Cascaded Modular Multilevel Converter and Cycloconverter Based Machine Drive System

This is a repository copy of Cascaded Modular Multilevel Converter and Cycloconverter Based Machine Drive System. White Rose Research Online URL for this paper: https://eprints.whiterose.ac.uk/189145/ Version: Accepted Version Article: Zhang, Yue, Deng, Fujin, Hou, Jiehua et al. (5 more authors) (2022) Cascaded Modular Multilevel Converter and Cycloconverter Based Machine Drive System. IEEE Transactions on Industrial Electronics. ISSN 0278-0046 https://doi.org/10.1109/TIE.2022.3169851 [email protected] https://eprints.whiterose.ac.uk/ Reuse Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the reason for the withdrawal request. 0278-0046 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2022.3169851, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS Abstract— Low-speed drive is one of the challenges for modular multilevel converters (MMCs) due to large capacitor voltage fluctuation. In this paper, a cascaded MMC and cycloconverter (CCV) based machine drive system is proposed to ensure stable operation of medium- -voltage and low-speed machine. The MMC provides medium-frequency ac voltage for the CCV, and the CCV converts the medium-frequency ac input to low-frequency ac output required by the machine. Detailed analysis about MMC’s operation frequency, device current stress and submodule (SM) capacitance are given in this paper. Proposed drive system can operate at zero/low frequency under rated load torque, while the SM capacitance is much smaller than that in existing methods. Simulation and experimental studies are conducted, and the results verify the effectiveness of proposed system. Index Terms— Capacitor voltage, cycloconverter, lowspeed machine drive, modular multilevel converter (MMC). I. INTRODUCTION The modular multilevel converter (MMC), which was firstly proposed in 2003 [1], has become the most potential topology for next-generation medium/high-voltage applications due to its advantages such as modularity, high efficiency, and flexible expandability [2]-[7]. In recent years, the MMC is attractive for the medium-voltage drive applications. The submodule (SM) capacitor voltage fluctuation is one of the important issues for the MMC working at low frequency. The voltage fluctuation is inversely proportional to the operation frequency of the MMC [8]. For the MMC’s zero/lowspeed high-torque scenarios such as hoister, conveyor and mill applications, the voltage fluctuation will be large and unacceptable, which would cause overmodulation and degrades the system reliability [9]. To date, the mainstream solution to suppress the capacitor voltage fluctuation in the MMC at low speed is the current injection based methods [10]-[14]. Kolb et al. [10] presents the injection of high-frequency sinusoidal common-mode voltage and circulating current, which can eliminate the low-frequency capacitor voltage fluctuation, but the device current stress is increased [11]. To reduce the device current stress, the improved injection methods [12]-[14] are proposed for the MMC. However, the injection of high-amplitude current is still needed. The current injection based methods require to inject high-amplitude circulating current and the device current stress is extremely high especially in low-speed high-torque scenarios. Alternatively, the capacitor voltage fluctuation in the MMC at low speed can be reduced by variable dc voltage methods [15]-[21]. Li et al. [15] proposes a hybrid MMC (HMMC) with a chopper on the dc side, which can change the average dc voltage along with the variation of output frequency. However, the average dc voltage cannot be reduced to zero, so the voltage fluctuation is still high at zero/low speed. Sau et al. [16] applies parallel SMs in [17], then the MMC operates with one SM in each arm at zero/low speed. However, the output voltage of parallel SMs is limited, which cannot satisfy the operation for medium-voltage low-speed machines. Kumar et al. [18] and [19] use a back-to-back (BTB) MMC, where the grid-side MMC is controlled as a current source, and the capacitor voltage fluctuation keeps unchanged. However, both the grid-side and machine-side MMCs require full-bridge SMs, which greatly increases the number of devices. Although Guan et al. [20] and Li et al. [21] reduce the devices of BTB-MMCs, the stable operation under rated torque at zero speed cannot be ensured. The variable dc voltage methods have limitation to suppress the capacitor voltage fluctuation of MMCs for medium-voltage low-speed drive, which require large SM capacitance [15], [18]. This paper proposes a cascaded MMC and cycloconverter (CCV) based machine drive system for the medium-voltage low-speed machine, which extends the work in [22]. Detailed analysis is conducted in this paper, including the operation frequency of MMCs, device current stress, and SM capacitance. In addition, a prototype of the proposed machine drive system is built in the lab and the experimental studies are conducted in this paper. In the proposed system, the MMC operates at medium frequency, providing constant ac voltage for the CCV, and the CCV converts the medium-frequency ac input to lowfrequency ac output required by the machine. The paper includes following contributions: 1) the proposed drive system can operate at zero/low frequency under rated load torque; 2) the MMC in the proposed drive system operates at medium frequency, which requires smaller SM capacitance compared to variable dc voltage methods [15]-[21]; 3) the device current Yue Zhang, Fujin Deng, Senior Member, IEEE, Jiehua Hou, Pengyuan Jiang, Hanlu Zhang, Kangshun Zhu, Yihua Hu, Senior Member, IEEE and Sergio Vazquez, Fellow, IEEE Cascaded Modular Multilevel Converter and Cycloconverter Based Machine Drive System This work was supported in part by the National Natural Science Foundation of China under Project 61873062. (Corresponding author: Fujin Deng.) Y. Zhang, J. Hou, P. Jiang, H. Zhang and K. Zhu are with the School of Electrical Engineering, Southeast University, Nanjing 210096, China (e-mail: [email protected]; 2202029[email protected].cn; 220192735 @seu.edu.cn; 2202029[email protected]du.cn; [email protected]). F. Deng is with the School of Electrical Engineering, Southeast University, and Jiangsu Key Laboratory of Smart Grid Technology and Equipment, Nanjing 210096, China (e-mail: [email protected]). Y. Hu is with the Department of Electronic Engineering, University of York, York, YO10 5DD, U.K. (e-mail: [email protected]). S. Vazquez is with the Department of Electronic Engineering, University of Seville, 41092 Seville, Spain (e-mail: [email protected]). Authorized licensed use limited to: University of York. Downloaded on July 15,2022 at 10:49:23 UTC from IEEE Xplore. Restrictions apply. 0278-0046 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2022.3169851, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS stress in the MMC with proposed method is much less than that with current injection based methods [10]-[14]. The rest of paper is organized as follows. Section II proposes the cascaded MMC and CCV based machine drive system. Section III proposes operating principles. Section IV discusses the proposed system. Sections V and VI present the simulation and experiment, respectively. Section VII gives conclusion. II. PROPOSED CASCADED MMC AND CCV BASED MACHINE DRIVE SYSTEM A. Proposed Drive System A cascaded MMC and CCV based machine drive system is proposed, as shown in Fig. 1. The MMC operates as the gridside converter, and the CCV operates as the machine-side converter. The MMC is connected to the dc grid and provides the ac voltage with medium-frequency fg for the CCV. The CCV converts the input medium-frequency ac voltage to the required ac voltage with low-frequency fm to drive the permanent magnet synchronous machine (PMSM). CCV MMC DC Grid DC PMSM Grid-side Machine-side Drive System Mediumfrequency fg Lowfrequency fm Fig. 1. Block diagram of proposed machine drive system. B. MMC Based Grid-Side Converter Fig. 2(a) shows the grid-side three-phase MMC, whose each phase includes an upper arm, a lower arm, a filter inductor Lf, and a compensation capacitor Ccom. Each arm consists of n identical SMs and an arm inductor Ls. Fig. 2(b) shows a SM, which consists of the switch/diode T1/D1, T2/D2 and a dc capacitor Csm. According to [5], in the MMC, the output voltage uj in phase j (j=a, b, c) can be expressed as 2 lj uj j j u u di uL dt − =− (1) with 2 s f L LL=+ (2) where uuj and ulj are the total SM output voltage of the upper arm and lower arm in phase j, respectively. ij is the ac-side current of phase j. L is the equivalent output inductance of the MMC. C. CCV Based Machine-Side Converter Fig. 3 shows the machine-side three-pulse half-wave CCV. The CCV consists of three phase units. Each phase unit contains three pairs of inverse parallel thyristors including Thp1 & Thn1, Thp2 & Thn2, and Thp3 & Thn3, where the thyristors Thp1-Thp3 constitute a positive converter and the thyristors Thn1-Thn3 constitute a negative converter. LT is the commutation inductor. Taking phase unit a for example and neglecting harmonics, Fig. 4 shows the fundamental components of the output voltage uma and current ima of the CCV, which can be expressed as sin( ) ma m m u U t  = (3) sin( ) ma m m i I t  =− (4) where Um and Im are the amplitudes of the machine phase voltage and current, respectively. ωm is the fundamental angular frequency. λ is the lagging displacement angle of machine, which decides the operation of the positive converter and negative converter, as follows. ⚫ ωmt∈[λ, λ+π]: ima is positive and the positive converter (Thp1a, Thp2a, Thp3a) works. ⚫ ωmt∈[0, λ] & [λ+π, 2π]: ima is negative and the negative converter (Thn1a, Thn2a, Thn3a) works. The Thp1a, Thp2a, Thp3a in the positive converter or the Thn1a, Thn2a, Thn3a in the negative converter are fired alternately, and only one thyristor is conducting simultaneously, where the thyristor’s firing angle α can be obtained based on the cosine SM SM SM SM SM Ls Ls iua ila uua ula idc SM ia ica Lfua ub uc ioa Ccom Phase a Phase b Phase c Oiob ioc 2 Udc 2 Udc T2D2 T1D1 usm Csm uc (a) (b) Fig. 2. (a) Block diagram of MMC. (b) SM unit. ima uma Positive converter Negative converter umb umc imb imc Thn3a Thn2a Thn1a Thp3a Thp2a Thp1a uc ub uaioa iob ioc LT LT LT iTp1a iTp2a iTp3a iTn1a iTn2a iTn3a Phase unit a Phase unit b Phase unit c Fig. 3. Block diagram of the CCV. uma ima t λππ λ 0ωmt λ λ+π2π Positive converter operation range Negative converter operation range Fig. 4. Fundamental frequency components of the CCV’s output. Authorized licensed use limited to: University of York. Downloaded on July 15,2022 at 10:49:23 UTC from IEEE Xplore. Restrictions apply. 0278-0046 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2022.3169851, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS wave crossing method [23], as _ arccos( ) ref ma y  = (5) with _sin( ) ref ma m y r t  = (6) where yref_ma is the reference for phase a of the CCV. r is modulation index with 0≤r≤1. III. CONTROL OF PROPOSED MACHINE DRIVE SYSTEM A. Control of Grid-Side MMC The MMC provides a constant medium-frequency ac output voltage for the CCV. The control structure of the MMC is shown in Fig. 5(a), including the output voltage control and circulating current suppression control (CCSC) [24]. Fig. 5(b) shows the output voltage control in detail, which adopts doubleloop vector control to ensure a constant output voltage of the MMC. ud, uq and iod, ioq are the dq-axis components of output voltages ua, ub, uc and output currents ioa, iob, ioc, respectively. id, iq are the dq-axis components of ac-side currents ia, ib, ic. ωg is the angular frequency of output voltage and ωg=2πfg, where fg is the MMC’s output frequency. Udc is the dc-side voltage of the MMC. According to the voltage commands ud* and uq*, where ud* is equal to the amplitude of MMC’s phase voltage and uq* is 0, the outer loop generates the current commands id* and iq*. The inner loop produces the dq-axis reference voltages uref_d and uref_q. And then, the reference voltage uref_j for phase j is derived by the inverse dq transformation. Fig. 5(c) shows the CCSC in detail, iuj and ilj are the upper and lower arm currents in phase j, respectively. icir_d and icir_q are the dq-axis components of circulating currents, respectively. The CCSC produces the dqaxis reference voltages ucir_d and ucir_q, then the reference voltage ucir_j for phase j is derived by the inverse dq transformation. Finally, the upper arm reference voltage and lower arm reference voltage can be obtained as uref_uj=(ucir_j−uref_j) and uref_lj=(ucir_j+uref_j), where the ucir_j is the reference for phase j produced by the CCSC, as shown in Fig. 5(a). Finally, the upper arm reference and lower arm reference signals can be obtained as __ __ 2/ 2/ ref uj ref uj dc ref lj ref lj dc y u U y u U =   =   (7) which are used for the upper arm and the lower arm in phase j of the MMC, respectively. B. Control of Machine-Side CCV The CCV is employed to control the machine and Fig. 6 shows the vector control of the CCV. imd, imq and Lmd, Lmq are the dq-axis components of machine currents and inductances, respectively. ψ is the permanent magnet flux linkage. θ is the electrical rotor position angle of the machine. According to the command ωm*, the outer loop produces the q-axis current command imq*. The d-axis current command imd* is 0. The inner loop produces the dq-axis reference voltages uref_md and uref_mq to make the current imd and imq follow their commands, and then three-phase reference voltage uref_mj is derived from the inverse dq transformation. According to [23], the relationship among CCV’s input phase voltage amplitude UP, output phase voltage amplitude Um, and modulation index r is 2 33 m P U rU  = (8) Substituting (8) into (6), the reference signal yref_mj can be derived as _ _ _ 22 3 33 ref mj ref mj ref mj L P y u u U U  == (9) where UL is the CCV’s input line voltages uab, ubc, uca. The yref_mj is used for the CCV to control the machine. IV. DISCUSSION OF PROPOSED DRIVE SYSTEM A. Studied Drive System In this paper, a 6.6 kV/5 MW low-speed PMSM based drive system is studied, which is normally operated at the rated situation in applications such as conveyor. The system parameters are shown in Table I. yref_ lj yref_ uj ij uj iuj ilj CCSC Output Voltage Control _ + + + uref_ j abc / dq ucir_ j uref_ uj uref_ lj ωgt Upper arm of phase j Lower arm of phase j 2 Udc 2 Udc (a) + _ + _ _ + + + + _ + _ _ + + + ud * uq * ud uq id iq id * iq * ud uq uref_d + + PI PI ωgL ωgL PI PI uref_q uref_ j ωgt ωgCcom ωgCcom dq to abc iod + ioq + (b) _ + + _ + _ + + icir_ducir_d PI PI 2ωgL 2ωgL ucir_q ucir_ j dq to abc icir_q abc to dq ωgt 1 2 0 0 iuj ilj ++ ωgt (c) Fig. 5. (a) Overall control diagram of the grid-side MMC. (b) Output voltage control diagram of the MMC. (c) Circulating current suppression control diagram of the MMC. +_ + _ _ + + + ωmψ + PI PI imd imq imq * θ PI + _ ωm * ωm uref_mj ωmLmd ωmLmq imd * dq to abc uref_md uref_mq yref_mj 2 3L U  CCV Fig. 6. Control diagram of the CCV. Authorized licensed use limited to: University of York. Downloaded on July 15,2022 at 10:49:23 UTC from IEEE Xplore. Restrictions apply. 0278-0046 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2022.3169851, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS TABLE I PARAMETERS OF PROPOSED MACHINE DRIVE SYSTEM Parameter Value PMSM Rated stator rms line voltage (kV) 6.6 Rated rms current (A) 462 Number of pole pairs 12 Rated speed (r/min) 50 Rated frequency (Hz) 10 Rated displacement factor 0.95 MMC DC grid voltage (kV) 20 Rated rms line voltage (kV) 8.9 Rated frequency (Hz) 100 SM number per arm n 12 SM capacitance (mF) 2.76 Arm inductance (mH) 3 Compensation capacitance (mF) 0.1 Carrier frequency (kHz) 1 CCV Commutation inductance (mH) 0.63 B. Commutation Inductor LT of CCV The commutation inductor LT, as shown in Fig. 3, is adopted to limit the rising rate of the CCV’s thyristor current during commutation between the thyristors. Taking the commutation in the positive converter of phase unit a as an example, Fig. 7 shows the commutation from outgoing thyristor Thp3a to incoming thyristor Thp1a in the commutation period μ, where the Thp3a’s current iTp3a is gradually reduced, the Thp1a’s current iTp1a is gradually increased, and the IT=iTp1a+iTp3a is nearly a constant. According to (4) and (5), the IT can be obtained as 0 iT 0 u uaub uc μδ α ua+uc 2 π IT iTp3a iTp1a ωgt ωgt ωgtq Commutation period Turn-off Fig. 7. Commutation from Thp3a to Thp1a. cos sin arcsin Tm II r    =−     (10) The rising rate of the thyristor current iT during commutation period μ is =2 TT g di I f dt   (11) with 4 =arccos cos g T T L f L I U      −−   (12) It can be observed that along with the increase of the commutation inductor LT, the diT/dt will reduce; along with the reduction of LT, the diT/dt will increase. Normally, the maximum diT/dt appears when the CCV works at the rated situation. According to (10) and (11), the diT/dt is related to α for the given LT and fg. Fig. 8(a) shows the range of α for the positive converter in phase unit a under various phase angle ωmt of uma, which is derived from Table I. Fig. 8(b) shows the diT/dt under various phase angles ωmt of ua and various fg, where LT=0.63 mH. It can be observed that the diT/dt reaches its minimum value when phase angle ωmt is close to π/2, and the diT/dt increases when the ωmt is far from π/2. The maximum diT/dt under various fg are all close to 10 A/μs. Taking the thyristor Infineon T2871N [25] as an example, whose nominal diT/dt is 10 A/μs. In order to ensure that the maximum diT/dt does not exceed the nominal value, LT should be more than 0.63 mH. 100 300 500 700 900 4 6 8 10 12 ωmt (rad) diT /dt (A/μs) ωmt (rad) fg (Hz) 0 α (rad) π λλ+π Positive converter operation range λ λ+π 10 A/us LT=0.63mH 0.32 3.46 π 4 π 23π 45π 4 π 4 π 2 3π 4 0 π5π 4 3π 4 π 2 π 4 (a) (b) Fig. 8. (a) The change of α in the operation range of positive converter. (b) diT/dt under various fg when LT=0.63 mH. C. Operation Frequency fg of MMCs In Fig. 7, the extinction angle δ is = ( )     −+ (13) The extinction time tδ is 1 2g tf    = (14) According to (13) and (14), it can be observed that along with the increase of (α+μ) and fg, the tδ will reduce, which is critical for the commutation. According to (5) and (12), (α+μ) can reach the maximum at rated power, which will result in the minimum δ. Taking the positive converter in phase unit a as an example, and according to (14), Fig. 9(a) shows the tδ in the operation range of positive converter under rated situation, where various fg are considered. Based on Fig. 9(a), the minimum extinction time tδ_min under various fg can be obtained, as shown in Fig. 9(b). Along with the increase of fg, the tδ_min will reduce, and vice versa. In order to avoid commutation failure, the minimum tδ_min of the thyristor must be more than the thyristor’s turn-off time tq. As a result, according to Fig. 9(b), the maximum fg should meet ( = ) |_min q g_max g t t ff   (15) The minimum fg of CCV is limited by its output frequency fm. Referring to [26], the minimum fg in three-pulse half-wave CCV should be 6 g_min m ff (16) Authorized licensed use limited to: University of York. Downloaded on July 15,2022 at 10:49:23 UTC from IEEE Xplore. Restrictions apply. 0278-0046 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2022.3169851, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS For the system in Table I, the thyristor Infineon T2871N [25] is considered, whose tq is 0.55 ms. According to Fig. 9(b) and (15), there is fg_max≤372 Hz. The rated frequency fm of the machine is 10 Hz. According to (16), there is fg_min≥60 Hz. Although a higher fg brings smoother output current, it requires higher sampling frequency. Here, the rated fg is set as 100 Hz. D. Compensation Capacitor Ccom of MMCs A compensation capacitor Ccom, as shown in Fig. 2, is adopted in the MMC, whose capacitive reactive power is 2 1 =2 NC g com L Q C U  (17) The Ccom is used to compensate the inductive reactive power QNV of the CCV at rated situation, which is caused by the CCV and results in the lagging displacement angle φN between the CCV’s input currents ioa, iob, ioc and phase voltages ua, ub, uc. Here, the inductive reactive power QNV of the CCV at rated can be calculated as = tan NV NV N QP  (18) where PNV is the rated power at the input side of the CCV. Neglecting the power loss in the CCV, the PNV equals to the rated power at the ac side of the machine as 3 = cos 2 NV mN mN P U I  (19) where UmN and ImN are the amplitude of machine’s rated phase voltage and current, respectively. According to (17)~(18), the Ccom can be obtained as 2 2 tan =NV N com gL P CU   (20) Substituting Table I into (20), the Ccom in the system can be obtained as 0.1 mF. E. Device Current Stress of MMCs Suppose that the circulating current in the MMC is suppressed by the CCSC, the upper arm current iuj and the lower arm current ilj in phase j of the MMC, as shown in Fig. 2, can be expressed as 32 32 j dc uj j dc lj i i i i i i =+    =−   (21) where idc is the dc current. The ac-side current ij in phase j is j cj oj i i i=+ (22) with j cj com du iCdt = (23) where icj is the compensation capacitor current, which mainly consists of the fundamental-frequency component. ioj is the output current in phase j. Due to the CCV, the MMC’s output current ioj contains fundamental-frequency component and harmonic components. Fig. 10(a) shows the frequency spectrum of ioj at rated situation, which is derived from the system in Table I. It can be observed that the frequencies of the harmonics mainly include 2fg±3fm, 4fg±3fm, 5fg & 5fg±6fm, 7fg & 7fg−6fm. Fig. 10(b) shows the frequency spectrum of ij at rated situation, whose harmonics are almost the same to those in ioj, as shown in Fig. 10(a). The amplitude of fundamental component in Fig. 10(b) is less than that in Fig. 10(a), because its reactive component is compensated by Ccom. 0100 200 300 400 500 600 700 Frequency (Hz) 0 0.2 0.4 0.6 0.8 1 1.2 0100 200 300 400 500 600 700 Frequency (Hz) 0 0.2 0.4 0.6 0.8 1 1.2 Amplitude (p.u. of ImN) 2fg ± 3 fm 4fg ± 3 fm Fundamental component 7fg &7fg 6fm 5fg & 5f g±6fm Harmonic components cosφN 0.21 0.14 0.13 0.08 Fundamental component 0.21 0.14 0.13 0.08 1 Amplitude (p.u. of ImN) (a) (b) Fig. 10. (a) Frequency spectrum of ioj at rated situation. (b) Frequency spectrum of ij at rated situation. Fig. 11 shows the peak value of MMC’s arm currents under various machine speeds, which is derived from the system in Table I. It can be seen that along with the increase of machine speed, the current peak value also increases. Fig. 11 also shows the current peak value of the MMC based machine drive system with square-wave circulating current injection method [11], whose current peak value is the minimum among various circulating current injection methods. It can be observed that the device current stress in the proposed machine drive system is much lower than that in the circulating current injection method, because the proposed method does not need to inject high-amplitude circulating currents. Machine speed (p.u.) Peak of arm current (kA) Circulating Current Injection [11]Proposed 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 1.2 0.45 0.39 0.34 0.27 0.71 0.78 0.86 0.97 1.12 0.51 Fig. 11. Comparison of arm current peak value between proposed method and current injection method [11]. F. SM Capacitor Csm of MMCs Taking the upper arm of phase a for example, according to (21) and Fig. 10(b), the rated arm current iuaN can be simplified 100300500700900 0 1 2 3 4 5 0 π tδ (ms) ωmt (rad) fg (Hz) 0.55 ms 100 300 500 700 900 0 0.7 1.4 2.1 0.55 ms fg (Hz) tδ_min (ms) 372 Hz 5π 4 3π 4 π 2 π 4 λ+π (a) (b) Fig. 9. (a) tδ under various fg in the operation range of positive converter. (b) tδ_min under various fg. Authorized licensed use limited to: University of York. Downloaded on July 15,2022 at 10:49:23 UTC from IEEE Xplore. Restrictions apply. 0278-0046 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2022.3169851, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS as (24), where only the fundamental component and harmonic components 2fg±3fm and 4fg±3fm are considered. 2 2 2 2 2 2 4 4 4 4 4 4 32 1 = + cos sin ( ) 32 1[ sin ( ) sin ( ) ] 2 1[ sin ( ) sin ( ) ] 2 d c N a N uaN d c N m N N g m N n n n p p p m N n n n p p p ii i iIt I k t k t I k t k t          =+ + + + + + + + + (24) where idcN is rated dc current. iaN is the rated ac-side current of phase a. k2n, k2p, k4n, k4p are respectively the p.u. values of harmonics 2fg−3fm, 2fg+3fm, 4fg−3fm and 4fg+3fm as shown in Fig. 10(b). ω2n, ω2p, ω4n, ω4p are respectively the angular frequency of these harmonics. φ2n, φ2p, φ4n, φ4p are respectively the phase angles of these harmonics. According to [27], the SM capacitor current in upper arm of phase a can be expressed as _ 1 2 r e f u a cuaN uaN y ii − = (25) Normally, the circulating current control has little effect on the yref_ua [28]. Therefore, it can be expressed as yref_ua=m·sin(ωgt), where m is the modulation index of MMC. Combining (24) and (25), the rated capacitor voltage fluctuation ∆ucuaN can be obtained as (26). The SM capacitor voltage fluctuation ratio ε can be defined as [] / cua N dc Ma x u Un   = (27) Fig. 12 shows the relationship between ε and Csm in the MMC of the proposed system, which is derived from (24)~(27) and Table I. It can be seen that along with the increase of Csm, ε will be reduced; along with the reduction of Csm, ε will be increased. Fig. 12 also shows relationship between the ε and Csm in the HMMC based machine drive system [15]. It can be observed that for the same capacitor voltage fluctuation, the required capacitance in the proposed machine drive system is far less than that in the HMMC based machine drive system. According to Fig. 12, the Csm of 2.76 mF corresponding to the capacitor voltage fluctuation of 2% is selected in the proposed system. V. SIMULATION STUDIES To verify the proposed machine drive system, the system simulation is conducted with professional tool PLECS. The system diagram is shown in Fig. 1 and the system parameters are shown in Table I. A. Performance of proposed system Fig. 13 shows the performance of the proposed machine drive system, where the machine operates under rated load from standstill to the rated speed. Fig. 13(a) shows the machine speed. The machine accelerates at 1s from standstill to 0.5 p.u. speed and accelerates at 2.5s from 0.5 p.u. to rated speed. Fig. 13(b) shows the machine line voltage. Fig. 13(c) shows the machine currents, whose frequency changes from 0 to 10 Hz. Fig. 13(d) shows the electrical torque. The torque ripple increases with the speed and reaches the maximum value 0.10 p.u. at rated situation. Fig. 13(e) shows the line voltages of the MMC, whose frequency fg is 100 Hz. Fig. 13(f) shows the output current of the MMC. Fig. 13(g) shows the MMC’s arm currents, whose peak value rises with with the increase of the machine speed. The peak of arm current is 514 A. Fig. 13(h) shows the SM capacitor voltages of upper and lower arm in phase a of MMC. The voltage fluctuation rises with the arm current, ranging from 1590 to 1749 V at the rated speed. The voltage fluctuation ratio is less than 5% when the Csm is 2.76 mF, which verifies the analysis in Fig. 12. Fig. 14 shows the harmonic spectrums of machine line voltage and current at rated situation. It can be observed that the main harmonic components of machine voltage are in the sidebands of 3fg and 6fg. The main harmonic components of machine current are in the sidebands of 3fg. B. Comparison with traditional MMC Fig. 15 shows the comparison of capacitor voltages between traditional MMC based drive system and proposed system, where the SM capacitance of traditional MMC is 7 times (19.32 mF) of proposed system (2.76 mF). Fig. 15(a) and (b) show the capacitor voltage fluctuation at 0.2 p.u. speed under rated load. Fig. 15(c) and (d) show the capacitor voltage fluctuation at rated situation. It can be observed that the voltage fluctuation of 42 42 4 4 4 4 2 2 2 2 4 4 2 2 2 cos ( ) cos sin (2 ) 1 = = cos cos( ) 6 4 4 = cos( ) cos( ) cos ( ) cos ( ) 4 sin[( 8 d c N g N g mN c u a N c u a N N g s m g s m s m g pp mN n n n n p p p p n n s m n p p n n mN sm m i t m t I u i d t t C C C kk I k k t t t t C k mI C                    − +     − + + + + + + +    +  2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 44 ) ] sin [( ) ] sin[( ) ] sin[( ) ] ( ) ( ) ( ) ( ) sin[( ) ] sin[( ) ] sin [( ) ] ++ ( ) ( ) ( n g n n n g n p p g p p p g p n g n g p g p g n n g n n n g n p p g p n g n g t k t k t k t k t k t k t                                   + + − + + + − + − + − + − + −   + + − + + + − +− 4 4 4 44 sin[( ) ] ) ( ) p p g p p g p g kt        −+  − +−   (26) ε (%) 510 15 20 25 30 Proposed HMMC in [15] Csm (mF) 0 10 20 30 40 1.38 0.92 0.69 0.55 2.76 16.81 11.21 8.40 6.72 33.62 Fig. 12. Comparison of SM capacitance between MMC in proposed system and HMMC [15]. Authorized licensed use limited to: University of York. Downloaded on July 15,2022 at 10:49:23 UTC from IEEE Xplore. Restrictions apply. 0278-0046 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2022.3169851, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS traditional MMC increases as machine speed reduces, which is 42.88% at 0.2 p.u. speed. Compared to traditional MMC, proposed system can operate stably at low speed with lower SM capacitance, and the voltage fluctuation is less than 5% in the whole speed range. 0 2 4 6 8 10 0 0.2 0.4 0.6 0.8 1 0100 200 300 400 500 600 700 Frequency (Hz) Amplitude (kV) Amplitude (kA) 0100 200 300 400 500 600 700 Frequency (Hz) fm (10 Hz) Sidebands of 3fg Sidebands of 6fg fm (10 Hz) Sidebands of 3fg (a) (b) Fig. 14. Harmonic spectrum at rated situation. (a) Machine line voltage. (b) Machine current. 1 1.25 1.5 1.75 2 Time (s) Csm Voltage (kV) ucua ucla 1709 V (+2.59%) 1628 V ( 2.24%) Csm=2.76 mF 1.5 1.6 1.7 1.8 1.9 0.5 1 1.5 2 2.5 3 1 1.25 1.5 1.75 2 Time (s) Csm Voltage (kV) ucua ucla 2380 V (+42.88%) 1077 V ( 35.36%) Csm=19.32 mF (a) (b) 1.4 1.6 1.8 2 1 1.25 1.5 1.75 2 Time (s) Csm Voltage (kV) ucua ucla 1749 V (+4.94%) 1590 V ( 4.60%) Csm=2.76 mF 1.4 1.6 1.8 2 1 1.25 1.5 1.75 2 Time (s) Csm Voltage (kV) ucua ucla 1769 V (+6.2%) 1529 V ( 8.24%) Csm=19.32 mF (c) (d) Fig. 15. Comparison of capacitor voltage fluctuation. (a) Traditional MMC at 0.2 p.u. speed. (b) Proposed system at 0.2 p.u. speed. (c) Traditional MMC at rated speed. (d) Proposed system at rated speed. VI. EXPERIMENTAL STUDIES A prototype of the proposed machine drive system is built in the lab, as shown in Fig. 16. A dc power supply is used to support the dc voltage. The ac side of the MMC is connected to the CCV. The output side of CCV is connected to the PMSM. The control algorithm is implemented by digital signal processor (DSP) and the drive signals are transferred to driving circuit of each device by optical fibers. The system parameters are listed in Table II. DC power supply DSP controllers CCV PMSM MMC Fig. 16. Photo of experimental platform. (a) Machine speed (r/min) Time (s) 0.5 11.5 22.5 33.5 4 0 20 40 60 rated speed (b) Machine voltage (kV) Time (s) 0.5 1 1.5 2 2.5 3 3.5 4 -20 -10 0 10 20 umab (c) Machine current (kA) Time (s) -4 -3 -2 -1 0 1 0.5 1 1.5 2 2.5 3 3.5 4 2.1 2.2 2.3 3.5 3.6 3.7 0.7 0.8 0.9 -1 0 1 -1 0 1 -1 0 1ima imb imc (d) Electrical torque (p.u.) Time (s) 0.5 1 1.5 2 2.5 3 3.5 4 2.1 2.2 2.3 3.5 3.6 3.70.7 0.8 0.90.8 1.0 1.2 0.8 1.0 1.2 0.8 1.0 1.2 0 0.2 0.4 0.6 0.8 1 1.2 Ripple=0.10 p.u.Ripple=0.07 p.u. Ripple=0.04 p.u. (e) -60 -40 -20 0 20 MMC line voltage (kV) Time (s) 0.5 11.5 22.5 33.5 4 2.1 2.15 3.5 3.550.7 0.75 -15 0 15 -15 0 15 -15 0 15 uab ubc uca (f) MMC output current (kA) Time (s) 0.5 11.5 22.5 33.5 4 2.1 2.15 3.5 3.550.7 0.75 -1 0 1 ioa iob ioc -1 0 1 -1 0 1 -4 -3 -2 -1 0 1 THD=30.03% THD=30.36% THD=36.77% (g) -20 -10 0 10 MMC arm current (kA) Time (s) 0.5 11.5 22.5 33.5 4 2.1 2.15 3.5 3.550.7 0.75 514 A -0.6 0 0.6 -0.6 0 0.6 -0.6 0 0.6 iua ila (h) 1.2 1.4 1.6 1.8 Csm voltage (kV) Time (s) 0.5 11.5 22.5 33.5 4 2.1 2.15 3.5 3.550.7 0.75 1.5 1749 V 1590 V 1.6 1.7 1.8 1.5 1.6 1.7 1.8 1.5 1.6 1.7 1.8 Fig. 13. Simulation waveforms. (a) Machine speed. (b) Machine line voltage. (c) Machine currents. (d) Electrical torque. (e) MMC line voltages. (f) MMC output currents. (g) Arm currents of phase a. (h) SM capacitor voltages of phase a. Authorized licensed use limited to: University of York. Downloaded on July 15,2022 at 10:49:23 UTC from IEEE Xplore. Restrictions apply. 0278-0046 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2022.3169851, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS TABLE II PARAMETERS OF EXPERIMENTAL SYSTEM Parameter Value PMSM Rated stator rms line voltage (V) 44 Rated rms current (A) 5.66 Number of pole pairs 4 Rated speed (r/min) 150 Rated frequency (Hz) 10 Rated displacement factor 0.95 MMC DC voltage (V) 140 Rated rms line voltage (V) 62 Rated frequency (Hz) 100 SM number per arm n 4 SM capacitance (mF) 2.7 Arm inductance (mH) 0.5 Compensation capacitance (mF) 0.18 Carrier frequency (kHz) 5 CCV Commutation inductance (mH) 1 A. Steady State Operation Fig. 17 shows the shows the line voltages of the MMC, whose frequency is 100Hz. Fig. 18 shows the steady state operation at standstill under rated load. Fig. 19 shows the steady state operation at 0.5 p.u. speed under rated load. Fig. 20 shows the steady state operation at rated speed under 0.5 p.u. load. Fig. 21 shows the steady state operation at rated speed under rated load. uab ubc uca Fig. 17. Experimental waveforms of uab, ubc, uca (50 V/div). Fig. 18(a), Fig. 19(a), Fig. 20(a) and Fig. 21(a) show the machine voltages umab, umbc, umca. Fig. 18(b), Fig. 19(b), Fig. 20(b) and Fig. 21(b) show the machine currents ima, imb, imc. Under rated load in Figs. 19~20, the fundamental frequency machine current amplitude is 8 A. Under 0.5 p.u. load in Fig. 21, the fundamental frequency machine current amplitude is 4 A. Fig. 18(c), Fig. 19(c), Fig. 20(c) and Fig. 21(c) show the spectrum of machine line voltage, where the main harmonic components are in the sidebands of 3fg and 6fg. Fig. 18(d), Fig. 19(d), Fig. 20(d) and Fig. 21(d) show the spectrum of machine current, where the main harmonic components are in the sidebands of 3fg. Fig. 18(e), Fig. 19(e), Fig. 20(e) and Fig. 21(e) show the MMC’s output current ioa, iob, ioc, whose THD reaches the maximum 34.06% at rated situation. Fig. 18(f), Fig. 19(f), Fig. 20(f) and Fig. 21(f) show the arm currents and the SM capacitor voltages in phase a of the MMC. It can be observed that the peak of arm current increases as the machine speed and torque increase. At rated situation, the peak of arm current umab umbc umca ima imb imc (a) (b) 0 2 4 6 8 10 0100 200 300 400 500 600 700 Frequency (Hz) Amplitude (V) Amplitude (A) 0 20 40 60 80 0100 200 300 400 500 600 700 fm (0 Hz) 3fg 6fg fm (0 Hz) 6fg Frequency (Hz) (c) (d) ioa iob ioc THD=28.54% 35.5 V 34.7 V 35 V ila iua 3.5 A ucua ucla (e) (f) Fig. 18. Experimental waveforms at standstill. (a) umab, umbc, umca (100 V/div). (b) ima, imb, imc (5 A/div). (c) Spectrum of umab. (d) Spectrum of ima. (e) ioa, iob, ioc (5 A/div). (f) iua, ila, (5 A/div), ucua, ucla (1 V/div). umab umbc umca ima imb imc (a) (b) Sidebands of 3fg Sidebands of 6fg fm (5 Hz) Sidebands of 3fg 0 2 4 6 8 10 0100 200 300 400 500 600 700 Frequency (Hz) Amplitude (V) Amplitude (A) 0 20 40 60 80 0100 200 300 400 500 600 700 fm (5 Hz) Frequency (Hz) (c) (d) ioa iob ioc THD=28.18% 35.6 V 34.6 V 35 V ila iua 4 A ucua ucla (e) (f) Fig. 19. Experimental waveforms at 0.5 p.u. speed. (a) umab, umbc, umca (100 V/div). (b) ima, imb, imc (5 A/div). (c) Spectrum of umab. (d) Spectrum of ima. (e) ioa, iob, ioc (5 A/div). (f) iua, ila, (5 A/div), ucua, ucla (1 V/div). Authorized licensed use limited to: University of York. Downloaded on July 15,2022 at 10:49:23 UTC from IEEE Xplore. Restrictions apply.