**3. Component Reliability Analysis**

Normally, the power device reliability is expressed in terms of lifetime consumption (*LC*), which indicates how much lifetime has been consumed since the beginning of th operation. In this paper, the *LC* is obtained according to the Miner's rule [28], which is expressed as

$$LC = \sum\_{i} \frac{n\_i}{(N\_t)\_i} \tag{1}$$

where *ni* is the number of cycles under certain stress conditions and (*<sup>N</sup>*f)*i* is the corresponding number of cycles to failure with the same stress conditions that is dependent on the lifetime model. Notably, the *LC* calculation according to (1) assumes that various stress cycle events are independent, and the caused damage can be linearly accumulated. The device is considered to reach its end of life when the *LC* exceeds one (or 100%).

In this paper, the number of cycles to failure *N*f is evaluated based on the Bayerer model [29]. This model is an empirical model describing *N*f in relation to certain stress conditions (i.e., the minimum junction temperature *<sup>T</sup>*j(min) and cycle amplitude Δ*T*j), which is expressed as

$$N\_{\rm f} = A \cdot \left(\Delta T\_{\rm f}\right)^{-\beta\_1} \cdot \exp\left(\frac{\beta\_2}{T\_{\rm f(min)} + 273}\right) \cdot t\_{\rm on}^{\beta\_3} \cdot I^{\beta\_4} \cdot V^{\beta\_5} \cdot D^{\beta\_6} \tag{2}$$

in which the impact of the heating time *t*on, current per wire bond *I*, blocking voltage *V*, and bond wire diameter *D* are also considered according to individual power laws. The model parameters and coefficients are summarized in Table 3. More discussions on this lifetime model are provided in [29].

**Table 3.** Parameters and coefficient of the Bayerer Model [29].


Additionally, the number of cycles *ni* in (1) is not directly available, since the temperature profiles obtained in the previous section, as shown in Figure 8; Figure 9, are irregular. In order to obtain the number of cycles *ni* at a certain stress condition (i.e., the cycle amplitude, mean junction temperature, and cycle period *t*cyc), a rainflow counting analysis [30] is performed, categorizing the irregular thermal cycles into several regular cycles. Subsequently, the number of cycles *ni* can be obtained.

Applying the above calculation, the one-year *LC* of all the IGBTs and diodes in the PV-battery systems can be obtained. Figure 10 summarizes the results. For the PV inverters, as expected, the DC-coupled configuration alleviates the loading on the PV inverter. It can be seen in Figure 10a,b that the IGBTs and diodes in the PV inverter with the DC-coupled BESS have much lower *LC* than the corresponding ones in the PV inverter with the AC-coupled BESS. Additionally, in both cases, the clamping diodes (e.g., D5 referring to Figure 4) are the most stressed devices (i.e., with the highest *LC*). This can be considered when designing the power converters, e.g., to select a high reliability diode. Regarding the power converters for the batteries, as can be seen in Figure 10c,d, several power devices in both converters have higher *LC* when compared with the devices in the PV inverters. For both the DC- and AC-coupled configurations, it can be expected that the converter-level reliability of the battery converters will be lower than that of the PV inverters. Although the battery inverter consumes less life

under the mission profile, it has more power components, when compared to the battery converter. The overall lifetime may be different.

So far, the component reliability of all the power interfacing converters within the DC- and AC-coupled PV-battery systems has been analyzed, with which the most fragile component can be identified. Furthermore, the corresponding *LC* results provide the basis for the next converter- and system-level reliability analysis.

**Figure 10.** One-year *LC* results of the power devices in different power converters: (**a**) PV inverter in the AC-coupled configuration, (**b**) PV inverter in the DC-coupled configuration, (**c**) battery inverter in the AC-coupled configuration, and (**d**) battery converter in the DC-coupled configuration.
