Lifetime Estimation Considering Short cycle Thermal Loading

phase angles are near to 0^◦ or 360^◦. This behavior can be explained based on the thermal impedance of the diodes and the thermal cycles presents in this component. In te next section, the short cycle thermal loading is explained.

for the battery bank, the harmonic current amplitude and phase angle are varied.

Finally, the junction temperature obtained from the BESS simulation is analyzed for each simulation.

This methodology demands a steady-state (SS) junction temperature value for a better estimation of lifetime consumption. Therefore, T_j is constantly monitored in order to obtain a SS cycle. If the SS is not obtained, the simulation time (t_sim) needs to be increased until the steady state condition is achieved. Otherwise, one cycle of the T_j is stored.

The PLECS thermal simulation is used in this work to obtain the junction temperature of the semiconductor device. This software enables the use of the semiconductor devices data provided by the manufacturer datasheets. The conduction losses, switching losses and thermal impedances parameters are used in the software simulation. The effectiveness of the junction temperature estimated by PLECS environment is validated in different works (Ma et al., 2015; Madhusoodhanan et al., 2016; Andresen et al., 2017). In addition, Zhang et al. (2019) shows the effectiveness of Tj

estimation by PLECS simulation when the converter sensitizes different frequency values of the output voltage.

The power cycling due to switching frequency is not considered. Previous studies have demonstrated that these cycles have a negligible effect on lifetime consumption, since the values of the fluctuation temperature are very small, compared to the power cycling due to grid frequency (Reigosa et al., 2016a). Therefore, to count only the effects caused by the HCC process, the peaks and valleys of the junction temperature are identified.

Then, these information are used to build the SS T_j cycle. This new signal is applied to the rainflow algorithm and the lifetime parameters are obtained.

Thus, all the parameters of ∆T_j, T_jm and t_on are estimated and applied to the lifetime. The lifetime model is the same used in the long cycle lifetime evaluation. It is important to observe that the resolution of the mission profile for the short cycle lifetime evaluation is hard to obtain, since it is necessary a very low sampling time value (T_s).

Therefore, for each interval of T_s, short cycles can be considered constant with the total number of cycles equal to T_sx f_n , as shown in Fig.39.

Then, LC is calculated and stored in a look-up table. As observed, the look-up table is created for a specific harmonic component. The same procedure can be applied for any harmonic characteristics and their combination. The flowchart for the LC, considering the short cycles, is shown in Fig. 40.

Considering a three-phase systems, the common harmonic components are the 5^th, 7^th and 11^th with their combination. Therefore, in this section, the short cycle analysis of the 5^th,7^th and the combination of them are analyzed. Only this two harmonic

Time (s)

T_s

(a)

Time (s)

T

(b)

...

T_s×f

P

n

Figure 39 – Exemplification of the total number of short cycles based on the mission profile resolution.

Source: Own authorship.

LC Look up

-I

T

LC Short-Term Table

P

θ

Time

-10 0 10

P(kW)bat

Zoom

Figure 40 – Flowchart of the LC calculation for the short cycles thermal load.

Source: Own authorship.

components are used since they are more present the electrical power system and because the reduction of the simulation time consumed in the lifetime evaluation process. In this context, the BESS with HCC operation is compared to the BESS without HCC operation to understand how the harmonic compensation can affect the semiconductors devices (IGBT and diodes) lifetime consumption. Since the stress in the power device depends on

the Ih/IBat, two different values of active power injected by the BESS are considered.

The LC values considering the injection of 5^th and 7^th harmonic current components are presented in Fig. 41, with phase angle ranging from 0^◦ to 360^◦. In this analysis, the BESS injects 500 of active power, the amplitude of each harmonic current component is fixed in 5 A and the ambient temperature is considered25^◦C. As noticed, the phase angle effects on lifetime consumption is more significant for low harmonic orders.

In this context, the LC variation due to the phase angle is higher when the BESS is compensating the 5^th harmonic current component. This fact is explained by the inverter current waveform, since it presents more shape variations due to the harmonic phase angle.

In addition, a phase shift is observed in the minimum and maximum LC values, which

can be explained by the different thermal impedances for each harmonic component.

θ (deg)

0.5 1.0

1.5 2.0 2.5 3.0 3.5

LC×10-7

5^th 7^th

0 90 135 270 360

h

Figure 41 – The effect on the semiconductor LC due to harmonic phase angle variation.

The active power is considered 500 kW, the ambient temperature 25^oC and the harmonic current amplitude is equal to 0.6 I_f.

Source: Own authorship.

The combination of multiple harmonics in the power system is usually observed under real operation conditions. In this context, the multiple harmonic compensation process should be considered. Thus, the LC is computed considering a nonlinear load composed of a sum of5^thand7^thharmonic current components. The phase angle variation for both harmonic components are considered. In Fig. 42, the BESS injects 500 kW, the ambient temperature is considered 25^◦C.

In Fig. 42(a),I₅ is considered equal to 0.6I_f andI₇is equal to 0.3 I_f . As observed, there are two critical LC areas for the IGBT. In Fig. 42(b) the I₅ was reduced to 0.3I_f and I₇ was equal to 0.6 I_f. As noticed, the critical areas are also present. However, the LC values are lightly lower than previous case. In addition, in Fig. 42(c), theI₅ andI₇ are both equal to 0.6I_f . In this case, there is a reduction in theLC critical areas. Thus, it is observed an increasing in the LC values with the harmonic current amplitude increasing.

In addition, the compensation of the 5^th harmonic component is lightly higher than the 7^th harmonic. In the next section, the lifetime evaluation considering the mission profile