- Email: [email protected]
Benchmarking of capacitor power loss calculation methods for wear-out failure prediction in PV inverters
Microelectronics Reliability xxx (xxxx) xxxx
Contents lists available at ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
Benchmarking of capacitor power loss calculation methods for wear-out failure prediction in PV inverters João M. Lenza, , Allan F. Cupertinob,c, Heverton A. Pereirad, Dao Zhoue, Huai Wange, José R. Pinheiroa ⁎
a
Power Electronics and Control Research Group (GEPOC), Federal University of Santa Maria – UFSM, Santa Maria, RS, Brazil Graduate Program in Electrical Engineering - Federal University of Minas Gerais, Belo Horizonte, MG, Brazil c Department of Material Engineering, Federal Center for Technological Education of Minas Gerais, Belo Horizonte, MG, Brazil d Department of Electrical Engineering, Federal University of Viçosa, Viçosa, MG, Brazil e Department of Energy Technology, Aalborg University, Aalborg, Denmark b
ABSTRACT
Aluminium electrolytic capacitors (e-caps) are among the components most prone to failure in power electronic systems. Thermal stress is a critical factor which affects the lifetime of dc-link capacitors. Therefore, the estimation of power loss and temperature are important steps in lifetime prediction of these components. This paper aims to carry out a qualitative benchmarking of different capacitor loss estimation methods, focusing on the component level reliability. Four different equivalent series resistance (ESR) models are benchmarked for 2 different mission profiles based on complexity, estimated losses, thermal stresses, and B1 lifetime: 1) constant ESR, 2) temperature dependent ESR, 3) frequency dependent ESR, and 4) frequency/temperature dependent ESR. Capacitors in the dc-link of a PV inverter are evaluated using an offline look-up table (LUT) approach, considering two different mission profiles (MP), and following a normal distribution parametric variation. For the lifetime model and parameters employed, the results for this case study indicated a maximum difference of 7.1% in the B1 lifetime estimated by approaches 1 and 4.
1. Introduction In single-stage photovoltaic (PV) inverters, the dc-link capacitor bank is an interface between the PV array and the switching power converter, as shown in Fig. 1a. Although industry based surveys indicate that Al e-caps are among the most prone to failure components in power electronics [1,2], they are still widely employed in products available in the market due to their low cost and high energy density. Considering the high competitiveness of the PV market, more reliable inverters are desired to reduce the cost of energy [3]. Thereby, many studies have recently developed methodologies to assess the reliability of renewable energy inverters [4–6]. High average operating temperature is one of the main factors that affect a capacitor's lifetime. As a rule of thumb, the lifetime of Al e-caps is reduced by half for every 10 °C increase [7]. Although estimating the operating temperature is critical for the reliability analysis, it is not trivial due to the intrinsic coupling among temperature, power losses, and heat transfer mechanisms in power electronic components. The complexity is also increased by the non-linear relationship between the temperature response and electric parameters. The power losses in Al e-caps are dependent on their equivalent series resistance (ESR) and different approaches have been proposed for ⁎
modelling such losses in dc-link capacitors. A simple model is used in [8,9] assuming a constant ESR and computing the power losses as a function of the RMS current ripple. While in [10,11] the dependence of ESR on frequency is considered to obtain a more accurate estimation. Alternatively, in [12] the relationship between the ESR and both the frequency and temperature is considered and modelled in look-up tables which demonstrates that offline LUT are a useful tool for decreasing the losses computing time. If the ESR relationship with frequency is included, the complexity of the needed methodology and algorithms increases considerably, since the Fast Fourier Transform (FFT) must be applied to compute the harmonic currents [8]. The complexity is even higher when the temperature is also included, which leads to the need for an iteration process. Therefore, this paper aims to benchmark different capacitor loss estimation methods, focusing on the reliability. Four different ESR models are compared based on complexity, estimated power losses and thermal stresses, and B1 lifetime: 1) constant ESR, 2) temperature dependent ESR, 3) frequency dependent ESR, and 4) frequency/temperature dependent ESR. A case study based on a 3.5 kW PV single-stage single-phase PV inverter in two different mission profiles is done.
Corresponding author. E-mail address: [email protected] (J.M. Lenz).
https://doi.org/10.1016/j.microrel.2019.113491 Received 15 May 2019; Received in revised form 25 June 2019; Accepted 6 August 2019 0026-2714/ © 2019 Published by Elsevier Ltd.
Please cite this article as: João M. Lenz, et al., Microelectronics Reliability, https://doi.org/10.1016/j.microrel.2019.113491
Microelectronics Reliability xxx (xxxx) xxxx
J.M. Lenz, et al.
Fig. 1. Flowchart evaluating a) PV inverter dc-link capacitors using an b) offline look-up tables approach under c) different power loss and ESR models.
Fig. 3. Variation of ESR with: a) frequency; b) temperature [15].
well as the ESR model shown in Fig. 3: Method #1: ESR is constant and equal to the value usually provided by the manufacturer's datasheet, e.g. ESR at grid frequency and ambient temperature. In this approach, only the RMS capacitor current look-up tables are needed. This is the simplest and fastest power method (Fig. 1b–c); Method #2: After an initial estimation of Eq. (2), the ESR value is corrected according to the temperature, using the datasheet information (Fig. 3b). An iterative method is needed, once TCAP is a function of the ESR; Method #3: Datasheet information is used to model the ESR value according to the frequency (Fig. 3a). Here, the Fast Fourier Transform (FFT) algorithm must be performed (Fig. 1b–c), which increases both processing time and needed memory; Method #4: No simplifications are carried out and methods 2 and 3 are combined. This is the most realistic and demanding method, since it requires both FFT and in iteration process to calculate the power loss to estimate the capacitor temperature.
Fig. 2. Dc-link capacitor wear-out prediction flowchart.
2. DC-link capacitor lifetime evaluation Fig. 2 shows the methodology used to predict the capacitor wear-out and evaluate the different ESR models, which are described as follows. 2.1. Electro-thermal model The simplified equivalent circuit of the electrolytic capacitor used is composed only of its capacitance (C) and equivalent series resistance. The thermal model estimates the capacitor core temperature (TCAP), where the power loss (Ploss) is dissipated in the thermal resistance (Rth) between the capacitor core and the atmosphere; τCAP is the capacitor's thermal time constant and Tamb, the ambient temperature. Thus, e-cap power loss and core temperature may be calculated through N
Ih2 (fh ) ESR (fh , TCAP ) ,
Ploss = h=1
TCAP = Ploss Rth 1
t
exp CAP + Tamb + THS ,
(1)
2.2. Lifetime model and damage accumulation Failures in e-caps may occur due to external and/or random factors, such as manufacturing defect, improper design, environmental overstress, abnormal operation condition, among others. However, they usually occur non-predictably and catastrophically – where a single event leads to failure. Thus, they are difficult to model or foresee and are usually deemed as random events. The electrolyte vaporization and wear-out of electrical parameters is one of the dominant mechanisms that may lead to the failure of either the capacitor itself or of the circuit/control scheme in which the capacitor is inserted. A typical and widely used approach for estimating the useful life of e-caps the simplification of the Arrhenius law [7,17], which yields in lifetime (L) as a function of the capacitor operating temperature and voltage (VCAP) as
(2)
where fh is the hth harmonic frequency, and Eq. (2) is calculated through and iterative process since it is a transcendental equation wherein TCAP is dependent on the ESR, and vice-versa. For a more comprehensive modelling, the inverter internal temperature increase (ΔTHS) relative to Tamb is calculated using the methodology and parameters given in [13,14]. As previously discussed, e-caps ESR relationship with both frequency and temperature is not always included and the impact of its model complexity has not yet been thoroughly evaluated in reliability analyses. The present work analyzes four different methods for describing the ESR and the e-cap electrical model, as shown in Fig. 1c as 2
Microelectronics Reliability xxx (xxxx) xxxx
J.M. Lenz, et al.
L (TCAP , VCAP ) = L0 2
T0 TCAP n1
VCAP V0
n2
,
(3)
where L0, T0, and V0 are the capacitor rated lifetime, temperature, and voltage, respectively, which are usually specified by the manufacturer. In this paper, n1 = 10 and n2 = 4 are adopted, which are within the typical range for e-caps [7]. Since the dc-link voltage is controlled and mainly dependent on ambient conditions, the values of VCAP in time are the same for all ESR methods throughout this analysis. During day-time, the energy flowing through the PV-inverter system is constantly fluctuating due to changes in weather conditions. This leads to a variability in voltage and thermal stresses in the dc-link capacitors. The latter is in reason of the varying ambient temperature and current levels, and the former, due to the MPPT voltage control of the single stage inverter. A simple solution to quantify the impact of this time-variant stresses on the overall lifetime is to use Miner's rule to calculate the ratio between the period in which the capacitor operated in each stress level, tLi, and the estimated lifetime Eq. (3) at that given condition [16], as follows
t Li
AD =
Li (TCAP VCAP )
.
(4)
Fig. 4. Solar irradiance and ambient temperature MPs used in the case studies for a) Lindenberg and b) Petrolina.
Typically, failure is assumed to occur when the accumulated damage (AD) calculated by Eq. (4) reaches one. It is highlighted that Miner's rule assumes a linear relationship between stress and AD, and it is known that capacitors follow a somewhat exponential degradation curve. However, there is no consensus yet in scientific literature nor in the information provided by the manufacturers about a generalized model for damage accumulation of e-caps electric parameters. Since the scope of this paper lies in a qualitative comparison of electro-thermal – and not of lifetime – models, Miner's rule is used as a rough estimation.
distinct mission profiles, following the methodology and data provided in [17]. The first mission profile (MP) is established as the PV system operating in a horizontal fixed mounting, e.g. as in a rooftop, at Lindenberg (LIN), Germany (52° N, 14° E). In the second MP, the PV system is assumed to be in a 2-axis mechanical tracker and is installed in Petrolina (PTR), Brazil (09° S, 40° W). These PV MPs are built using PV modelling combined with real weather data measured over 7+ years and averaged minute-by-minute using the same timestamp for different years, forming a typical average year (TAY) of ambient conditions. The 1-year typical average surface irradiance and ambient temperature for each scenario are shown in Fig. 4. The main parameters of the studied PV system and dc-link capacitor bank are described in Table 1. The analyses are carried out using the capacitors manufactured by Cornell Dubillier [15].
2.3. Monte-Carlo simulation and Bx lifetime Since not all capacitors are identical and even their degradation may occur differently for the same stress level, a statistical approach is combined with a parametric variation in order to calculate the Bx lifetime – which is the time when x% of the samples would fail [4]. A normal distribution with ± 20% in a 3σ range of the rated lifetime (L0) and estimated hotspot temperature (TCAP) is assumed in order to include a parameter deviation analysis, to consider the difference among multiple components. A Monte Carlo simulation is performed using these parametric variations to obtain the lifetime of 10,000 random samples. The stochastic parameters TCAP and VCAP are initially converted into static values T′CAP and V′CAP, using Eqs. (3) and (4) for the condition in which the AD is equal to one, based on the methodology proposed in [4]. The Monte Carlo simulation output is the capacitor lifetime distribution, which usually follows the Weibull distribution given by:
f (x ) =
x
1 exp
x
,
3.1. Look-up table approach The energy flow from the PV array into the grid is mainly dependent on ambient temperature and the available solar power. Therefore, by changing these both variables in alternate intervals, the PV system entire range of operation is assessed offline. Current and voltage values of the inverter and dc-link capacitors are stored in look-up tables (LUT) as function of the input irradiance and Table 1 Parameters of the PV system analysed.
(5)
where β is the shape parameter, η is the scale parameter, and x is the operation time. The wear-out failure probability curve F(x) is obtained through a cumulative density function (CDF), where
F (x ) =
x 0
f (x ) dx .
(6)
The B1 lifetime – time when 1% of the samples have failed – is then obtained from Eq. (6). B1 is used as the comparison criteria for the different power loss models analysed in this paper. 3. Case study: single-phase PV inverter Two long-term case studies of a PV system are conducted using two 3
Parameter
Value
Panel SunEarth TPB60-60-235p rated power Number of PV panels in series Inverter rated power Switching frequency DC-link nominal voltage DC-link maximum ripple voltage Grid frequency Grid voltage (line-to-neutral, RMS) Capacitor rated capacitance Number of parallel capacitors in dc-link ESR @ 120 Hz, 25 °C Capacitor thermal resistance Capacitor thermal time constant
235 W 14 3.5 kW 10 kHz 380 V 14 V 60 Hz 220 V 0.68 mF 6 0.293 Ω 12.58 K/W 480 s
Microelectronics Reliability xxx (xxxx) xxxx
J.M. Lenz, et al.
Fig. 5. Power loss in an individual capacitor for different irradiance levels and 25 °C of ambient temperature.
ambient temperature, as depicted in Fig. 1b. These LUTs are later accessed and interpolated during the long-term mission profile analysis.
Fig. 7. Wear-out failure probabilities of the dc-link capacitors for all methods: (a) Detailed view for PTR MP; (b) detailed view for LIN MP.
4. Results Firstly, the steady-state power losses in the dc-link capacitors are evaluated for different irradiance levels. The results are presented in Fig. 5. As expected, the increase of solar irradiance results in higher power generation and higher losses. Method 1 (constant ESR) results in an overestimation of the power losses when compared to the other methods. Method 4 (frequency and temperature dependent) presents the lowest losses, since the ESR decreases with both temperature and frequency. After estimating the capacitor temperature throughout 1-year, electro-thermal histograms are built to count the number of hours the capacitor operated in each stress level in that MP, according to each power loss model. These yearly frequency distributions of TCAP are shown in Fig. 6 for the methods 1 and 4. Due to the higher average and lower variability of ambient temperature at PTR (Fig. 4), dc-link capacitors operate in a considerably higher temperature range and for longer periods throughout the year than in LIN. Notably, the constant ESR model results in higher values of TCAP. This is consistent in both analysed MPs and indicates that the constant ESR method gives a worstcase scenario when estimating thermal stresses. After computing the AD and Monte Carlo simulation of both mission profiles, the lifetime distribution CDF for each model are obtained and shown in Fig. 7. The failure probability in the B1 region is shown in detail in Fig. 7a and b, for PTR and LIN MPs, respectively. As previously observed, the higher core temperatures at PTR resulted in higher capacitor damage and reduced lifetime. The failure probability curves indicate that method 1 is the most conservative. Table 2 gives the calculated B1 lifetime for all scenarios. In accordance to the previous results, the constant ESR method presented the lowest values for both MPs, in reason of the higher thermal stresses. Furthermore, the results indicate that the ESR dependence to
Table 2 B1 lifetime of the dc-link capacitors for the evaluated methods. Method
LIN PTR
B1 lifetime Error relative to ESR(f,TCAP) B1 lifetime Error relative to ESR(f,TCAP)
1
2
3
4
13.50 −5.3% 4.61 −7.1%
13.90 −2.5% 4.89 −1.4%
13.89 −2.6% 4.72 −4.8%
14.26 – 4.96 –
temperature affects more the lifetime estimation than the frequency. The maximum difference observed is lower than 7.1%. Nevertheless, the lifetime values and model errors shown in Table 2 are bound to the parametric variations, current harmonic spectrum, and the mission profile used in this paper. The B1 values may also differ if a non-linear cumulative of damage assumption is made. Finally, Table 3 benchmarks the discussed power loss evaluation methods as good (blue), average (grey), and poor performance (red). 5. Conclusions In order to obtain fast tools for reliability evaluation of multiple components on long-term analyses, methods with reduced complexity and still acceptable accuracy are desirable. Therefore, this paper benchmarked four capacitor power loss calculation methods and compared their impact on the wear-out failure prediction of PV inverters. Method 1 (constant ESR) is the simplest, since it requires knowledge only of the capacitors RMS current. The frequency dependence (included in methods 3 and 4) requires the harmonic components of the capacitor current. Thereby, an FFT is employed and the computational effort increases. The maximum difference observed in the dc-link B1 lifetime was 7.1% for Petrolina and 4.6% for Lindenberg mission profiles. For Table 3 Benchmarking of the power losses methods. Good, average, and poor performance.
Fig. 6. Core temperature distribution in the dc-link capacitors for methods 1 and 4: (a) LIN; (b) PTR. 4
Microelectronics Reliability xxx (xxxx) xxxx
J.M. Lenz, et al.
methods 2 and 4, these values reduced to 5.3% and 1.7%, respectively. It is also observed that the capacitor average core temperature is the dominant factor in lifetime estimation. Thus the mission profiles of ambient temperature and current harmonic content significantly affect these deviations. Therefore, the results presented are viewed as a qualitative comparison between these power loss models. A compromise between model error and complexity should be assessed considering the application requirements.
[4] [5] [6] [7]
Declaration of competing interest
[8]
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
[9] [10]
Acknowledgements
[11]
This wok was financed by the Energy Technology Department (ET) of Aalborg University (AAU), by the Brazilian National Council for Scientific and Technological Development (CNPq) – process 206373/ 2017, and by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES/PROEX) - Finance Code 001.
[12] [13] [14]
References
[15]
[1] S. Yang, A. Bryant, P. Mawby, An industry-based survey of reliability in power electronic converters, 2009 IEEE Energy Convers. Congr. Expo, 2009, pp. 3151–3157. [2] J. Falck, C. Felgemacher, A. Rojko, M. Liserre, P. Zacharias, Reliability of power electronic systems: an industry perspective, IEEE Ind. Electron. Mag. 12 (June) (2018) 24–35. [3] A. Sangwongwanich, Y. Shen, A. Chub, E. Liivik, D. Vinnikov, Mission profile-based accelerated testing of DC-link capacitors in photovoltaic inverters, Applied Power
[16] [17]
5
Electronics Conference and Exposition (APEC) (2019), https://doi.org/10.1109/ APEC.2019.8721794. F.H. Aghdam, M. Abapour, Reliability and cost analysis of multistage boost converters connected to PV panels, IEEE J. Photovoltaics 6 (4) (2016) 981–989 Jul. D. Zhou, Y. Song, Y. Liu, F. Blaabjerg, Mission profile based reliability evaluation of capacitor banks in wind power converters, IEEE Trans. Power Electron. 34 (5) (2019) 4665–4677 May. Y. Shen, A. Chub, H. Wang, D. Vinnikov, E. Liivik, F. Blaabjerg, Wear-out failure analysis of an impedance-source PV microinverter based on, IEEE Trans. Ind. Electron. 66 (5) (2019) 3914–3927. H. Wang, F. Blaabjerg, Reliability of capacitors for DC-link applications in power electronic converters - an overview, IEEE Trans. Ind. Appl. 50 (5) (2014) 3569–3578. B. Basler, T. Greiner, Power loss reduction of DC link capacitor for multi-phase motor drive systems through shifted control, 2015 9th Int. Conf. Power Electron. ECCE Asia (ICPE-ECCE Asia), 2015, pp. 2451–2456. H. Matsumori, K. Urata, T. Shimizu, K. Takano, H. Ishii, Capacitor loss analysis method for power electronics converters, Microelectron. Reliab. 88–90 (September) (2018) 443–446. A. Braham, A. Lahyani, P. Venet, N. Rejeb, Recent developments in fault detection and power loss estimation of electrolytic capacitors, IEEE Trans. Power Electron. 25 (1) (2010) 33–43 Jan. P. Kulsangcharoen, C. Klumpner, M. Rashed, G. Asher, G.Z. Chen, S.A. Norman, Assessing the accuracy of loss estimation methods for supercapacitor energy storage devices operating under constant power cycling, 16th European Conference on Power Electronics and Applications, 2014, pp. 1–11. Y. Yang, K. Ma, H. Wang, F. Blaabjerg, Instantaneous thermal modeling of the DClink capacitor in PhotoVoltaic systems, 2015 IEEE Appl. Power Electron. Conf. Expo, vol. 2015-May, no. May, Mar. 2015, pp. 2733–2739. Z. Zhang, et al., Operating temperatures of open-rack installed photovoltaic inverters, Sol. Energy 137 (2016) 344–351. J.M. Lenz, J.R. Pinheiro, Mission profile impact on capacitor reliability in PV singlestage inverters, 2018 7th International Conference on Renewable Energy Research and Applications (ICRERA), 5 2018, pp. 976–981. CDM Cornell Dubilier, Type 380LQ 85 °C compact, high capacitance, snap-in aluminum, Technical Datasheet, 2019. D. Zhou, H. Wang, F. Blaabjerg, Lifetime estimation of electrolytic capacitors in a fuel cell power converter at various confidence levels, 2016 IEEE 2nd Annual Southern Power Electronics Conference (SPEC), 2016, pp. 1–6. J.M. Lenz, H.C. Sartori, J.R. Pinheiro, Mission profile characterization of PV systems for the specification of power converter design requirements, Sol. Energy 157 (2017) 263–276 Nov.
Contents lists available at ScienceDirect
Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel
Benchmarking of capacitor power loss calculation methods for wear-out failure prediction in PV inverters João M. Lenza, , Allan F. Cupertinob,c, Heverton A. Pereirad, Dao Zhoue, Huai Wange, José R. Pinheiroa ⁎
a
Power Electronics and Control Research Group (GEPOC), Federal University of Santa Maria – UFSM, Santa Maria, RS, Brazil Graduate Program in Electrical Engineering - Federal University of Minas Gerais, Belo Horizonte, MG, Brazil c Department of Material Engineering, Federal Center for Technological Education of Minas Gerais, Belo Horizonte, MG, Brazil d Department of Electrical Engineering, Federal University of Viçosa, Viçosa, MG, Brazil e Department of Energy Technology, Aalborg University, Aalborg, Denmark b
ABSTRACT
Aluminium electrolytic capacitors (e-caps) are among the components most prone to failure in power electronic systems. Thermal stress is a critical factor which affects the lifetime of dc-link capacitors. Therefore, the estimation of power loss and temperature are important steps in lifetime prediction of these components. This paper aims to carry out a qualitative benchmarking of different capacitor loss estimation methods, focusing on the component level reliability. Four different equivalent series resistance (ESR) models are benchmarked for 2 different mission profiles based on complexity, estimated losses, thermal stresses, and B1 lifetime: 1) constant ESR, 2) temperature dependent ESR, 3) frequency dependent ESR, and 4) frequency/temperature dependent ESR. Capacitors in the dc-link of a PV inverter are evaluated using an offline look-up table (LUT) approach, considering two different mission profiles (MP), and following a normal distribution parametric variation. For the lifetime model and parameters employed, the results for this case study indicated a maximum difference of 7.1% in the B1 lifetime estimated by approaches 1 and 4.
1. Introduction In single-stage photovoltaic (PV) inverters, the dc-link capacitor bank is an interface between the PV array and the switching power converter, as shown in Fig. 1a. Although industry based surveys indicate that Al e-caps are among the most prone to failure components in power electronics [1,2], they are still widely employed in products available in the market due to their low cost and high energy density. Considering the high competitiveness of the PV market, more reliable inverters are desired to reduce the cost of energy [3]. Thereby, many studies have recently developed methodologies to assess the reliability of renewable energy inverters [4–6]. High average operating temperature is one of the main factors that affect a capacitor's lifetime. As a rule of thumb, the lifetime of Al e-caps is reduced by half for every 10 °C increase [7]. Although estimating the operating temperature is critical for the reliability analysis, it is not trivial due to the intrinsic coupling among temperature, power losses, and heat transfer mechanisms in power electronic components. The complexity is also increased by the non-linear relationship between the temperature response and electric parameters. The power losses in Al e-caps are dependent on their equivalent series resistance (ESR) and different approaches have been proposed for ⁎
modelling such losses in dc-link capacitors. A simple model is used in [8,9] assuming a constant ESR and computing the power losses as a function of the RMS current ripple. While in [10,11] the dependence of ESR on frequency is considered to obtain a more accurate estimation. Alternatively, in [12] the relationship between the ESR and both the frequency and temperature is considered and modelled in look-up tables which demonstrates that offline LUT are a useful tool for decreasing the losses computing time. If the ESR relationship with frequency is included, the complexity of the needed methodology and algorithms increases considerably, since the Fast Fourier Transform (FFT) must be applied to compute the harmonic currents [8]. The complexity is even higher when the temperature is also included, which leads to the need for an iteration process. Therefore, this paper aims to benchmark different capacitor loss estimation methods, focusing on the reliability. Four different ESR models are compared based on complexity, estimated power losses and thermal stresses, and B1 lifetime: 1) constant ESR, 2) temperature dependent ESR, 3) frequency dependent ESR, and 4) frequency/temperature dependent ESR. A case study based on a 3.5 kW PV single-stage single-phase PV inverter in two different mission profiles is done.
Corresponding author. E-mail address: [email protected] (J.M. Lenz).
https://doi.org/10.1016/j.microrel.2019.113491 Received 15 May 2019; Received in revised form 25 June 2019; Accepted 6 August 2019 0026-2714/ © 2019 Published by Elsevier Ltd.
Please cite this article as: João M. Lenz, et al., Microelectronics Reliability, https://doi.org/10.1016/j.microrel.2019.113491
Microelectronics Reliability xxx (xxxx) xxxx
J.M. Lenz, et al.
Fig. 1. Flowchart evaluating a) PV inverter dc-link capacitors using an b) offline look-up tables approach under c) different power loss and ESR models.
Fig. 3. Variation of ESR with: a) frequency; b) temperature [15].
well as the ESR model shown in Fig. 3: Method #1: ESR is constant and equal to the value usually provided by the manufacturer's datasheet, e.g. ESR at grid frequency and ambient temperature. In this approach, only the RMS capacitor current look-up tables are needed. This is the simplest and fastest power method (Fig. 1b–c); Method #2: After an initial estimation of Eq. (2), the ESR value is corrected according to the temperature, using the datasheet information (Fig. 3b). An iterative method is needed, once TCAP is a function of the ESR; Method #3: Datasheet information is used to model the ESR value according to the frequency (Fig. 3a). Here, the Fast Fourier Transform (FFT) algorithm must be performed (Fig. 1b–c), which increases both processing time and needed memory; Method #4: No simplifications are carried out and methods 2 and 3 are combined. This is the most realistic and demanding method, since it requires both FFT and in iteration process to calculate the power loss to estimate the capacitor temperature.
Fig. 2. Dc-link capacitor wear-out prediction flowchart.
2. DC-link capacitor lifetime evaluation Fig. 2 shows the methodology used to predict the capacitor wear-out and evaluate the different ESR models, which are described as follows. 2.1. Electro-thermal model The simplified equivalent circuit of the electrolytic capacitor used is composed only of its capacitance (C) and equivalent series resistance. The thermal model estimates the capacitor core temperature (TCAP), where the power loss (Ploss) is dissipated in the thermal resistance (Rth) between the capacitor core and the atmosphere; τCAP is the capacitor's thermal time constant and Tamb, the ambient temperature. Thus, e-cap power loss and core temperature may be calculated through N
Ih2 (fh ) ESR (fh , TCAP ) ,
Ploss = h=1
TCAP = Ploss Rth 1
t
exp CAP + Tamb + THS ,
(1)
2.2. Lifetime model and damage accumulation Failures in e-caps may occur due to external and/or random factors, such as manufacturing defect, improper design, environmental overstress, abnormal operation condition, among others. However, they usually occur non-predictably and catastrophically – where a single event leads to failure. Thus, they are difficult to model or foresee and are usually deemed as random events. The electrolyte vaporization and wear-out of electrical parameters is one of the dominant mechanisms that may lead to the failure of either the capacitor itself or of the circuit/control scheme in which the capacitor is inserted. A typical and widely used approach for estimating the useful life of e-caps the simplification of the Arrhenius law [7,17], which yields in lifetime (L) as a function of the capacitor operating temperature and voltage (VCAP) as
(2)
where fh is the hth harmonic frequency, and Eq. (2) is calculated through and iterative process since it is a transcendental equation wherein TCAP is dependent on the ESR, and vice-versa. For a more comprehensive modelling, the inverter internal temperature increase (ΔTHS) relative to Tamb is calculated using the methodology and parameters given in [13,14]. As previously discussed, e-caps ESR relationship with both frequency and temperature is not always included and the impact of its model complexity has not yet been thoroughly evaluated in reliability analyses. The present work analyzes four different methods for describing the ESR and the e-cap electrical model, as shown in Fig. 1c as 2
Microelectronics Reliability xxx (xxxx) xxxx
J.M. Lenz, et al.
L (TCAP , VCAP ) = L0 2
T0 TCAP n1
VCAP V0
n2
,
(3)
where L0, T0, and V0 are the capacitor rated lifetime, temperature, and voltage, respectively, which are usually specified by the manufacturer. In this paper, n1 = 10 and n2 = 4 are adopted, which are within the typical range for e-caps [7]. Since the dc-link voltage is controlled and mainly dependent on ambient conditions, the values of VCAP in time are the same for all ESR methods throughout this analysis. During day-time, the energy flowing through the PV-inverter system is constantly fluctuating due to changes in weather conditions. This leads to a variability in voltage and thermal stresses in the dc-link capacitors. The latter is in reason of the varying ambient temperature and current levels, and the former, due to the MPPT voltage control of the single stage inverter. A simple solution to quantify the impact of this time-variant stresses on the overall lifetime is to use Miner's rule to calculate the ratio between the period in which the capacitor operated in each stress level, tLi, and the estimated lifetime Eq. (3) at that given condition [16], as follows
t Li
AD =
Li (TCAP VCAP )
.
(4)
Fig. 4. Solar irradiance and ambient temperature MPs used in the case studies for a) Lindenberg and b) Petrolina.
Typically, failure is assumed to occur when the accumulated damage (AD) calculated by Eq. (4) reaches one. It is highlighted that Miner's rule assumes a linear relationship between stress and AD, and it is known that capacitors follow a somewhat exponential degradation curve. However, there is no consensus yet in scientific literature nor in the information provided by the manufacturers about a generalized model for damage accumulation of e-caps electric parameters. Since the scope of this paper lies in a qualitative comparison of electro-thermal – and not of lifetime – models, Miner's rule is used as a rough estimation.
distinct mission profiles, following the methodology and data provided in [17]. The first mission profile (MP) is established as the PV system operating in a horizontal fixed mounting, e.g. as in a rooftop, at Lindenberg (LIN), Germany (52° N, 14° E). In the second MP, the PV system is assumed to be in a 2-axis mechanical tracker and is installed in Petrolina (PTR), Brazil (09° S, 40° W). These PV MPs are built using PV modelling combined with real weather data measured over 7+ years and averaged minute-by-minute using the same timestamp for different years, forming a typical average year (TAY) of ambient conditions. The 1-year typical average surface irradiance and ambient temperature for each scenario are shown in Fig. 4. The main parameters of the studied PV system and dc-link capacitor bank are described in Table 1. The analyses are carried out using the capacitors manufactured by Cornell Dubillier [15].
2.3. Monte-Carlo simulation and Bx lifetime Since not all capacitors are identical and even their degradation may occur differently for the same stress level, a statistical approach is combined with a parametric variation in order to calculate the Bx lifetime – which is the time when x% of the samples would fail [4]. A normal distribution with ± 20% in a 3σ range of the rated lifetime (L0) and estimated hotspot temperature (TCAP) is assumed in order to include a parameter deviation analysis, to consider the difference among multiple components. A Monte Carlo simulation is performed using these parametric variations to obtain the lifetime of 10,000 random samples. The stochastic parameters TCAP and VCAP are initially converted into static values T′CAP and V′CAP, using Eqs. (3) and (4) for the condition in which the AD is equal to one, based on the methodology proposed in [4]. The Monte Carlo simulation output is the capacitor lifetime distribution, which usually follows the Weibull distribution given by:
f (x ) =
x
1 exp
x
,
3.1. Look-up table approach The energy flow from the PV array into the grid is mainly dependent on ambient temperature and the available solar power. Therefore, by changing these both variables in alternate intervals, the PV system entire range of operation is assessed offline. Current and voltage values of the inverter and dc-link capacitors are stored in look-up tables (LUT) as function of the input irradiance and Table 1 Parameters of the PV system analysed.
(5)
where β is the shape parameter, η is the scale parameter, and x is the operation time. The wear-out failure probability curve F(x) is obtained through a cumulative density function (CDF), where
F (x ) =
x 0
f (x ) dx .
(6)
The B1 lifetime – time when 1% of the samples have failed – is then obtained from Eq. (6). B1 is used as the comparison criteria for the different power loss models analysed in this paper. 3. Case study: single-phase PV inverter Two long-term case studies of a PV system are conducted using two 3
Parameter
Value
Panel SunEarth TPB60-60-235p rated power Number of PV panels in series Inverter rated power Switching frequency DC-link nominal voltage DC-link maximum ripple voltage Grid frequency Grid voltage (line-to-neutral, RMS) Capacitor rated capacitance Number of parallel capacitors in dc-link ESR @ 120 Hz, 25 °C Capacitor thermal resistance Capacitor thermal time constant
235 W 14 3.5 kW 10 kHz 380 V 14 V 60 Hz 220 V 0.68 mF 6 0.293 Ω 12.58 K/W 480 s
Microelectronics Reliability xxx (xxxx) xxxx
J.M. Lenz, et al.
Fig. 5. Power loss in an individual capacitor for different irradiance levels and 25 °C of ambient temperature.
ambient temperature, as depicted in Fig. 1b. These LUTs are later accessed and interpolated during the long-term mission profile analysis.
Fig. 7. Wear-out failure probabilities of the dc-link capacitors for all methods: (a) Detailed view for PTR MP; (b) detailed view for LIN MP.
4. Results Firstly, the steady-state power losses in the dc-link capacitors are evaluated for different irradiance levels. The results are presented in Fig. 5. As expected, the increase of solar irradiance results in higher power generation and higher losses. Method 1 (constant ESR) results in an overestimation of the power losses when compared to the other methods. Method 4 (frequency and temperature dependent) presents the lowest losses, since the ESR decreases with both temperature and frequency. After estimating the capacitor temperature throughout 1-year, electro-thermal histograms are built to count the number of hours the capacitor operated in each stress level in that MP, according to each power loss model. These yearly frequency distributions of TCAP are shown in Fig. 6 for the methods 1 and 4. Due to the higher average and lower variability of ambient temperature at PTR (Fig. 4), dc-link capacitors operate in a considerably higher temperature range and for longer periods throughout the year than in LIN. Notably, the constant ESR model results in higher values of TCAP. This is consistent in both analysed MPs and indicates that the constant ESR method gives a worstcase scenario when estimating thermal stresses. After computing the AD and Monte Carlo simulation of both mission profiles, the lifetime distribution CDF for each model are obtained and shown in Fig. 7. The failure probability in the B1 region is shown in detail in Fig. 7a and b, for PTR and LIN MPs, respectively. As previously observed, the higher core temperatures at PTR resulted in higher capacitor damage and reduced lifetime. The failure probability curves indicate that method 1 is the most conservative. Table 2 gives the calculated B1 lifetime for all scenarios. In accordance to the previous results, the constant ESR method presented the lowest values for both MPs, in reason of the higher thermal stresses. Furthermore, the results indicate that the ESR dependence to
Table 2 B1 lifetime of the dc-link capacitors for the evaluated methods. Method
LIN PTR
B1 lifetime Error relative to ESR(f,TCAP) B1 lifetime Error relative to ESR(f,TCAP)
1
2
3
4
13.50 −5.3% 4.61 −7.1%
13.90 −2.5% 4.89 −1.4%
13.89 −2.6% 4.72 −4.8%
14.26 – 4.96 –
temperature affects more the lifetime estimation than the frequency. The maximum difference observed is lower than 7.1%. Nevertheless, the lifetime values and model errors shown in Table 2 are bound to the parametric variations, current harmonic spectrum, and the mission profile used in this paper. The B1 values may also differ if a non-linear cumulative of damage assumption is made. Finally, Table 3 benchmarks the discussed power loss evaluation methods as good (blue), average (grey), and poor performance (red). 5. Conclusions In order to obtain fast tools for reliability evaluation of multiple components on long-term analyses, methods with reduced complexity and still acceptable accuracy are desirable. Therefore, this paper benchmarked four capacitor power loss calculation methods and compared their impact on the wear-out failure prediction of PV inverters. Method 1 (constant ESR) is the simplest, since it requires knowledge only of the capacitors RMS current. The frequency dependence (included in methods 3 and 4) requires the harmonic components of the capacitor current. Thereby, an FFT is employed and the computational effort increases. The maximum difference observed in the dc-link B1 lifetime was 7.1% for Petrolina and 4.6% for Lindenberg mission profiles. For Table 3 Benchmarking of the power losses methods. Good, average, and poor performance.
Fig. 6. Core temperature distribution in the dc-link capacitors for methods 1 and 4: (a) LIN; (b) PTR. 4
Microelectronics Reliability xxx (xxxx) xxxx
J.M. Lenz, et al.
methods 2 and 4, these values reduced to 5.3% and 1.7%, respectively. It is also observed that the capacitor average core temperature is the dominant factor in lifetime estimation. Thus the mission profiles of ambient temperature and current harmonic content significantly affect these deviations. Therefore, the results presented are viewed as a qualitative comparison between these power loss models. A compromise between model error and complexity should be assessed considering the application requirements.
[4] [5] [6] [7]
Declaration of competing interest
[8]
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
[9] [10]
Acknowledgements
[11]
This wok was financed by the Energy Technology Department (ET) of Aalborg University (AAU), by the Brazilian National Council for Scientific and Technological Development (CNPq) – process 206373/ 2017, and by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES/PROEX) - Finance Code 001.
[12] [13] [14]
References
[15]
[1] S. Yang, A. Bryant, P. Mawby, An industry-based survey of reliability in power electronic converters, 2009 IEEE Energy Convers. Congr. Expo, 2009, pp. 3151–3157. [2] J. Falck, C. Felgemacher, A. Rojko, M. Liserre, P. Zacharias, Reliability of power electronic systems: an industry perspective, IEEE Ind. Electron. Mag. 12 (June) (2018) 24–35. [3] A. Sangwongwanich, Y. Shen, A. Chub, E. Liivik, D. Vinnikov, Mission profile-based accelerated testing of DC-link capacitors in photovoltaic inverters, Applied Power
[16] [17]
5
Electronics Conference and Exposition (APEC) (2019), https://doi.org/10.1109/ APEC.2019.8721794. F.H. Aghdam, M. Abapour, Reliability and cost analysis of multistage boost converters connected to PV panels, IEEE J. Photovoltaics 6 (4) (2016) 981–989 Jul. D. Zhou, Y. Song, Y. Liu, F. Blaabjerg, Mission profile based reliability evaluation of capacitor banks in wind power converters, IEEE Trans. Power Electron. 34 (5) (2019) 4665–4677 May. Y. Shen, A. Chub, H. Wang, D. Vinnikov, E. Liivik, F. Blaabjerg, Wear-out failure analysis of an impedance-source PV microinverter based on, IEEE Trans. Ind. Electron. 66 (5) (2019) 3914–3927. H. Wang, F. Blaabjerg, Reliability of capacitors for DC-link applications in power electronic converters - an overview, IEEE Trans. Ind. Appl. 50 (5) (2014) 3569–3578. B. Basler, T. Greiner, Power loss reduction of DC link capacitor for multi-phase motor drive systems through shifted control, 2015 9th Int. Conf. Power Electron. ECCE Asia (ICPE-ECCE Asia), 2015, pp. 2451–2456. H. Matsumori, K. Urata, T. Shimizu, K. Takano, H. Ishii, Capacitor loss analysis method for power electronics converters, Microelectron. Reliab. 88–90 (September) (2018) 443–446. A. Braham, A. Lahyani, P. Venet, N. Rejeb, Recent developments in fault detection and power loss estimation of electrolytic capacitors, IEEE Trans. Power Electron. 25 (1) (2010) 33–43 Jan. P. Kulsangcharoen, C. Klumpner, M. Rashed, G. Asher, G.Z. Chen, S.A. Norman, Assessing the accuracy of loss estimation methods for supercapacitor energy storage devices operating under constant power cycling, 16th European Conference on Power Electronics and Applications, 2014, pp. 1–11. Y. Yang, K. Ma, H. Wang, F. Blaabjerg, Instantaneous thermal modeling of the DClink capacitor in PhotoVoltaic systems, 2015 IEEE Appl. Power Electron. Conf. Expo, vol. 2015-May, no. May, Mar. 2015, pp. 2733–2739. Z. Zhang, et al., Operating temperatures of open-rack installed photovoltaic inverters, Sol. Energy 137 (2016) 344–351. J.M. Lenz, J.R. Pinheiro, Mission profile impact on capacitor reliability in PV singlestage inverters, 2018 7th International Conference on Renewable Energy Research and Applications (ICRERA), 5 2018, pp. 976–981. CDM Cornell Dubilier, Type 380LQ 85 °C compact, high capacitance, snap-in aluminum, Technical Datasheet, 2019. D. Zhou, H. Wang, F. Blaabjerg, Lifetime estimation of electrolytic capacitors in a fuel cell power converter at various confidence levels, 2016 IEEE 2nd Annual Southern Power Electronics Conference (SPEC), 2016, pp. 1–6. J.M. Lenz, H.C. Sartori, J.R. Pinheiro, Mission profile characterization of PV systems for the specification of power converter design requirements, Sol. Energy 157 (2017) 263–276 Nov.