I. INTRODUCTION
Wind Turbine Power Converter Systems (WTPCSs) are critical in terms of the reliable operation of wind energy conversion systems (WECS). According to market feedback, WTPCSs are more prone to failure than generators and gearboxes [1]. Surveys also indicate that WTPCSs and their power semiconductors vary significantly in terms of failure rates depending on the WTPCS topologies and operating environments. Tavner et al. [2], [3] suggest that both the average wind speed and wind turbulence significantly affect the reliability of WTPCS power devices based on several statistical analyses. Nonetheless, the effects of wind turbulence on the reliability of WTPCS power devices has not gained adequate attention. Hence, a reliability assessment that considers the effect of average wind speed and wind turbulence intensity in such devices is essential.
Studies on the reliability of the power devices used in wind power converters can be categorized into two main classes:
The failure mechanism caused by these physical stresses can be traced as thermomec fatigue stresses which is the dominant wear-out mechanism in modern insulated gate bipolar transistor (IGBT)-based power converters [4]. Thermomec fatigue stresses are caused by the operational thermal level and thermal cycling, whose mission profiles are generated by variable wind speeds and the Pulse-Width Modulation (PWM) caused alternating currents, for long-term and short-term thermal loadings.
Most of the articles on this subject only address the short-term thermal cycling stresses caused by periodic converter commutations [5]. However, some articles have suggested that long-term temperature cycles are more damaging, since the solders creep and crack propagation [6], [7]. Considering this fact, the authors in [8] have derived a multi-state reliability assessment model, which addresses the influence of long-term thermal cycling. In the proposed model, both the effect of wind speed and wind turbulence are taken into consideration. The pitfall of this article is that short-term thermal cycling is omitted. Ma et al. [9] considered different timespans of the thermal behavior in the WTPCS thermal loading profile. Thus, the lifetime of these power devices are estimated. In this article, most of the lifetime models are based on accelerating test results that can cover only limited ranges of amplitudes, durations, and maximum values of thermal cycles. In addition, some test conditions are difficult to implement. Taking this into consideration, the method proposed in [9] is hard to put forward into practical application. Comparatively, the FIDES [10] reliability guide is proposed based on a lot of industrial reliability data and several acceleration models. This guide considers technological and physical factors, precise mission profiles, and almost all of the thermal behavior in various timespans that are shorter than one year. Thus, it may be suitable for reliability evaluations of the power semiconductors used in variable wind speeds applications. Xie et al. [11] conducted some preliminary studies that referenced the FIDES guide in the reliability assessment of WTPCS. However, in this article only average wind speeds are considered, while the influence of wind turbulence is ignored. As a result, the obtained failure rate is lower than the actual value.
A reliability assessment model for the power semiconductors used in WTPCS is proposed in this paper. Four basic concepts contribute to this methodology:
The paper is organized as follows. Section II analyzes the timescale characteristics of thermal cycling in power devices under variable wind speed operation conditions. Section III proposes a reliability assessment model that considers the effect of long-term thermal behavior. Section IV presents a reliability assessment model that accounts for the influences of short-term thermal behavior. Section V demonstrates the reliability through a case study, and the influences of parameters such as cut-in, rated and cut-out wind speed to the failure rate are analyzed. Section VI concludes the study.
II. THERMAL BEHAVIOR OF WTPCSS UNDER VARIABLE WIND SPEED
Based on the principle analysis and the simulated thermal loading profiles under variable wind speeds [11], [12], the reasons for power device thermal loading can generally be classified into two different types from the timescale perspective:
Fig. 1.Thermal mission profiles of power semiconductors in wind power converters under different time scales.
To sum up the aforementioned analysis of the reliability assessment model, two timescales of thermal cycling should be considered: long-term thermal cycling ÄTj_L, which considers the influence of wind speed variations; and short-term thermal cycling ÄTj_S, which accounts for the influence of alternating converter currents under a constant wind speed. Here different time-scale damages are independently accumulated. According to Miner’s rule, the final fatigue damage can be concluded by linearly adding the different timescales of thermal loading contributions.
III. PROFILES OF LONG-TERM THERMAL LOADING AND RELIABILITY EVALUATION
This section addresses long-term reliability assessment which is mainly caused by variations in wind speed. Considering the period for monsoon climate change is generally one year, one year’s operation data is required to evaluate the influence of variable wind speed on the failure rate of power devices [2], [10], [11].
A. Generation of the Long-Term Thermal Loading Profile
To illustrate the general construction of a thermal loading profile, the thermal loading profile of power devices in the permanent magnetic synchronous generators (PMSG) of wind turbine power converters is calculated. The randomly changing thermal loading profiles are computed according to the values of wind speed samples. The full-scale output power of the wind power converter can be expressed as [11]:
where Pr is the rated power of the wind turbine generator. The constants A, B, and C are denoted by vci, vr, and vco,[20].
where Kfv=pλop/2πR; p denotes the pole pair numbers; λop is the tip speed ratio (TSR); and R is the radius of the wind turbine blade.
Based on the electromotive force equation the peak voltage of the PMSG can be written as:
where N denotes the winding turns; KN is the winding coefficient; and Φ is the magnetic flux of each pole.
The conduction power losses of a diode and a IGBT can be given as [11]:
where fsw denotes the switching frequency; Eon and Eoff represent the energy losses in active and inactive states, respectively; Vref and Iref correspond to the rated voltage and current, respectively; ESR represents the power loss in the diode conduction; cosα denotes the power factor; and M indicates the modulation index. The principle behind the use of “±” is that the top sign corresponds to the grid side converter and the bottom one is used on the generator side. Iom is the peak of the phase current on the grid side converter and can be approximated as:
The mean value of the steady-state junction temperature is related to the total thermal resistance alone in this study. Fig. 2 depicts the model of the diodes and IGBTs.
Fig. 2.Equivalent model of thermal resistance of the IGBT and the diode.
In this figure, Ta, Tc, and Th are the ambient, heat sink, and case temperatures, respectively; Tj,IGBT and Tj,D are the junction temperatures of the IGBT and the diode; Rthjc,IGBT and Rthjc,D are the junction-to-case thermal resistances for the IGBT and the diode, respectively; Rthch is the case-to-heatsink thermal resistance; and Rthha is the heatsink-to-ambient thermal resistance.
Based on the thermal resistance model, the junction temperature for the IGBTs and diodes can be expressed as:
where Ploss denotes the total power loss of the IGBTs and the diodes.
B. Reliability Evaluation given Long-Term Thermal Loading
Wind speed and turbulence significantly affect the reliability of WTPCS power devices. Therefore, in this section, the operation state of a wind power converter is partitioned into different phases based on these two factors.
The probability of each state in a 2D multistate probability model of a WTPCS can be expressed as:
where p(i, j) denotes the annual cumulative frequency of the (i, j)th state of the WTPCS at the ith average wind speed and the jth division of the wind turbulence intensity; t(i, j) represents the cumulative time for the states (i, j); T corresponds to the period considered, which is typically one year; and Nth and NCy are the division numbers for the average wind speed and wind turbulence intensity, respectively. The wind turbulence intensity is defined as the ratio of the standard deviation of wind speed to the average wind speed:
where vtur denotes the wind turbulence intensity; vmean represents the average wind speed; and σ indicates the standard deviation of the wind speed for each hourly partitioned phase.
Based on FIDES, the thermal stress factor for the state (i, j) can be expressed as the Arrhenius law as:
where Vapplied is the working voltage; Vrated is the rated voltage; Sreference is the reference level for the electrical stress and p is the acceleration power for the electrical stress, which are both referred in the FIDES guide [10]; and Ea is the activation energy, where for different components the value is different. Tmean_i is the mean steady-state temperature of the components.
Based on the Norris—Landzberg acceleration model, the thermal cycling factor is written as:
where tj denotes the cumulative operation time for each state; N0 and Ncyj represent the number of reference and actual temperature cycles for each state phase, respectively; θ0 and θcyj are the reference and actual temperature cycle durations, respectively; ΔTCyj denotes the thermal amplitude of the cycle; Tmax_cyj is the maximum thermal value of the cycle; and γ, p and n are specific constants that correspond to different types of components.
By combing the results of the partition of the WTPCS operation state and the FIDES philosophy regarding the assessment of multi-phase failure rates, the proposed failure rate calculation method for WTPCS power devices can be represented by
where λ0Th and λ0TC denote the base failure rates of a component, which can be referred in the FIDES guide[10], both of which correspond to the thermal stress factor πty and the thermal cycling factor πTC, respectively. πIn represents overstress, which is determined by the coefficient of sensitivity to the application field of the component; πPm indicates component quality; and πPr denotes the aging status in terms of the lifespan of a component, whose recommended value in a normal life stage is 4.
Based on the aforementioned analysis, Fig. 3 depicts the proposed reliability assessment diagram for the WTPCS. The procedure mainly includes the following steps:
Fig. 3.Schematic of the assessment of power device reliability induced by long-term thermal cycling.
1) Partition of the WTPCS Operation States: As suggested in Equ.(8), the process of partitioning the WTPCS operation states involves the following steps: a) The sampled time series wind speed data is divided into equivalent time-span segments. Each segment spans one hour as indicated by the FIDES. vmean and vtur should be calculated for each segment. b) These segments are then partitioned into Nth parts based on their minimum and maximum average wind speeds. c) For each segment based on the average wind speed, an advanced partition is conducted into Ncy parts based on a wind turbulence value that ranges from the minimum to the maximum value. As a result, the WTPCS operation state is divided into Nth× Ncy parts. d) The cumulative operation time t(i, j) for each Nth× Ncy of the parts is also recorded to calculate the occurrence frequency p(i, j) for each state.
2) Calculation of the Thermal Loading Profiles of the Power Devices: The power losses can be calculated using Equs.(1)-(5) based on the sampled wind speed. The thermal loading profile can then be computed with Equ. (7).
3) Regulation of the Random Thermal Loading Profile using the Rain-flow Cycling Count Algorithm: As shown in Equ. (11), the thermal cycling factor in each separate phase of the WTPCS operation state is affected by ΔTcyj and Tmax_cyj as well as the duration time θcyj and cycle values Ncyj. Thus, the cycle counting method must be applied to extract the regular thermal cycling information from the randomly changing thermal profile. The rain-flow algorithm is a popular method for cycle counting. Fig. 4 displays the process when the rain-flow algorithm is used to regulate the randomly changing thermal profiles for each partitioned phase of the WTPCS operation. The average thermal value Ti, cycle number Ncyj, amplitude ΔTcyj, maximum value Tmax_cyj, and duration time θcyj are computed for each phase. These values are the arguments in the calculation of the failure rate thermal factor πth in Equ. (10) and of the thermal cycling factor πcy in Equ. (11).
Fig. 4.Rain-flow cycle counting algorithm in relation to junction temperature.
4) Failure Rate Calculation: The failure rate of a power device can be determined using Equ. (12) based on the partition results p(i, j), the failure rate thermal factor πth, and the thermal cycling factor πcy.
IV. PROFILES OF THE SHORT-TERM THERMAL LOADING AND RELIABILITY EVALUATION
As indicated in Fig.1, this type of thermal loading is mainly caused by alternating currents in the power converter that change periodically. This variation is observed even under the constant wind speeds that are omitted in the long-term thermal loading profile. As a result, the thermal cycling information should be extracted from a zoomed in perspective with a more detailed model. In this section, a reliability assessment model that considers short-term thermal behavior is established.
A. Characteristics and Thermal Profile of Short-term Thermal Loading
The amplitude of the short-term thermal loading is lower than that of the long-term thermal loading. However, the oscillation frequency is much higher than the long-term thermal cycling. The simulation results indicate that the mean junction temperature and temperature fluctuations are constant under stable operating states over the entire wind speed range [16]. Thus, the thermal cycling information regarding the mean junction temperature, temperature fluctuation, and cycling duration can be calculated at different wind speeds and can be directly applied to the FIDES model of failure rate without the rain-flow counting.
The mean temperature of the thermal cycling can be computed using the analytical functions of Equs. (1)-(7). The cycling duration θcyj represents half of the oscillation cycle, which can be determined with Equ.(2). The cycling amplitude ΔTcy can be calculated as in [16]:
where Zth is the thermal impedance in the datasheet of the power device; and f0 is the fundamental frequency of the converter output. At the grid side, this frequency is 50Hz. Meanwhile, that on the generator side can be calculated using Equ.(2).
B. Reliability Evaluation Given Short-Term Thermal Loading
In this subsection, the reliability assessment model of the multi-average wind speed is introduced in consideration of the fact that the cycling information of the short-term thermal loading varies with the wind speed. According the FIDES guide, the failure rate can be calculated as:
where tannual_i denotes the accumulated time for each wind speed distribution phases.
As presented in Fig. 5, the reliability assessment flow generated by the short-term thermal loading differs from that induced by the long-term thermal loading. The long-term thermal loading changes with variable wind speeds. Meanwhile, the short-term thermal loading is caused by alternating converter currents, the amplitude and mean junction temperature of which are related to the average wind speed. The reliability assessment caused by the short-term thermal loading involves three main steps:
Fig. 5.Schematic of the assessment of power device reliability induced by short-term thermal cycling.
V. CASE STUDY
To apply the proposed reliability assessment method, a typical field-sampled wind speed and a wind turbine system are established for a case study. The parameters of the WECS are presented in Table I, and the information on the main components are presented in the Appendix.
TABLE IWECS PARAMETERS
A. Reliability Assessment under Long-Term Thermal Loading
The WTPCS operation states are partitioned as shown in Fig. 6, the result shows that most of the states are centered on the point of the average wind speed 7.5m/s and the wind turbulence intensity 10%.
Fig. 6.Distributions of wind speed and wind turbulence intensity.
The effect of the operation state partition numbers Nth and Ncy on the WTPCS failure rate is investigated as depicted in Fig. 7. When Nth and Ncy reach a certain level, the failure rates of the power devices stabilize at approximately 0.042 and 0.026 occ./year on the generator side and grid sides, respectively. Conceptually, larger partition numbers generate more accurate results, but require additional calculation time. Fig. 7 indicates that both Nth and Ncy can be set at 20.
Fig. 7.Results of power device reliability assessment as induced by long-term thermal cycling under different average wind speeds and wind turbulence division numbers.
B. Reliability Assessment under Short-Term Thermal Loading
Using the proposed approach for power device reliability assessment based on short-term thermal loading, the failure rate calculation results are shown in Fig. 8. The power devices in the generator side and grid side finally stabilize at 0.053 occ./year and 0.034 occ./year, respectively. The wind speed division number can be set as 50 to get the table results.
Fig. 8.Results of power device reliability assessment as induced by short-term thermal cycling under different wind speed division number.
The contributions of different wind speeds to this failure rate are plotted in Fig. 9. As Fig. 9 shows, wind speeds around the rated value contribute the most to this failure rate, since the converter power losses at around rated operation state are significant. Furthermore, the contribution of the rated wind speed for the generator side power device is larger than the grid side, which occupies 60% of the total failure rate. This finding is ascribed to the fact that at the grid side, the converter output power variation is partially smoothened by the direct current (DC)-link capacitors.
Fig. 9.Failure rate contribution of different wind speeds.
C. Assessment Result of the Total Power Device Failure Rate
Fig. 10 displays the total failure rate of a power device by summing up the contributions of the short-term and long-term thermal behaviors. The total failure rates for the generator and grid sides are 0.096 and 0.060 occ./year, respectively. The long-term and short-term thermal loading are compared in terms of their contributions, as indicated in Fig. 10. The short-term thermal loading contributes more than the long-term thermal loading because its cycling numbers are significantly larger even though its cycling amplitude is smaller, as indicated in Fig.1.
Fig.10.Assessment result of total power device failure rate given different timescales of thermal loading.
D. Effects of WECS Parameters on the Failure Rate of WTPCS Power Devices
To accommodate the distribution of different wind speed resources, the WTPCS manufacturers may set various cut-in, rated, and cut-out wind speeds. In [19], these WECS parameters are investigated in different farms, and the results show that the cut-in wind speed is generally 0.6vm, the rated wind speed ranges from 1.6vm to 1.75 vm, and the cut-out wind speed is generally set at 3vm. In this case, vm is the annual mean wind speed. As stated in Section III, these parameters are directly related to the power loss, junction temperature, and power device failure rate. Hence, this section analyzes the effects of WECS parameters on the failure rate of WTPCS power devices based on the aforementioned reliability assessment model.
The relationship between the cut-in wind speed and the reliability of WTPCS power devices is determined as shown in Fig. 11, where the cut-in wind speed is varied, and the other parameters remain constant. The failure rate decreases as the cut-in wind speed increases, and this effect can be primarily attributed to the fact that the WTPCS standby time increases with a cut-in wind speed increase.
Fig. 11.Effect of the cut-in wind speed of wind turbines on the failure rate of WTPCS power devices.
Fig. 13 presents the effect of the cut-out wind speed on the reliability of WTPCS power devices when the cut-out wind speed varies. This effect may be complicated. The reliability of the generator side remains almost stable, whereas the grid side increases. To trace the influential contributors, two factors that contribute opposite effects on the failure rate are considered: the first is that an increase in the cut-out speed implies a prolonged annual operation time, which may cause the failure rate to be higher; the second is that an increase in the cut-out speed also implies a fewer frequently cut-in and recut-in behaviors, which corresponds to a variation in the junction temperature from the rated stress level to a circumstance temperature. As a result, these two factors balance out in the generator side converter. Meanwhile, in the grid side converter, the DC link flattens the variation. Therefore, the first influential factor is dominant.
Fig. 12.Effect of the rated wind speed of wind turbines on the failure rate of WTPCS power devices.
Fig. 13.Effect of the cut-out wind speed of wind turbines on the failure rate of WTPCS power devices.
To conclude, the effect of the rated wind speed on the failure rate is stronger than those of the cut-in and cut-out wind speeds.
VI. CONCLUSION
In this study, a failure rate assessment model is proposed for WTPCS power devices. This model considers thermal behavior at different timescales. For the assessment of long-term thermal loading, the operation state of the WTPCS is partitioned into different phases in terms of average wind speed and wind turbulence intensity, which correspond to different thermal factors and thermal cycling factors. Therefore, the contributions of these phases to reliability are considered. The feature of this model is that it considers both the influences of the average wind speed and the wind turbulence intensity. For short-term thermal loading, the wind profile is first converted into a wind speed distribution. The contributions of different wind speeds on the failure rate are then calculated. A multi-state reliability assessment model is then developed with the proportional addition of the different failure rate contributions. With the establishment of the failure rate assessment model, the influences of cut-in, rated, and cut-out wind speeds on the failure rate of the WTPCS power devices can be acquired. Among these factors, the rated wind speed has the greatest impact on the failure rate.
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