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Quasi-resonant inverter-fed direct torque controlled induction motor drive
Electric Power Systems Research 77 (2007) 946–955
Quasi-resonant inverter-fed direct torque controlled induction motor drive S. Behera ∗ , S.P. Das 1 , S.R. Doradla 1 Power Electronics Laboratory, Electrical Engineering., Indian Institute of Technology, Kanpur 208016, India Received 13 February 2006; received in revised form 8 August 2006; accepted 16 August 2006 Available online 18 September 2006
Abstract A quasi-resonant inverter-fed induction motor operated under direct torque control (DTC) scheme is modeled and analyzed with SABER simulator. The dc link voltage is clamped to source voltage. All the devices in the resonant link and inverter except auxiliary switch in the resonant link are operated soft under zero-voltage switching (ZVS). The auxiliary switch is turned on under zero-current switching (ZCS), but turned off hard. This scheme has been implemented on a laboratory-sized experimental setup. A comparison of simulation and experimental results under identical operating conditions were presented. © 2006 Elsevier B.V. All rights reserved. Keywords: Quasi-resonant inverter; SABER simulation; Direct torque control (DTC) scheme
1. Introduction Variable voltage and variable frequency operation of induction motors are generally used for speed and torque control of induction motor drives. The literature related to ac drives covering scalar control, field-oriented control, and direct torque control (DTC) has been well documented [1]. The induction motor drives employing DTC strategies with various variables have been reported [2–4]. In all these schemes, a better torque profile and current response have been focused. Because of hard-switching in conventional PWM inverters, the switching losses in the devices are high and the windings of induction motor are subjected to high switching stresses. The limitations of hard-switchings are restriction in switching frequency, acoustic noise, larger filter size and EMI, etc. These shortcomings can be overcome using soft-switching techniques (zero-voltage/zerocurrent switchings). Various soft-switching strategies for both static and dynamic loads are being discussed in literatures [5–17]. The soft-switching inverter-fed three-phase induction motor drive is lacking in the literature. In the area of softswitching inverter-fed induction motor drives, only a few papers ∗
Corresponding author at: Department of Electrical Engineering, University College of Engineering, Burla 768018, Orissa, India. Tel.: +91 663 2432608. E-mail address: [email protected] (S. Behera). 1 Department of Electrical Engineering, Indian Institute of Technology, Kanpur 208016, India. 0378-7796/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2006.08.011
[15,16] have appeared in the literature, but still they suffer considerably from hard-switchings. Out of various soft-switching techniques (i.e., load resonant, resonant link and resonant transition), the quasi-resonant technique that comes under resonant transition category is the latest and most popular one as far as the soft-switchings of the devices are concerned. The quasiresonant topology [17], which is meant for static RL load, has been actively considered for dynamic load (i.e., induction motor drive under DTC scheme) in the present paper. The control scheme used for dynamic load in this paper is different than that of static load [17]. The complete scheme is modeled and simulated by SABER to analyze its performance. A laboratory-sized model is fabricated and experimentally tested in order to verify with the simulation results under identical operating conditions. 2. Quasi-resonant inverter topology and basic operation The proposed quasi-resonant inverter topology is shown in Fig. 1. The current input to the inverter is designated as dc link/load current ‘ilink ’, which is assumed to be ripple free for explanation shown in Fig. 2. This topology has the ability to provide zero-voltage switching (ZVS) of all inverter switches for both positive and negative dc link current ilink . The switching waveforms of gating pulses of all resonant link switches, resonant capacitor voltage and resonant inductor current under common control strategy (i.e., either positive or negative dc link current) are shown in Fig. 2. The gating pulses for the link
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Fig. 1. Circuit diagram of quasi-resonant dc link inverter topology.
switches shown in Fig. 2(a) allow soft-switching of inverter devices for both negative and positive dc link current. The waveforms of resonant capacitor voltage and resonant inductor current shown in Fig. 2(b) correspond to the case when the link current is negative. Fig. 2(c) corresponds to the case when the dc link current is positive. The link current may be positive or negative during a switching cycle. In order to initiate soft-switching process, the gating pulse to the main switch is withdrawn at to . In case of negative dc link current, the diode Dp conducts and the link voltage is clamped to the source voltage. On the other hand if the link current is positive, the resonant capacitor
across the dc link discharges to zero through the inverter and load. The shunt switches SW1−SH , SW2−SH are turned on at t1 with the release of gate pulses. In case of negative link current the dc link voltage continues to be clamped at the source voltage due to conduction of the diode DP . The current through the shunt inductor increases linearly from zero to the dc link current while the current through DP decreases linearly and turns off at t2 . From t2 onwards, the link voltage is no more clamped to the source voltage due to reverse-biased diode DP . The resonant capacitor starts discharging through the shunt inductor LSh . The shunt inductor current increases resonantly from its initial
Fig. 2. Switching waveforms under independent direction of dc link current (a) gating pulses to dc link switches, (b) waveforms of VCr and ilr when dc link current is negative and (c) waveforms of VCr and ilsh when dc link current is positive.
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value of ilink . The resonant capacitor discharges resonantly to zero at t3 . The soft-switching of inverter devices under ZVS is achieved during t3 –t4 . The diode D1−SH is forward biased by the trapped energy in LSh and conduction of shunt switch SW2−SH . This continues until the removal of gating pulses from the shunt switches at t4 . In case of positive link current, the link voltage continues to be held at zero value until the auxiliary switch is turned on. However, the switching status of inverter device is changed during t3 –t4 as in the case of negative dc link current. This ensures that the link voltage is held at zero before switching of inverter devices is initiated independent of the direction of link current. The gating pulses from the shunt switches are removed at t4 . The energy trapped in the shunt inductor is recovered to the source through conduction of diodes D1−SH and D2−SH . The resonant capacitor is charged linearly by the negative dc link current and it continues until the link voltage becomes equal to the source voltage. Then, the diode DP gets forward biased and conducts the negative link current. The gating signal to the auxiliary switch SWA is released. This does not affect the operation when the link current is negative. In case of positive link current, the auxiliary switch turns on under ZCS due to resonant inductor Lr . The current through the resonant inductor increases linearly until it becomes equal to the link current. At t6 , the excess current through the resonant inductor charges the link capacitor resonantly. This continues until the link voltage becomes equal to the source voltage. At this instant t7 , SWM is turned on and SWA is turned off. The excess current in the resonant inductor is fed back to the source through diode DP . When the inductor current becomes equal to the link current, the diode DP turns off. The main switch turns on under ZVS and supplies the load current along with the resonant inductor. As the resonant inductor current falls to zero, the main switch carries the link current. In case of negative link current, the operation of main and auxiliary switches does not have any effect. This explains soft-switching operation independent of direction of dc link current. Now the dc link is ready for the next soft-switching operation. Above all, the roles of auxiliary and other switches in dc link are summarized as follows: The role of auxiliary switch (SWA ) is not only to prevent the main switch (SWM ) from short circuit through resonating capacitor (Cr ) during turn-on of the later (i.e., the resonating capacitor Cr retains zero charge/voltage), but also from discharging current of snubber capacitor (Csnub ). The auxiliary switch assists in resonating dc link voltage with the help of Lr and Cr , by which the voltage across resonating capacitor builds up and is clamped to input voltage due to anti-parallel diode across the main switch. This enables the main switch to turn-on soft under ZVS as the voltage across it is zero. The main switch turns off soft under ZVS due to snubber capacitor across it. Every time, the auxiliary switch is enabled, whenever the main switch is needed to turn on irrespective load conditions. All the switches in dc link are operated in sequence (i.e., essential to make the topology independent of direction of link current shown in Fig. 2) for soft-switching operation of its own and inverter devices. When the link current is from source to inverter, the auxiliary switch (SWA ) and main switch (SWM ) remain active as they handle link current and voltage. The shunt
switches (SW1−SH , SW2−SH ) do not handle link current as the link voltage being already clamped down to zero. On the other hand, when the link current is in opposite direction (i.e., from inverter to source), the shunt switches remain active by handling current and voltage of dc link. The switches SWA and SWM that are operated prior to the shunt do not handle link current, as these are reverse-biased. 3. Control strategy for soft-switching scheme The soft-switching strategies for three-phase static and dynamic loads are different and explained in following two sections. 3.1. Soft-switching inverter for three-phase static load In the conventional SVM technique [14], each fundamental cycle is divided into six sectors as shown in Fig. 3. In each sector, the reference vector (Vr ) is realized by two adjacent non-zero vectors and two zero vectors. There are six non-zero vectors (V1 , . . ., V6 ) and two zero vectors (V0 , V7 ), and thus there are in total eight vectors. The zero vectors in this case are realized by switching on either the upper half or the lower half devices of the three-phase bridge inverter. By this, the three-phase load terminals become short-circuited and as input of the conventional bridge inverter is directly connected to source, the link voltage remains unchanged. The non-zero vectors in conventional PWM are operated adjacent to each other. So the soft-switching for inverter devices is not possible during transition from one nonzero vector to another non-zero vector. Thus, the ZVS operation of inverter devices is necessary between the two consecutive non-zero vectors. In order to achieve soft-switching operation, the inverter is operated under modified space vector modulation (MSVM) [17]. In MSVM, the zero vectors are realized by clamping down the link voltage to zero whereas the non-zero vectors are realized in the same way as obtained in conventional space vector modulation (SVM) [14]. In this proposed topology under MSVM, the zero vectors are realized by turning off the main and
Fig. 3. Representation of phase voltage space vector under space vector modulation (SVM).
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Fig. 4. Control technique of switching under modified space vector modulation (MSVM).
Fig. 5. Conventional direct torque control (DTC) scheme.
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Table 1 Optimum switching table Flux status
Torque status
Sector-I
Sector-II
Sector-III
Sector-IV
Sector-V
Sector-VI
ψst = 1
Tst = 1 Tst = 0 Tst = −1
Vs (1, 1, 0) Vs (1, 1, 1) Vs (1, 0, 1)
Vs (0, 1, 0) Vs (0, 0, 0) Vs (1, 0, 0)
Vs (0, 1, 1) Vs (1, 1, 1) Vs (1, 1, 0)
Vs (0, 1, 1) Vs (0, 0, 0) Vs (0, 1, 0)
Vs (1, 0, 1) Vs (1, 1, 1) Vs (0, 1, 1)
Vs (1, 0, 0) Vs (0, 0, 0) Vs (0, 0, 1)
ψst = 0
Tst = 1 Tst = 0 Tst = −1
Vs (0, 1, 0) Vs (0, 0, 0) Vs (0, 0, 1)
Vs (0, 1, 1) Vs (1, 1, 1) Vs (1, 0, 1)
Vs (0, 1, 1) Vs (0, 0, 0) Vs (1, 0, 0)
Vs (1, 0, 1) Vs (1, 1, 1) Vs (1, 1, 0)
Vs (1, 0, 0) Vs (1, 0, 0) Vs (0, 1, 1)
Vs (1, 1, 0) Vs (0, 0, 0) Vs (0, 1, 1)
auxiliary switch and turning on the shunt switches without any change in switching status of the inverter devices. The control technique of switching devices in MSVM in a sector-I is shown in Fig. 4, where the two non-zero vectors are V1 and V2 . The zero vectors Vz1 and Vz2 in MSVM replace the zero vectors V0 and V7 in conventional SVM. Similar operations repeat for other sectors. In this technique, in each fundamental cycle, the non-zero-voltage vectors are operated sequentially (V1 –V6 ) and then this process repeats. 3.2. Soft-switching inverter for DTC scheme In static load the non-zero vectors are operated sequentially with intermediate zero vectors [17]. But in conventional DTC scheme (Appendix A) shown in Fig. 5, the non-zero vectors are operated randomly based upon the flux, torque and the sector status. So a technique is developed to formulate the co-ordination among the switches in the quasi-resonant link (SWM , SWA , SW1−SH and SW2−SH ) so that the soft-switching of all devices in the quasi-resonant inverter must be ensured when the voltage vectors are operated randomly in the DTC
scheme. Once the status of the incoming voltage vector is known from the optimum switching table (Table 1), it is compared with the outgoing voltage vector that has already been latched. When the incoming voltage vector differs from the outgoing one, the soft-switching steps I–VI are adopted as follows. • Step-I: Gate pulses to both main and auxiliary switches SWM and SWA are withdrawn. • Step-II: Shunt switches, SW1−SH and SW2−SH are turned on with releasing gate pulses. • Step-III: The status of inverter switches is changed after the resonant capacitor Cr discharges to zero. • Step-IV: The shunt switches are turned off. • Step-V: The auxiliary switch is turned on for a small interval. • Step-VI: As the dc link attains the source voltage, the main switch is turned on while the auxiliary switch SWA is turned off. The control technique to be adopted here is different than that of static load [17]. Fig. 6 shows the control strategy for
Fig. 6. Control technique of switching devices between two different voltage vectors under soft-switching DTC scheme.
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the soft-switching DTC scheme with randomly chosen voltage vectors for the sake of illustration. During the transition from vector V1 to V3 , steps I–VI ensure soft-switching operation independent of direction of the dc link current. If it is found that both incoming and outgoing voltage vectors are the same, then there is no need to disable the outgoing voltage vector. Also the transitions from outgoing to incoming voltage vectors need to be handled in such a way that soft-switching of all switching devices is ensured during step change in rotor speed. The switching sequences of inverter and the resonant link devices are programmed for soft-switching by software control. During regenerative mode, the anti-parallel diode Dp remains forward biased due to negative link current. The gating pulse to the main switch SWM is present, but the device does not conduct. The auxiliary switch is in the off state. When soft-switching of inverter devices is desired, the gating pulse to SWM is withdrawn and the shunt switches (SW1−SH and SW2−SH ) are activated by releasing the gate pulses. This operation is similar to that of when dc link current is negative shown in Fig. 2(b).
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4. Hardware implementation The hardware implementation of the proposed scheme has been shown in Fig. 7. The topology permits easy implementation of ZVS technique for inverter devices independently whether the voltage vectors operate sequentially or randomly. The implementation is carried out through a combination of both software and hardware. The hardware section comprises IGBT drivers (for both quasi-resonant link and inverter), current sensors, voltage sensor, and a tacho-generator coupled with induction motordc generator set. The data-acquisition card used is ACL-8112PG and it has been attached to a PC having Pentium-IV. The control strategies of conventional DTC scheme are given in Refs. [2–4]. In case of quasi-resonant inverter, the switches in the resonant link are synchronized with the appropriate switches in the inverter after a voltage vector is chosen from optimum switching table shown in Table 1. The synchronization of link switches with the inverter switches from randomly chosen voltage vectors (i.e., between two different random voltage vectors for ex. V1 and V3 ) has been shown in Fig. 6.
Fig. 7. Hardware implementation of soft-switching DTC scheme.
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5. Simulation and experimental results The quasi-resonant inverter is initially modeled with RL load under PWM technique and simulated by SABER to validate the soft-switching scheme. The input dc voltage is 120 V. The values of resonant components are: Lr = 8 H, Lsh = 6 H and Cr = 20 nF. The procedure for the designing the components are detailed in Ref. [17]. Initially, the experiment is conducted for a static load. Typical simulation and experimental results with static load are given in Figs. 8 and 9 (i.e., with parameters sampling time Ts = 69.5 s, modulation index = 0.7, fundamental frequency = 400 Hz, power factor = 0.6, per phase load parameters: Rd = 8 , Ld = 4.2 mH). Fig. 8 shows the current and voltage across the auxiliary switch. In this figure, a vertical bi-directional arrow mark shows the turn-off of auxiliary switch. When the auxiliary switch is turned off, there appears a corresponding transient voltage (i.e., limited to input voltage) showing turn-off hard. It is also observed that the current and the voltage transient across auxiliary switch are of different amplitudes. These changes in magnitude of current and voltage across SWA are due to continuous changes in instantaneous values of (ilink , iCr ) and VCr , respectively (i.e., iSWA = ilink + iCr , vSWA = Vdc − VCr ). The gate pulses of shunt switch, main switch and their corresponding link voltage within a sector (i.e., 1/6th of a fundamental
Fig. 8. Current (iSWA ) through and voltage (vSWA ) across the auxiliary switch SWA when the inverter is operated under PWM technique with RL load (sampling interval Ts = 69.5 s, modulation index = 0.7, fundamental frequency = 400 Hz, power factor = 0.6, per phase load parameters: Rd = 8 , Ld = 4.2 mH). (a) Simulation result (scale: 1:1) and (b) experimental result (scale—iSWA : 2 A/V, vSWA : 1:10).
Fig. 9. Gate pulse GM for switch SWM , and GSH for shunt switches (SW1−SH , SW2−SH ) and dc link voltage in a sector (i.e., 1/6th of a fundamental period) when inverter is operated under PWM technique with RL-load. (a) Simulation result (scale—1:1) and (b) experimental (scale—GM , GSH : 1:1, Vlink : 1:10).
Fig. 10. GA , GM , GSH : gate pulses of switches SWA , SWM , and (SW1−SH , SW2−SH ) and dc link voltage when inverter is operated under DTC scheme during steady-state condition. (a) Simulation (scale: 1:1) and (b) experimental (scale—GA , GM , GSH : 1:1, Vlink : 1:10).
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Fig. 11 (i.e., during a step change in the reference input speed command (0–500 rpm)). It may be noted that both stator flux and rotor speed are unaffected due to load torque. Fig. 12 shows the experimental result of the speed and stator flux under fourquadrant operation. This indicates that the response of flux is unaffected during four-quadrant operation. Fig. 13 shows the rotor speed during four-quadrant operation. The theoretical and experimental efficiencies of quasi-resonant inverter are found to be 94% and 91%, respectively. Fig. 11. Response of stator flux (Ψ s ) during step change in reference speed from 0 to 500 rpm and load torque (TL ) of 1 N m for 1 s. Scale: Ψ s − 1 Wb/5 V, Tload − 1 N m/5 V.
Fig. 12. Response of rotor speed Nr during step change in reference speed from 0 to 500 rpm and load torque (TL ) of 1 N m for 1 s. Scale: Nr : 1000 rpm/6 V, Tload : 1 N m/5 V.
cycle) in Fig. 9. It is observed that except auxiliary switch, all the devices both in inverter and resonant link are soft-switched. The auxiliary switch suffers only from turn off stress particularly during positive dc link current. This limitation is less significant as compared to other soft-switching devices. Such case does not arise under when dc link current is negative. Once the soft-switching is ensured with static RL load, the scheme is extended to induction motor load operated under DTC scheme. The machine parameters are given in Appendix B. Fig. 10 shows the gate pulses of auxiliary, main, shunt switches, and link voltage for both simulation and experiment under DTC scheme. The ZVS operation can clearly be seen from the waveforms of the link voltage. The typical experimental response of flux and speed during a change in load torque for a small interval are shown in
Fig. 13. Rotor speed (Nr ) and stator flux (Ψ s ) during four-quadrant operation (scale—Nr : 1000 rpm/6 V, Ψ s : 1 Wb/5 V).
6. Conclusion The quasi-resonant inverter has been implemented in a direct torque controlled induction machine. The switching sequence of various switches in the resonant link is formulated to permit softswitching devices in the inverter. The transient and steady-state responses from quasi-resonant inverter-fed DTC scheme have shown good agreement between simulation and experimental results. All switches except auxiliary in quasi-resonant inverter are operated under soft-switching condition during both turn-on and turn-off. The auxiliary switch turn on soft, but turn on hard particularly under positive dc link current. Though the quasiresonant inverter adds extra switches in addition to a normal inverter, but on the other hand it reduces overall switching losses compared to the later and facilitating in reduction of switching stresses across motor windings. It is expected that inclusion of the soft-switching quasi-resonant inverter in DTC scheme will lead to an efficient, compact, and high performance drive system. Appendix A. Conventional direct torque control (DTC) scheme The conventional direct torque control scheme [2–4], which is known for fast transient response and less complication as compared to field-oriented control, is shown in Fig. 5. The reference speed is compared with actual speed and error is processed through PI controller and limiter to provide reference torque. The actual torque and stator flux are calculated from motor model that in turn requires three-phase currents, dc link voltage and switching status (Sa, Sb, Sc) of the devices in three-phases of the inverter. The reference torque and stator flux are compared with their respective actual values. The torque and flux error are processed through three-level hysteresis and two level hysteresis controller to generate the status of torque and flux, respectively. The sector status, which is one of the six sectors in a fundamental cycle, is determined from the d- and q-axes stator fluxes of the motor model. Based on the torque, flux and sector status, the voltage vectors are decided from optimum switching table shown in Table 1. The devices to be on/off during particular voltage vector are shown in Table 1. The generalized stator voltage vector (Vs ) can be expressed as follows in terms of Sa , Sb , and Sc . Vs (Sa , Sb , Sc ) 2 j2π j4π = Vdc Sa + Sb exp + Sc exp 3 3 3 (A.1)
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where Vdc is the dc link voltage of the inverter. Sa , Sb , and Sc are the status of the switching devices in phases (a, b, and c) of inverter, respectively. Their values are either ‘1’ or ‘0’. Each vector represents switching status in each phase. Considering this generalized equation, the six non-zero/active vectors are Vs (1, 0, 0), Vs (1, 1, 0), Vs (0, 1, 0), Vs (0, 1, 1), Vs (0, 0, 1), Vs (1, 0, 1) and the two zero vectors are Vs (0, 0, 0), Vs (1, 1, 1). The stator flux linkage Ψ s is given by the integral of the induced voltage vector behind the stator resistance. (A.2) Ψs = (Vs − is rs )dt If the voltage drop due to stator resistance ‘is rs ’ is neglected, then the trajectory of stator flux is found to move in the direction of the applied stator voltage vector. When the output is one of the active or non-zero-voltage vectors, Ψ s moves at a constant velocity that is proportional to the magnitude of the stator voltage. On the other hand, when a zero-voltage vector is selected, the velocity is nearly zero, as the drop in the stator resistance is negligible. Thus, the trajectory of Ψ s can be made to follow a specified path by a proper choice of stator voltage vectors. The magnitude of Ψ s is kept constant within a hysteresis band and the rotating velocity is regulated by the zero vectors and active vectors. Thus, a judicious selection of active and zero-voltage vectors forms the key to DTC control. Accordingly, the direction of rotation can also be changed. The magnitude of flux is maintained at a constant through a twolevel hysteresis controller. The control of flux by the two-level hysteresis controller is based on the following inequality. (Ψs∗ − Ψs ) < Ψs ≤ (Ψs∗ + Ψs )
(A.3)
where Ψs∗ is the magnitude of the reference stator flux, Ψ s the magnitude of the actual flux, and Ψ s is the flux band. Eq. (A.3) is interpreted through software control as follows: If Ψs ≥
(Ψs∗
+ Ψs ),
then Ψst = 0
(A.4)
If Ψs < (Ψs∗ − Ψs ),
then Ψst = 1
(A.5)
where Ψ st is the status of flux having the value ‘0’ or ‘1’. The flux status Ψ st = 1 indicates that the actual flux is below the lower limit of hysteresis and the voltage vectors are selected in such a way that the flux level is increased. Similarly, the flux status Ψ st = 0 indicates that the actual flux level is beyond the upper limit of hysteresis band and accordingly the voltage vectors are selected to reduce the flux. The error between the reference and actual torque is passed through a three-level hysteresis controller to realize torque control in both clockwise and anti-clockwise directions. This is implemented by the following inequalities: For clockwise rotation: (Te∗ − T ) ≤ Te ≤ Te∗
(A.6)
For anti-clockwise rotation: Te∗
≤ Te ≤ (Te∗ + T )
(A.7)
where Te is the actual torque developed, Te∗ the reference torque, and T is the torque band. While implementing under software
control, Eqs. (A.5) and (A.6) are interpreted as follows: If (Te∗ − Te ) ≥ T,
Tst = 1
(A.8)
If T > (Te∗ − Te ) ≥ 0 and Tst = 0,
Tst = 0
(A.9)
If T > (Te∗ − Te ) ≥ 0 and Tst = 1,
Tst = 1
(A.10)
If (Te∗ − Te ) ≤ −T,
Tst = −1
If − T < (Te∗ − Te ) ≤ 0 and Tst = 0, If − T < (Te∗ − Te ) ≤ 0 and Tst = −1,
(A.11) Tst = 0 Tst = −1
(A.12) (A.13)
where Tst is status of torque. Torque status ‘1’ means actual torque less than the lower limit of torque reference and hence the torque needs to be increased. Torque status ‘−1’ means the actual torque is more than the upper limit of torque reference and a reduction of the torque is necessary. For both torque status ‘−1’ and ‘1’, it requires active voltage vectors. Torque status ‘0’ means the actual torque need not change and it requires zero vectors. The voltage vector changes at the beginning of every sector and each sector is equal to an interval of π/3 radian. Appendix B. Induction machine parameters • 1 HP, line-to-line volt: 400 V, Iph (rated) = 2.6 A. • Stator resistance per phase (Rs ) = 8.4 ; rotor resistance per phase (Rr ) = 4.1 . • Stator leakage inductance per phase (ls ) = 0.026 H; rotor leakage inductance per phase (lr ) = 0.026 H. • Magnetizing inductance per phase (Lm ) = 0.377 H; moment of inertia (J) = 0.02 kg m2 . References [1] B.K. Bose, High performance control of induction motor drives, IEEE Ind. Electron. Soc. Newslett. (1998) 7–11. [2] I. Takashashi, T. Nouguchi, A new quick-response and high-efficiency control strategy of an induction motor, IEEE Trans. Ind. Appl. IA. 22 (5) (1986) 820–827. [3] M. Depenbrock, Direct self-control (DSC) of inverter-fed induction machine, IEEE Trans. Power Electron. 3 (4) (1988) 420–429. [4] J.N. Nash, Direct torque control, induction motor vector control without encoder, IEEE Trans. Ind. Appl. 33 (2) (1997) 333–341. [5] D.M. Divan, A resonant dc link converter—a new concept in static power conversion, IEEE Trans. Ind. Appl. 25 (2) (1989) 317–325. [6] D.M. Divan, G. Sibinsky, Zero switching loss inverters for high power applications, IEEE Trans. Ind. Appl. 25 (4) (1989) 634–643. [7] Y. Murai, H. Nakamura, T.A. Lipo, M.T. Aydemir, Pulse-split concept in series resonant dc link power conversion for induction motor drives, IEEE Trans. Ind. Appl. 30 (1) (1992) 45–51. [8] M.T. Aydemir, P. Caldeira, T.A. Lipo, Y. Murai, R.C. da Silva, G. Ledwich, Utilization of a series resonant dc link for a dc motor drive, IEEE Trans. Ind. Appl. 29 (5) (1993) 949–957. [9] J. He, N. Mohan, B. Wold, Zero-voltage switching PWM inverter for high frequency dc-ac power conversion, IEEE Trans. Ind. Appl. 29 (5) (1993) 959–968. [10] T.M. Johns, R.W.A.A.De. Doncker, A.V. Radun, P.M. Szczesny, F.G. Turnbull, System design considerations for a high-power aerospace resonant link converter, IEEE Trans. Power Electron. 8 (4) (1993) 663– 671.
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[15] J.S. Lai, Resonant snubber-based soft-switching inverters for electric propulsion drives, IEEE Trans. Ind. Appl. 44 (1) (1997) 71– 80. [16] D. Andrade, R.M.F. Neto, L.C. Freitas, J.B. Vieira, V.J. Farias, A softswitched current-controlled converter for induction machine drives, IEEE Trans. Power Electron. 16 (1) (2001) 63–71. [17] S. Behera, S.P. Das, S.R. Doradla, A Novel quasi-resonant soft-switching Inverter for Low and high power factor loads, IEE Proc. Electr. Power Appl. (EPA) 151 (4) (2004) 451–459.
Quasi-resonant inverter-fed direct torque controlled induction motor drive S. Behera ∗ , S.P. Das 1 , S.R. Doradla 1 Power Electronics Laboratory, Electrical Engineering., Indian Institute of Technology, Kanpur 208016, India Received 13 February 2006; received in revised form 8 August 2006; accepted 16 August 2006 Available online 18 September 2006
Abstract A quasi-resonant inverter-fed induction motor operated under direct torque control (DTC) scheme is modeled and analyzed with SABER simulator. The dc link voltage is clamped to source voltage. All the devices in the resonant link and inverter except auxiliary switch in the resonant link are operated soft under zero-voltage switching (ZVS). The auxiliary switch is turned on under zero-current switching (ZCS), but turned off hard. This scheme has been implemented on a laboratory-sized experimental setup. A comparison of simulation and experimental results under identical operating conditions were presented. © 2006 Elsevier B.V. All rights reserved. Keywords: Quasi-resonant inverter; SABER simulation; Direct torque control (DTC) scheme
1. Introduction Variable voltage and variable frequency operation of induction motors are generally used for speed and torque control of induction motor drives. The literature related to ac drives covering scalar control, field-oriented control, and direct torque control (DTC) has been well documented [1]. The induction motor drives employing DTC strategies with various variables have been reported [2–4]. In all these schemes, a better torque profile and current response have been focused. Because of hard-switching in conventional PWM inverters, the switching losses in the devices are high and the windings of induction motor are subjected to high switching stresses. The limitations of hard-switchings are restriction in switching frequency, acoustic noise, larger filter size and EMI, etc. These shortcomings can be overcome using soft-switching techniques (zero-voltage/zerocurrent switchings). Various soft-switching strategies for both static and dynamic loads are being discussed in literatures [5–17]. The soft-switching inverter-fed three-phase induction motor drive is lacking in the literature. In the area of softswitching inverter-fed induction motor drives, only a few papers ∗
Corresponding author at: Department of Electrical Engineering, University College of Engineering, Burla 768018, Orissa, India. Tel.: +91 663 2432608. E-mail address: [email protected] (S. Behera). 1 Department of Electrical Engineering, Indian Institute of Technology, Kanpur 208016, India. 0378-7796/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2006.08.011
[15,16] have appeared in the literature, but still they suffer considerably from hard-switchings. Out of various soft-switching techniques (i.e., load resonant, resonant link and resonant transition), the quasi-resonant technique that comes under resonant transition category is the latest and most popular one as far as the soft-switchings of the devices are concerned. The quasiresonant topology [17], which is meant for static RL load, has been actively considered for dynamic load (i.e., induction motor drive under DTC scheme) in the present paper. The control scheme used for dynamic load in this paper is different than that of static load [17]. The complete scheme is modeled and simulated by SABER to analyze its performance. A laboratory-sized model is fabricated and experimentally tested in order to verify with the simulation results under identical operating conditions. 2. Quasi-resonant inverter topology and basic operation The proposed quasi-resonant inverter topology is shown in Fig. 1. The current input to the inverter is designated as dc link/load current ‘ilink ’, which is assumed to be ripple free for explanation shown in Fig. 2. This topology has the ability to provide zero-voltage switching (ZVS) of all inverter switches for both positive and negative dc link current ilink . The switching waveforms of gating pulses of all resonant link switches, resonant capacitor voltage and resonant inductor current under common control strategy (i.e., either positive or negative dc link current) are shown in Fig. 2. The gating pulses for the link
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Fig. 1. Circuit diagram of quasi-resonant dc link inverter topology.
switches shown in Fig. 2(a) allow soft-switching of inverter devices for both negative and positive dc link current. The waveforms of resonant capacitor voltage and resonant inductor current shown in Fig. 2(b) correspond to the case when the link current is negative. Fig. 2(c) corresponds to the case when the dc link current is positive. The link current may be positive or negative during a switching cycle. In order to initiate soft-switching process, the gating pulse to the main switch is withdrawn at to . In case of negative dc link current, the diode Dp conducts and the link voltage is clamped to the source voltage. On the other hand if the link current is positive, the resonant capacitor
across the dc link discharges to zero through the inverter and load. The shunt switches SW1−SH , SW2−SH are turned on at t1 with the release of gate pulses. In case of negative link current the dc link voltage continues to be clamped at the source voltage due to conduction of the diode DP . The current through the shunt inductor increases linearly from zero to the dc link current while the current through DP decreases linearly and turns off at t2 . From t2 onwards, the link voltage is no more clamped to the source voltage due to reverse-biased diode DP . The resonant capacitor starts discharging through the shunt inductor LSh . The shunt inductor current increases resonantly from its initial
Fig. 2. Switching waveforms under independent direction of dc link current (a) gating pulses to dc link switches, (b) waveforms of VCr and ilr when dc link current is negative and (c) waveforms of VCr and ilsh when dc link current is positive.
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value of ilink . The resonant capacitor discharges resonantly to zero at t3 . The soft-switching of inverter devices under ZVS is achieved during t3 –t4 . The diode D1−SH is forward biased by the trapped energy in LSh and conduction of shunt switch SW2−SH . This continues until the removal of gating pulses from the shunt switches at t4 . In case of positive link current, the link voltage continues to be held at zero value until the auxiliary switch is turned on. However, the switching status of inverter device is changed during t3 –t4 as in the case of negative dc link current. This ensures that the link voltage is held at zero before switching of inverter devices is initiated independent of the direction of link current. The gating pulses from the shunt switches are removed at t4 . The energy trapped in the shunt inductor is recovered to the source through conduction of diodes D1−SH and D2−SH . The resonant capacitor is charged linearly by the negative dc link current and it continues until the link voltage becomes equal to the source voltage. Then, the diode DP gets forward biased and conducts the negative link current. The gating signal to the auxiliary switch SWA is released. This does not affect the operation when the link current is negative. In case of positive link current, the auxiliary switch turns on under ZCS due to resonant inductor Lr . The current through the resonant inductor increases linearly until it becomes equal to the link current. At t6 , the excess current through the resonant inductor charges the link capacitor resonantly. This continues until the link voltage becomes equal to the source voltage. At this instant t7 , SWM is turned on and SWA is turned off. The excess current in the resonant inductor is fed back to the source through diode DP . When the inductor current becomes equal to the link current, the diode DP turns off. The main switch turns on under ZVS and supplies the load current along with the resonant inductor. As the resonant inductor current falls to zero, the main switch carries the link current. In case of negative link current, the operation of main and auxiliary switches does not have any effect. This explains soft-switching operation independent of direction of dc link current. Now the dc link is ready for the next soft-switching operation. Above all, the roles of auxiliary and other switches in dc link are summarized as follows: The role of auxiliary switch (SWA ) is not only to prevent the main switch (SWM ) from short circuit through resonating capacitor (Cr ) during turn-on of the later (i.e., the resonating capacitor Cr retains zero charge/voltage), but also from discharging current of snubber capacitor (Csnub ). The auxiliary switch assists in resonating dc link voltage with the help of Lr and Cr , by which the voltage across resonating capacitor builds up and is clamped to input voltage due to anti-parallel diode across the main switch. This enables the main switch to turn-on soft under ZVS as the voltage across it is zero. The main switch turns off soft under ZVS due to snubber capacitor across it. Every time, the auxiliary switch is enabled, whenever the main switch is needed to turn on irrespective load conditions. All the switches in dc link are operated in sequence (i.e., essential to make the topology independent of direction of link current shown in Fig. 2) for soft-switching operation of its own and inverter devices. When the link current is from source to inverter, the auxiliary switch (SWA ) and main switch (SWM ) remain active as they handle link current and voltage. The shunt
switches (SW1−SH , SW2−SH ) do not handle link current as the link voltage being already clamped down to zero. On the other hand, when the link current is in opposite direction (i.e., from inverter to source), the shunt switches remain active by handling current and voltage of dc link. The switches SWA and SWM that are operated prior to the shunt do not handle link current, as these are reverse-biased. 3. Control strategy for soft-switching scheme The soft-switching strategies for three-phase static and dynamic loads are different and explained in following two sections. 3.1. Soft-switching inverter for three-phase static load In the conventional SVM technique [14], each fundamental cycle is divided into six sectors as shown in Fig. 3. In each sector, the reference vector (Vr ) is realized by two adjacent non-zero vectors and two zero vectors. There are six non-zero vectors (V1 , . . ., V6 ) and two zero vectors (V0 , V7 ), and thus there are in total eight vectors. The zero vectors in this case are realized by switching on either the upper half or the lower half devices of the three-phase bridge inverter. By this, the three-phase load terminals become short-circuited and as input of the conventional bridge inverter is directly connected to source, the link voltage remains unchanged. The non-zero vectors in conventional PWM are operated adjacent to each other. So the soft-switching for inverter devices is not possible during transition from one nonzero vector to another non-zero vector. Thus, the ZVS operation of inverter devices is necessary between the two consecutive non-zero vectors. In order to achieve soft-switching operation, the inverter is operated under modified space vector modulation (MSVM) [17]. In MSVM, the zero vectors are realized by clamping down the link voltage to zero whereas the non-zero vectors are realized in the same way as obtained in conventional space vector modulation (SVM) [14]. In this proposed topology under MSVM, the zero vectors are realized by turning off the main and
Fig. 3. Representation of phase voltage space vector under space vector modulation (SVM).
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Fig. 4. Control technique of switching under modified space vector modulation (MSVM).
Fig. 5. Conventional direct torque control (DTC) scheme.
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Table 1 Optimum switching table Flux status
Torque status
Sector-I
Sector-II
Sector-III
Sector-IV
Sector-V
Sector-VI
ψst = 1
Tst = 1 Tst = 0 Tst = −1
Vs (1, 1, 0) Vs (1, 1, 1) Vs (1, 0, 1)
Vs (0, 1, 0) Vs (0, 0, 0) Vs (1, 0, 0)
Vs (0, 1, 1) Vs (1, 1, 1) Vs (1, 1, 0)
Vs (0, 1, 1) Vs (0, 0, 0) Vs (0, 1, 0)
Vs (1, 0, 1) Vs (1, 1, 1) Vs (0, 1, 1)
Vs (1, 0, 0) Vs (0, 0, 0) Vs (0, 0, 1)
ψst = 0
Tst = 1 Tst = 0 Tst = −1
Vs (0, 1, 0) Vs (0, 0, 0) Vs (0, 0, 1)
Vs (0, 1, 1) Vs (1, 1, 1) Vs (1, 0, 1)
Vs (0, 1, 1) Vs (0, 0, 0) Vs (1, 0, 0)
Vs (1, 0, 1) Vs (1, 1, 1) Vs (1, 1, 0)
Vs (1, 0, 0) Vs (1, 0, 0) Vs (0, 1, 1)
Vs (1, 1, 0) Vs (0, 0, 0) Vs (0, 1, 1)
auxiliary switch and turning on the shunt switches without any change in switching status of the inverter devices. The control technique of switching devices in MSVM in a sector-I is shown in Fig. 4, where the two non-zero vectors are V1 and V2 . The zero vectors Vz1 and Vz2 in MSVM replace the zero vectors V0 and V7 in conventional SVM. Similar operations repeat for other sectors. In this technique, in each fundamental cycle, the non-zero-voltage vectors are operated sequentially (V1 –V6 ) and then this process repeats. 3.2. Soft-switching inverter for DTC scheme In static load the non-zero vectors are operated sequentially with intermediate zero vectors [17]. But in conventional DTC scheme (Appendix A) shown in Fig. 5, the non-zero vectors are operated randomly based upon the flux, torque and the sector status. So a technique is developed to formulate the co-ordination among the switches in the quasi-resonant link (SWM , SWA , SW1−SH and SW2−SH ) so that the soft-switching of all devices in the quasi-resonant inverter must be ensured when the voltage vectors are operated randomly in the DTC
scheme. Once the status of the incoming voltage vector is known from the optimum switching table (Table 1), it is compared with the outgoing voltage vector that has already been latched. When the incoming voltage vector differs from the outgoing one, the soft-switching steps I–VI are adopted as follows. • Step-I: Gate pulses to both main and auxiliary switches SWM and SWA are withdrawn. • Step-II: Shunt switches, SW1−SH and SW2−SH are turned on with releasing gate pulses. • Step-III: The status of inverter switches is changed after the resonant capacitor Cr discharges to zero. • Step-IV: The shunt switches are turned off. • Step-V: The auxiliary switch is turned on for a small interval. • Step-VI: As the dc link attains the source voltage, the main switch is turned on while the auxiliary switch SWA is turned off. The control technique to be adopted here is different than that of static load [17]. Fig. 6 shows the control strategy for
Fig. 6. Control technique of switching devices between two different voltage vectors under soft-switching DTC scheme.
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the soft-switching DTC scheme with randomly chosen voltage vectors for the sake of illustration. During the transition from vector V1 to V3 , steps I–VI ensure soft-switching operation independent of direction of the dc link current. If it is found that both incoming and outgoing voltage vectors are the same, then there is no need to disable the outgoing voltage vector. Also the transitions from outgoing to incoming voltage vectors need to be handled in such a way that soft-switching of all switching devices is ensured during step change in rotor speed. The switching sequences of inverter and the resonant link devices are programmed for soft-switching by software control. During regenerative mode, the anti-parallel diode Dp remains forward biased due to negative link current. The gating pulse to the main switch SWM is present, but the device does not conduct. The auxiliary switch is in the off state. When soft-switching of inverter devices is desired, the gating pulse to SWM is withdrawn and the shunt switches (SW1−SH and SW2−SH ) are activated by releasing the gate pulses. This operation is similar to that of when dc link current is negative shown in Fig. 2(b).
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4. Hardware implementation The hardware implementation of the proposed scheme has been shown in Fig. 7. The topology permits easy implementation of ZVS technique for inverter devices independently whether the voltage vectors operate sequentially or randomly. The implementation is carried out through a combination of both software and hardware. The hardware section comprises IGBT drivers (for both quasi-resonant link and inverter), current sensors, voltage sensor, and a tacho-generator coupled with induction motordc generator set. The data-acquisition card used is ACL-8112PG and it has been attached to a PC having Pentium-IV. The control strategies of conventional DTC scheme are given in Refs. [2–4]. In case of quasi-resonant inverter, the switches in the resonant link are synchronized with the appropriate switches in the inverter after a voltage vector is chosen from optimum switching table shown in Table 1. The synchronization of link switches with the inverter switches from randomly chosen voltage vectors (i.e., between two different random voltage vectors for ex. V1 and V3 ) has been shown in Fig. 6.
Fig. 7. Hardware implementation of soft-switching DTC scheme.
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5. Simulation and experimental results The quasi-resonant inverter is initially modeled with RL load under PWM technique and simulated by SABER to validate the soft-switching scheme. The input dc voltage is 120 V. The values of resonant components are: Lr = 8 H, Lsh = 6 H and Cr = 20 nF. The procedure for the designing the components are detailed in Ref. [17]. Initially, the experiment is conducted for a static load. Typical simulation and experimental results with static load are given in Figs. 8 and 9 (i.e., with parameters sampling time Ts = 69.5 s, modulation index = 0.7, fundamental frequency = 400 Hz, power factor = 0.6, per phase load parameters: Rd = 8 , Ld = 4.2 mH). Fig. 8 shows the current and voltage across the auxiliary switch. In this figure, a vertical bi-directional arrow mark shows the turn-off of auxiliary switch. When the auxiliary switch is turned off, there appears a corresponding transient voltage (i.e., limited to input voltage) showing turn-off hard. It is also observed that the current and the voltage transient across auxiliary switch are of different amplitudes. These changes in magnitude of current and voltage across SWA are due to continuous changes in instantaneous values of (ilink , iCr ) and VCr , respectively (i.e., iSWA = ilink + iCr , vSWA = Vdc − VCr ). The gate pulses of shunt switch, main switch and their corresponding link voltage within a sector (i.e., 1/6th of a fundamental
Fig. 8. Current (iSWA ) through and voltage (vSWA ) across the auxiliary switch SWA when the inverter is operated under PWM technique with RL load (sampling interval Ts = 69.5 s, modulation index = 0.7, fundamental frequency = 400 Hz, power factor = 0.6, per phase load parameters: Rd = 8 , Ld = 4.2 mH). (a) Simulation result (scale: 1:1) and (b) experimental result (scale—iSWA : 2 A/V, vSWA : 1:10).
Fig. 9. Gate pulse GM for switch SWM , and GSH for shunt switches (SW1−SH , SW2−SH ) and dc link voltage in a sector (i.e., 1/6th of a fundamental period) when inverter is operated under PWM technique with RL-load. (a) Simulation result (scale—1:1) and (b) experimental (scale—GM , GSH : 1:1, Vlink : 1:10).
Fig. 10. GA , GM , GSH : gate pulses of switches SWA , SWM , and (SW1−SH , SW2−SH ) and dc link voltage when inverter is operated under DTC scheme during steady-state condition. (a) Simulation (scale: 1:1) and (b) experimental (scale—GA , GM , GSH : 1:1, Vlink : 1:10).
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Fig. 11 (i.e., during a step change in the reference input speed command (0–500 rpm)). It may be noted that both stator flux and rotor speed are unaffected due to load torque. Fig. 12 shows the experimental result of the speed and stator flux under fourquadrant operation. This indicates that the response of flux is unaffected during four-quadrant operation. Fig. 13 shows the rotor speed during four-quadrant operation. The theoretical and experimental efficiencies of quasi-resonant inverter are found to be 94% and 91%, respectively. Fig. 11. Response of stator flux (Ψ s ) during step change in reference speed from 0 to 500 rpm and load torque (TL ) of 1 N m for 1 s. Scale: Ψ s − 1 Wb/5 V, Tload − 1 N m/5 V.
Fig. 12. Response of rotor speed Nr during step change in reference speed from 0 to 500 rpm and load torque (TL ) of 1 N m for 1 s. Scale: Nr : 1000 rpm/6 V, Tload : 1 N m/5 V.
cycle) in Fig. 9. It is observed that except auxiliary switch, all the devices both in inverter and resonant link are soft-switched. The auxiliary switch suffers only from turn off stress particularly during positive dc link current. This limitation is less significant as compared to other soft-switching devices. Such case does not arise under when dc link current is negative. Once the soft-switching is ensured with static RL load, the scheme is extended to induction motor load operated under DTC scheme. The machine parameters are given in Appendix B. Fig. 10 shows the gate pulses of auxiliary, main, shunt switches, and link voltage for both simulation and experiment under DTC scheme. The ZVS operation can clearly be seen from the waveforms of the link voltage. The typical experimental response of flux and speed during a change in load torque for a small interval are shown in
Fig. 13. Rotor speed (Nr ) and stator flux (Ψ s ) during four-quadrant operation (scale—Nr : 1000 rpm/6 V, Ψ s : 1 Wb/5 V).
6. Conclusion The quasi-resonant inverter has been implemented in a direct torque controlled induction machine. The switching sequence of various switches in the resonant link is formulated to permit softswitching devices in the inverter. The transient and steady-state responses from quasi-resonant inverter-fed DTC scheme have shown good agreement between simulation and experimental results. All switches except auxiliary in quasi-resonant inverter are operated under soft-switching condition during both turn-on and turn-off. The auxiliary switch turn on soft, but turn on hard particularly under positive dc link current. Though the quasiresonant inverter adds extra switches in addition to a normal inverter, but on the other hand it reduces overall switching losses compared to the later and facilitating in reduction of switching stresses across motor windings. It is expected that inclusion of the soft-switching quasi-resonant inverter in DTC scheme will lead to an efficient, compact, and high performance drive system. Appendix A. Conventional direct torque control (DTC) scheme The conventional direct torque control scheme [2–4], which is known for fast transient response and less complication as compared to field-oriented control, is shown in Fig. 5. The reference speed is compared with actual speed and error is processed through PI controller and limiter to provide reference torque. The actual torque and stator flux are calculated from motor model that in turn requires three-phase currents, dc link voltage and switching status (Sa, Sb, Sc) of the devices in three-phases of the inverter. The reference torque and stator flux are compared with their respective actual values. The torque and flux error are processed through three-level hysteresis and two level hysteresis controller to generate the status of torque and flux, respectively. The sector status, which is one of the six sectors in a fundamental cycle, is determined from the d- and q-axes stator fluxes of the motor model. Based on the torque, flux and sector status, the voltage vectors are decided from optimum switching table shown in Table 1. The devices to be on/off during particular voltage vector are shown in Table 1. The generalized stator voltage vector (Vs ) can be expressed as follows in terms of Sa , Sb , and Sc . Vs (Sa , Sb , Sc ) 2 j2π j4π = Vdc Sa + Sb exp + Sc exp 3 3 3 (A.1)
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where Vdc is the dc link voltage of the inverter. Sa , Sb , and Sc are the status of the switching devices in phases (a, b, and c) of inverter, respectively. Their values are either ‘1’ or ‘0’. Each vector represents switching status in each phase. Considering this generalized equation, the six non-zero/active vectors are Vs (1, 0, 0), Vs (1, 1, 0), Vs (0, 1, 0), Vs (0, 1, 1), Vs (0, 0, 1), Vs (1, 0, 1) and the two zero vectors are Vs (0, 0, 0), Vs (1, 1, 1). The stator flux linkage Ψ s is given by the integral of the induced voltage vector behind the stator resistance. (A.2) Ψs = (Vs − is rs )dt If the voltage drop due to stator resistance ‘is rs ’ is neglected, then the trajectory of stator flux is found to move in the direction of the applied stator voltage vector. When the output is one of the active or non-zero-voltage vectors, Ψ s moves at a constant velocity that is proportional to the magnitude of the stator voltage. On the other hand, when a zero-voltage vector is selected, the velocity is nearly zero, as the drop in the stator resistance is negligible. Thus, the trajectory of Ψ s can be made to follow a specified path by a proper choice of stator voltage vectors. The magnitude of Ψ s is kept constant within a hysteresis band and the rotating velocity is regulated by the zero vectors and active vectors. Thus, a judicious selection of active and zero-voltage vectors forms the key to DTC control. Accordingly, the direction of rotation can also be changed. The magnitude of flux is maintained at a constant through a twolevel hysteresis controller. The control of flux by the two-level hysteresis controller is based on the following inequality. (Ψs∗ − Ψs ) < Ψs ≤ (Ψs∗ + Ψs )
(A.3)
where Ψs∗ is the magnitude of the reference stator flux, Ψ s the magnitude of the actual flux, and Ψ s is the flux band. Eq. (A.3) is interpreted through software control as follows: If Ψs ≥
(Ψs∗
+ Ψs ),
then Ψst = 0
(A.4)
If Ψs < (Ψs∗ − Ψs ),
then Ψst = 1
(A.5)
where Ψ st is the status of flux having the value ‘0’ or ‘1’. The flux status Ψ st = 1 indicates that the actual flux is below the lower limit of hysteresis and the voltage vectors are selected in such a way that the flux level is increased. Similarly, the flux status Ψ st = 0 indicates that the actual flux level is beyond the upper limit of hysteresis band and accordingly the voltage vectors are selected to reduce the flux. The error between the reference and actual torque is passed through a three-level hysteresis controller to realize torque control in both clockwise and anti-clockwise directions. This is implemented by the following inequalities: For clockwise rotation: (Te∗ − T ) ≤ Te ≤ Te∗
(A.6)
For anti-clockwise rotation: Te∗
≤ Te ≤ (Te∗ + T )
(A.7)
where Te is the actual torque developed, Te∗ the reference torque, and T is the torque band. While implementing under software
control, Eqs. (A.5) and (A.6) are interpreted as follows: If (Te∗ − Te ) ≥ T,
Tst = 1
(A.8)
If T > (Te∗ − Te ) ≥ 0 and Tst = 0,
Tst = 0
(A.9)
If T > (Te∗ − Te ) ≥ 0 and Tst = 1,
Tst = 1
(A.10)
If (Te∗ − Te ) ≤ −T,
Tst = −1
If − T < (Te∗ − Te ) ≤ 0 and Tst = 0, If − T < (Te∗ − Te ) ≤ 0 and Tst = −1,
(A.11) Tst = 0 Tst = −1
(A.12) (A.13)
where Tst is status of torque. Torque status ‘1’ means actual torque less than the lower limit of torque reference and hence the torque needs to be increased. Torque status ‘−1’ means the actual torque is more than the upper limit of torque reference and a reduction of the torque is necessary. For both torque status ‘−1’ and ‘1’, it requires active voltage vectors. Torque status ‘0’ means the actual torque need not change and it requires zero vectors. The voltage vector changes at the beginning of every sector and each sector is equal to an interval of π/3 radian. Appendix B. Induction machine parameters • 1 HP, line-to-line volt: 400 V, Iph (rated) = 2.6 A. • Stator resistance per phase (Rs ) = 8.4 ; rotor resistance per phase (Rr ) = 4.1 . • Stator leakage inductance per phase (ls ) = 0.026 H; rotor leakage inductance per phase (lr ) = 0.026 H. • Magnetizing inductance per phase (Lm ) = 0.377 H; moment of inertia (J) = 0.02 kg m2 . References [1] B.K. Bose, High performance control of induction motor drives, IEEE Ind. Electron. Soc. Newslett. (1998) 7–11. [2] I. Takashashi, T. Nouguchi, A new quick-response and high-efficiency control strategy of an induction motor, IEEE Trans. Ind. Appl. IA. 22 (5) (1986) 820–827. [3] M. Depenbrock, Direct self-control (DSC) of inverter-fed induction machine, IEEE Trans. Power Electron. 3 (4) (1988) 420–429. [4] J.N. Nash, Direct torque control, induction motor vector control without encoder, IEEE Trans. Ind. Appl. 33 (2) (1997) 333–341. [5] D.M. Divan, A resonant dc link converter—a new concept in static power conversion, IEEE Trans. Ind. Appl. 25 (2) (1989) 317–325. [6] D.M. Divan, G. Sibinsky, Zero switching loss inverters for high power applications, IEEE Trans. Ind. Appl. 25 (4) (1989) 634–643. [7] Y. Murai, H. Nakamura, T.A. Lipo, M.T. Aydemir, Pulse-split concept in series resonant dc link power conversion for induction motor drives, IEEE Trans. Ind. Appl. 30 (1) (1992) 45–51. [8] M.T. Aydemir, P. Caldeira, T.A. Lipo, Y. Murai, R.C. da Silva, G. Ledwich, Utilization of a series resonant dc link for a dc motor drive, IEEE Trans. Ind. Appl. 29 (5) (1993) 949–957. [9] J. He, N. Mohan, B. Wold, Zero-voltage switching PWM inverter for high frequency dc-ac power conversion, IEEE Trans. Ind. Appl. 29 (5) (1993) 959–968. [10] T.M. Johns, R.W.A.A.De. Doncker, A.V. Radun, P.M. Szczesny, F.G. Turnbull, System design considerations for a high-power aerospace resonant link converter, IEEE Trans. Power Electron. 8 (4) (1993) 663– 671.
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