Performance improvement in six‐phase symmetrical induction motor by using synthetic voltage vector based direct torque control
2019; Institution of Engineering and Technology; Volume: 13; Issue: 11 Linguagem: Inglês
10.1049/iet-epa.2018.5983
ISSN1751-8679
AutoresSohit Sharma, Mohan V. Aware, Apekshit Bhowate, E. Levi,
Tópico(s)Electric Motor Design and Analysis
ResumoIET Electric Power ApplicationsVolume 13, Issue 11 p. 1638-1646 Special Issue: Multiphase Electric Drives and Generation SystemsFree Access Performance improvement in six-phase symmetrical induction motor by using synthetic voltage vector based direct torque control Sohit Sharma, Corresponding Author Sohit Sharma sohitee@students.vnit.ac.in Electrical Engineering Department, Visvesvaraya National Institute of Technology, Nagpur, IndiaSearch for more papers by this authorMohan Aware, Mohan Aware Electrical Engineering Department, Visvesvaraya National Institute of Technology, Nagpur, IndiaSearch for more papers by this authorApekshit Bhowate, Apekshit Bhowate Electrical Engineering Department, Visvesvaraya National Institute of Technology, Nagpur, IndiaSearch for more papers by this authorEmil Levi, Emil Levi Liverpool John Moores University, Liverpool, L3 3AF UKSearch for more papers by this author Sohit Sharma, Corresponding Author Sohit Sharma sohitee@students.vnit.ac.in Electrical Engineering Department, Visvesvaraya National Institute of Technology, Nagpur, IndiaSearch for more papers by this authorMohan Aware, Mohan Aware Electrical Engineering Department, Visvesvaraya National Institute of Technology, Nagpur, IndiaSearch for more papers by this authorApekshit Bhowate, Apekshit Bhowate Electrical Engineering Department, Visvesvaraya National Institute of Technology, Nagpur, IndiaSearch for more papers by this authorEmil Levi, Emil Levi Liverpool John Moores University, Liverpool, L3 3AF UKSearch for more papers by this author First published: 20 May 2019 https://doi.org/10.1049/iet-epa.2018.5983Citations: 4AboutSectionsPDF 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 In this paper, direct torque control (DTC) scheme for a symmetrical six-phase induction motor by incorporating five-level torque comparator is presented. The five-level torque comparator in DTC provides the benefit of torque ripple reduction, compared to a three-level torque comparator. Adoption of five-level torque comparator generates the flux in xy-subspace which leads to flow of increased stator current. The xy-subspace flux is also not responsible for torque production. The synthetic voltage vectors are therefore developed to minimise the xy-subspace flux and thus improve performance of the symmetrical six-phase induction motor. The comparative analysis of the developed switching schemes is presented. The common mode voltage of the drive is also taken care of by the proposed switching scheme. Experimental results are provided to verify the proposed scheme. 1 Introduction In 1986, Takahashi and Noguchi [1] proposed an alternative to field oriented control for controlling the induction motor in a faster and simpler way. The advantages of the direct torque control (DTC) algorithm are that neither coordinate transformation nor current control loops are required, and technique is hardly affected by parameter variations [2, 3]. The implementation of DTC algorithm for three-phase induction motors has been discussed extensively and various techniques are available to improve its performance [4-9]. In recent years, multiphase induction machines are emerging as a substitute of the three-phase induction machines because of the various inherent advantages, such as lower power per phase, lower space magneto-motive force (mmf) harmonics, higher torque density and fault tolerance property [10-12]. The first feasible phase number higher than three is five. The construction of a five-phase induction motor requires a stator with the minimum number of 20 slots in four-pole configuration [13], a slot number normally not available for three-phase machines. Hence, a six-phase motor is more attractive because it can be obtained by rewinding a three-phase induction motor as a six-phase one, with the minimum number of 24 slots for four-pole topology. The basic principle of switching table based DTC algorithm for multiphase motors is similar to the one for three-phase motors. A switching table is developed and it takes flux error, torque error, and sector number as the inputs for the selection of an appropriate voltage vector. However, this method is not directly extendable to the multiphase motors due to the presence of the extra two-dimensional subspaces (, ,…). In the multiphase machines with sinusoidal mmf distribution, electromagnetic torque production depends only on the dq-subspace and other available subspaces are responsible for losses only. When one voltage vector is selected in the dq-subspace for application, its projections in other subspaces are not zero and this deteriorates the performance of the drive [14]. Therefore, projections in other subspaces should be reduced for better drive performance. In [15], an extension of the three-phase induction motor DTC to five-phase induction motor is presented, using a two-level voltage source inverter (VSI). A DTC algorithm for five-phase induction motors supplied from a three-level neutral point clamped inverter is presented in [16], in conjunction with a seven-level torque comparator for reducing the torque ripples. The projection of the chosen vectors in xy-subspace is reduced by using the virtual voltage vectors. A generalised switching table for DTC of induction motors supplied from multilevel inverters is discussed in [17]. A modified switching table based DTC algorithm is proposed for reducing the current harmonics due to the presence of xy-subspace in an asymmetrical six-phase (30° spatial shift between two three-phase windings) permanent magnet synchronous machine (PMSM) [18]. In the modified switching table, selection of the voltage vectors is based on the location of the flux in xy-subspace. The incorporation of synthetic voltage vectors in DTC algorithm is developed for reducing current harmonics in dual three-phase PMSM [19]. The requirement of monitoring the stator flux in xy-subspace is eliminated with the utilisation of synthetic voltage vectors. In [20], the concept of synthetic voltage vectors is extended for asymmetrical six-phase induction motor in the view of simplified implementation of the scheme by using pulse-width modulation (PWM) module. When the conventional DTC algorithm is employed, the common mode voltage (CMV) generally appears in the drives; it leads to flow of common-mode current through parasitic capacitance of the induction motor. This reduces the life expectancy of the bearings and causes unexpected tripping of ground current protection [21, 22]. Electromagnetic noise interference is also a consequence of CMV [23, 24]. To alleviate these problems, a synchronised PWM-based technique has been developed for the elimination of CMV in six-phase symmetrical drives [25]. A space vector modulation based method has also been presented for symmetrical six-phase AC drives for reducing the CMV [26]. Another DTC technique, based on application of even voltage vectors in even sectors, and odd vectors in odd sectors without considering null vectors for the minimisation of common-mode voltage was proposed in [9]. Therefore, torque and flux ripples are increased. The reduction of CMV with DTC algorithm for five-phase induction motor is discussed in [27], where suitable vectors are selected from the available vectors for the generation of virtual voltage vectors. This scheme additionally eliminates the xy-subspace flux as well. A DTC scheme, similar to the conventional DTC switching scheme for three-phase induction motors, is proposed in [28] for the symmetrical six-phase induction motor supplied from a two-level VSI. Here, only large voltage vectors (LVVs) are applied along with a three-level torque comparator. Therefore, it results in high torque ripples. This DTC scheme, based on the three-level torque comparator (DTC-3TC), is considered here for the comparative purpose. As DTC algorithm for a three-phase induction motor is not directly applicable to any multiphase motor drive, it is necessary to introduce appropriate modifications and each number of phases has to be considered separately. The structure analysed here, a symmetrical six-phase induction motor, has not been addressed previously except in [28], where a very basic DTC was considered. Hence, this paper provides an addition to the existing knowledge by introducing a DTC scheme for the said stator phase disposition, based on the use of synthetic voltage vectors. Such an improved DTC, with the utilisation of synthetic voltage vectors, has been developed for five-phase and asymmetrical six-phase machines in the past, but not for a symmetrical six-phase winding disposition. Since voltage vector selection has to meet simultaneously requirements for desired flux/torque error change using the first plane voltage vector projections, while at the same time keeping as close as possible to zero voltage vector (ZVV) projections in other planes, a detailed study of the suitable vector choices for designing the synthetic voltage vectors is provided first. It is found to be advantageous here that LVVs of a symmetrical six-phase VSI map into ZVVs in the xy-subspace. Next, to reduce the torque ripple, a five-level torque comparator (used previously in relation to other phase numbers but not in the context of a symmetrical six-phase induction machine's DTC) is utilised. The implementation of a five-level torque comparator in the DTC algorithm reduces the torque ripples of the drive. This torque comparator permits utilisation of the small voltage vectors (SVVs) of the dq-subspace. Due to the involvement of SVVs, xy-subspace flux is generated. The synthetic voltage vector based five-level torque comparator scheme (DTC-5TC) is therefore developed for reducing the projections of voltage vectors in the xy-subspace. The CMV of the drive with all available switching states of the inverter is also analysed. The three-level torque comparator based switching scheme is modified (MDTC-3TC) to eliminate the CMV of drive. The CMV, produced when the five-level torque comparator based table is used, is examined next. The redundancy of available voltage vectors provides the freedom to modify the five-level torque comparator based scheme (MDTC-5TC), so that it can simultaneously reduce the xy-subspace flux and torque ripples, and eliminate the CMV of the drive. Finally, the comparative analysis of the considered switching table based DTC techniques (DTC-3TC, MDTC-3TC, DTC-5TC and MDTC-5TC) is provided. The paper is organised as follows. Section 2 summarised the modelling of symmetrical six-phase induction motor and the voltage vector mapping for a two-level VSI. The conventional DTC algorithm, based on three-level torque comparator, is further modified by introducing the five-level torque comparator. Formulation of synthetic voltage vectors for suppressing the xy-subspace flux and CMV with the available switching states is discussed in Section 3. Section 4 provides the experimental results and is followed by the conclusions, summarised in Section 5. 2 Six-phase symmetrical induction motor model and voltage vectors of a two-level VSI 2.1 Symmetrical six-phase induction motor modelling Symmetrical six-phase induction motors have two three-phase windings displaced by 60 electrical degrees. The transformation matrix, based on vector space decomposition theory, transforms the six-dimensional space into two two-dimensional orthogonal subspaces and two zero-sequence axes (dq, xy, ). The neutrals of both three-phase windings (n and n′) are isolated, as shown in Fig. 1, so that -component equations are omitted. The symmetrical six-phase induction machine is thus modelled using (1) Fig. 1Open in figure viewerPowerPoint Symmetrical six-phase induction motor drive with two-level VSI supply The voltage equations for stator and rotor are given in stationary reference frame as (2) (3) (4) The stator and rotor flux components in the stationary reference frame are written as (5) (6) (7) where and are stator and rotor resistance, and are stator and rotor leakage inductance, is mutual inductance, and are stator and rotor current, and and are stator and rotor flux. Rotor xy voltage and flux equations are omitted since they are always zero due to the short-circuited rotor winding [10]. The electromagnetic torque () of the six-phase induction motor is given by (8) The rotor motion equation is finally (9) where is load torque, J is inertia constant, P is pole pair number, is rotor electrical speed. 2.2 Six-phase two-level VSI A two-level VSI is shown in Fig. 1. The two switching states are possible for each leg. Therefore, there are in total 26 = 64 switching states. The relationship between switching states (), where {0, 1} (i = a, b, c, d, e, f) and phase voltages is given by (10) Phase voltages are represented in the two-subspaces (dq and xy) by using (11) All the 64 voltage vectors are mapped in both subspaces, as shown in Fig. 2. For example, vector is plotted in dq and xy-subspace by considering its binary form as the switching state (, , , , , , where 1 denotes the 'ON' state of the upper switches and 0 represents the 'ON' state of the lower switches). With reference to the mapping in the first plane, there are 6 LVVs, 12 medium voltage vectors (MVVs), 36 SVVs, and 10 ZVVs. Fig. 2Open in figure viewerPowerPoint Voltage vectors in dq and xy-subspace 3 Direct torque control algorithm The basic block diagram of the DTC scheme is presented in Fig. 3. The conventional DTC algorithm works on the basis of the selection of voltage vectors from the pre-defined switching tables. The choice of voltage vector for firing the inverter depends on the location of stator flux in dq-subspace, and output status of flux and torque hysteresis comparators. The stator flux is continuously monitored for getting the location of the stator flux in dq-subspace in terms of sectors, by means of sector identification block. The dq and xy-subspace are divided into six sectors, as shown in Fig. 2. The voltage estimator uses (10) and (11) for calculating the stator voltage components. Stator flux is estimated using (2) and the electromagnetic torque is obtained by means of (8). The two-level flux comparator is used for comparing the reference flux and actual flux. Two torque comparators, three-level torque comparator and five-level torque comparator, are considered further on. Fig. 3Open in figure viewerPowerPoint Block diagram of DTC algorithm 3.1 Three-level and five-level torque comparators based switching scheme In what is called here the conventional DTC algorithm, a three-level torque comparator is used in conjunction with 6 LVVs and 2 ZVVs, out of the 64 available voltage vectors. The switching table for three-level torque comparator (DTC-3TC) is shown in Table 1. The positions of selected voltage vectors are in essence the same as for the three-phase two-level VSI. The ZVVs, and , are also obtained by switching 'ON' all the lower switches and all the upper switches, respectively. All vectors of this table have zero projections in the xy-subspace. Therefore, there is no need to deal separately with the xy-subspace. Table 1. Three-level torque comparator (DTC-3TC) Sectors 1 2 3 4 5 6 +1 +1 0 −1 −1 +1 0 −1 The output of flux and torque comparators depends on the correlation between reference value and actual value. These relationships are, for the two-level flux comparator and three-level torque comparator, given with (12) (13) where and are the reference flux and actual flux, respectively, and are the reference torque and actual torque, respectively, and HB represents the width of the torque hysteresis band. The output of comparators +1, −1, and 0 demands the increase, decrease, and no change in the respective values of flux and torque. The is selected from the switching table when the stator flux is in the first sector and there is a requirement of increase in flux and torque of the induction motor. The torque ripple of the symmetrical six-phase induction motor can be reduced by incorporating the five-level torque comparator. The available SVVs are also incorporated in the switching table for obtaining the five-level torque comparator operation. The formation of the switching table is similar to DTC-3TC, but with two more torque levels. The switching table with five-level torque comparator is presented in Table 2. Table 2. Five-level torque comparator switching scheme Sectors 1 2 3 4 5 6 +1 +2 +1 0 −1 −2 −1 +2 +1 0 −1 −2 The hysteresis band size of the five-level torque comparator is governed by (14) Here, and represent the inner and outer hysteresis band, respectively. The length of SVVs is half of the LVVs. Therefore, if is equal to HB then is equal to . The operational relationships of the five-level torque comparator are given by (15) while they remain the same as in (12) for the flux comparator. 3.2 Five-level torque comparator based switching scheme using synthetic voltage vectors The implementation of the switching scheme, presented in Table 2, reduces the torque ripples. However, it employs voltage vectors that have non-zero projections in the xy-subspace and hence lead to formation of the xy-subspace flux. From (3) and (6), it is observed that current flowing in this plane is only limited by leakage inductance of the machine. Due to this, high currents will flow and thus increases the losses. The xy-subspace does not contribute to the torque production. For these reasons, the synthetic voltage vectors are formed next, in order to reduce the xy-subspace flux. 3.2.1 Formulation of synthetic voltage vectors The synthetic voltage vectors are developed by combining two small active vectors of the dq-subspace. The selected vectors have the same magnitude () and angle (), so that the effect on torque and flux is the same with both vectors. In the xy-subspace, they map as SVVs, which are out of phase. The dwell time for the selected vectors is calculated by using volt-second balancing equation in the xy-subspace. The balancing equation is written in such a manner that it neutralises the effect in xy-subspace. In dq-subspace (16) where and for six synthetic vectors. In xy-subspace (17) where and for six synthetic vectors (18) (19) where is the sampling time and , are the times of application, calculated for the respective vectors. From (18) and (19), it is observed that = = . In one sampling time, both selected voltage vectors are applied for half of the time. All the developed synthetic voltage vectors are mapped in the dq and xy-subspaces as shown in Fig. 4. The projection of synthetic vectors in xy-subspace is zero. For vector, value of both and in the dq-subspace is (here, k of (16) is 1). Projection in xy-subspace is given by (17) as and (j = 2 for the second synthetic vector). Therefore, they cancel each other leading to zero total projection in the xy-subspace. Fig. 4Open in figure viewerPowerPoint Voltage vectors of DTC-5TC and MDTC-5TC scheme in both subspaces (dq and xy) 3.2.2 Switching scheme based on synthetic voltage vectors The switching scheme based on synthetic voltage vectors is given in Table 3. The selection of vectors is similar as in the switching scheme presented in Table 2. The difference is that, instead of small vectors, synthetic voltage vectors are applied, which are capable of reducing the xy-subspace flux. However, torque ripples remain unaltered. Table 3. Five-level torque comparator with synthetic voltage vectors (DTC-5TC) Sectors 1 2 3 4 5 6 +1 +2 +1 0 −1 −2 −1 +2 +1 0 −1 −2 3.3 MDTC-3TC and MDTC-5TC based switching scheme for CMV elimination In the above developed switching schemes for the DTC algorithm, CMV of the drive is not considered. Therefore, CMV due to all available voltage vectors is explored in order to reduce its value to zero. The DTC-3TC switching table is modified to MDTC-3TC for eliminating the CMV. For the five-level torque comparator, MDTC-5TC switching scheme is proposed by considering synthetic voltage vectors for the elimination of CMV. 3.3.1 CMV in six-phase symmetrical induction motor with two-level VSI The CMV of six-phase symmetrical induction motor drive with two-level VSI is given with (20) which is the average of the CMV of the two individual three-phase windings, as shown by (21) where and . The and are common-mode voltages of the first and the second three-phase winding, respectively, in terms of pole voltages ('z' is the mid-point of the dc bus). When the lower switch of the inverter is 'ON' then pole voltage of that phase is and pole voltage is when the upper switch is 'ON'. For example, 54th ([1 1 0 1 1 0]) switching state generates pole voltage for each phase as , , , , , and , which gives the overall CMV of . Different switching states generate different pole voltages and value of CMV is obtained by using (20). The CMV obtained due to all 64 switching states is presented in Table 4. Table 4. CMV in symmetrical six-phase induction motor drive with two-level VSI Number of VVs VVs CMV 1 0 1 63 6 1, 2, 4, 8, 16, 32 6 31, 47, 55, 59, 61, 62 15 3, 5, 6, 9, 10, 12, 17, 18, 20, 24, 33, 34, 36, 40, 48 15 15, 23, 27, 29, 30, 39, 43, 45, 46, 51, 53, 54, 57, 58, 60 20 7, 11, 13, 14, 19, 21, 22, 25, 26, 28, 35, 37, 38, 41, 42, 44, 49, 50, 52, 56 3.3.2 Switching scheme for eliminating the CMV From Table 4, it is observed that all LVVs are not responsible for the CMV generation. In the DTC-3TC switching table, LVVs and ZVVs are adopted. The ZVVs (, ) produce CMV. Therefore, for this switching table, generated CMV has three levels (, , ). When the ZVVs (, ) are replaced by (, ) vectors, then CMV of the drive is eliminated. The modified switching table for three-level torque comparator (MDTC-3TC) is presented in Table 5. Table 5. Three-level torque comparator (MDTC-3TC) Sectors 1 2 3 4 5 6 +1 +1 0 −1 −1 +1 0 −1 In the DTC-5TC, ZVVs (, ) are employed. Therefore, CMV due to LVVs and ZVVs is zero. But for small vectors, CMV is . The developed MDTC-5TC switching scheme incorporates those voltage vectors which have zero CMV. A total of 20 voltage vectors are available, which provide zero CMV, as shown in Table 4. These 20 voltage vectors are composed of 6 large, 12 small, and 2 zero vectors. The projection of LVVs and ZVVs in xy-subspace is zero. But the small vectors are mapped as MVVs in the xy-subspace. For reducing the flux in the xy-subspace, synthetic voltage vectors are formed by above stated principle, and are plotted in Fig. 4. The projection of these synthetic vectors in xy-subspace is also zero. The final switching scheme for DTC with five-level torque comparator for CMV elimination is presented in Table 6. Table 6. Five-level torque comparator with synthetic voltage vectors (MDTC-5TC) for zero CMV Sectors 1 2 3 4 5 6 +1 +2 +1 0 −1 −2 −1 +2 +1 0 −1 −2 4 Experimental results The developed switching schemes (MDTC-3TC, DTC-5TC, and MDTC-5TC) for the DTC are verified on the laboratory prototype of symmetrical six-phase induction motor of 1.5 kW and compared with conventional switching scheme (DTC-3TC). The experimental set-up is shown in Fig. 5 and its parameters are presented in Table 7. Texas instrument's digital signal processor is used (TMS320F28377S) for the implementation of the algorithm. The Hall effect voltage and current sensors and a high-resolution encoder are used for sensing the feedback signals. Table 7. System parameters Parameters Values dc bus voltage 200 V pole pairs 2 fundamental frequency 50 Hz rated power 1.5 kW rated flux 0.35 Wb 5.17 Ω, 2.3 Ω 20.8 mH 215 mH Fig. 5Open in figure viewerPowerPoint Experimental rig An eddy current brake is used to load the motor. The sampling frequency of 10 kHz is maintained in all the switching schemes. The results are collected at the speed of 1200 rpm, in closed-loop operation. The dq-subspace flux for all switching schemes is maintained at 0.35 Wb. The current flowing through the machine windings under no-load is presented in Fig. 6a with DTC-3TC and MDTC-3TC, and its values are 1.18 A (RMS) and 1.12 A (RMS), respectively. Fig. 6b shows the dq-subspace flux. The xy-subspace flux with the corresponding switching tables is shown in Fig. 6c. When the five-level torque comparator based switching scheme is employed, current flowing through the motor winding is as shown in Fig. 7. Fig. 6Open in figure viewerPowerPoint Experimental results for DTC-3TC and MDTC-3TC (a) C1 = a-phase current, C2 = d-axis current, C3 = x-axis current [3 A/div, 20 ms/div], (b) C3 = d-flux, C2 = q-flux [0.2 Wb/div, 20 ms/div], (c) C1 = x-flux, C2 = y-flux [0.04 Wb/div, 20 ms/div] Fig. 7Open in figure viewerPowerPoint Experimental results for five-level torque comparator by using Table 2 (without synthetic voltage vectors) (a) C1 = a-phase current, C2 = d-axis current, C3 = x-axis current [3 A/div, 20 ms/div], (b) C3 = d-flux, C2 = q-flux [0.2 Wb/div, 20 ms/div], (c) C1 = x-flux, C2 = y-flux [0.04 Wb/div, 20 ms/div] Due to the presence of SVVs, xy-subspace flux is generated. As a consequence, 2.1 A (RMS) current is drawn by the machine. As the xy-subspace flux can be reduced by using the synthetic voltage vectors for the DTC-5TC and MDTC-5TC schemes, current flowing through the windings is reduced to 1.17 A (RMS) and 1.21 A (RMS), respectively. This is confirmed with results shown in Fig. 8, where stator current, dq and xy-subspace flux for DTC-5TC and MDTC-5TC are shown. In no-load operation, current drawn by the five-level torque comparator based DTC without synthetic voltage vectors is very high, compared to other switching schemes, due to the presence of xy-subspace flux. Therefore, it is not feasible to apply load on the motor without reducing the xy-subspace flux, if overload is to be avoided. Fig. 8Open in figure viewerPowerPoint Experimental results for DTC-5TC and MDTC-5TC (a) C1 = a-phase current, C2 = d-axis current, C3 = x-axis current [3 A/div, 20 ms/div], (b) C3 = d-flux, C2 = q-flux [0.2 Wb/div, 20 ms/div], (c) C1 = x-flux, C2 = y-flux [0.04 Wb/div, 20 ms/div] The step speed response is observed next, for DTC-3TC, MDTC-3TC, DTC-5TC, and MDTC-5TC, with loading of 2 Nm load. The initial speed of the motor is 600 rpm. The step change of 600 rpm is commanded; therefore due to action of the speed controller, speed of motor increases to 1200 rpm, as shown in Fig. 9a. The dynamic response for the load disturbance is presented in Figs. 9b and c. The speed of the motor is governed with the 1200 rpm reference and the initial load is 2 Nm. The load of 5 Nm is then applied to the motor, with the resulting dynamics illustrated in Fig. 9b. The speed of the motor momentarily reduces due to step loading. The proportional–integral controller comes in action and motor regains its speed. The torque response when motor is unloaded from 4 to 2 Nm load is further presented in Fig. 9c and similar, but with inverse speed change sign, effects are observed. Fig. 9Open in figure viewerPowerPoint Transient response for DTC-3TC, MDTC-3TC, DTC-5TC, and MDTC-5TC switching scheme (a) Step speed response [C1 = speed (300 rpm/div, 200 ms/div), C2 = torque (1 Nm/div, 200 ms/div)], (b) Torque response with increment in load [C1 = speed (300 rpm/div, 200 ms/div), C2 = torque (1 Nm/div, 200 ms/div)], (c) Torque response with decrement in load [C1 = speed (300 rpm/div, 200 ms/div), C2 = torque (1 Nm/div, 200 ms/div)] The torque ripples for the DTC-3TC and MDTC-3TC are higher due to the three-level torque comparator. The torque ripples are reduced by incorporating the five-level torque comparator, as confirmed by Fig. 9. Both algorithms (DTC-5TC and MDTC-5TC) use five-level torque comparator based table and therefore both have similar torque ripples. The torque ripples are calculated by using (22) as suggested in [19] (22) where and are instantaneous and average value of the estimated torque. The calculated values of torque ripples are presented in Table 8 for the respective switching schemes. Here it is observed that selection of voltage vectors under the same torque comparator does not affect the torque ripples. However, employment of the five-level torque comparator significantly reduces the torque ripples when compared to the three-level comparator, by up to 44%. The variation of torque ripples and average switching frequency with change in load is observed at speed of 1200 rpm; next, variation of the torque ripples and average switching frequency with change in rotor speed at 2 Nm load is also investigated. The results are presented in Fig. 10. It is observed that, in the whole range, torque ripples are almost constant with either three-level or five-level torque comparator. In the MDTC-3TC, average switching frequency reduces with respect to DTC-3TC due to replacement of ZVVs , with , . It is observed that implementation of synthetic voltage vectors for the five-level torque comparator scheme increases the average switching frequency of the drive and MDTC-5TC has also slightly higher average switching frequency compared to DTC-5TC. Table 8. Comparison of torque ripples for different switching schemes at 4 Nm load with speed of 1200 rpm Switching scheme DTC-3TC MDTC-3TC DTC-5TC MDTC-5TC torque ripple, Nm 0.311 0.307 0.175 0.179 Fig. 10Open in figure viewerPowerPoint Torque ripple and average switching frequency variation with change in load and rotor speed The CMV of the drive with different switching scheme is observed and presented in Fig. 11. In the symmetrical six-phase motor, two three-phase windings are present. The CMV due to both individual three-phase windings is shown along with its resultant value. In the conventional DTC (DTC-3TC), CMV of is generated due to the involvement of (, ) voltage vectors. In the MDTC-3TC, all employed voltage vectors are applied in such a manner that they generate opposite CMV in two windings. Therefore, resultant CMV is zero. However, in individual windings CMV has two values and . The DTC-5TC table uses voltage vectors which generate CMV of . Therefore, corresponding synthetic voltage vectors also generate the same CMV with three levels (, 0, ). The voltage vectors of DTC-5TC scheme are modified in MDTC-5TC scheme to eliminate the CMV of the drive. Fig. 11Open in figure viewerPowerPoint CMV of drive with DTC-3TC, MDTC-3TC, DTC-5TC, and MDTC-5TC switching schemes [Trace 1 – C1 = CMV-I, Trace 2 – C2 = CMV-II (50 V/div, 20 ms/div), Trace 3 – F1 = CMV (100 V/div, 20 ms/div)] 5 Conclusion In this paper, a DTC method using synthetic voltage vectors is introduced for a symmetrical six-phase induction motor drive. The conventional switching table of DTC (DTC-3TC) employs only LVV and ZVV. The five-level torque comparator based switching scheme is therefore proposed, which utilises the available SVVs of the dq-subspace. The projection of these vectors in xy-subspace is reduced by developing synthetic voltage vectors. The incorporation of synthetic voltage vectors in the scheme with five-level torque comparator effectively reduces the xy-subspace flux and the torque ripples by up to 44%. By a proper selection of the voltage vectors, CMV of the drive is also eliminated. The conventional three-level torque comparator (DTC-3TC) based table is modified to MDTC-3TC by replacing the redundant ZVVs for eliminating the CMV, with an additional benefit of reduced average switching frequency. Similarly, such voltage vectors are selected which impress zero CMV for the formulation of synthetic voltage vectors. Therefore, proposed switching table (MDTC-5TC) effectively minimises the xy-subspace flux, reduces the torque ripples, and eliminate the CMV of the drive at the expense of an increase in the average switching frequency. The experimental results are presented to validate the performance improvements realised with the MDTC-5TC switching scheme. 6 Acknowledgments This work was supported by the Visvesvaraya Ph.D. scheme, Ministry of Electronics and Information Technology (MeitY), Government of India, under Grant PhD-MLA/4{14}/2015-16 7 References 1Takahashi, I., Noguchi, T.: 'A new quick-response and high-efficiency control strategy of an induction motor', IEEE Trans. Ind. Appl., 1986, 22, (5), pp. 820– 827 2Buja, G.S., Kazmierkowski, M.P.: 'Direct torque control of PWM inverter-fed AC motors – a survey', IEEE Trans. Ind. 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