Microelectronics Reliability 76–77 (2017) 549–555

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Microelectronics Reliability

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Fundamental-frequency and load-varying thermal cycles effects onlifetime estimation of DFIG power converter

G. Zhang a, D. Zhou b,⁎, J. Yang a, F. Blaabjerg b

a School of Information Science and Engineering, Central South University, Changsha, Chinab Department of Energy Technology, Aalborg University, Aalborg, Denmark

⁎ Corresponding author.E-mail address: zda@et.aau.dk (D. Zhou).

http://dx.doi.org/10.1016/j.microrel.2017.06.0690026-2714/© 2017 Elsevier Ltd. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 30 May 2017Received in revised form 14 June 2017Accepted 27 June 2017Available online 16 July 2017

In respect to aDoubly-Fed Induction Generator (DFIG) system, its corresponding time scale varies frommicrosec-ond level of power semiconductor switching to second level of the mechanical response. In order to map annualthermal profile of the power semiconductors, different approaches have been adopted to handle the fundamen-tal-frequency thermal cycles and load-varying thermal cycles. Their effects on lifetime estimation of the powerdevice in the Back-to-Back (BTB) power converter are evaluated.

© 2017 Elsevier Ltd. All rights reserved.

Keywords:DFIG wind power systemLifetime estimationThermal cycles

1. Introduction

In the field of thewind energy generation, the Doubly-Fed InductionGenerator (DFIG) has evolved as amainstream solution [1], as the rotor-side of the generator only handles the slip power of the stator-side. Dueto the high cost of the maintenance and the downtime, the reliabilityissue of the wind power converter is investigated and addressed inmany studies [2–5].

The DFIG system is basically configured with the mechanical andelectrical parts, and its multi-timescale feature challenges the mappingof the annual thermal profile due to the huge difference of the time con-stants (e.g., from themicrosecond level of thepower device switching tothe second level of the mechanical response). As a result, the thermalcycles of a power semiconductor include small cycles (e.g., current com-mutation within one fundamental frequency) and large cycles (e.g., thefluctuation of wind speed and environment temperature) [4]. On theother hand, the lifetime of the power components of the Back-to-Back(BTB) power converter are unequal [5], which makes the maintenanceof the DFIG system difficult. In this case, the studies of the reliability ofthe power converter are able to provide guidance to design the systemmore appropriately.

In addition, the Mean Time Between Failure (MTBF) term is fre-quently used to describe the reliability, which is the inverse of failurerate λ. Usually, the development of failure intensity with operationaltime is often described by a bathtub curve [6], which divides the lifetime

of a system into three phases as shown in Fig. 1, where the spontaneousfails usually contribute to the failure rate of “early life” and “useful life”parts. However, the estimated consumed lifetime discussed heremainlystudies on the “wearout period” part.

In this paper, the fundamental-frequency and load-varying thermalcycles of a power semiconductor are discussed, and their effects onthe lifetime estimation are studied.

In Fig. 2, the lifetime of the IGBT and diode of the DFIG power con-verter is estimated with a one-year mission profile, and a schematic di-agram of the estimation process is given. In terms of fundamental-frequency thermal cycles, the consumed lifetime is estimated with theannual wind speed distribution, while a rain flow counting method isused in respect to varying-loading thermal cycles. Then, a comparisonof these two effects is carried out between the power components ofthe power converter.

2. Mission profile of DFIG-based wind energy system

The configuration of a DFIG-based wind energy power system isshown in Fig. 3, which consists of a turbine, a gear box, a DFIG, volt-age-type-source BTB power converters, a transformer and an inputfilter. The filter is featured to prevent the high frequencies causedby the converter from polluting the power grid and avoid the effectsof power grid fluctuations on power converter. Compared with theGrid-Side Converter (GSC) of the BTB converters, the Rotor-SideConverter (RSC) carries a higher current because of a lower outputvoltage, thus two bridges are paralleled in one arm of the RSC as in-dicated in Fig. 3.

Fig. 1. The failure rate function shaped by a theoretical bathtub curve.

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In this study, a one-year wind speed and ambient temperature pro-file with a sample rate of 10 min is used, as shown in Fig. 4(a) and (b).Alternatively, the annual wind speed distribution obtained from the

Fig. 2. Schematic diagram of the

Fig. 3.Wind energy power system based o

sampling data is shown in Fig. 4(c), and the wind speed of 9 m/shas the largest probability within one year, belonging to class IEC Iwith the average wind speed of 10 m/s. According to Fig. 4, thewind speed and ambient temperature are constant for each 10 min,but they fluctuate considerably within one year, both the constantand fluctuation factors affect the lifetime of the power converter.Therefore, two cases of the lifetime estimation are studied in thispaper. One is considering the constant wind speed and ambient tem-perature, and the fundamental-frequency thermal cycles for each10 min are discussed, where the thermal model is described as anRC impedance network. The other is the load-varying case by consid-ering the fluctuations between each speed and temperature, wherethe thermal model is simplified to an R impedance network, andthe effects of thermal capacitance are ignored.

In terms of the output power profile of the wind turbine, both thewind speed distribution and the power control method have importanteffects. In order to simplify the analysis, a Maximum Power PointTracking (MPPT) scheme is applied, the turbine parameters are givenin Table 1, and the output power of the wind turbine with differentwind speeds is shown in Fig. 5. When the wind speed is higher thanthe cut-in speed, the generator starts to produce the active power,while the output power of the generator is zero when the wind speedis higher than the cut-off speed.

lifetime estimation process.

n the doubly fed induction generator.

Fig. 4. Yearly mission profile. (a) Real-time wind speed. (b) Real-time ambienttemperature. (c) Wind speed distribution.

Fig. 5. Generator power at different wind speeds.

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3. Lifetime estimation caused by fundamental-frequency thermalcycling

In this section, as the fundamental period of the power converter issmaller than the mechanical inertia of the wind turbine, a constantwind speed can be considered within a fundamental period. As shownin Fig. 2, the process of the lifetime estimation is calculated by the fol-lowing parts: the steady-state modeling of the DFIG system, converterpower losses calculation,mean junction temperature and junction tem-perature fluctuation mapping of the power components, and lifetimeestimation of the power converter on the basis of the lifetime modelwithin the specific wind speed distribution.

Under the stator voltage orientation frame, ignoring the effects ofthe stator resistance and the rotor resistance, the stator voltage followsusd = Us, usq = 0, the dq stator current components are isd = −Ps/(1.5usd), isq = Qs/(1.5 usd), and the steady-state model of the DFIG systemis obtained as

urd ¼1ks

LrUs

LmþωsδLmisq

� �ð1Þ

urq ¼ 1ks sign sð Þð ÞωsδLmisd ð2Þ

Table 1Wind turbine parameters.

Parameters Values

Cut-in speed (m/s) 4Cut-off speed (m/s) 25Air density (kg/m3) 1.225Maximum turbine speed (rpm) 19Minimum turbine speed (rpm) 11Blade radius (m) 41.3Optimal tip speed ratio 8.1

ird ¼ −kLsLm

isd ð3Þ

irq ¼ −kUs

ωsLmþ sign sð Þð Þ Ls

Lmisq

� �ð4Þ

where k is the turns ratio, s is the slip, Lm, Lr, Ls are the magnetic induc-tance, rotor inductance and stator inductance, δ = (LrLs − Lm

2 )/Lm2 , urd,urq, ird, irq are the dq components of the rotor voltage and current, andωs is the power grid frequency.

Assuming that no reactive power flows between the GSC and powergrid, the GSC current is igd= sPs/(1.5 usd), igq=0, and the GSC voltage is

ugd ¼ Us þωsLgigqugq ¼ −ωsLgigd

ð5Þ

where ugd, ugq are the dq components of the voltage of the GSC, and Lg isthe input filter of the GSC.

In respect to the power losses of the power converter, the switchinglosses and conduction losses of IGBTs and diodes are taken into account.The conventional space vector pulse width modulation scheme is used,the power losses with different wind speeds is calculated according tothe hash temperature in the datasheet [5]. As shown in Fig. 6, the IGBTlosses are larger than that of the diodes, and the power losses of theRSC is lower than that of the GSC in the super-synchronous mode, be-cause two-parallel bridges decrease the burden of each power devices.When the DFIG works in synchronous mode, no power flows from theDFIG to the power grid theoretically, and the smallest power losses ofthe GSC occur. On the above basis, according to the conventionalthermal model network with Foster structure [7], the mean junction

Fig. 6. Power losses distribution of the power converter with different wind speeds.

Fig. 7.Mean junction temperature Tjm and junction temperature fluctuation dTj of the power devices at different wind speeds.

552 G. Zhang et al. / Microelectronics Reliability 76–77 (2017) 549–555

temperature Tjm and the junction temperature fluctuation dTj are calcu-lated as

Tjm T=D ¼ Ploss �X4i¼1

Rthjc T=D ið Þ þ Ploss �X3j¼1

Rthca jð Þ þ Ta

dT j T=D ¼ 2Ploss �X4i

Rthjc T=D ið Þ �1−e

− tonτthjc T=D ið Þ

� �2

1−e−Ts

τthjc T=D ið Þ

ð6Þ

where Rthjc and Rthca are the thermal resistance from the junction to thecase of the powermodule and the cooling, subscripts T andD denote theIGBT and the diode, respectively, subscripts i and j denote layer number,ton denotes the ON-state time within each fundamental period Ts, and τdenotes each Foster layer's thermal time constant, Ploss is the power lossof each power semiconductor. Ta is the ambient temperature, and it is

Fig. 8. Waveforms of the rotor current, mean junction temperature Tjm and junctiontemperature fluctuation.

40 °C considering the harsh ambient temperature. Thus, themean junc-tion temperature Tjm and the junction temperature fluctuation dTj cal-culated by (6) are shown in Fig. 7, the junction temperature of theIGBT of the GSC is maximum, whereas the junction temperature fluctu-ation of the diode of the RSC is maximum. As the junction temperaturefluctuates with the fundamental frequency of the flowing current, thewaveforms of the rotor current, Tjm and dTj at different slips are simulat-ed in Fig. 8. In Fig. 8(a), the frequency of rotor current is 15 Hz corre-sponding to the wind speed of 5.9 m/s, and the output power is0.26 MW, where Tjm of the IGBT is higher than that of the diode, anddTj of the IGBT and diode are similar; In Fig. 8(b), the frequency ofrotor current is 10 Hz corresponding to the wind speed of 14 m/s, andthe output power reaches the maximum 2 MW, where both the Tjmand dTj of the diode are higher than that of the IGBT. Obviously, the re-sults shown in Fig. 8 are consistent with the results in Fig. 7.

In this case, the lifetime model follows the Coffin-Manson model[8–9], and the relationship between cycle-to-failure of the power de-vice and its thermal stress can be found as

Nf vð Þ ¼ A � dT j vð Þβ1 � eβ2

273þTjm vð Þ � ton vð Þ0:7

� �β3

ð7Þ

whereNf is the number of power cycles, and it is closely related to thejunction temperature Tjm and the junction temperature fluctuationdTj, as well as the on-time duration ton. Besides, A, β1, β2, β3 are fittingparameters based on test results provided by the manufacturer, butthe provided data only covers limited ranges of Tjm, dTj and ton. Con-sidering the thermal behaviors of power devices in the wind powerapplications, Tjm, dTj are interpolated or extrapolated linearly withlog scale by the multiple linear regression method [8]. For the stud-ied IGBT module in this paper, A = 1.27e6, β1 = −5.039, β2 =

Fig. 9. Total consumed lifetime of the IGBT and diode of RSC and GSC.

Fig. 10. Process of the total consumed lifetime estimation caused by load-varying thermal cycling.

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7166.7, β3 =−0.463, respectively. However, it should be noted thatthe values of these parameters could be varied depending on differ-ent lifetime definitions and confidence levels because the IGBT mod-ules have the different number of cycles to failure.

According to the Miner's rule-linear damage hypothesis [10], thefailure occurs when the same of stress cycles to failure Nf reaches 1,and the total consumed lifetime is calculated as

CL ¼X25v¼4

nf vð ÞNf vð Þ

¼X25v¼4

Dwind vð Þ365 � 24 � 3600 � f c vð ÞNf vð Þ

� � ð8Þ

whereDwind is the annual percentage of eachwind speed obtained fromFig. 4(c), and fc is the fundamental frequency of the flowing current andequals the slip frequency.

From (8), the total consumed lifetime of the IGBT and diode of theRSC and GSC is plotted in Fig. 9. It can be seen that the consumed life-time of the GSC is only 1/100 of the RSC. Moreover, the consumed life-time of diode of the RSC is larger than its IGBT, whereas the IGBT hashigher consumed lifetime than the diode in the GSC.

4. Lifetime estimation caused by load-varying thermal cycling

Due to the stochastic characteristics of the wind, the fluctuations ofthewind speed occur as shown in Fig. 4(a). However, these fluctuations

554 G. Zhang et al. / Microelectronics Reliability 76–77 (2017) 549–555

cannot be taken into account in the aforementioned process by the fun-damental-frequency. As discussed before, the thermal capacitance ofthe power devices and the heat sink are ignored because their time con-stants are too small compared with the sampling time of 10 min of theload-varying. Under this circumstance, a rainflow counting method isapplied to obtain the regular thermal cycles from the randomly changedannual temperature profile. The estimation process is shown in Fig. 10,the power losses corresponding to the yearly wind speed profile are ob-tained with the look-up table method, and a rainflow counting methodis applied to extract the mean junction temperature, junction tempera-ture fluctuation, as well as the period of the power cycles.

The results obtained from the rainflow counting method are shownin Fig. 11, where the thermal cycles of the GSC and the RSC are 8255 and

Fig. 11. Results obtained by rain flow counting method. (a) Mean junction temperature.(b) Junction temperature fluctuation. (c) The ON-state time.

7655, respectively. Comparedwith the results shown in Fig. 7, the junc-tion temperatures are similar, while the junction temperature fluctua-tions are higher than that in the fundamental-frequency thermalcycles, and the on-time periods are much higher because this case con-siders the effects of a long time-scale thermal cycles. Then, the total con-sumed lifetime is also obtained by the Miner's rule, and it is expressedas.

CL ¼X nf

N f

� �ð9Þ

where Nf is the number of thermal cycles calculated by (7), and nf is 0.5or 1 thermal cycle that is obtained by the rainflow counting method.

Then, the total Consumed Lifetime CL calculated by (9) is shown inFig. 12. It can be seen that the IGBT of theGSC and diode of the RSC dom-inates the consumed lifetime in terms of the varying-load thermal cy-cles, which is consistent with the fundamental-frequency causedannual damage. On the other hand, the lifetime consumption betweenthe IGBT and diode in the RSC stage is more balanced, as they are inthe same level with e−4 magnitude.

Compared with the consumed lifetime caused by fundamental-frequency thermal cycle shown in Fig. 9, the lifetime of GSC is mainlydetermined by the load-varying caused thermal cycles due to itsmuch higher junction temperature fluctuation. In respect to theRSC, although load-varying caused thermal cycles have higher junc-tion temperature compared to that caused by the fundamental-fre-quency, the cycle numbers of the load-varying caused thermalcycles is lower than that of the fundamental-frequency. As a result,these two kind of thermal cycles have almost the same effect onthe consumed lifetime.

5. Conclusion

In this paper, the consumed lifetime of the power converter in theDFIG system is discussed from the viewpoint of the fundamental-fre-quency thermal cycling and the load-varying thermal cycling. The GSClifetime is mainly dominant by the load-varying thermal cycles, whilethe fundamental-frequency and load-varying thermal cycles almosthave the same effect on the RSC lifetime. Besides, the IGBT of the GSCand the diode of the RSC are the most stressed component regardlessof the thermal cycle types. Generally, the lifetime of the RSC and GSCis in the same level with e−3 magnitude.

On the other hand, the low reliability of power devices can be com-pensated by increasing the number of the paralleled power module inthe GSC and RSC, or by selecting the power devices with larger capacityand higher reliability.

Fig. 12. Total consumed lifetime caused by varying-load.

555G. Zhang et al. / Microelectronics Reliability 76–77 (2017) 549–555

Acknowledgements

This work was supported by the Centre of Reliable Power Elec-tronics, Aalborg University, Denmark, and the China ScholarshipCouncil.

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