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The Influence of MPPT Algorithms in the Lifespan of the Capacitor Across the PV Array

Márquez Alcaide, Abraham; Gómez Merchán, Rubén; Zafra Ratia, Eduardo; Pérez, E.; López, Juan M.; León Galván, José Ignacio; Vázquez Pérez, Sergio; García Franquelo, Leopoldo

Abstract

PV systems efficiency highly depends on the MPPT strategy to be implemented in the PV converter. Many MPPT methods on the literature are focused on improving the steady state and transient system performance extracting the maximum energy from the sun. In this paper, the impact of the MPPT methods in the PV converter is analyzed focusing the study on the capacitor across the PV array lifespan. The obtained results demonstrate that the low frequency PV voltage oscillations that are present in many MPPT methods have a large negative impact on this capacitor lifespan. Experimental and simulation results are presented in order to show that advanced MPPT methods, which avoid these low frequency oscillations, achieve higher capacitor lifespan values compared with the values obtained by applying well-known MPPT methods such as the perturb and observe or incremental conductance strategies

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Received March 11, 2022, accepted March 23, 2022, date of publication April 4, 2022, date of current version April 21, 2022. Digital Object Identifier 10.1109/ACCESS.2022.3164411 The Influence of MPPT Algorithms in the Lifespan of the Capacitor Across the PV Array ABRAHAM M. ALCAIDE 1, (Member, IEEE), RUBEN GOMEZ-MERCHAN1,2, EDUARDO ZAFRA 1, (Graduate Student Member, IEEE), EMILIA P. MARTIN1, JUAN M. LOPEZ RODRIGUEZ1, JOSE I. LEON 1,3, (Fellow, IEEE), S. VAZQUEZ 1, (Fellow, IEEE), AND LEOPOLDO G. FRANQUELO1,3, (Life Fellow, IEEE) 1Electronic Enginering Department, Universidad de Sevilla, 41092 Seville, Spain 2Instituto de Microelectronica de Sevilla, IMSE-CNM (CSIC), Universidad de Sevilla, 41092 Seville, Spain 3Department of Control Science and Engineering, Harbin Institute of Technology, HIT, 150001 Harbin, China Corresponding author: Abraham M. Alcaide ([email protected]) This work was supported in part by the Research Projects under Project PID2020-115561RB-C31, Project H2020-821381, Project P18-RT-1340, and Project US-1381331; and in part by the European Social Fund and Junta de Andalucía through the Contratación de Personal Investigador Doctor (Convocatoria 2019) 43 Contratos Capital Humano Línea 2. Paidi 2020. ABSTRACT PV systems efficiency highly depends on the MPPT strategy to be implemented in the PV converter. Many MPPT methods on the literature are focused on improving the steady state and transient system performance extracting the maximum energy from the sun. In this paper, the impact of the MPPT methods in the PV converter is analyzed focusing the study on the capacitor across the PV array lifespan. The obtained results demonstrate that the low frequency PV voltage oscillations that are present in many MPPT methods have a large negative impact on this capacitor lifespan. Experimental and simulation results are presented in order to show that advanced MPPT methods, which avoid these low frequency oscillations, achieve higher capacitor lifespan values compared with the values obtained by applying well-known MPPT methods such as the perturb and observe or incremental conductance strategies. INDEX TERMS Harmonic analysis, pulse width modulation, motor drives. I. INTRODUCTION In the last decades, power demand is constantly increasing in most modern societies. In this electrification process, the power conversion systems, and particularly power electronics, are playing a key role [1]–[3]. Among the energy sources, renewable energy sources such as hydroelectric, wind energy conversion systems or photo-voltaic systems (PV), are the most attractive in terms of taking care of the environment [4], [5]. In particular, PV energy has become one of the most promising alternatives due to its massive availability as well as its easy installation, fast deployment and cost reduction in the last decades [5]–[7]. It can be affirmed that the grid-connected PV systems will play a main role to solve the future energy requirements. Depending on the power level of the PV installation, the optimal implementation of the PV power system is different [5]. For instance, in high-power PV facilities the most common solution is to use three-phase two-level inverters to connect the solar arrays directly to the grid through a The associate editor coordinating the review of this manuscript and approving it for publication was Jiajie Fan . low frequency transformer. In other cases such as industrial, residential, or low-power applications (power level lower than 200 kW), the mainstream solution is to use a two-stage power conversion system. Usually, it is composed of a dc-dc power converter to step-up the PV voltage plus an inverter to perform the grid connection [8]–[10]. A generalized PV power system based on two power converter stages (dc-dc and dc-ac) is shown in Fig. 1, where the most conventional control methods for each stage are also represented. The technical literature presents multiple control strategies to connect an inverter to the grid [11]–[14]. Among them, the PI-based on the synchronous dq frame shown in Fig. 1 is widely adopted by the industry. This control scheme performs the power converter grid-connection allowing unity power factor with minimum grid currents harmonic distortion. On the other hand, the optimal operation of the PV string is achieved by the maximum power point tracking (MPPT) algorithm which targets to obtain the maximum power from the instantaneous ambient conditions (solar radiation and temperature). In a PV system with two power stages (as shown in Fig. 1), the MPPT algorithm is executed by the dc-dc power converter. However, in high-power PV systems, VOLUME 10, 2022 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ 40945 A. M. Alcaide et al.: Influence of MPPT Algorithms in Lifespan of Capacitor Across PV Array FIGURE 1. Generalized PV system with two power converter stages (dc-dc and dc-ac). the dc-dc stage is usually avoided and the MPPT is implemented in the central PV inverter (leading to the development of global MPPT methods). The catalog of MPPT algorithms is very wide. Among the MPPT strategies that are available in the technical literature, the perturb and observe (P&O) and the incremental conductance (INC) techniques are the most successful solutions implemented in the industry [15], [16]. However, many other options can be found such as those based on neural networks, fuzzy logic, or other more complex strategies in order to optimize the MPPT performance [17], [18]. The objective of this paper is to analyze the impact of the MPPT execution on the expected lifespan of the most critical power component of the PV power electronic converter, that is, the power capacitor that is connected in parallel with the PV arrays (called CPV and highlighted in red in Fig. 1). It is important to note that the calculations to estimate this impact have been done just considering the steady state performance of the MPPT methods, but this does not represent a limitation of the obtained conclusions. It can be affirmed that PV systems are normally operating in steady state because of the extremely slow dynamic behavior of the weather conditions compared with the execution period of the MPPT method. It is also important to highlight that the PV capacitor lifetime depends on two different factors. In one hand, it depends on the capacitor equivalent series resistance (ESR) value, and the low frequency capacitor current oscillations provoked by the MPPT method being executed each Tmppt . On the other hand, the capacitor lifetime degradation also depends on the high frequency current ripple provoked by the operation of the power converter at fsw that is directly related by the PV converter topology. In any case, the PV converter topology, including the capacitor bank technology, is mainly defined by the nominal power of the system, regulations to be fulfilled, efficiency, weight, size and cost. Once the converter topology is defined, a useful method to improve the capacitor CPV lifetime is to look for the most suitable MPPT method, which is the focus of this work. In section II, a brief summary of the P&O and INC methods is addressed considering also, for comparison purposes, an advanced MPPT technique based on a binary search (called BNS [19]). Section III highlights the impact of the MPPT algorithms in the capacitor CPV lifespan of the PV system. Finally, in sections IV and V, the experimental validation and the conclusions are shown. II. IMPLEMENTATION OF SOME MPPT TECHNIQUES Among the existing MPPT techniques, P&O and INC are the most popular ones being vastly adopted by the industry [15], [16]. This is because of their simplicity, relatively good performance, low computational requirements as well as their easy implementation using an off-the-shelf mid-range micro-controller control platforms. However, in recent years, new MPPT techniques have emerged in order to achieve faster convergence, also avoiding low frequency PV voltage oscillations around the optimal MPPT voltage value. Among these advanced MPPT techniques, for performance comparison purposes, the binary-search MPPT algorithm (BNS) has been included in this section [19]. The P&O technique is the most common method used in the PV industry because of its simplicity. It is important to highlight that the P&O algorithm is constantly perturbing the system, which means that the PV voltage always oscillates around its optimal value [20]–[22]. A good alternative to the P&O strategy is the well-known INC algorithm, since it studies the P-V curve trend in a more sophisticated way, estimating the derivative of the P-V curve in order to find its maximum point. However, as it happens when the P&O method is applied, in practical applications the INC MPPT strategy also presents PV voltage oscillations around its optimal value. Finally, the application of BNS method in PV systems consists in the modification of the operational region limits to efficiently look for the optimal PV voltage value [19]. In addition to fastly achieve the final value of the PV voltage, the BNS algorithm is prepared to develop a flexible MPPT where the power to be generated can be the maximum 40946 VOLUME 10, 2022 A. M. Alcaide et al.: Influence of MPPT Algorithms in Lifespan of Capacitor Across PV Array available or an specific power value imposed by the PV system operator. It is important to highlight that, at the contrary of the conventional P&O and INC strategies, the BNS method considers a threshold band leads to a steady state performance that avoids the oscillations around the optimal PV voltage in order to look for the required power. III. IMPACT OF THE MPPT TECHNIQUE OVER THE RELIABILITY OF THE CAPACITOR ACROSS THE PV SYSTEM Capacitors are key components in power conversion systems [23]. Their capacitance and voltage rating are selected to be minimized in order to reduce the system costs. Additionally, regarding reliability in power converters, capacitors are identified among the most frequent failure case [24]. Among capacitor technologies in manufacturer portfolio for power electronics applications, multi-layer ceramic capacitors, metallized polypropylene film capacitors and aluminum electrolytic capacitors are the most common [23]. In particular, aluminum electrolytic are the cheapest technology, but with reduced reliability. On the contrary, film capacitors are considered the most reliable at the expense of a higher cost [9], [23], [25]. It is important to highlight that in solar PV applications, depending on the nominal power of the facility, the PV array maximum voltage is in the range 50-1500 volts considering applications from domestic to utility-scale systems respectively. Taking into account typical capacitance values of PV systems, that is usually in the mF range, capacitors to be connected in parallel to the PV arrays are aluminum electrolytic capacitors (connected in series and/or parallel to achieve the expected capacitance and voltage ratings) because of their vast capacitance values, high maximum voltage ratings and low cost at the expense of high ESR values. In any case, the capacitor lifespan intrinsically depends on the rated voltage, the current as well as the temperature of the device Th. In order to estimate the power capacitor lifetime (Lc), it is usual to model the capacitor as: Lc=L0V V0−n eEa kBT−1 h−T−1 0(1) where L0is the rated lifetime at voltage V0and temperature T0.Eais the activation energy and kBis the Boltzmann constant. Additionally, considering electrolytic capacitors, the model can be simplified to: Lc=L0V V0−n 2 T0−Th 10K(2) From (2), it is possible to conclude that increasing the capacitor temperature in 10 K, its remaining lifetime is reduced in 50%, which highlights the importance of the hotspot temperature. The hotspot temperature can be modeled as the ambient temperature Taplus the convolution of the capacitor losses Pdwith the thermal impedance Zth. In this sense, in steady state operation, it is necessary to consider the thermal resistance Rth as: Th=RthPd+Ta=1Th+Ta(3) In (3), Pddepends on the current through the capacitor as well as the ESR. It has to be noticed that the ESR has higher importance at low frequencies, while the equivalent series inductance (ESL) value affects to the capacitor impedance at higher frequencies (generating EMI and malfunctions in high-frequency applications). In this way, as the MPPT methods are executed at very low frequency (because of the very slow dynamic behavior of the ambient conditions, i.e. temperature and solar radiation), it can be derived that the ESL value does not significantly affect to the influence of the MPPT method on the lifespan of the capacitor CPV that is connected in parallel to the PV array. Considering the frequency dependence of the ESR, it is possible to use the Fourier representation as: Pd= ∞ X h=0 I2 c,hRESR,h(4) where Ic,his the h−harmonic of the capacitor current and RESR,his the ESR value for the corresponding frequency component. The ESR value depends on the capacitor technology as well as the frequency. For instance, the ESR of electrolytic capacitors is higher for low frequency harmonic content than for high frequency components [26]. The ESR of a capacitor can be separated in three different terms: RESR =RESR,0+RESR,f+R T0−Th E T=R0+R T0−Th E T(5) The first term RESR,0is constant, the second term RESR,f depends on the frequency content of the capacitor current and the third term RTexponentially depends on the hotspot temperature [27]. In this work, the first two terms are represented by R0. Taking all these facts into account, it is clear that Lcclearly depends on the power capacitor technology (because of the ESR value) and the way the capacitor is operating (because of its voltage, and mainly the harmonic components of the capacitor current). As the power capacitor voltage and its ESR inherently depend on the power capacitor technology and the specific power application, the capacitor lifetime is closely related to its operation in terms of its current quality. In this way, in a PV system the evaluation of the capacitor CPV current, that directly depends on the MPPT method, will show the direct impact in the capacitor CPV lifetime. This is the focus of the experimental results included in this work. IV. EXPERIMENTAL RESULTS The impact of the MPPT algorithms on the capacitor CPV lifespan has been evaluated in the laboratory using a traditional dc-dc scheme based on a boost converter topology, which is shown in Fig. 2a. The PV string has been emulated using the E4360 PV Emulator from Keysight [28]. The E4360 PV emulator has been configured considering the waveforms VOLUME 10, 2022 40947 A. M. Alcaide et al.: Influence of MPPT Algorithms in Lifespan of Capacitor Across PV Array FIGURE 2. Experimental setup used in the experiments. a) Electrical diagram with the experimental rig used. b) Configuration of the PV emulator. TABLE 1. Parameters of the experimental setup and the MPPT algorithms. shown in 2b. The most relevant parameters of the dc-dc prototype are summarized in Table 1. In order to evaluate the impact of these MPPT methods on the capacitor CPV lifespan taking into account the capacitor current harmonic components, the PV emulator has been configured to operate with two different solar radiation conditions. This fact enables the possibility to evaluate the techniques considering an abrupt change in the weather conditions as well as in the steady state operation. The most relevant parameters for all techniques are listed in Table 1, where it can be observed that the P&O and INC MPPT strategies share the same operation parameters. The experimental results are represented in Fig. 3. As it can be observed, the experiment consists in an abrupt variation in the solar radiation. In the beginning of the experiment, the PV system is working normally and the MPPT methods are being executed successfully achieving PV voltages around its optimal value (that depends on the solar radiation and the temperature). From this steady state operational point, in t=10sthe solar radiation, and therefore the available PV power, drops abruptly forcing to the MPPT algorithms to look for the new optimal PV voltage value. After some time, in t=30sthe solar radiation is restored to its previous value. As it can be observed in Fig. 3, it is clear that the MPPT strategies performance is good because the final optimal PV voltage value is achieved. It is clear that the BNS method has superior dynamic performance because the optimal PV voltage value is fastly achieved. On the other hand, it can be seen that the application of the BNS strategy leads to have a constant PV voltage while the other methods present PV voltages with low-frequency oscillations. The frequency of these voltage oscillations depends on the frequency of the execution of the MPPT methods (Tmppt ) that is fixed to 0.5 seconds. The performance of the MPPT techniques can be evaluated considering the following expression: η=Rt1 t0ppv(t)dt Rt1 t0pav(t)dt ·100 (6) where ppv is the power generated by the PV and pav is the available power from the PV string. Thus, as higher is η, the performance of the MPPT method is better. This figure of merit has been firstly evaluated taking into account the complete experimental results considering the three MPPT methods. It can be seen that ηvalues are similar considering the P&O and INC MPPT techniques. However, the BNS strategy obtains a higher ηvalue equal to 97.52%. If the ηfactor is evaluated only taking into account the instants where the solar radiation changes, the performance difference among the MPPT methods becomes more evident. The terms ηfand ηrare the values of the ηfactor but only evaluated in some specific time intervals. ηfis evaluated taking into account the time interval from t=10sto t=15s, while ηris evaluated taking into account the time interval 40948 VOLUME 10, 2022 A. M. Alcaide et al.: Influence of MPPT Algorithms in Lifespan of Capacitor Across PV Array FIGURE 3. Comparison of the MPPT techniques considering an abrupt solar radiation variation a) PV array voltage b) Power extracted from the PV array. TABLE 2. Performance of the MPPT algorithms considering the ηfactor as figure of merit. from t=30 sto t=35s. The obtained values are summarized in Table 2 where it can be observed that the BNS method is superior compared with the other methods. It is very important to highlight that this result is not surprising and it is not the focus of this paper. The focus of the paper is to evaluate the impact of the MPPT methods in the capacitor CPV lifespan. In this sense, the current that is flowing through this capacitor has been captured and analyzed in the frequency domain. The corresponding current spectra have been represented in Fig. 4 considering the same color palette that was used in Fig. 3. As shown in Fig. 4a and Fig. 4c, both P&O and INC methods present undesirable harmonic components at very low frequency whereas the BNS strategy presents a better quality harmonic spectrum. From the measured capacitor currents and considering the hotspot temperature estimation presented in (3)-(4), the resulting corresponding capacitor temperatures have been estimated considering different Rth values. The most important parameters to carry out this estimation and the obtained results are presented in Table 3. In the table, the resulting CPV hotspot temperatures depending on the MPPT methods are determined by using (3)-(5). With these calculations, and applying (2) it is possible to determine the corresponding capacitor CPV lifetime Lcapplying each MPPT method. In order to develop the MPPT method comparison, the result obtained by the P&O algorithm is used to normalize the results obtained by the other MPPT strategies in order to calculate the corresponding capacitor CPV lifespan increment 1Lcpresent in MPPT method x(where xcan be INC or BNS) as 1Lc=Lcx LcP&O ·100 (7) It can be observed that, in all cases depending on Rth, P&O and INC present very similar results in terms of the capacitor CPV lifetime Lc. However, because of the superior quality of the capacitor CPV current, the application of the BNS method leads to improve the capacitor lifespan Lcwith values from 2% up to 20%. In order to extend the results for higher power PV installations, not available in our laboratory facilities, multiple scenarios have been simulated. The nominal power in multi-string PV systems is in the range up to [100 −150]kW whereas the required capacitance CPV to be connected in parallel to the PV array (for an optimal system controllability) is in the range of [6−15] mF. These data have been taken from the industrial solution PV100 by GPTech [29]. First of all, the impact of the MPPT methods in CPV lifespan has been evaluated considering a 100kW PV array with a capacitance value equal to C=10mF. Several frequencies of MPPT execution have been evaluated in order to check the influence of the Tmppt factor in the capacitor CPV lifespan. Tmppt equal to 0.5, 1 and 2 and 5 seconds have been evaluated. The obtained results have been summarized in Table 4, where the results of the INC method are not included because, as presented in Table 3, it presents very VOLUME 10, 2022 40949 A. M. Alcaide et al.: Influence of MPPT Algorithms in Lifespan of Capacitor Across PV Array FIGURE 4. a) Capacitor CPV current harmonic spectrum for P&O MPPT b) A low-order harmonic spectrum detail c) Capacitor CPV current harmonic spectrum for INC MPPT d) A low-order harmonic spectrum detail e) Capacitor CPV current harmonic spectrum for BNS MPPT f) A low-order harmonic spectrum detail. TABLE 3. Evaluation of the impact of the MPPT technique on the capacitor hotspot temperature and the corresponding impact on the capacitor lifetime. similar results compared with the P&O strategy. From the obtained results, it can be observed that the BNS method again presents a superior performance in terms of extended capacitor CPV lifespan. Also, it can be also observed that the Tmppt value does not affect at all the capacitor CPV lifespan because the corresponding very-low order harmonic content in the CPV capacitor CPV current is always present (but at FIGURE 5. Impact of application the BNS method over the capacitor CPV lifetime with different thermal impedance characteristic and capacitance values. different frequencies) leading to degrade the CPV lifespan in the P&O and INC methods. The obtained improvement in the capacitor CPV lifespan 1Lcapplying the BNS method compared with the P&O performance considering a 100kW PV array has been evaluated also considering different capacitance values. The results are summarized in Fig. 5, where it can be observed that the benefits obtained by the application of the BNS method in 40950 VOLUME 10, 2022 A. M. Alcaide et al.: Influence of MPPT Algorithms in Lifespan of Capacitor Across PV Array TABLE 4. Evaluation of the impact of the MPPT technique on the hotspot temperature reduction for different thermal impedances, PV power = 100 kW,CPV =10mF and Tmppt =[0.5,1,2,5]s terms of increasing the 1Lcvalue are more evident with higher values of C. V. CONCLUSION MPPT strategies are a key part of PV systems seeking to obtain the maximum power taking into account the current weather conditions (solar radiation and temperature). These MPPT methods are normally evaluated considering the transient and steady state responses of the PV system but their influence on the PV system reliability is not usually explored. In this work, the influence of the MPPT methods on the capacitor CPV that is connected in parallel to the PV array, that is one of the most critical components of the PV system in terms of reliability, is addressed. In this paper simulation and experimental results show that the low frequency voltage oscillations present in this capacitor, typical in MPPT methods such as the P&O and INC, provoke the presence of low-order harmonic components in the current that flows through the capacitor CPV . This fact leads to a non negligible capacitor degradation reducing the overall PV system reliability. In this way, from the obtained results, the application of an advanced MPPT method where the oscillations around the optimal maximum power PV voltage becomes fundamental. REFERENCES [1] B. K. Bose, ‘‘Power electronics, smart grid, and renewable energy systems,’’ Proc. IEEE, vol. 105, no. 11, pp. 2011–2018, Nov. 2017. [2] J. I. Leon, S. Kouro, L. G. Franquelo, J. Rodriguez, and B. Wu, ‘‘The essential role and the continuous evolution of modulation techniques for voltage-source inverters in the past, present, and future power electronics,’’ IEEE Trans. Ind. Electron., vol. 63, no. 5, pp. 2688–2701, May 2016. [3] S. Rivera, S. Kouro, S. Vazquez, S. M. Goetz, R. Lizana, and E. Romero-Cadaval, ‘‘Electric vehicle charging infrastructure: From grid to battery,’’ IEEE Ind. Electron. Mag., vol. 15, no. 2, pp. 37–51, Jun. 2021. [4] F. Blaabjerg and K. Ma, ‘‘Wind energy systems,’’ Proc. IEEE, vol. 105, no. 11, pp. 2116–2131, Nov. 2017. [5] M. Malinowski, J. I. Leon, and H. Abu-Rub, ‘‘Solar photovoltaic and thermal energy systems: Current technology and future trends,’’ Proc. IEEE, vol. 105, no. 11, pp. 2132–2146, Nov. 2017. [6] E. Romero-Cadaval, G. Spagnuolo, L. G. Franquelo, C. A. Ramos-Paja, T. Suntio, and W. M. Xiao, ‘‘Grid-connected photovoltaic generation plants: Components and operation,’’ IEEE Ind. Electron. Mag., vol. 7, no. 3, pp. 6–20, Sep. 2013. [7] S. Kouro, J. I. Leon, D. Vinnikov, and L. G. Franquelo, ‘‘Grid-connected photovoltaic systems: An overview of recent research and emerging PV converter technology,’’ IEEE Ind. Electron. Mag., vol. 9, no. 1, pp. 47–61, Mar. 2015. [8] T. Jalakas, R. Kosenko, A. Chub, D. Vinnikov, and A. Blinov, ‘‘Current-fed partial power converter for photovoltaic applications in DC microgrids,’’ in Proc. 47th Annu. Conf. Ind. Electron. Soc., Oct. 2021, pp. 1–5. [9] A. Sangwongwanich, Y. Shen, A. Chub, E. Liivik, D. Vinnikov, H. Wang, and F. Blaabjerg, ‘‘Design for accelerated testing of DC-link capacitors in photovoltaic inverters based on mission profiles,’’ IEEE Trans. Ind. Appl., vol. 57, no. 1, pp. 741–753, Jan. 2021. [10] A. Blinov, O. Korkh, A. Chub, D. Vinnikov, D. Peftitsis, S. Norrga, and I. Galkin, ‘‘High gain DC–AC high-frequency link inverter with improved quasi-resonant modulation,’’ IEEE Trans. Ind. Electron., vol. 69, no. 2, pp. 1465–1476, Feb. 2022. [11] S. Vazquez, A. Marquez, R. Aguilera, D. Quevedo, J. I. Leon, and L. G. Franquelo, ‘‘Predictive optimal switching sequence direct power control for grid-connected power converters,’’ IEEE Trans. Trans. Ind. Electron., vol. 62, no. 4, pp. 2010–2020, Mar. 2015. [12] P. Montero-Robina, K. Rouzbehi, F. Gordillo, and J. Pou, ‘‘Grid-following voltage source converters: Basic schemes and current control techniques to operate with unbalanced voltage conditions,’’ IEEE Open J. Ind. Electron. Soc., vol. 2, pp. 528–544, 2021. [13] T. Dragicevic, S. Vazquez, and P. Wheeler, ‘‘Advanced control methods for power converters in DG systems and microgrids,’’ IEEE Trans. Ind. Electron., vol. 68, no. 7, pp. 5847–5862, Jul. 2021. [14] Y. Yin, S. Vazquez, A. Marquez, J. Liu, J. I. Leon, L. Wu, and L. G. Franquelo, ‘‘Observer-based sliding-mode control for gridconnected power converters under unbalanced grid conditions,’’ IEEE Trans. Ind. Electron., vol. 69, no. 1, pp. 517–527, Jan. 2022. [15] A. Mohapatra, B. Nayak, P. Das, and K. B. Mohanty, ‘‘A review on MPPT techniques of PV system under partial shading condition,’’ Renew. Sustain. Energy Rev., vol. 80, pp. 854–867, Dec. 2017. [16] J. P. Ram, T. S. Babu, and N. Rajasekar, ‘‘A comprehensive review on solar PV maximum power point tracking techniques,’’ Renew. Sustain. Energy Rev., vol. 67, pp. 826–847, Jan. 2017. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S1364032116305706 [17] R. B. Bollipo, S. Mikkili, and P. K. Bonthagorla, ‘‘Critical review on PV MPPT techniques: Classical, intelligent and optimisation,’’ IET Renew. Power Gener., vol. 14, no. 9, pp. 1433–1452, 2020. [18] A. Ali, K. Almutairi, S. Padmanaban, V. Tirth, S. Algarni, K. Irshad, S. Islam, M. H. Zahir, M. Shafiullah, and M. Z. Malik, ‘‘Investigation of mppt techniques under uniform and non-uniform solar irradiation condition a retrospection,’’ IEEE Access, vol. 8, pp. 127368–127392, 2020. [19] R. Gomez-Merchan, S. Vazquez, A. M. Alcaide, H. D. Tafti, J. I. Leon, J. Pou, C. A. Rojas, S. Kouro, and L. G. Franquelo, ‘‘Binary search based flexible power point tracking algorithm for photovoltaic systems,’’ IEEE Trans. Ind. Electron., vol. 68, no. 7, pp. 5909–5920, Jul. 2021. [20] H. D. Tafti, A. I. Maswood, G. Konstantinou, C. D. Townsend, P. Acuna, and J. Pou, ‘‘Flexible control of photovoltaic grid-connected cascaded H-bridge converters during unbalanced voltage sags,’’ IEEE Trans. Ind. Electron., vol. 65, no. 8, pp. 6229–6238, Aug. 2018. [21] H. D. Tafti, G. Konstantinou, C. D. Townsend, G. G. Farivar, A. Sangwongwanich, Y. Yang, J. Pou, and F. Blaabjerg, ‘‘Extended functionalities of photovoltaic systems with flexible power point tracking: Recent advances,’’ IEEE Trans. Power Electron., vol. 35, no. 9, pp. 9342–9356, Sep. 2020. [22] A. Kumaresan, H. D. Tafti, N. K. Kandasamy, G. G. Farivar, J. Pou, and T. Subbaiyan, ‘‘Flexible power point tracking for solar photovoltaic systems using secant method,’’ IEEE Trans. Power Electron., vol. 36, no. 8, pp. 9419–9429, Aug. 2021. [23] H. Wang and F. Blaabjerg, ‘‘Reliability of capacitors for DC-link applications in power electronic converters—An overview,’’ IEEE Trans. Ind. Appl., vol. 50, no. 5, pp. 3569–3578, Sep. 2014. [24] S. Yang, A. Bryant, P. Mawby, D. Xiang, L. Ran, and P. Tavner, ‘‘An industry-based survey of reliability in power electronic converters,’’ IEEE Trans. Ind. Appl., vol. 47, no. 3, pp. 1441–1451, May/Jun. 2011. [25] Y. Shen, A. Chub, H. Wang, D. Vinnikov, E. Liivik, and F. Blaabjerg, ‘‘Wear-out failure analysis of an impedance-source PV microinverter based on system-level electrothermal modeling,’’ IEEE Trans. Ind. Electron., vol. 66, no. 5, pp. 3914–3927, May 2018. [26] Y. J. Ko, H. Jedtberg, G. Buticchi, and M. Liserre, ‘‘Analysis of DC-link current influence on temperature variation of capacitor in a wind turbine application,’’ IEEE Trans. Power Electron., vol. 33, no. 4, pp. 3441–3451, Apr. 2018. [27] M. L. Gasperi, ‘‘Life prediction modeling of bus capacitors in AC variable frequency drives,’’ in Proc. Conf. Rec. Annu. Pulp Paper Ind. Tech. Conf., Jun. 2005, pp. 141–146. VOLUME 10, 2022 40951 A. M. Alcaide et al.: Influence of MPPT Algorithms in Lifespan of Capacitor Across PV Array [28] E4360 Series Modular Solar Array Simulators. Accessed: Mar. 10, 2022. [Online]. Available: https://www.keysight.com/ [29] Pv100 SKT Solar Power Converter. Accessed: Mar. 10, 2022. [Online]. Available: https://www.greepower.es/ ABRAHAM M. ALCAIDE (Member, IEEE) was born in Huelva, Spain, in 1985. He received the B.S., M.S., and Ph.D. degrees in telecommunications engineering from the Universidad de Sevilla (US), Seville, Spain, in 2014, 2016, and 2019, respectively. His main research interests include modulation techniques, multilevel converters, model-based predictive control of power converters and drives, renewable energy sources, and power devices lifetime extension. He was a recipient as the coauthor of the 2015 and 2021 Best Paper Award of the IEEE Industrial Electronics Magazine. RUBEN GOMEZ-MERCHAN was born in Cáceres, Spain, in 1997. He received the bachelor’s degree in electronics, robotics, and mechatronics engineering and the master’s degree in microelectronics from the University of Seville (US), Seville, Spain, in 2019 and 2020, respectively, where he is currently pursuing the Ph.D. degree in physics-electronics. His work is supported by the Spanish Government through FPU. From 2018 to 2019, he was with the Department of Electronic Engineering, US. His main research interests include dc/dc converters and PV systems. In 2019, he was granted by the Spanish National Research Council (CSIC), starting his activity at the Instituto de Microelectronica de Sevilla (IMSE), US. His main research interests include smart complementary metal oxide semiconductor (CMOS) sensors and address event representation (AER) vision systems. He was acknowledged as the Top Student of the Graduating Class in the Escuela Técnica Superior de Ingeniería, US. EDUARDO ZAFRA (Graduate Student Member, IEEE) was born in Seville, Spain, in 1994. He received the B.S. and M.S. degrees in industrial engineering from the University of Seville (US), in 2016 and 2019, respectively, where he is currently pursuing the Ph.D. degree in automatics, electronics and telecommunications. His main research interests include control and modulation of power converters and drives, model predictive control, and design for digital embedded systems. EMILIA P. MARTIN was born in Seville, Spain, in 1999. She received the B.S. degree in industrial engineering from the University of Seville (US), in 2021, where she is currently pursuing the dual master’s degree in industrial engineering and electronic, robotic and automatic engineering. Her main research interests include modulation and control of power electronic converters applied to renewable energy technologies and HIL techniques. JUAN M. LOPEZ RODRIGUEZ was born in Seville, Spain, in 1998. He received the B.S. degree in industrial engineering from the Universidad de Sevilla (US), Seville, where he is currently pursuing the master’s degree in industrial engineering. He started working with the Department of Electronic Engineering, in 2021, where his main research interests include dc/dc converters. He is yet to publish an educational book about dc/dc converters, a work that allowed him to pass his final degree project, obtaining the maximum grade with honors. JOSE I. LEON (Fellow, IEEE) was born in Cadiz, Spain. He received the B.S., M.S., and Ph.D. degrees in telecommunications engineering from the Universidad de Sevilla (US), Seville, Spain, in 1999, 2001, and 2006, respectively. Since 2019, he has been a Chair Professor at the Department of Control Science and Engineering, Harbin Institute of Technology, China. He is currently an Associate Professor with the Department of Electronic Engineering, US. His research interests include modulation and control of power converters for high-power applications and renewable energy systems. In 2017, he was elevated to the IEEE Fellow grade with the following citation ‘‘For Contributions to High-Power Electronic Converters.’’He was a recipient of the 2014 IEEE J. David Irwin Industrial Electronics Society Early Career Award, the 2017 IEEE Bimal K. Bose Energy Systems Award, and the 2017 Manuel Losada Villasante Award for Excellence in Research and Innovation. He was a co-recipient of the 2008 Best Paper Award of IEEE Industrial Electronics Magazine, the 2012 Best Paper Award of the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, and the 2015 Best Paper Award of IEEE Industrial Electronics Magazine. S. VAZQUEZ (Fellow, IEEE) was born in Seville, Spain, in 1974. He received the M.S. and Ph.D. degrees in industrial engineering from the University of Seville (US), in 2006 and 2010, respectively. Since 2002, he has been with the Power Electronics Group working in research and development projects. He is currently an Associate Professor with the Department of Electronic Engineering, US. His research interests include power electronics systems, modeling, modulation, and control of power electronics converters applied to renewable energy technologies. Dr. Vazquez was a recipient as the coauthor of the 2012 Best Paper Award of the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS and the 2015 Best Paper Award of the IEEE Industrial Electronics Magazine. He is involved in the Energy Storage Technical Committee of the IEEE Industrial Electronics Society and is also serving as an Associate Editor for the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS. LEOPOLDO G. FRANQUELO (Life Fellow, IEEE) was born in Málaga, Spain. He received the M.Sc. and Ph.D. degrees in electrical engineering from the Universidad de Sevilla, Seville, Spain, in 1977 and 1980, respectively. From 1982 to 1986, he was an Associate Professor at the Electronics Engineering Department, Sevilla University, where he has been a Professor, since 1986, and a 1000 Talent Professor at the Department of Control Science and Engineering, Harbin Institute of Technology, since 2016. He has participated in more than 100 industrial and research and development projects and has published more than 300 articles, 76 of them in IEEE journals. His current research interests include modulation techniques for multilevel inverters and application to power electronic systems for renewable energy systems. He is an IES AdCom Life Member. In 2009 and 2013, he received the Prestigious Andalusian Research Award and FAMA Award Recognizing the Excellence of his Research Career. He has received a number of best paper awards from IEEE journals. In 2012 and 2015, he was a recipient of the Eugene Mittelmann Outstanding Research Achievement Award and the Antohny J. Hornfeck Service Award from IEEEIES, respectively. In the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, he became an Associate Editor, in 2007, the Co-Editor-in-Chief, in 2014, and the Editor-in-Chief, since 2016. He was a Member-At-Large of the IES AdCom (2002–2003), the Vice President for Conferences (2004–2007), and the President Elect of the IES (2008–2009). He was the President of the IES (2010–2011). He has been an IEEE Industrial Electronics Society (IES) Distinguished Lecturer, since 2006. 40952 VOLUME 10, 2022