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Relationship between SVPWM and carrier‐based PWM of eight‐switch three‐phase inverter

2015; Institution of Engineering and Technology; Volume: 51; Issue: 13 Linguagem: Inglês

10.1049/el.2015.0356

1350-911X

Yong‐Chao Liu, Xinglai Ge, Xiaoyun Feng, Rongjun Ding,

Silicon Carbide Semiconductor Technologies

Electronics LettersVolume 51, Issue 13 p. 1018-1019 Power electronics, energy conversion and sustainabilityFree Access Relationship between SVPWM and carrier-based PWM of eight-switch three-phase inverter Yong-Chao Liu, Yong-Chao Liu School of Electrical Engineering, Southwest Jiaotong University, Chengdu, 610031 Sichuan, People's Republic of ChinaSearch for more papers by this authorXing-Lai Ge, Corresponding Author Xing-Lai Ge xlgee@163.com School of Electrical Engineering, Southwest Jiaotong University, Chengdu, 610031 Sichuan, People's Republic of ChinaSearch for more papers by this authorXiao-Yun Feng, Xiao-Yun Feng School of Electrical Engineering, Southwest Jiaotong University, Chengdu, 610031 Sichuan, People's Republic of ChinaSearch for more papers by this authorRong-Jun Ding, Rong-Jun Ding School of Electrical Engineering, Southwest Jiaotong University, Chengdu, 610031 Sichuan, People's Republic of ChinaSearch for more papers by this author Yong-Chao Liu, Yong-Chao Liu School of Electrical Engineering, Southwest Jiaotong University, Chengdu, 610031 Sichuan, People's Republic of ChinaSearch for more papers by this authorXing-Lai Ge, Corresponding Author Xing-Lai Ge xlgee@163.com School of Electrical Engineering, Southwest Jiaotong University, Chengdu, 610031 Sichuan, People's Republic of ChinaSearch for more papers by this authorXiao-Yun Feng, Xiao-Yun Feng School of Electrical Engineering, Southwest Jiaotong University, Chengdu, 610031 Sichuan, People's Republic of ChinaSearch for more papers by this authorRong-Jun Ding, Rong-Jun Ding School of Electrical Engineering, Southwest Jiaotong University, Chengdu, 610031 Sichuan, People's Republic of ChinaSearch for more papers by this author First published: 08 June 2015 https://doi.org/10.1049/el.2015.0356Citations: 15AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Space-vector pulse-width modulation (SVPWM) and carrier-based PWM (CBPWM) of eight-switch three-phase inverters (ESTPIs) which are the post-fault reconfigured topologies for the three-level neutral-point-clamped inverter with an open-circuit fault in a leg are introduced. On the basis of the PWM regular sampling method, the modulating functions of CBPWM which are equivalent to SVPWM of ESTPIs are derived, therefore the relationship between SVPWM and CBPWM of ESTPIs is revealed. The validity of the theoretical analysis is verified by experimental results. Introduction Compared with the two-level inverter, the three-level neutral-point-clamped (NPC) inverter has many advantages, such as less du/dt stress and lower EMI in systems [1]. However, the increase in the number of switch devices, which are one of the most vulnerable components in converters, leads to a reduction in the reliability of the three-level NPC inverter, and the open-circuit fault in a leg will seriously threaten the safe operation of the overall system [2, 3]. Therefore, to maintain the working performance under a leg open-circuit fault condition as far as possible, the three-level NPC inverter can be reconfigured to the topology the named eight-switch three-phase inverter (ESTPI) as shown in Fig. 1a by isolating the faulty leg (taking the leg a as an example) [4, 5]. Fig 1Open in figure viewerPowerPoint Topologies and voltage vector distribution of ESTPI a Topology of ESTPI b Voltage vector distribution of ESTPI Space-vector pulse-width modulation (SVPWM) and carrier-based PWM (CBPWM) are two strategies that have been widely used to achieve PWM control. Although starting from different points of view, the nature of the control principle of the two strategies is the same, and the relationship between SVPWM and CBPWM provides a platform not only to transform from one to another, but also to develop different PWM modulators [6]. To reveal the relationship between SVPWM and CBPWM of the ESTPI, based on the PWM regular sampling method, the modulating functions of CBPWM which are equivalent to SVPWM of the ESTPI are derived in this Letter. Theoretical analysis As shown in Fig. 1a, assuming that Vd is constant, Vc1 = Vc2 = Vd/2. Owing to the DC-link midpoint in connection with phase a, Vao is always zero. For convenient analysis, the pole voltage Vxo (x = b, c) for two normal legs described by the DC-link voltage Vd and the switching function Sx (equal to '1', '0' or '−1', where '1' means TX1 and TX2 are on and TX3 and TX4 are off, '0' means TX2 and TX3 are on and TX1 and TX4 are off and '−1' means TX3 and TX4 are on and TX1 and TX2 are off) can be depicted as (1)The basic voltage vector Vs in two-phase stationary coordinate, namely the αβ-plane, can be obtained by the following expression: (2)According to expressions (1) and (2), because of having nine different switch combinations, there are two medium vectors, six small vectors and one zero vector for the ESTPI in the αβ-plane as shown in Fig. 1b. Taking switching losses limitations into account, it is a good choice to use the six small vectors and one zero vector to achieve the SVPWM strategy, and the αβ-plane is divided into six sectors as shown in Fig. 1b by the seven basic vectors [5]. In any sector, as shown in Fig. 1b, the reference voltage vector labelled Vr should be synthesised by two adjacent small vectors and a zero vector. Therefore, based on the voltage–second balancing principle, the duration time of the three vectors in the six sectors can be obtained by the following expression: (3)where Ts is the switching period, T1, T2 and T0 are the duration times of two adjacent small vectors and zero vectors, respectively, θ is the phase angle of Vr and symbol n represents the sector number. Defining Vr(t), V1(t) and V2(t) as the modulating wave, upper and lower high-frequency triangular carrier wave, respectively, and assuming that the amplitude of the triangular wave is 1, based on the PWM regular sampling method, the principle of CBPWM of the ESTPI is presented in Fig. 2a. Comparing Vr(t) with V1(t) or V2(t), there are three possible results as shown in Fig. 2a, and the relationship between these comparison results and the on–off conditions of power switches are presented in Table 1. Fig 2Open in figure viewerPowerPoint Principle of CBPWM of ESTPI and timing sequence of switching signal in sector Ia Principle of CBPWM of ESTPI b Timing sequence of switching signal in sector I Table 1. Relationship between comparison results and on–off conditions of power switches Comparison result Vr(t) > V1(t) V1(t) > Vr(t) > V2(t) V2(t) > Vr(t) Duration time δ1 δ2 δ3 Switching state Sx = 1 Sx = 0 Sx = −1 Closed power switches Tx1, Tx2 Tx2, Tx3 Tx3, Tx4 According to Table 1, the on–off condition of Tx1 only depends on the comparison results between Vr(t) and V1(t), the on–off condition of Tx4 only depends on the comparison results between Vr(t) and V2(t) and the on–off conditions of Tx1 and Tx2 are always opposite to Tx3 and Tx4, respectively. Therefore, in order to obtain the modulating functions of CBPWM which is equivalent to SVPWM, as shown in Fig. 2a, Vr(t) can be decomposed into Vr+(t) which is the component that Vr(t) is more than 0 and Vr−(t) which is the component that Vr(t) is less than 0. Thus the on–off conditions of Tx1 and Tx3 rely on the comparison results between Vr+(t) and V1(t) and the on–off conditions of Tx2 and Tx4 rely on the comparison results between Vr−(t) and V2(t). Taking the leg b as an example, according to expression (3) and Fig. 2b, in sector I, δ1 = 0 and δ3 = T1. According to Fig. 2, the two components of the modulating wave of leg b labelled Vrb+(t) and Vrb−(t) in sector I can be written as (4)Substituting (3) into (4), Vrb+(t) and Vrb−(t) in sector I can be obtained by the following expression: (5)where m = 2|Vr|/Vd is defined as the modulation index. Fig 3Open in figure viewerPowerPoint Experimental results a Output line voltage (SVPWM) b Output line voltage (CBPWM) c Spectrum of Vab (SVPWM) d Spectrum of Vab (CBPWM) e Spectrum of Vbc (SVPWM) f Spectrum of Vbc (CBPWM) g Spectrum of Vca (SVPWM) h Spectrum of Vca (CBPWM) Similarly, Vrb+(t) and Vrb−(t) of other sectors can be derived. Therefore, in a sampling period, Vrb+(t) and Vrb−(t) can be written as (6) (7)By combining expression (6) with (7), the modulating wave of leg b named Vrb(t) in a sampling period can be obtained by the following expression: (8)Similarly, the modulating wave of leg c labelled Vrc(t) can be derived. The expression of the modulating functions of CBPWM which is equivalent to the SVPWM of the ESTPI in a sampling period is shown as the following equations: (9)Therefore, the CBPWM which is equivalent to the SVPWM of the ESTPI can be achieved by comparing two sine waves as shown in expression (9) with two high-frequency triangular waves. Experimental results To verify the equivalence of SVPWM and CBPWM whose modulating functions can be written as expression (9), an experimental test was performed with a DSP TMS320F2812 and a dSPACE. The circuit parameters are Vd = 3000 V, Ts = 1 ms and modulation index m = 0.51. The output line voltage of the ESTPI with the SVPWM and the CBPWM strategy and the fast Fourier transform analysis results of them are as shown in Fig. 3. The experimental results indicate that not only the total harmonic distortion but also the harmonic distribution of the output line voltage is much the same. Conclusion On the basis of the PWM regular sampling method, the relationship between SVPWM and CBPWM of ESTPIs is revealed. It is shown that the SVPWM of ESTPIs is a special type of CBPWM which can be achieved by comparing two sine waves of 60° phase difference with two high-frequency triangular waves. The validity of the theoretical analysis is verified by experimental results. Acknowledgments This work was supported by the National Natural Science Foundation of China (grants 51207131 and 51277153), and the National Natural Science Foundation and High Speed Railway Joint Key Foundation Project of China (grant U11344205). References 1Figarado, S., Bhattacharya, T., Mondal, G., Gopakumar, K.: 'Three-level inverter scheme with reduced power device count for an induction motor drive with common-mode voltage elimination', IET Power Electron., 2008, 1, (1), pp. 84– 92 (https://doi/org/10.1049/iet-pel:20070110) 2Song, Y.T., Wang, B.S.: 'Survey on reliability of power electronic systems', IEEE Trans. Power Electron., 2013, 28, (1), pp. 591– 604 (https://doi/org/10.1109/TPEL.2012.2192503) 3Zhang, W.P., Xu, D.H., Enjeti, P.N., Li, H.J., Hawke, J.T., Krishnamoorthy, H.S.: 'Survey on fault-tolerant techniques for power electronic converters', IEEE Trans. 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