Applications and Modulation Methods for Modular Converters Enabling Unequal Cell Power Sharing

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/352386087 Applications and Modulation Methods for Modular Converters Enabling Unequal Cell Power Sharing: Carrier Variable-Angle Phase-displacement Modulation Methods ArticleinIEEE Industrial Electronics Magazine · June 2021 DOI: 10.1109/MIE.2021.3080232 CITATIONS 0 READS 46 7 authors, including: Some of the authors of this publication are also working on these related projects: DFG - Formal stability assessment of hybrid distribution grids based on the correct modeling of the effect of synchronization of the power electronics interfaces View project Development of fast and accurate analytical sizing and modelling techniques for synchronous reluctance machines. View project Vito Giuseppe Monopoli Politecnico di Bari 70 PUBLICATIONS1,225 CITATIONS SEE PROFILE A. Marquez Universidad de Sevilla 57 PUBLICATIONS1,474 CITATIONS SEE PROFILE Jose I. Leon Universidad de Sevilla 155 PUBLICATIONS15,131 CITATIONS SEE PROFILE Marco Liserre Christian-Albrechts-Universität zu Kiel 582 PUBLICATIONS28,586 CITATIONS SEE PROFILE All content following this page was uploaded by A. Marquez on 18 July 2021. The user has requested enhancement of the downloaded file. 1 Applications and Modulation Methods for Modular Converters Enabling Unequal Cell Power Sharing Vito G. Monopoli, Senior Member,IEEE, Abraham Marquez, Member,IEEE, Jose I. Leon, Fellow Member,IEEE, Marco Liserre, Fellow Member,IEEE, Giampaolo Buticchi, Senior Member,IEEE, Leopoldo G. Franquelo, Fellow Member,IEEE and Sergio Vazquez, Fellow Member,IEEE Abstract Modular converters based on the connection of multiple power cells have become a competitive solution for many applications achieving high performance with reduced production and maintenance cost. However, their performance is degraded if the power modules present an unbalanced operation which is a common case in some applications and/or when they implement active thermal control methods. Variable-angle carrier-based PWM strategies face this challenge minimizing the negative impact of unequal power sharing among the cells by improving the output waveforms harmonic quality what has a direct impact on the output filters and/or components’ lifetime. I. INTRODUCTION In the last decades the increasing power demand has come hand by hand with the non-stop evolution of power systems in order to face the current technical challenges with maximum efficiency, reliability and cost reduction [1]. One of the mainstream solutions to develop power systems with enhanced reliability, scalability, fault tolerant capability and reduced production and maintenance cost is to consider the power converters as modular systems formed by multiple cloned cells connected in series or parallel as shown in Manuscript received December 29th, 2020; revised February 7th, 2021; accepted April 29th, 2021. This paper was made possible by the Andalusian Science and Innovation project P18-RT-1340 and the European Union under project H2020-821381. Vito G. Monopoli is with Politecnico di Bari, Italy (e-mail: [email protected]). Abraham Marquez, Jose I. Leon, Sergio Vazquez and Leopoldo G. Franquelo are with Universidad de Sevilla, Spain (e-mail: [email protected]). Jose I. Leon and Leopoldo G. Franquelo are also with the Harbin Institute of Technology, China. Marco Liserre is with the Christian-Albrechts-Universit¨ at zu Kiel, Germany (email: [email protected]) Giampaolo Buticchi is with the University of Notthingham at Ningbo, China (email: giampaolo.b[email protected]). 2 Fig. 1 [2], [3]. These cloned cells, usually called power electronic building blocks (PEBBs) present inherent reduced cost in terms of PEBB design and manufacturing because the same power cell design can be used to cover different applications [4]–[8]. Also, PEBB-based converters, also called in general modular converters, present reduced maintenance cost because if one PEBB failures, just a direct replacement is needed in order to keep the power system with proper operation. A. Series-connected PEBB-based Converters One possible solution to develop modular converters based on the connection of multiple PEBBs is to connect them in series to achieve high voltage ratings [9], [10]. If the voltage rating of a PEBB is Vc, the voltage rating of the complete series-connected PEBB-based converter with NPEBBs is NVc, what is an interesting feature in applications such as medium-voltage high-power motor drives or high-voltage dc transmission systems [11]. Among the series-connected PEBB-based converters, the cascaded H-bridge converter (CHB) [12] or the modular multilevel converter (MMC) [13], represented in Fig. 1, can be cited. The basic PEBBs of these converters are normally full-bridges or half-bridges for the CHB and the MMC respectively. B. Parallel-connected PEBB-based converters A second option to develop modular converters is to connect cloned cells in parallel (parallel connection at the input, output or or even both sides) [14]–[16]. The most important feature of the parallel connection of PEBBs is the equal distribution of the power system nominal current among the modules. For instance, this is the case of the Vensys 60/1200 Wind power system represented in Fig. 1, where parallel-connected boost converters carry out the dc-voltage stage [17]. The advantages obtained by the parallel-connected PEBB-based converters become fundamental in applications where the nominal current rating is above the limits of the power semiconductors, or it is very high forcing to implement the converter with very expensive high-current power devices and hardware. Another interesting parallel-connected PEBB-based converter can be found in residential and industrial photovoltaic applications where several independent PV arrays are connected to a multi-string PV inverter, as shown in Fig. 1 [18], [19]. In this case, a boost converter is connected to each PV array but all boost converters have output parallel connection to the common dc-link of the inverter. Another example can be found in dc power supplies where the output waveforms requirements are strict in terms of reduced ripples [20]. 3 II. PHASE DISPLACEMENT PULSE-WIDTH MODULATION METHODS FOR PEBB-BASED CONVERTERS A proper operation of series/parallel PEBB-based converters is required in order to squeeze all their potential performance. In most of the cases, they are operated using PWM methods based on the phase displacement of the carriers [21]. Considering a series-connected PEBB-based converter such as the CHB topology, the carrier phasedisplacement PWM method is called phase-shifted PWM (PS-PWM) strategy [22], [23]. If a N-cell CHB is considered (assuming that a unipolar PWM method is applied to each H-bridge), the analytical expression of the phasor representing the k-th harmonic component of the CHB output voltage Hkcan be determined by adding up all the terms of each PEBB output voltage as follows: Hk= 4 cos [m+n−1]π 2πm N X x=1 Ax(1) where the coefficient Axis defined by Ax=Vdc xJ2n−1mπMxej(2mφx) =Vdc xJ2n−1mπMxhcos(2mφx) + jsin(2mφx)i(2) It is clear that Hkdepends on φxthat represent the carriers phase-displacement of cell x(x=1,. . .,N). J2n−1represents the Bessel function of the first kind of order 2n−1.Vdc xand Mxare the dc voltage and the modulation index of the x-th cell. The coefficients mand nare two indexes that identify each harmonic order k, represented in Fig. 2 fulfilling that k= 2mR + (2n−1), where Ris the ratio between the carrier signal frequency fcand the modulating signal frequency fm(R=fc /fm= 20). The conventional PS-PWM method applied to the CHB considers carrier phase-displacement angles φxin the PEBBs equal to [24]: φx= (x−1) π N.(3) On the other hand, considering parallel-connected PEBB-based converters, another PS-PWM method, that is well-known as interleaved operation [25]–[27], is applied where φx= (x−1)2π N.(4) 4 A. Conventional Phase-displacement PWM Methods Performance Under Balanced Operational Conditions The usual operation of modular converters considers balanced operational conditions for all the PEBBs. Taking the CHB converter as an example, applying the conventional PS-PWM angles, and assuming balanced operational conditions in all PEBBs, i. e., equal dc voltages (Vdc x=Vdc), and equal cell reference voltages leading to Mx=M, the CHB operation is optimal in terms of equalized power and equally distributed PEBBs aging. In addition, the application of the PS-PWM method reduces the output voltage ripple (limited to the dc voltage of one cell, Vdc) reducing the filtering stage. In addition, related to the harmonic distortion, from expressions (1) and (2), in order to eliminate one particular k-th harmonic, it has to be fulfilled that Hk= 0 ⇒                N X x=1 Vdc xJ2n−1mπMxcos(2mφx) = 0 N X x=1 Vdc xJ2n−1mπMxsin(2mφx)=0 (5) By applying the conventional φxdefined in (3) under balanced operational conditions, it can be observed that all the harmonic components in the CHB output voltage with m=1,2,. . .,N-1 are zero (independently of the value of n). In other words, the harmonic distortion is inherently eliminated up to frequencies around 2Nfc[28]. This phenomenon can be observed in Fig. 2, where the cell voltages and the total output voltage (and their corresponding harmonic spectra) of a three-cell CHB with fc=1 kHz are shown. It can be observed that the cell voltages and the CHB output voltage present the lowest-order harmonic distortion around 2fcand 2Nfc= 6fcrespectively, as expected. A dual case can be found if a parallel-connected PEBB-based converter is considered. In the interleaved operation of a N-cell parallel-connected PEBB-based converter such as the parallel-boost converters in the multi-string application, the output current ripple is limited leading to a superior harmonic performance [29]. In this case, the output current harmonic spectrum presents the first harmonic distortion around Nfc. As an example, a dc/dc converter based on three parallel-connected boost interleaved converter has been tested. The obtained PEBB currents and the total output current and their corresponding harmonic spectra are represented in Fig. 2. 5 B. Conventional Phase-displacement PWM Methods Performance Under Unbalanced Operational Conditions The balanced operation of PEBB-based converters is not always present. On one hand, there are applications where the balanced operation of PEBB-based converters is inherently impossible. An example is the multi-string converter shown in Fig. 1. The input of each boost converter is an independent PV string that, in general, presents a unique solar radiation and temperature leading to an inherent unbalanced operation. On the other hand, PEBB-based converters present an unbalanced operation if an active thermal control method, such as the power routing method, is applied [30]. This is a recent research topic that takes into account the actual state of health of the PEBBs to manage their power smartly in order to extend their lifetime reducing the maintenance cost [31]. In any case, if a modular converter operates under unbalanced conditions (i.e. unequal dc voltages and/or unequal modulation indices in the PEBBs), the performance applying the conventional carrier phase-displacement PWM methods is degraded leading to higher output waveform ripples and low-order harmonic distortion. Good features such as the inherent equalized power and equally distributed PEBBs aging are also lost [32]. As an example to show this phenomenon, considering a three-cell CHB converter, Fig. 3 illustrates what happens if the converter operates under the unbalanced conditions applying the conventional PS-PWM technique. It results that the low-order side-bands harmonic components of the CHB output voltage are not canceled anymore. The main consequence of this fact is the necessity of increasing the output filter size, weight and cost. The same negative phenomenon appears if a parallel-connected PEBB-based converter is operated with unbalanced conditions as can be also observed in Fig. 3. The parallel-connected PEBB-based converter presents an output current with higher ripple and degraded harmonic performance. This creates different drawbacks depending on the converter specific application. In the case of the multi-string PV converter shown in Fig. 1, the unbalanced operation of the parallel-connected dc/dc stage leads to a degraded harmonic performance of the current that flows through the dc-link capacitor of the PV inverter. This critically affects to its remaining useful lifetime making its lifespan shorter than expected. III. VARIABLE-ANGLE MULTICARRIER PWM METHODS FOR MODULAR CONVERTERS In order to address the issue of the harmonic performance worsening for the PEBB-based converters operated with unbalanced operational conditions, a modification in the modulation strategy, that is called 6 Variable-Angle Phase-Shifted PWM (VAPS-PWM) technique, has been developed [33]–[36]. The main concept underlying this new approach is based on adapting the φxvalues according to the converter operational conditions. Doing it cleverly, the low-order side-bands harmonics of the output waveforms can be mitigated even under unbalanced operational conditions. The VAPS-PWM methods were initially introduced for modular converters with three PEBBs, which is the focus of this section. In Section IV, the methods are extended to be used in modular converters with larger number of PEBBs. A. Fundamental-Period Based VAPS-PWM Method for Three-Cell PEBB-based Converters As a first approach of a VAPS-PWM method, the strategy considered a three-cell CHB aiming to eliminate the most important low-order harmonic component, that is described by m= 1 and n= 1 in (5). In this approach the harmonic analysis is conducted adopting the modulating signal fundamental period as time-window and using a double fourier integral [24] to determine the analytical expression of the harmonics to be canceled and hence the required φxvalues [33], [34] leading to the expression introduced in Fig. 4. The main advantage of this approach is based on the capability of optimizing the converter harmonic performance with low computational burden taking into account the relatively large fundamental period window. As an example, this method has been applied to a three-cell CHB with the operational conditions shown in Fig. 4. It can be observed that the dominant low-order harmonic component defined by m=1 and n=1 is canceled. The methodology used for the series-connected PEBB-based converter such as the CHB, can be applied in a similar manner to parallel-connected modular converters. In this case, the VAPS-PWM method considers the converter output current as the waveform to be analyzed in order to determine its corresponding side-bands harmonic expression. Once this is known, φxcan be determined with the objective of eliminating the most dominant low-order harmonic component or, in general, improving its harmonic content. In order to show this concept, Fig. 6 is included where the current that is flowing through the output capacitor in a three-cell parallel-connected boost converter is represented. Different operational conditions are imposed in the converter applying the conventional interleaved angles and those obtained by the VAPS-PWM method. In this case, the VAPS-PWM strategy applies the φxangles in order to minimize the current harmonic components even under unbalanced operational conditions. As it can be observed in Fig. 6, applying the VAPS-PWM strategy, the first harmonic group (Case III) or the three first harmonic groups (Case IV) of the capacitor current harmonic spectrum are reduced. This fact has a decisive positive impact in the output capacitor average temperature leading to extend its expected lifetime. 7 B. Sampling-Time Based VAPS-PWM Method for Three-Cell PEBB-based Converters An alternative approach of the harmonic analysis of a modular converter can be derived taking into account the carrier signal period as time-window [35]. Every carrier period it is possible to determine the time-based phasor (hk(t)) representing the k-th harmonic component of the output waveform, as introduced in Fig. 4 where Dxis the duty cycle applied to PEBB number x. It is important to notice that in this method, the parameter kis defined related to the PEBB output waveform effective switching frequency what means that k=1 represents the most dominant lowest-order harmonic component. Taking this fact into account, a VAPS-PWM method can be developed in order to eliminate the harmonic distortion located at the first harmonic group by forcing h1(t) = 0. Doing this, the envelope of that signal is eliminated what leads to the elimination of the complete harmonic group described by m= 1 with any value of n. In addition, a prompt and rapid optimization of the converter harmonic performance is achieved also during transients. The φxdetermination every carrier signal period, introduced in Fig. 4, does not represent a limitation of the applicability of the method in three-PEBB modular converters because the computational burden is very reduced. As an example to show the performance of this method, it has been applied to the three-cell CHB with the operational conditions summarized in Fig. 4. The obtained results show that in the CHB output voltage the harmonic group defined by m=1 is highly mitigated. On the other hand, the method can be also applied to parallel-connected PEBB-based converters considering the output current as the waveform to be analyzed [37]. IV. VARIABLE-ANGLE MULTICARRIER PWM METHODS FOR MODULAR CONVERTERS IF N > 3 A. Fundamental-Period Based VAPS-PWM Method Implemented with Artificial Intelligence The fundamental-period based VAPS-PWM method introduced in Section III-A presents two challenges. On one hand, this strategy just achieves the elimination of one specific harmonic component (defined by m=1 and n=1). The method lets the other components completely uncontrolled what could cause a distortion increase in other frequencies. On the other hand, applying the method to converters with N > 3, the angles φxare very complex to be determined in an analytical manner as can be observed in [38]. In order to overcome both issues, it is possible to adapt the method looking for the φxthat minimize a well-defined cost function ρthat includes not only one specific harmonic but the harmonics of interest in an specific application [39]. Typically, a well-suited option to define ρis to use the weighted total 8 harmonic distortion (WTHD) which is a good figure of merit to improve the design of the output lowpass filter as it is introduced in Fig. 5, where harmonics up to N-1 are included in the cost function (but other figures of merit can also be used). In any case, any mathematical search algorithm can be used to look for the minimum value of the cost function [39], [40]. In [39], the Exchange Market Algorithm (EMA) was used to determine φxto minimize the cost function in a CHB with four, five and six cells. Some of the obtained results (represented in Fig. 5) show that, applying this VAPS-PWM method, an improved CHB output voltage harmonic spectrum is obtained. B. Extension of the Sampling-Time Based VAPS-PWM Method In the case of the sampling-time based VAPS-PWM method addressed in Section III-B, as the number of cells increases, it becomes progressively more difficult to determine the φxvalues imposing hk(t) = 0. In this case, an efficient way to come to a valid solution is to force some conditions to φxin order to simplify the mathematical approach fitting with the solution given if N=3 introduced in Fig. 4 [41]. As an example, if N=4 and forcing h1(t) = 0, the resulting equations to be solved are complex. However, the angle φ1can be fixed to one specific value in order to reduce the number of angles to be determined. Doing this, the obtained solution if N=3 would be valid but it represents only one of the infinite solutions to achieve the harmonic cancellation. Another way to simplify the calculations when Nis large is to associate the cells forming groups of three cells and again using the well-known analytical solution when N=3. In this method, the carrier phase-displacement angles are determined in order to eliminate the envelope of the harmonics Ackintroduced in Fig. 5. In particular, in [41] the φxvalues are obtained eliminating the envelope of the lowest-order side-bands harmonic (k=1) and minimizing the envelopes of other side-bands harmonic groups (defined by k=1 and k=2). The obtained enhanced CHB total output voltage harmonic spectrum applying this VAPS-PWM method considering a six-cell CHB converter is represented in Fig. 5. Another strategy to implement a sampling-time based VAPS-PWM method is based on a geometrical approach that also achieves similar results [42]. In any case, the elimination of the first group of harmonic components lead to an increase of the magnitude higher harmonic groups compared to the result obtained by applying the fundamental-period VAPS-PWM method. V. FUTURE TRENDS In many current and future applications, strict requirements in terms of fault tolerant capability, extended lifespan converters and reduced maintenance cost will lead to consider modular converters as the most 15 Fig. 3: Unbalanced operation of three-cell CHB and three-cell parallel boost converters applying the conventional carrier phase displacement PWM methods with carrier frequency equal to 1 kHz and 5 kHz respectively. PEBB voltages/currents and total output voltage/current with their corresponding harmonic spectra 16 Fig. 4: Basic concepts and results applying PWM methods for three-cell CHB converters. From left to right: conventional PS-PWM, fundamental-period VAPS-PWM and sampling-time VAPS-PWM strategies 17 Fig. 5: Basic concepts and results applying PWM methods for six-cell CHB converters. From left to right: conventional PS-PWM, fundamental-period VAPS-PWM and sampling-time VAPS-PWM strategies 18 Fig. 6: Experimental results of a three-cell parallel-connected boost converter working under balanced and unbalanced operational conditions applying the conventional interleaved PWM technique and the VAPSPWM method View publication statsView publication stats