 1, the proposed method assures a cell energy saving of about 45%, which is consistent with the fact that the experimental converter is operating with a mid-range *ξ* value.

#### **7. Additional Losses Numerical Example**

In order to better evaluate the relative impact of the cell loss reduction introduced by the proposed method, other losses occurring in the system should be considered. These are principally switching and conduction losses occurring in the power electronic devices. For an MMC with a large number of modules driven by NLM, the switching losses are negligible, since the power devices switch at the fundamental output frequency. The VSI is

instead characterized by both conduction and switching losses. A rapid example can be developed by completing the analysis of [11] (which compares the power electronics losses of a traditional VSI to those of a DS-MMC) with the electrochemical cell losses evaluation of the present work. While the VSI is equipped with FZ300R12KE3G IGBT, the MMC is built upon AUIRFS8409-7P power MOSFET. Both solutions constitute a 80 kW–220 V–250 A converter, fed by a 24 kWh battery system based on 11 Ah Kokam SLPB55205130H cells with an internal resistance of approximately 1.6 mΩ each.

The procedure given in [11] only considers the losses occurring in the power electronic devices; at half full-load, with *ξ* = 0.7 and cos*ϕ* = 1, the power electronics losses are as shown in Figure 7a.

**Figure 7.** (**a**) Power losses of an 80 kW–24 kWh converter realized by the MMC and VSI solution: (**a**) Power electronics losses and (**b**) all losses.

Cell losses may be added to the analysis of [11], by applying Equations (21), (24) and (27), resulting in the loss breakdown given in Figure 7b. As expected, the MMC cell losses are higher than those of VSI and represent an important fraction of the total losses. In this example, the proposed technique produces a 42% reduction in cell losses, which equates to an overall 19% loss reduction. As a consequence of applying the proposed technique, the total efficiency is increased by 1.8%.

Naturally, the actual increase of the MMC overall efficiency achieved through the proposed technique depends on the particular operating condition. It is important to highlight that loss reduction in electrochemical cells is doubly beneficial as it leads to a direct reduction in detrimental cell heating and increase in the service life.
