Study and analysis of the effects of varied PWM techniques and power sharing ratios on the current ripple in open‐ended, three‐level traction motor drives
2019; Institution of Engineering and Technology; Volume: 10; Issue: 2 Linguagem: Inglês
10.1049/iet-est.2018.5100
ISSN2042-9746
AutoresRishi Menon, Najath Abdul Azeez, Arvind H. Kadam, Sheldon S. Williamson,
Tópico(s)Advanced DC-DC Converters
ResumoIET Electrical Systems in TransportationVolume 10, Issue 2 p. 154-161 Research ArticleFree Access Study and analysis of the effects of varied PWM techniques and power sharing ratios on the current ripple in open-ended, three-level traction motor drives Rishi Menon, Corresponding Author Rishi Menon rishi.menon@ieee.org orcid.org/0000-0002-6913-7385 Department of Electrical, Computer and Software Engineering, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, ON, L1G 0C5 CanadaSearch for more papers by this authorNajath Abdul Azeez, Najath Abdul Azeez Department of Electrical, Computer and Software Engineering, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, ON, L1G 0C5 CanadaSearch for more papers by this authorArvind H. Kadam, Arvind H. Kadam orcid.org/0000-0003-4008-0765 Department of Electrical, Computer and Software Engineering, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, ON, L1G 0C5 CanadaSearch for more papers by this authorSheldon S. Williamson, Sheldon S. Williamson orcid.org/0000-0002-4617-5418 Department of Electrical, Computer and Software Engineering, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, ON, L1G 0C5 CanadaSearch for more papers by this author Rishi Menon, Corresponding Author Rishi Menon rishi.menon@ieee.org orcid.org/0000-0002-6913-7385 Department of Electrical, Computer and Software Engineering, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, ON, L1G 0C5 CanadaSearch for more papers by this authorNajath Abdul Azeez, Najath Abdul Azeez Department of Electrical, Computer and Software Engineering, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, ON, L1G 0C5 CanadaSearch for more papers by this authorArvind H. Kadam, Arvind H. Kadam orcid.org/0000-0003-4008-0765 Department of Electrical, Computer and Software Engineering, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, ON, L1G 0C5 CanadaSearch for more papers by this authorSheldon S. Williamson, Sheldon S. Williamson orcid.org/0000-0002-4617-5418 Department of Electrical, Computer and Software Engineering, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, ON, L1G 0C5 CanadaSearch for more papers by this author First published: 01 June 2020 https://doi.org/10.1049/iet-est.2018.5100AboutSectionsPDF 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 A dual inverter feeding an open-ended motor load is a feasible solution for high-power traction applications. The topology supplied from isolated DC sources has a power-sharing capability. Different pulse width modulation (PWM) techniques have been proposed for the dual inverter. The performance of these modulation schemes can be compared by analysing the current ripple output of the dual inverter drive. There are various methods in the literature to analyse the ripple content in the output current of the dual inverter. However, the existing work on ripple analysis has been done only for equal power sharing between the isolated DC sources. This study presents an output current ripple analysis for carrier-based PWM techniques for different power-sharing ratios. The variation in the current ripple with varied power-sharing ratios for different PWM techniques is demonstrated. The results to validate the analysis have been obtained using MATLAB/Simulink and real-time simulator. Based on the discussion, an optimal PWM technique under different sharing conditions has been identified. 1 Introduction The demand for high power and high-voltage drives increased the popularity of multilevel inverters. In these topologies, a higher voltage with reduced harmonic distortion and better electromagnetic compatibility can be synthesised from lower voltage inputs. The enhancement in the output quality made the multilevel inverter to be adopted in grid connected systems and motor load applications [1]. There has been an evolution of many multilevel structures, one of which is a dual inverter. This topology feeds an AC machine in which both stator ends are open. Owing to the structural simplicity, modularity, and reported benefits of multilevel operation, this topology has been widely explored for transportation electrification [2]. A dual inverter can be fed from single or isolated DC sources. However, the circulation of zero sequence current can be intrinsically eliminated by powering isolated DC sources to the dual inverter [3]. Moreover, with isolated DC supplies each inverter can be independently modulated with different types of pulse width modulation (PWM) strategies. For electric vehicular systems, it would be feasible to form isolated supplies by splitting the whole battery pack into two equal sub-packs [4]. Being isolated, the DC sources may differ in voltage level or capacity, caused by aging or manufacturing tolerances. Hence, it would be essential to control the power drawn from the DC sources to have balanced operation and prevent the weaker battery pack from being over drained. With power regulation it would also be possible to operate the system as a conventional three-phase drive during a half-bridge fault in one of the two-level inverters. This will make the system more reliable and fault tolerant. The power regulation can be achieved by suitable PWM techniques applied to the dual inverter system [5]. The PWM techniques for the dual inverter can be broadly categorised as space-vector PWM and carrier-based PWM (CBPWM). In each of these, the switching pattern can be continuous or discontinuous. Since both modulation techniques can have similar results [6], CBPWM will be more suitable for the dual inverter due to its reduced computational complexities in digital domain [7, 8]. The PWM techniques play a vital role in the overall performance of the inverter drive. One of the techniques proposed in the literature to evaluate the performance is analysing the ripple content of the motor phase current [9, 10]. The knowledge of ripple content can be used to estimate the torque ripple due to switching as well as the peak current. The latter is used for designing the protection circuitries in the drive systems [11, 12]. In voltage source inverters, each switching state corresponds to a voltage vector. There will be always a difference between the required vector and the applied vector. This error voltage between the reference and the instantaneous output voltage results in the inverter output ripple current [13]. For current ripple analysis, the inductive load can be taken as a leakage inductance circuit, and the cumulative sum of error voltage in a switching cycle will give the magnitude of current ripple [14]. Several methods have been suggested to estimate and reduce the effect of output current ripple for conventional three-phase inverters [15-17], which were extended for multiphase [18, 19] and multilevel inverters [20-23]. Owing to structural similarity with the conventional three-phase inverter, the current ripple in dual inverter topology with isolated DC sources has been extensively investigated. A mathematical approach has been reported in [24], to determine the root mean squared current ripple for different PWM variants. It was suggested that the ripple in the dual inverter can be reduced with a discontinuous PWM technique. A concept of pivot voltage vector and its switching duty cycle can be used to estimate the instantaneous current ripple in three-level inverter, as presented in [23]. A similar method has been used for the dual inverter to evaluate its peak current ripple for centred PWM techniques [25]. In the above literature, the authors emphasised on the ripple analysis for an equal power sharing ratio, i.e. when both inverters share the load power equally. However, the effect of the modulation schemes on the current ripple with varying power sharing ratios has not been presented yet. This study predominantly focuses on the error voltage vector-based current ripple analysis for different power sharing factors in the dual inverter. The analysis is performed for CBPWM techniques which include continuous and discontinuous switching schemes. It has been shown that the current ripple changes with different sharing factors in dual inverter topology. MATLAB/Simulink was used for the analytical study. The PWM control techniques are implemented on Texas Instruments DSP controller kit. For the experimental result, an open-ended 5 kW Induction Motor (IM) with a dual inverter was used. The current ripple output is analysed by processing real-time data using MATLAB and hardware-in-loop. 2 Power sharing in dual inverter The dual inverter shown in Fig. 1 is configured by connecting the six open terminals of an AC machine to the two conventional three-phase inverters. In order to generate a three-level voltage output, each inverter on either side is supplied equal DC voltage. The principle of superposition theorem is applied to obtain the effective pole voltages. The three-level space vector (SV) structure shown in Fig. 2 has 64 voltage vectors, which are formed by the combination of the individual SV of the two inverters. The side length of SV polygon is and each equilateral triangles is . Fig. 1Open in figure viewerPowerPoint Schematic of dual inverter drive with isolated DC sources Fig. 2Open in figure viewerPowerPoint SV diagram for the three-level inverter In the dual inverter fed from isolated DC sources, different power can be delivered to the motor from the individual two-level inverters [23, 24]. The power sharing in this topology based on the voltage levels of isolated DC sources can be realised by offset power sharing and decoupled power sharing, which are discussed in the subsections below. 2.1 Offset power sharing The offset power sharing is a modification of the conventional PWM generation in three-level inverters. The block representation of this technique is shown in Fig. 3. The three-phase components of the reference vector are converted to the modulating waves, which are compared to two level-shifted carrier waves in a contiguous band. Fig. 3Open in figure viewerPowerPoint Block representation of offset power sharing In Fig. 4a, it can be seen that the modulating waves are placed at the centre of the carrier band, which inherently provides a per cycle average power sharing in the dual inverter. It can be observed that the active vectors placed in the centre can be shifted to either of the carriers by adding a common DC offset. This provides a provision for power regulation by moving the modulating waves on either side of the carrier band. The limit of DC offset, , can be expressed as [26, 27] (1) When the value of is , no offset will be applied and the modulating waves will be at the centre of the carrier region. For a positive value of , the offset will shift the modulating wave to the upper carrier zone as shown in Fig. 4b and more power will be fed by Inverter-1 to the load. The opposite will happen when the value of is negative. For better understanding, the carriers used for comparison are shown at a reduced frequency in the figures. Fig. 4Open in figure viewerPowerPoint Modulating waves at compared with carriers (a) For , (b) For 2.2 Decoupled power sharing The decoupled power sharing is realised by splitting the reference vector into two-phase opposed vectors [28] as shown in Fig. 5. The reference vector can be split by a factor , which denotes the power-sharing ratio in the dual inverter. For operation in the linear range, the limit of can be expressed in the terms of modulation index m as [29] (2) and the decoupled reference vectors and for the two inverters can be written as (3) where is the reference vector of the dual inverter. As shown in the block diagram, the orthogonal components of the individual reference vectors, converted to three-phase components, are applied to the modulating signal generator. The output of the modulating signal generator can be continuous or discontinuous signals with instantaneous amplitude proportional to the multiplication factor . The modulating signals are then compared to the carrier wave with the same comparison logic to generate two sets of gate signals for the individual two-level inverters. This is unlike the offset method, in which the comparison logics for the carrier wave are opposite. Fig. 5Open in figure viewerPowerPoint Block representation of decoupled modulation Fig. 6 illustrates the decoupled power-sharing method. When the value of is 0.5, the reference is divided into two equal parts as shown in Fig. 6a, resulting in equal load sharing in the dual inverter [30]. For , the reference is divided unequally as shown in Fig. 6b, resulting in inverter-1 delivering more power to the load. The opposite will happen when . Fig. 6Open in figure viewerPowerPoint Modulating waves at compared with the carrier for different (a) For , (b) For From this section, it can be seen that the power can be regulated in dual inverter using the carrier-based modulation. The factors and are applied based on the desired power sharing between the two-level inverters. In the case of battery powered vehicles, the power regulation in the dual inverter can be based on the difference of instantaneous state-of-charge of the isolated battery packs. 3 Switching sequences for the power-sharing techniques In the CBPWM technique, the instantaneous three-phase references are converted to modulating waves by placing of effective time period in a switching cycle [6, 28]. For the dual inverter, standard clamp, clamp, and triplen harmonic injected (THI) PWM schemes could be used for each inverter. The former two methods are types of discontinuous switching patterns, also known as split clamp and continual clamp PWM schemes, respectively [10], whereas the latter method is a form of continuous switching pattern [8]. When the clamping PWM schemes are used in offset power sharing, it will result in more power being drawn from one of the sources. Since control of power sharing is desired in electric vehicular applications, only THI scheme is considered for offset power sharing. The SV approach is considered to study the switching sequence. For analysis, first sectorial triangle OGI from Fig. 2 is examined and the reference vector at the centre of each sub-triangle (OAB, AHB, AGH, BHI) are considered as shown in Fig. 7a. Figs. 7b–e show the corresponding gating sequence in the dual inverter when power sharing is done using decoupled split clamp (DSC), decoupled continual clamp (DCC), decoupled THI (DTHI) and offset THI (OTHI) PWM schemes. The total switching cycle time period is and the gate signals for inverter-1 and inverter-2 are represented by and , respectively. These sets of waveforms are for unequal power sharing in which inverter-1 is delivering maximum possible share of the load power. Similar waveforms can be drawn for other power-sharing conditions. Fig. 7Open in figure viewerPowerPoint Switching pattern for different voltage vector positions in the first sectorial triangle OGI for different PWM schemes (a) Sub-triangles, (b) DSC, (c) DCC, (d) DTHI, (e) OTHI In the inner sub-triangle OAB, the modulation index is small. It can be seen from the first column of Figs. 7b–e that in all schemes, the active vectors are generated by inverter-1 alone, keeping the inverter-2 clamped to its zero vector state. In the DTHI scheme, inverter-2 is switched from one zero vector state to other. This shows that the entire power has been shifted to inverter-1. When the vector is in the middle sub-triangle AHB and outer sub-triangles AGH and BHI, the overall switching in the dual inverter has increased for the decoupled power-sharing schemes. In the OTHI scheme, for the applied value of , it can be observed that the total switching in the dual inverter is minimum compared to other methods. It is also worth noting that nearest three vectors are always applied in OTHI. This is not the case in decoupled power sharing and the switching vectors used do not form an equilateral triangle. The effect of these switching sequences on the motor phase current is discussed in the next section. 4 Current ripple in dual inverter The various conventional PWM techniques for three-level inverters can be compared in the frequency domain by calculating the total harmonic distortion (THD) in the fundamental output. However, the computation of THD in the frequency domain could be complex. An alternative method for comparison is the time domain analysis in which the error between reference and the applied voltage is analysed [10]. The cumulative addition of error voltages in a switching cycle will give the current error trajectory for an inductive load as expressed below: (4) where is the stator leakage inductance, and are the voltage and current errors, respectively. 4.1 Derivation of current ripple In general, the reference vector can be resolved into the orthogonal stationary components shown in (5) (5) The two sets of three-phase pole voltages due to the application of gate pulses are transformed into and components as given in (6) (6) On applying the superposition principal to the real and imaginary components in the above equations, the applied orthogonal components of the dual inverter become: (7) From (5) and (7), the equations for the error voltage can be written as (8) The error voltages can be resolved to the orthogonal revolving reference frame components, and , using standard Park's transformation. On integrating the error voltages in a switching cycle, the current errors are given as (9) In the equations above, and corresponds to the flux and the torque ripple in the motor, respectively [9]. The difference of the maximum and minimum values of and gives the expression of a peak-to-peak current ripple as (10) 4.2 Current ripple trajectory The error currents derived in (9) can be plotted in a two-dimensional plane as illustrated in Figs. 8 and 9. The current error trajectories for equal and unequal power sharing are represented. All the plots are normalised with respect to the leakage inductance. It can be seen that the double-triangular shape of the dq current ripple changes for the different PWM schemes. In Figs. 8a–d, the ripple trajectories for both sharing conditions corresponding to low values of m are shown. It can be seen that the DTHI scheme is having the highest q-axis ripple and lowest d-axis ripple projection when the sharing is equal. In the unequal case, the OTHI scheme is having the lowest ripple in both axes. Though the magnitudes of ripples for DTHI and OTHI schemes are different, the current error trajectories in both schemes are similar for unequal sharing. Fig. 8Open in figure viewerPowerPoint dq current error plots for equal and unequal sharing at and (a) DSC, (b) DCC, (c) DTHI, (d) OTHI Fig. 9Open in figure viewerPowerPoint dq current error plots for equal and unequal sharing at and (a) DSC, (b) DCC, (c) DTHI, (d) OTHI Figs. 9a–d show the ripple trajectory of current error for a higher value of m. It can be noted that the d-axis ripple for the DCC scheme is the lowest for an equal share ratio. However, the shape of the trajectory changed to multiple triangles for unequal sharing. In DTHI and DSC, the ripple locus area for equal and unequal sharing conditions is higher and the ripple shape has changed to rectangular. In the OTHI scheme, the double-triangular shape is maintained in either of the sharing condition with minimum ripple. From the above discussion, it is clear that the current error trajectory not only changes with the modulation index but also with the power-sharing ratio. The mathematical expression for ripple content can be easily derived for equal power sharing. However, this will be complex for unequal power sharing. It will be easier to calculate the ripple analytically using MATLAB or similar software. The peak-to-peak ripple obtained from the MATLAB analysis and experimental results is discussed in the next section. 5 Experimental analysis The peak-to-peak current ripple amplitude is calculated by post processing the experimental current data using the analytical method. The experimental setup shown in Fig. 10 includes semikron inverter stacks and the Texas Instruments DSP microcontroller kit with 90 MHz clock frequency. The three-phase power modules consist of SKM50GB12T4 (1200 V, 50 A). Fig. 10Open in figure viewerPowerPoint Experimental setup A three-phase open ended winding induction motor was used as the load. The rated motor parameters are Pn = 5.6 kW, Vn = 480 V, fn = 60 Hz, N = 3600 rpm, and two pole pairs. The dc-link voltages was kept at 135 V and the fundamental frequency was 60 Hz. For the analysis, the carrier frequency of each PWM scheme has been appropriately scaled to maintain the same effective switching frequency. A Lecroy MDA800A motor drive analyser with differential voltage probes and current probes was used for voltage and current measurements, respectively. The analyser built-in noise filter was applied for the current signal. In MATLAB for processing the instantaneous current ripple, a numerical high-pass filter was used to essentially remove the fundamental current component. 5.1 Peak-to-peak current ripple comparison The polar plots of minimum peak to peak current ripple for different decoupled power-sharing schemes are displayed in Fig. 11. Owing to different limits of sharing factors, the offset power-sharing technique is not included in this comparison and it will be considered later in this section. For better understanding, the minimum ripple content in both d-axis and q-axis are plotted separately and the sharing factor in decoupled power-sharing schemes is changed from 0.5 to 1. The radius of the plot is fixed by m and as defined by (1). In the figures, colour shades represent the PWM schemes having least ripple, at that m and angle. If two or more PWM schemes have the least ripple, they are also represented by different colour shades. Fig. 11Open in figure viewerPowerPoint Polar plot representation of peak-to-peak ripple current for decoupled power sharing with different sharing factor (a) , (b) , (c), (d) Fig. 11a shows the plot for equal sharing ratio (i.e. ) and radius of the plot will be 1. In the q-axis, for , DCC has the minimum ripple, whereas DSC has the least ripple for lower m. In d-axis, for , DCC is better at most of the angles. The DTHI scheme has minimum ripple for a small portion at every interval in the plot. When as shown in Fig. 11b, the results are similar to the previous case, except that the plot area is reduced due to the limit set by . The d-axis ripple shown in Fig. 11c for is approximately the same for both DSC and DCC schemes. However, in the q-axis plot, DSC is better for a larger portion. When the power is completely shifted to one side (i.e. ), the q-axis ripple for the DTHI scheme is minimum, which can be predicted from the ripple trajectory in Fig. 8c. In the d-axis, similar to , DSC and DCC have minimum ripples. Although the discontinuous switching pattern has minimum ripple content for equal power sharing () as claimed in [24], it changes for unequal power sharing. In the extreme case, when power is completely shifted to one of the inverters, DTHI has the least ripple. For the current ripple comparison of offset and decoupled power sharing, extreme cases of half and full power from inverter-1 is considered. It can be seen from Fig. 11 that in the q-axis, DCC and DTHI, respectively, have the least ripple for and . Hence, these PWM schemes can be compared with similar power sharing of OTHI as shown in Fig. 12. The peak-to-peak ripples are plotted for the first sector of the SV structure in –-plane. The radii of the plots are fixed by (1) and (3). It can be noted that for equal sharing in DCC and OTHI schemes, the difference in the shape of the plot and the ripple amplitude is very small. For unequal sharing, the ripple in DTHI is double than that of the OTHI. This shows that power sharing with offset power sharing can be a suitable alternative to decoupled power sharing. Fig. 12Open in figure viewerPowerPoint Map of peak-to-peak ripple current amplitude for decoupled and offset power sharing at different sharing factor (a) DCC with , (b) OTHI with , (c) DTHI with , (d) OTHI with Fig. 13 shows the motor phase voltage and current at no-load with unequal power sharing at higher m. It can be noted that the waveforms are very distinct for decoupled and offset power sharing. In decoupled power-sharing schemes, the voltage waveform has deviated from its ideal multilevel shape. However, a proper multilevel voltage waveform has been maintained using OTHI as shown in Fig. 13d, even for unequal power sharing. It can also be observed that the currents for discontinuous patterns (DSC and DCC) are similar and has considerable glitches at the peak of the waveform. In DTHI, the current is uniform but there are large transitions in voltage from minimum to maximum level. However, for the OTHI scheme, the current and voltage are not affected by the offsets applied. Therefore it can have improved performance in dual inverter drive compared to decoupled power-sharing schemes. Fig. 13Open in figure viewerPowerPoint Experimental results at (X-axis; 4 ms/div). (i) Phase voltage (100 V/div), (ii) phase current (2 A/div) (a) DSC, (b) DCC, (c) DTHI, (d) OTHI 6 Conclusion This study presents a time-domain analysis of output current ripple for different PWM techniques in dual inverter with varying power-sharing ratios. The peak-to-peak ripple evaluation is performed based on the error voltage vector and compared between decoupled and offset power-sharing technique in dual inverter. From the studies, it can be observed that the ripple is not only dependent on the modulation index, but also on the sharing ratio. In decoupled power sharing, the DCC scheme can be more effective for equal sharing. When the full power is shifted to one inverter, DTHI is preferred. There is an attractive scope for interchanging between the PWM schemes in decoupled power sharing to provide minimum current ripple when the sharing ratio changes. Only continuous PWM schemes are suitable for the offset power sharing technique. It is worth noting that in decoupled power sharing, switching instances in a sub-cycle are more than that of the offset power sharing irrespective of sharing ratio. Overall it can be stated that decoupled power sharing has more flexibility while compromising the waveform quality. In contrast, offset power sharing has better waveform quality with reduced power-sharing flexibility. 7 References 1Kouro, S., Malinowski, M., Gopakumar, K. et al.: 'Recent advances and industrial applications of multilevel converters', IEEE Trans. Ind. Electron., 2010, 57, (8), pp. 2553– 2580 2Hong, J., Lee, H., Nam, K.: 'Charging method for the secondary battery in dual-inverter drive systems for electric vehicles', IEEE Trans. Power Electron., 2015, 30, (2), pp. 909– 921 3Lakhimsetty, S., Surulivel, N., Somasekhar, V.T.: 'Improvised svpwm strategies for an enhanced performance for a four-level open-end winding induction motor drive', IEEE Trans. Ind. Electron., 2017, 64, (4), pp. 2750– 2759 4Grandi, G., Ostojic, D.: ' Dual inverter space vector modulation with power balancing capability'. IEEE EUROCON 2009, St. Petersburg, Russia, 2009, pp. 721– 728 5Welchko, B.A., Nagashima, J.M.: 'The influence of topology selection on the design of EV/HEV propulsion systems', IEEE Power Electron. Lett., 2003, 1, (2), pp. 36– 40 6Wu, B.: ' Cascaded h-bridge multilevel inverters', High-Power Converters and AC Drives, 2006 7Yao, W., Hu, H., Lu, Z.: 'Comparisons of space-vector modulation and carrier-based modulation of multilevel inverter', IEEE Trans. Power Electron., 2008, 23, (1), pp. 45– 51 8Wang, F.: 'Sine-triangle versus space-vector modulation for three-level PWM voltage-source inverters', IEEE Trans. Ind. Appl., 2002, 38, (2), pp. 500– 506 9Narayanan, G., Zhao, D., Krishnamurthy, H.K. et al.: 'Space vector based hybrid PWM techniques for reduced current ripple', IEEE Trans. Ind. Electron., 2008, 55, (4), pp. 1614– 1627 10Zhao, D., Hari, V.S.S.P.K., Narayanan, G. et al.: 'Space-vector-based hybrid pulsewidth modulation techniques for reduced harmonic distortion and switching loss', IEEE Trans. Power Electron., 2010, 25, (3), pp. 760– 774 11Binojkumar, A.C., Saritha, B., Narayanan, G.: 'Acoustic noise characterization of space-vector modulated induction motor drives—an experimental approach', IEEE Trans. Ind. Electron., 2015, 62, (6), pp. 3362– 3371 12Grandi, G., Loncarski, J.: ' Evaluation of current ripple amplitude in three-phase PWM voltage source inverters'. 2013 Int. Conf.-Workshop Compatibility And Power Electronics, Ljubljana, Slovenia, 2013, pp. 156– 161 13Sekhar, K.R., Srinivas, S.: 'Torque ripple reduction PWMs for a single dc source powered dual-inverter fed open-end winding induction motor drive', IET Power Electron., 2018, 11, (1), pp. 43– 51 14Narayanan, G., Ranganathan, V.T.: 'Analytical evaluation of harmonic distortion in PWM ac drives using the notion of stator flux ripple', IEEE Trans. Power Electron., 2005, 20, (2), pp. 466– 474 15Casadei, D., Serra, G., Tani, A. et al.: 'Theoretical and experimental analysis for the RMS current ripple minimization in induction motor drives controlled by SVM technique', IEEE Trans. Ind. Electron., 2004, 51, (5), pp. 1056– 1065 16Das, S., Binojkumar, A.C., Narayanan, G.: 'Analytical evaluation of harmonic distortion factor corresponding to generalised advanced bus-clamping pulse width modulation', IET Power Electron., 2014, 7, (12), pp. 3072– 3082 17Jiang, D., Wang, F.: 'Current-ripple prediction for three-phase PWM converters', IEEE Trans. Ind. Appl., 2014, 50, (1), pp. 531– 538 18Jiang, D., Wang, F.F.: 'A general current ripple prediction method for the multiphase voltage source converter', IEEE Trans. Power Electron., 2014, 29, (6), pp. 2643– 2648 19Dujic, D., Jones, M., Levi, E.: 'Analysis of output current ripple RMS in multiphase drives using space vector approach', IEEE Trans. Power Electron., 2009, 24, (8), pp. 1926– 1938 20Bhattacharya, S., Sharma, S.K., Mascarella, D. et al.: 'Subfundamental cycle switching frequency variation based on output current ripple analysis of a three-level inverter', IEEE J. Emerging Sel. Top. Power Electron., 2017, 5, (4), pp. 1797– 1806 21Sun, K.W., Summers, T.J., Coates, C.E.: ' Evaluation of peak-to-peak current ripple of phase shifted carrier PWM multilevel cascaded h-bridge converters'. 2017 IEEE Southern Power Electronics Conf. (SPEC), Puerto Varas, Chile, 2017, pp. 1– 6 22Christe, A., Dujic, D.: ' Novel insight into the output current ripple for multilevel and multiphase converter topologies'. 2017 IEEE 18th Workshop on Control and Modeling for Power Electronics (COMPEL), Stanford, USA, 2017, pp. 1– 8 23Grandi, G., Loncarski, J., Dordevic, O.: 'Analysis and comparison of peak-to-peak current ripple in two-level and multilevel PWM inverters', IEEE Trans. Ind. Electron., 2015, 62, (5), pp. 2721– 2730 24Srinivas, S., Sekhar, K.R.: 'Theoretical and experimental analysis for current in a dual-inverter-fed open-end winding induction motor drive with reduced switching PWM', IEEE Trans. Ind. Electron., 2013, 60, (10), pp. 4318– 4328 25Loncarski, J., Leijon, M., Srndovic, M. et al.: 'Comparison of output current ripple in single and dual three-phase inverters for electric vehicle motor drives', Energies, 2015, 8, (5), pp. 3832– 3848 26Menon, R., Azeez, N.A., Kadam, A.H. et al.: ' Carrier based power balancing in three-level open-end drive for electric vehicles'. 2018 IEEE 12th Int. Conf. on Compatibility, Power Electronics and Power Engineering (CPE-POWERENG 2018), Doha, Qatar, 2018, pp. 1– 6 27Menon, R., Azeez, N.A., Kadam, A.H. et al.: 'An instantaneous power balancing technique for an open-end IM drive using carrier based modulation for vehicular application', IEEE Trans. Ind. Electron., 2018, 66, pp. 1– 1 28Sekhar, K.R., Srinivas, S.: 'Discontinuous decoupled PWMs for reduced current ripple in a dual two-level inverter fed open-end winding induction motor drive', IEEE Trans. Power Electron., 2013, 28, (5), pp. 2493– 2502 29Grandi, G., Ostojic, D.: ' Carrier-based discontinuous modulation for dual three-phase two-level inverters'. SPEEDAM 2010, Pisa, Italy, 2010, pp. 839– 844 30Levi, E., Satiawan, I.N.W., Bodo, N. et al.: 'A space-vector modulation scheme for multilevel open-end winding five-phase drives', IEEE Trans. Energy Convers., 2012, 27, (1), pp. 1– 10 Volume10, Issue2June 2020Pages 154-161 FiguresReferencesRelatedInformation
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