A Hybrid Modulation Technique for Operating Medium-Voltage High-Power CHB Converters Under Grid Voltage Disturbances

Depósito de investigación de la Universidad de Sevilla https://idus.us.es/ This is an Accepted Manuscript of an article published IEEE Transactions on Industrial Electronics available at: 10.1109/TIE.2023.3241246 “© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other Works” IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 1 A Hybrid Modulation Technique for Operating Medium-Voltage High-Power CHB Converters under Grid Voltage Disturbances Vito Giuseppe Monopoli, Senior Member,IEEE, Abraham M. Alcaide, Member,IEEE, Lara Bruno, Giuseppe Rendine, Jose I. Leon, Fellow Member,IEEE, Marco Liserre, Fellow Member,IEEE, and Leopoldo G. Franquelo, Life Member,IEEE. Index Terms—Harmonic analysis, Pulse width modulation, Multilevel converters. Abstract—Power converters, and particularly multilevel converters, are key elements in the current energy scenario. Among them, Cascaded H-Bridge Converters (CHB) are a popular and versatile solution for many industrial applications. Technical literature provides multiple modulation techniques for its operation. Among them, hybrid-PWM modulation techniques provide a good trade-off between switching loss and output voltage quality. In this work a hybrid modulation technique is presented which allows not only the fundamental block switching operation of some power cells but also a harmonic control over a specific harmonic distortion present in the grid. To validate the operation of the proposal, several experimental results have been reported to demonstrated the good behaviour of the proposed modulation technique. I. INTRODUCTION Worldwide power demand is increasing every year hand by hand with the restricted policies to fight against climate change avoiding fossil fuels. In many of these actions, high power levels and/or high voltages are required [1], [2]. To fulfill these requirements the academia and industry have put many effort to develop efficient power converter structures to achieve high performance limiting costs [3]. In this sense, multilevel converters have become a mature and very attractive solution since decades because these structures can achieve high voltage ratings by using medium-voltage power semiconductors with high quality output wave-forms [4]–[6]. The authors gratefully acknowledge financial support provided Ministerio de Ciencia e Innovaci´ on under the project PID2020-115561RB-C31, Junta de Andaluc´ ıa under the project P18-RT-1340. Abraham M. Alcaide gratefully acknowledges the financial support provided by Contrataci´ on de Personal Investigador Doctor. (Convocatoria 2019) 43 Contratos Capital Humano L´ ınea 2. Paidi 2020, supported by the European Social Fund and Junta de Andaluc´ ıa V. G. Monopoli and Lara Bruno are with the Department of Electrical and Information Engineering, Politecnico di Bari, 70126 Bari, Italy (e-mail: [email protected]). Abraham M. Alcaide is with the Electronic Engineering Department, Universidad de Sevilla, Seville, 41092 Spain (e-mail: [email protected]g). Giusseppe Rendine is with Automation Engineer in EMS Group M. Liserre is with the Chair of Power Electronics, Christian-Albrechts- University of Kiel, Kiel 24143, Germany (e-mail: [email protected]). Jose I. Leon and Leopoldo G. Franquelo are with ENGREEN Laboratory of Engineering for Energy and Environmental Sustainability, Universidad de Sevilla, Seville, 41092 Spain and also are chair professors with the School of Astronautics, Harbin Institute of Technology, Harbin (China). Cell 1 Cell 2 Cell 3 v1 v2 v3 v a n + - + - + - S 31 S 31 + S 32 S 32 V dc ,3 +- Fig. 1: Three-cell multilevel cascaded H-bridge converter Among multilevel converter structures, the cascaded H-Bridge converter (CHB) is one of the most successful solutions for many high-power applications such as motor drive, pumps and fans, among others [7]–[9]. The CHB is built under the Power Electronics Block Building (PEBB) paradigm by the series connection of power modules leading to a high modularity, fault-tolerant capability, easy replacement of failed modules among others benefits. These features are very appreciated by the manufactures in the industry because production and maintenance cost reduction is intrinsically enabled [10], [11]. As an example, a single-phase three-cell CHB converter is represented in Fig. 1. Among the modulation techniques to operate a CHB present in the technical literature, the phase-shifted pulse-width modulation (PS-PWM) is the most conventional method because of its well-known advantages [12]–[14]. In this modulation strategy, each power cell is operated considering an unipolar PWM strategy with a triangular carrier of frequency fckHz. In order to achieve the optimum performance in the output voltages and currents, the PS-PWM method requires a specific phase displacement among the carriers of each power cell [15], [16]. The operation of the semiconductors switching at the carrier frequency can be challenging for high-power applications where the switching loss have to be very limited requiring bulky, heavy and complex cooling systems, although researchers have presented optimized solutions for thermal compensation using PS-PWM in CHB converters [17], [18]. On the opposite side there is the staircase operation of the CHB This article has been accepted for publication in IEEE Transactions on Industrial Electronics. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/TIE.2023.3241246 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 2 that allows very low switching losses because semiconductor devices only switch once per cycle of the fundamental period of the output voltage waveforms. Nevertheless, this technique do not allow to have any kind of control on the harmonics of the output voltage waveforms. In particular, very low frequency baseband harmonics are generated with this technique heavily affecting the harmonic quality of the output vaweforms and the size of output filters [12]. As an alternative, it is possible to operate the converter using the well-known selective harmonic elimination/mitigation (SHE/SHM) techniques in order to reduce the switching loss achieving a specific output voltage spectrum. The quality of the resulting output voltage and current as well as the switching loss of the system highly depends on the number of the switching angles considered in the pre-programmed switching pattern for each power cell [19]–[22]. In some cases, in order to simplify the definition of the pre-programmed switching pattern and also looking for the equalization of the power losses among the CHB power cells, one switching angle is related to each power module minimizing the switching loss of the modules (i.e. the staircase modulation method). This fundamental block switching (BS) modulation provides the minimum power loss in the overall power converter at the expense of degradation of the resulting output voltage and current spectra that could be not appropriated depending on the final application [23]. It is also worth to remind that all the afore-mentioned techniques do not allow to achieve an optimal dynamic performance of the power system. Therefore, through these techniques a trade-off between switching losses and harmonic quality can be achieved. Nevertheless, it has to be taken into consideration that the lower are the switching losses, the lower is the computational complexity but the worse is the harmonic quality. On the opposite side, the higher are the switching losses, the higher is the computation complexity and the better is the harmonic quality. An option to achieve good trade-off between switching losses and harmonic quality for CHB converters is represented by the hybrid PWM methods that consider some power cells operated at low frequency and some power cells operated with PWM [24], [25]. The power cells operated at low switching frequency or fundamental BS modulation greatly reduce their corresponding switching losses whereas the power cells operated with PWM increase the controllability of the system and improve the quality of the resulting output waveforms. However, these approaches are defined to be applied to asymmetric CHB converters. In order to deal with the loss imbalance among the power modules, the PWM-based modulation strategy is assigned to the power module with lowest dc voltage while the fundamental frequency modulation is used in the power module with highest dc voltage. In addition, these methods does not consider the possibility to compensate a distorted grid, which is one of the objectives of the proposed modulation strategy. In grid connected applications the injected current into the power grid should fulfil the minimum requirements defined in the corresponding grid codes and standards [26]. In this sense, if the grid presents some undesired distortion (which is very usual mainly in low-order harmonics), this disturbance L i R vg1(t)=A1sin(w1 t +©1 ) vg3(t)=A3sin(w3 t +©3 ) vg(t)=v g1 (t)+v g3 (t) Grid sideConverter side + + + v(t) Fig. 2: Equivalent circuit of the single-phase CHB connected to a grid with a non-negligible third harmonic distortion 0 40 80 120 Magnitude (A) Current (A) 0 4 1 32 85.4A 0 1 32 4 5 6 7 8 9 10 Harmonic order (n) Time (ms) 0 20 40 60 80 100 -120 -80 -40 0 40 80 120 Uncompensated Compensated a b Fig. 3: a) Injected currents in presence of grid voltage disturbance. b)Harmonic spectra will be also present in the current unless a proper action is considered [27]. In order to meet the power quality standards, this issue has to be considered in the design of the control and modulation techniques of the grid-tied converters connected to that point of common-coupling. In Fig. 2 is shown the mathematical representation of the previously mentioned phenomenon. As an example, in Fig. 3 an undesirable third harmonic distortion in the power grid is shown in blue. However, if the power converter generates the appropriated voltage it is possible to compensate this harmonic distortion as it is also shown in Fig. 3, drawn in red. In this work, an innovative hybrid PWM strategy for a single-phase three-cell CHB is presented. The main original contribution of the work is to consider a mix between the preprogrammed PWM methods and the unipolar PWM technique to operate the CHB converter with the objective of generating an specific fundamental voltage capable of considering a distorted grid. In this way, the proposed modulation strategy is able to simultaneously compensate the harmonic distortion of the grid voltage achieving high quality grid currents. The proposed modulation method also achieves a reduction in This article has been accepted for publication in IEEE Transactions on Industrial Electronics. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/TIE.2023.3241246 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 3 2 2 2 ®1¼-®1 ®2¼-®2 Power modules output voltages (vx) µo µo µo Fig. 4: Power modules output voltages applying the proposed hybrid PWM scheme for a three-cell CHB the power loss, also obtaining the power loss equalization in order to obtain an equally distributed ageing among the power cells keeping the modularity feature that is fundamental for industrial solutions of the CHB converter. II. PROPOSED HYBRID PWM TECHNIQUE (HHC-PWM) FOR CHB CONVERTER The proposed hybrid PWM technique for the three-cell CHB is based on applying a fundamental frequency waveform in two power modules while a conventional unipolar PWM technique is applied to the other one. The fundamental frequency operation of power modules is an attractive solution for very high-power applications because of its inherent reduced switching loss at the expense of reduced output waveforms quality. The power module operating with an unipolar PWM method mitigates this drawback achieving output waveforms with harmonic quality above the required limits imposed by grid codes. In summary, the proposed hybrid PWM method, called HHC-PWM, obtains power modules output voltages as it is represented in Fig. 4. As it is shown in Fig. 4, the HHC-PWM technique looks for reducing the switching loss of two power modules by generating fundamental frequency power modules output waveforms. In this sense, it is well-known that the resulting harmonic spectrum of this type of output waveform contains multiple non desired low-order harmonic components. To mitigate this effect, the HHC-PWM method considers variable fundamental frequency power module output waveforms defined by the value of corresponding switching angles (α1and α2) in the power modules. These switching angles are used by the HHCPWM method following the well-known basic concept used in the Selective Harmonic Elimination/Mitigation [28], [29], where the values of these angles are defined in order to manage the harmonic distortion of a converter output voltage. Prior to define how to determine the switching angles values, some definitions are required: M=1 3 N=3 X x=1 Mx(1) where Vdc,x and Mx(x= 1,2,3) are the dc voltage and modulation index of the power cell x. Additionally, Mxis defined as Mx=H1,x Vdc,x (2) where H1,x is the amplitude of the fundamental harmonic produced by the power cell x. Expression 2 is imposed because in this work, a symmetrical CHB converter is considered. This means that all the power modules have the same dc voltage, assuming that Vdc=Vdc,1=Vdc,2=Vdc,3, that is the case of most of the industrial CHB solutions present in the manufacturer ˆ A´s portfolios. A. Operation of the BS power cells The resulting fundamental harmonic of the output voltage of the CHB converter is the summation of the fundamental component of the voltages produced by each single power cell. On one hand, it is required to calculate the amplitude of the harmonic components produced by the fundamental frequency power modules. In this way, using the Fourier Series with Fourier coefficients anand bn(where bnis zero by choosing the proper waveform symmetry), the harmonic components of the summation of the output voltages of the fundamental frequency power modules can be determined as: Hn=an 2Vdc =4 nπ cos(nα1) + cos(nα2)(3) where nrepresents the harmonic order. From (3), the amplitude of the resulting fundamental harmonic (H1), as well as the resulting third harmonic (H3) can be expressed as: H1=4 πcos(α1) + cos(α2)(4) H3=4 3πcos(3α1) + cos(3α2)(5) It is possible to find an analytic solution to the system of equation given by (4) and (5) [28]. In this sense, the constrains are 2 /3of the fundamental required voltage and a H3component equal to 0. That is: 2 3 Mπ 4=cos(α1) + cos(α2)(6) 0 = cos(3α1) + cos(3α2)(7) After some mathematical manipulation and solving the system of equation with an appropriated symbolic mathematical solver tool, the analytical solution is given by: α1= 2π−arccos πM′ 8−σ α2= 2π−arccos πM′ 8+σ(8) where M′is the portion of the required fundamental voltage and σis an auxiliary variable defined as: This article has been accepted for publication in IEEE Transactions on Industrial Electronics. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/TIE.2023.3241246 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 4 Shareholders Ranking (according their ¿i ) Evaluate Cost Function ¿ (10) Balanced Market Evolution [23] Trading Market Evolution [23] Switching angles restriction M=0? Shareholder evolution M =1 M =0 YES NO InitEMA() Shareholders M=0 Stock ®10 ®11 ¿1 ¿2 ¿p ®20 ®21 ®p0 ®p1 Evaluate Market Rank Sharedholder [®10 ®11 ]Solution Fig. 5: EMA implementation to determine the most proper switching angles in order to minimize the cost function τ σ=1 24√3√48 −M′2π2(9) However, the analytical solution obtained does not provide the required waveform symmetry required by the fundamental BS modulation technique as it is shown in Fig. 4. In addition, the mathematical expressions become complex and the system of equations should be re-written as a multi-variable optimization problem where the main constrain is to generate the required portion of the fundamental harmonic component with a zero third harmonic injection. In general, it is possible to write the cost function as: τ=2H1 3+λnHn+λA (10) where λnand λare weighting factors, and the factor A considers the rest of the harmonic spectrum. Afactor can be considered as the well-known figure of merit WTHD or WTHD0. These are defined as follows: WTHD =1 H1 v u u t ∞ X n=1 Hn n2 (11) WTHD0 = 1 3Vdc v u u t ∞ X n=2 Hn n2 (12) Due to complexity of this optimization problem, it is very usual the use of meta-heuristic algorithms in power electronics and the technical literature offers multiple options [30]. For instance, the Genetic Algorithm (GA) is inspired by the natural selection, the process that drives biological evolution [31]. Particle Swarm Optimization (PSO) algorithm is inspired by animal’s social behavior [32]. As a combination of both 0 22.5 45.0 67.5 90.0 Switching angles (º) 0.5 0.6 0.7 0.8 0.9 1.0 Modulation index 2 3 4 5 6 WTHD, WTHD0 (%) ®1 ®2 WTHD0 WTHD a b Fig. 6: Results of the optimization cost function τ. a) optimal switching angles b) Resulting value of the figure of merit WTHD0 and WTHD techniques, the Exchange Market Algorithm (EMA) mixes the benefits from both techniques achieving a good trade-off between computational burden and convergence performance avoiding the local minima [18], [33], [34]. EMA is inspired by shares trading in the stock market and it is the selected method for the harmonic optimization in this work. However it is worth to be mentioned that any other meta-heuristic method can be applied. The EMA has been executed in order to minimize the cost function τdefined in (10) depending on the modulation index that has to be applied to the power cells forcing also the required output voltage quarter symmetry in the power cells operated with BS modulation. The obtained results are represented in Fig. 6, where the values of the switching angles α1and α2, and the corresponding values of the WTHD and WHTD0 of the summation of the output voltages of the two power modules operating with fundamental switching frequency are plotted as well. B. Unipolar PWM with Third Harmonic Injection In the proposed HHC-PWM method, one power cell of the CHB is operated with a unipolar PWM strategy. In this work, a distorted grid is considered assuming that the grid voltage presents a non-negligible harmonic distortion located at low frequency order. For instance, it is considered a grid voltage with a third harmonic component with a specific magnitude and phase. As it was shown in Fig. 2 and Fig. 3 can be observed that if the CHB output voltage vonly presents a fundamental harmonic, it leads to generate a grid current ithat presents a third harmonic distortion. However, measuring the magnitude of the third harmonic component in the grid voltage, and taking into account the grid filter (an inductance plus resistance in Fig. 2) in order to determine the third harmonic phase, it is possible to generate grid currents eliminating the third harmonic distortion. It can be done by generating a This article has been accepted for publication in IEEE Transactions on Industrial Electronics. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/TIE.2023.3241246 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 5 0 0.2 0.4 0.6 0.8 1.0 Magnitude 3rd harmonic (V) 0 90 180 270 360 Phase 3rd harmonic (º) Fig. 7: Limitations of the third harmonic injection (considering magnitude and phase) of the power module operated with a unipolar PWM strategy CHB voltage vwith the corresponding fundamental harmonic component and a third harmonic with the same magnitude of the grid voltage third harmonic component. Also, the third harmonic component of the CHB output voltage must have the opposite phase of the third harmonic component of the non-compensated grid current. This concept has been shown clearly in Fig. 3, where the grid current with and without applying a compensation in the CHB output voltage is also represented. It can be observed that high quality grid currents can be obtained even with distorted grid voltages by generating converter output voltages that are able to compensate the distortion. This idea is taken by the remaining power cell in the CHB, that is in charge of the generation of the remaining part of the fundamental harmonic. At the same time, this power module also generates the required amplitude and phase of the third harmonic component to cancel the undesirable harmonic content present in the power grid. In this way, in this power module it has to be fulfilled that H1=MVdc H3=Hvg3∠(Hig3+π)(13) where Hvg3is the third harmonic content of the grid voltage. Also, (Hig3is the third harmonic content of the grid current without applying any compensation. It is important to notice that there is a limitation in the generation of the third harmonic component generated by the power module operated with a unipolar PWM strategy. This limitation appears due to the requirement to avoid overmodulation is the power module operation, leading to introduce Fig. 7 where the possible values of third harmonic component (magnitude and phase) are represented. C. Power loss and controlability analysis comparison An important issue for the design and the operation of the converter is the achieved efficiency as well as the power loss that the cooling system should sink. In this sense, the proposed modulation technique can be compared with conventional state-of-the-art modulation techniques in terms of generated 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.2 0.4 0.6 0.8 1.0 PS-PWM Proposed Staircase Power load (p.u.) Switching loss factor (p.u.) Fig. 8: Switching loss evaluation for different power load power loss and the achieved harmonic injection ability against disturbances as follows: •Classical BS-based SHE modulation presents the lower switching loss since each power cell is only switching one time per fundamental period. This fact has a strong limitation effect on the resulting output voltage harmonic spectrum and its ability to neglect harmonic disturbances during the operation of the converter. •In SHE/SHM modulation techniques, the generated power loss as well as the quality of the resulting output voltage and current are highly depending on the number of switching angles considered in each power cell. Thus, it is possible to achieve a reasonable output voltage quality with a reduced number of switching angles maintaining the power loss under control. On the contrary, SHE/SHM has a serious limitation in terms of the ability of harmonic disturbance suppression. In this sense, it is mandatory to to consider half-wave symmetry (instead of conventional quarter-wave symmetry) which has an impact on the losses and the complexity of the operation of the converter. In addition, the dynamic performance of the proposed modulation technique can be comparable with conventional dynamic performance shown in SHE/SHM techniques since the switching patterns have be maintained during a complete fundamental period. •PS-PWM present the best controlability performance for the system operation since the modulating reference for each power cell can be composed by the required harmonic content but unfortunately PS-PWM also present the higher power loss and therefore the frequency of the carriers should be limited as much as possible. The proposed hybrid modulation technique offers a tradeoff solution in terms of achieved power loss since it combines the lower switching loss in the power cells operated with BS modulation. On the other hand, the proposed modulation technique also provides the ability to neglect a harmonic disturbance present in the system in a wide operation range. Finally, a quantitative switching power loss analysis for the presented techniques has been performed for validation of the previous dissertation. The results are presented in Fig. 8. The passive element values and other required parameters for calculation has been reported in Table I. The switching power loss for PW-PWM at nominal power has been used as reference for the normalization of the switching loss of the rest of the modulation techniques. This article has been accepted for publication in IEEE Transactions on Industrial Electronics. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/TIE.2023.3241246 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 6 Fig. 9: Down-scaled single-phase three-cell CHB prototype used for the experimental tests D. Power loss mismatch management in the CHB converter Another important issue to take into account in the power module operated with an unipolar PWM is related to its power loss. Compared with the two cells operating with fundamental BS frequency, this power cell presents much higher switching losses making a power loss unbalance effect among the CHB modules. This fact would provoke also a negative unbalance effect on the remaining useful lifetime of the converter [35]. This issue can be solved considering multiples alternatives by applying a superior control layer. As an example, a simple rotation strategy in the role assumed by each power cell in a similar way that [36]. In this sense after a some fundamental periods, the role of each power module can be changed. In the long-term, the power modules will be operated with BS modulation 2 /3time fractions whereas the remaining 1 /3time fraction will be operated applying an unipolar PWM strategy. This simple role rotation strategy equalizes the power loss among the modules leading to a equally distributed ageing. As an alternative, an active thermal control can be deployed considering the accumulation of the conducting and switching loss in order to decide the most appropriate role for the power cell for the aging equalization [35]. However, it is worth to be mentioned that it is not the focus of the present paper. III. EXPERIMENTAL RESULTS In order to test the performance of the proposed technique, the experimental setup shown in Fig. 9 has been used. The experimental rig is composed by a single-phase CHB converter tailored by three power cells connected to a grid emulator. The most representative parameters of the experimental setup and the operational conditions for the considered experiments are summarized in Table II. For the operation of the converter and the implementation of the proposed HHC-PWM method, the low-cost mid-range TMS320F28379D micro-controller platform from Texas Instruments has been considered [37]. TABLE I: Parameters used for loss calculation Parameter Value DC Voltage Vdc,x (V) 400 Capacitance C(mF) 2.0 Resistance R(Ω) 5 Inductance L(mH) 4.16 PWM Carrier frequency (when required) fc(kHz) 1 The experimental test performed are split-off in three different cases. In all reported experimental scenarios (also summarized in Table II), the power modules working with fundamental switching frequency are operated to achieve 2 /3 of the desired fundamental harmonic magnitude with a third harmonic component equal to 0as a main constraint. Additionally, it is also looking for the minimum WTHD value as previously described in the definition of the cost function τ(10). The obtained experimental results of the proposed HHCPWM strategy applied to the single-phase three-cell CHB considering the operational conditions described in scenarios I, II and III are presented in Fig. 10, Fig. 11 and Fig. 12, respectively. As it can be observed from these results, the operation of the CHB converter achieves the expected output voltage since the fundamental as well as third harmonic injection (including magnitude and phase) fulfil the imposed requirements to cancel the undesired third harmonic component in the output current. In order to make a comparison of the proposed method with the most conventional modulation methods, extra experimental results have been taken considering scenario I. First of all, a BS-based SHE modulation method is applied obtaining a CHB output voltage with the desired fundamental component, eliminating also the fifth harmonic component and imposing the desired magnitude in the third harmonic component (12 V). The switching angles to achieve these objectives are [α1, α2, α3]=[22.61◦,22.64◦,79.62◦]. The obtained result is represented in Fig. 13, where it can be observed that a nonnegligible third harmonic component appears in the output current because the obtained third harmonic phase of the generated output voltage is not the appropriated. In addition, a conventional PS-PWM method (implementing in each power module a unipolar PWM technique with carrier frequency equal to 3 kHz) has been applied where each power module generates a third part of the fundamental and desired third harmonic components. The obtained results are shown in Fig. 14, where it can be observed that the third harmonic com- TABLE II: Example of Operational conditions of the Block switching power cells in the CHB converter Experimental CHB set-up parameter Power module DC Voltage Vdc,x (V) 120 Desired modulation index M0.9 Fundamental frequency fo(Hz) 50 PWM Carrier frequency fc(kHz) 3 Scenario I - Operational case I Unipolar-PWM magnitude injection [H1, H3](V) [108,12] Unipolar-PWM phase injection [P1, P3](◦)[0,120] Scenario II - Operational case II Unipolar-PWM magnitude injection [H1, H3](V) [108,21] Unipolar-PWM phase injection [P1, P3](◦)[0,130] Scenario III - Operational case III Unipolar-PWM magnitude injection [H1, H3](V) [108,21] Unipolar-PWM phase injection [P1, P3](◦)[0,60] This article has been accepted for publication in IEEE Transactions on Industrial Electronics. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/TIE.2023.3241246 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 7 0 10 20 30 40 -10 -5 0 5 10 Time (ms) Harmonic order (n) Current (A)Current (A) 0 10 20 30 40 50 0 1 2 c d -400 -200 0 200 400 Voltage (V)Voltage (V) 0 30 60 Harmonic order (n) 0 10 20 30 40 50 0 10 20 30 40 Time (ms) a bTHD = 11.4% Fig. 10: Experimental results for case I applying the HHC-PWM method. a) CHB output voltage, b) CHB output voltage harmonic spectrum c) Phase current d) Phase current harmonic Spectrum 0 10 20 30 40 -10 -5 0 5 10 Time (ms) Harmonic order (n) Current (A)Current (A) 0 10 20 30 40 50 0 1 2 c d -400 -200 0 200 400 Voltage (V)Voltage (V) 0 30 60 Harmonic order (n) 0 10 20 30 40 50 0 10 20 30 40 Time (ms) a bTHD = 11.3% Fig. 11: Experimental results for case II applying the HHC-PWM method. a) CHB output voltage, b) CHB output voltage harmonic spectrum c) Phase current d) Phase current harmonic Spectrum ponent is eliminated in the output current because a specific third harmonic component has been imposed in magnitude and phase in the CHB output voltage. Additionally has to be notice the increasing of the switching loss of the CHB converter. Finally, a comparative analysis of the modulation methods to operate the three-cell CHB converter is addressed in III, where the advantages and disadvantages of each method are summarized. It can be highlighted that the proposed HHCPWM method achieves a good trade-off between harmonic rejection ability and efficiency, being a attractive solution for industrial applications where the switching loss have to be limited. IV. CONCLUSIONS Multilevel converters are an attractive solution for many industrial applications. As the control strategy as the selected modulation technique considered to operate the power converter become crucial to achieve high performance, highquality in the resulting output wave-forms with reduced power loss. A good trade-off between power loss and output waveform quality has also benefits from the build operational and maintenance costs of the power converter. In this paper, a hybrid-PWM technique which allows the operation of the power converter considering a specific harmonic cancellation with reduced power loss is presented. In order to validate the effectiveness of the proposal several experimental test have This article has been accepted for publication in IEEE Transactions on Industrial Electronics. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/TIE.2023.3241246 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 8 0 10 20 30 40 -10 -5 0 5 10 Time (ms) Harmonic order (n) Current (A)Current (A) 0 10 20 30 40 50 0 1 2 c d -400 -200 0 200 400 Voltage (V)Voltage (V) 0 30 60 Harmonic order (n) 0 10 20 30 40 50 0 10 20 30 40 Time (ms) a bTHD = 11.0% Fig. 12: Experimental results for case III applying the HHC-PWM method. a) CHB output voltage, b) CHB output voltage harmonic spectrum c) Phase current d) Phase current harmonic Spectrum 0 10 20 30 40 -10 -5 0 5 10 Time (ms) Harmonic order (n) Current (A)Current (A) 0 10 20 30 40 50 0 1 2 c dTHD = 12.5% -400 -200 0 200 400 Voltage (V)Voltage (V) 0 30 60 Harmonic order (n) 0 10 20 30 40 50 0 10 20 30 40 Time (ms) a b Fig. 13: Experimental results for case I applying the BS-based SHE method. a) CHB output voltage, b) CHB output voltage harmonic spectrum c) Phase current d) Phase current harmonic Spectrum been conducted. It can be observed that the proposed method represents a good trade-off solution for industrial applications achieving the ability to compensate grid disturbance with limited loss. REFERENCES [1] 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 Industrial Electronics Magazine, vol. 7, no. 3, pp. 6–20, Sep. 2013. [2] G. Rituraj, G. R. C. Mouli, and P. Bauer, “A comprehensive review on off-grid and hybrid charging systems for electric vehicles,” IEEE Open Journal of the Industrial Electronics Society, vol. 3, pp. 203–222, 2022. [3] H. Abu-Rub, J. Holtz, J. Rodriguez, and G. Baoming, “Medium-voltage multilevel converters-state of the art, challenges, and requirements in industrial applications,” IEEE Transactions on Industrial Electronics, vol. 57, no. 8, pp. 2581–2596, 2010. [4] B. Wu and M. Narimani, Cascaded H-Bridge Multilevel Inverters. 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Citation information: DOI 10.1109/TIE.2023.3241246 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information.