*3.2. Device Selection Consideration*

After the candidate topologies were determined, IGBT modules were then selected for each topology. In order to guarantee a reliable margin in an aerospace application, a 2/3 voltage derating fact was applied to IGBT modules. It meant that the standard of selection for a ±400 V DC system in aerospace is the same as for a ±600 V DC system in an industrial drive. In other words, this system can also operate under ±600 V DCs, if insulation can be guaranteed. Based on this criterion, the voltage rating of IGBTs in each topology is marked and shown in Figure 1.

Commercially available IGBT modules were considered. In order to guarantee a fair comparison, several types of IGBT modules from the same manufacturer were selected (Infineon in this paper). The results of the selection are given in Table 3. According to Table 3, with the increase of voltage level, the total number of modules to form one three-phase circuit increased. Twelve modules were required to form one three-phase 5L-HANPC circuit, which had the maximum number among all topologies. The total weight of these modules and the minimum heatsink surface area were calculated according to the number of required modules. These two results were quite important for power density evaluation. It is because all these IGBT modules accounted for a large portion of the total weight. On the other hand, the minimum heatsink surface area represented the rectangular baseplate area of all the IGBT modules added together. Although for most converter designs the heatsink surface area is much larger than this minimum area, a well-designed heatsink makes these two numbers similar. Under this condition, the heatsink weight is decided not only by the power loss, but also by how many modules are installed. Based on the comparison given in Table 3, without considering the power loss, the 2L-VSC would be the most suitable topology, since it had the smallest minimum heatsink area as well as the lowest total module weight. On the other hand, the 3L converter was a moderate solution, which showed a similar performance.


**Table 3.** Selection and comparison of active components for each candidate topology.

### *3.3. Power Loss Comparison*

As discussed before, the power loss performance is more critical in designing high-power-density converter systems. In order to evaluate the loss performance for each topology under different load conditions, the power loss on each device was calculated individually. The conduction loss and the switching loss were separately calculated.

A generalized equation to calculate an average conduction loss of an IGBT and a diode in one AC cycle was given by:

$$P\_{\rm con} = \frac{\int\_{\rm cl}^{2\pi} v\_{\rm cl}(\theta) i\_{\rm c}(\theta) d\_{\rm con}(\theta) \,\mathrm{d}\theta}{2\pi} \tag{1}$$

where *vce*(θ) represents the on-state voltage drop on the IGBT, *ice*(θ) represents the instantaneous current going through the IGBT when it is turned on, and *dcon*(θ) indicates the duty cycle of the device. For diodes, *vf*(θ) and *if*(θ) are used in Equation (1). The voltage drops, instantaneous current, and duty cycle are all variables related to the phase angle θ in one AC cycle. Furthermore, the on-state voltage drop characteristic can be modeled as a constant equivalent voltage source *V*<sup>0</sup> for both IGBTs and diodes in zero-current-condition series connected with an on-state resistor *r*0. Equation (1) can be rewritten as:

$$P\_{\rm conv} = \frac{\int\_0^{2\pi} (V\_0 + r\_0 \cdot i\_\varepsilon(\theta)) i\_\varepsilon(\theta) d\_{\rm com}(\theta) \mathrm{d}\theta}{2\pi} \tag{2}$$

The switching loss was calculated under the assumption that the relationships between the switching loss and the on-state current and off-state voltage were linear. From the datasheet, the turn-on energy loss *Eon* and the turn-off energy loss *Eo*ff of an IGBT and the reverse recovery energy loss *Erec* of a diode under rated test conditions can be found. Then, by integrating the total energy loss within one output period and then multiplying it with the output frequency, Equation (3) was obtained as:

$$P\_{\rm sw} = \frac{\int\_0^{2\pi} E\_k \frac{i\_c(\theta)}{I\_{\rm tot}} \frac{v\_c}{\mathcal{U}\_{\rm tot}} S\_{\rm sw}(\theta) d\theta}{2\pi} f\_{\rm out}, S\_{\rm sw}(\theta) = \begin{cases} 1 & \text{device has switching loss} \\ 0 & \text{device has no switching loss} \end{cases} \tag{3}$$

where the switching energy loss coefficient *Ek* represents *Eon* + *Eo*ff for the IGBT or *Erec* for the diode, *Itest* and *Utest* are the rated test conditions noted on the datasheet, and *Ssw*(θ) indicates whether the IGBT or diode has the switching loss or not at a certain phase angle θ in one AC cycle. All topologies were evaluated in both the rated rectifier mode and inverter mode. The results in the inverter mode with the rated conditions are given in Figure 2. According to the results, the 2L-VSC showed a much higher total loss than the other multilevel topologies, because that the 1700 V IGBT module had a poor switching loss performance, which was identified by analyzing the datasheet of devices and the loss distribution. On the other hand, half of IGBT modules in the 3L-T2C were 1700 V-type, and thus the total loss was also too high. Among all the topologies, 5L-HANPC had the lowest switching loss and the lowest total loss. The extremely low switching loss is not only because that the voltage step decreased to 1/4 of the DC link voltage, but also because the 650 V IGBT modules in the 5L-HANPC were the only devices under high-frequency switching after applying a commonly used low-loss modulation scheme. The results in the rectifier mode under the rated conditions are given in Figure 3. It can be found that the tendency kept the same and the 5L-HANPC was the one with the best performance.

**Figure 2.** Power loss comparison under ±400 V DC in the inverter mode (power factor: 0.76, *M* = 0.94, *f* s = 15 kHz, and *I*ac = 100 A).

Another comparison was made by fixing the modulation index and power factor in the rated conditions while varying the switching frequency or output current. The results in the inverter mode and the rectifier mode are shown in Figures 4 and 5, respectively, and showed that changing output currents did not affect the tendency since the loss was almost proportional to the output current for all topologies. However, after the switching frequency was decreased to be lower than 7 kHz, the power losses of the 3L-NPC and the 2L-FB became lower than that of the 5L-HANPC. It is because, under low switching frequencies, the conduction loss dominated the total loss and the 5L-HANPC had the highest conduction loss.

**Figure 3.** Power loss comparison under ±400 V DC in the rectifier mode (power factor: −1, *M* = 0.47, *f* <sup>s</sup> = 15 kHz, and *I*ac =150 A).

**Figure 4.** Loss performance comparison in the inverter mode (power factor = 0.76, *M* = 0.94) under different conditions: (**a**) varied AC currents and a fixed switching frequency (*f* s = 15 kHz); and (**b**) varied switching frequencies and a fixed AC current (*I*ac = 100 A).

**Figure 5.** Loss performance comparison in the inverter mode (power factor = −1, *M* = 0.47) under different conditions: (**a**) varied AC currents and a fixed switching frequency (*f* s = 15 kHz); and (**b**) varied switching frequencies and a fixed AC current (*I*ac = 100 A).

By summarizing the results of the loss comparison, a clear tendency can be discovered. The 2L-VSC was unacceptable because of huge power losses. At the selected operational frequency of 15 kHz, its total loss was 2–3 times higher than those of the other multilevel converter solutions. On the other hand, compared to the 3L-NPC, 2L-FB, and 5L-HANPC, the 3L-T2C showed no advantages. Its total power loss was 75% higher than those of the 5L-HANPC and 27% higher than those of the 3L-FB and the 2L-FB under the inverter-mode operation. Considering that it also showed no benefit in module weight and total area comparisons according to Table 3, it will not be considered in further evaluation. The 5L-HANPC should be the first choice considering the loss performance, because its total loss was reduced by 30% compared to that of our second choice the 3L-NPC.
