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16 msivasathyanarayana 171-184
 

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The International Institute for Science, Technology and Education (IISTE) , International Journals Call for papaers: http://www.iiste.org/Journals

The International Institute for Science, Technology and Education (IISTE) , International Journals Call for papaers: http://www.iiste.org/Journals

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    16 msivasathyanarayana 171-184 16 msivasathyanarayana 171-184 Document Transcript

    • Computer Engineering and Intelligent Systems www.iiste.orgISSN 2222-1719 (Paper) ISSN 2222-2863 (Online)Vol 2, No.3VSI fed IM drive employing look –up tables with 6&12 sectors M. Siva Sathyanarayana1, D. Subba Rayudu2, T. Brahmananda Reddy3 ,V. Sowmya Sree4 1 Department of Electrical and Electronics Engineering, G.Pulla Reddy Engineering College (Autonomous), Kurnool, Andhra Pradesh, India sathya_varma@rediffmail.com, tbnr@rediffmail.comAbstract: Since the IM drives play a vital role for variable speed applications from fractional horse powerto multi Mega-watt power, the control and estimation of induction motor drives constitute a vast subject.Nowadays, vector control and direct torque control (DTC) are popular for high performance drives. Eventhough these methods give better performance, the vector control method needs reference frametransformations and direct torque control gives large steady state ripples. To overcome these problems inthe above methods mentioned, this paper presents an advanced vector control method for voltage-sourceinverter fed induction motors using sophisticated look-up tables. This method uses a predetermined look-uptable instead of a much more time consuming pulse width modulation (PWM) procedure in conventionalvector control for generating inverter gate signals. This approach gives faster torque response like in vectorcontrol methods and it also reduces ripples as in DTC method. To validate the proposed method numericalsimulations have been carried out and compared with the existing algorithms. The simulation resultsconfirm the effectiveness of the proposed method.Key Words— Induction Motor Drive, Look-up table, Vector Control 1. Introduction High performance induction motor drives require decoupled torque and flux control. This controlis commonly provided through vector control. Vector control schemes require reference frametransformation. DTC as compared to FOC is advantageous in aspects such as absence of co-ordinatetransformation and PWM modulator. DTC is also very simple in its implementation as it needs only twohysteresis comparators and a lookup table for both flux and torque control. A detailed comparison betweenvector control and DTC has given in. Though, DTC gives fast transient response, it gives large ripple insteady state. Hence to overcome the drawbacks of vector control and DTC, this paper presents a new vectorcontrol scheme, which combines the principles of both vector control and DTC. For the current controllers,several look-up tables have given in. This paper also presents, a sophisticated look-up table based vectorcontrol algorithm. The proposed method does not require reference frame transformations and give goodsteady state and transient responses. 2. Mathematical Modeling of Induction Motor The voltage expressions of a three-phase induction motor in stator reference frame are given as in(1) d s v s  Rs i s  (1) dt dr vr  Rr ir  j r r  (2) dt The dynamic equations of the induction motor can be represented by using flux linkages asvariables, which involves the reduction of a number of variables in the dynamic equations. The stator androtor flux linkages in the stator reference frame are defined as in (2). 171
    • Computer Engineering and Intelligent Systems www.iiste.orgISSN 2222-1719 (Paper) ISSN 2222-2863 (Online)Vol 2, No.3 s  Ls is  Lmir (3) r  Lmis  Lr ir (4)The electromagnetic torque and electromechanical expressions of the induction motor are given by Te  3 P Lm 2 2 Lr  dr iqs  qr ids  (5) d m 2 d rAnd Te  TL  J  TL  J (6) dt P dt 3. Vector Control of Induction Motor The induction motor’s dynamic model equations are non-linear and multi-variable. Also, anadditional non-linearity is seen in the machine model due to variation of machine parameters withsaturation temperature and skin effect. There are also coupling effects between input and output variablesi.e., both torque and flux are functions of voltage and frequency. In the vector control algorithm, themachine torque and rotor flux linkage are controlled through stator current vector control. The stator * *current vector is divided into a torque producing component ( iqs ) and flux producing component ( i ds ) in *a rotating frame of reference. The flux component i ds is along the machine flux linkage vector and the *torque component iqs is perpendicular to the flux component. This represents the decoupling effectbetween torque and flux. The electromagnetic torque expression for an induction motor is given by 3 P Lm  *  3 P L Te  2 2 Lr Re j r  is    m   2 2 L dr iqs  qr ids  (7)   rFor decoupling control, the q-axis flux component must be made equal to zero. Then the torque expressioncan be modified as given in (8). Te  3 P Lm 2 2 Lr  dr iqs  (8)Hence, the total rotor flux equal to r  dr and given as in (9). r  dr  Lmids (9) From (9), it can be observed that the rotor flux is directly proportional to ids and is maintainedconstant. Hence, the torque linearly depends on i qs , and provides a faster torque response than the current( i qs ) response. Then, the slip frequency sl is added to the rotor speed to generate unit vectors. Theblock diagram of indirect vector controlled induction motor drive is as shown in Fig.1. 172
    • Computer Engineering and Intelligent Systems www.iiste.orgISSN 2222-1719 (Paper) ISSN 2222-2863 (Online)Vol 2, No.3 Fig. 1 Block diagram of indirect vector controlled induction motor drive The d-q axes currents then transformed from rotating to stationary and then converted from two-phase to three-phase currents. Then, the reference three-phase currents are compared with the actual three-phase stator currents in the hysteresis band type current controller, from which the pulses can be generatedand given to the voltage source inverter. 4. Proposed Vector Control Algorithm for Induction Motor The electromagnetic torque expression for an induction motor, which is given in (7), can berepresented as 3 P Lm Te  r is sin  (10) 2 2 Lrwhere  is the angle between stator current and rotor flux linkage vectors as shown in Fig. 2. q is ji qs  r ids d 173
    • Computer Engineering and Intelligent Systems www.iiste.orgISSN 2222-1719 (Paper) ISSN 2222-2863 (Online)Vol 2, No.3 Fig. 2 Representation of stator current vector and rotor flux linkage space vectorsFrom (10), it can be observed that the torque dynamics depends on the variation of  . Hence, fast torquecontrol can be achieved by rapidly changing ‘  ’ in the required direction. This is the basic objective of“proposed vector control”. During a short transient, the rotor flux remains almost unchanged, thus rapidchanges of electromagnetic torque can be produced by rotating the d and q components of stator currentvector in the required direction. By ignoring the stator resistance drop, the stator voltage expression can berepresented as d s vs  (11) dtFrom (3) and (4), the stator flux linkage space vector can be represented as given in (12). Lm L2  s  Ls i s  r  m i s (12) Lr LrThen the stator voltage expression can be represented as given in (13). d s di L d L2 di vs   Ls s  m r  m s (13) dt dt Lr dt Lr dtAs the rotor time constant is high, the rotor flux linkage space vector will move slowly. Hence, for shorttime durations, the rotor flux linkage vector is assumed as constant. This simplifies the voltage expressionas follows. d s  2   L  Lm  dis  L di s vs   s (14) dt  Lr  dt s dt  For a short time interval of t , the stator current expression can be represented as given in (15). 1 is  v s t (15) LsThus, the stator current space vector moves by i s in the direction of the stator voltage space vector at aspeed proportional to magnitude of voltage space vector (i.e. dc link voltage). By selecting the appropriatestator voltage vector step-by-step, it is then possible to change the stator current in the required direction.Decoupled control of the torque and stator flux is achieved by acting on the radial (flux component currentids ) and tangential components (torque component current iqs ) of the stator current vector in the locus. Considering the three-phase, two-level, six pulse voltage source inverter (VSI), there are six non-zero active voltage space vectors and two zero voltage space vectors as shown in Fig.3. The six activevoltage space vectors can be represented as 3  Vk  Vdc exp j k  1 2 3  k  1,2,...,6 (16)Depending on the position of stator current vector, it is possible to switch the appropriate voltage vectors tocontrol both d and q axes stator currents. As an example if stator current vector is in sector I, then voltagevectors V2 and V6 can increase ids and V3 and V5 can decrease the ids . Similarly V2 and V3 can 174
    • Computer Engineering and Intelligent Systems www.iiste.orgISSN 2222-1719 (Paper) ISSN 2222-2863 (Online)Vol 2, No.3increase the torque component current i qs and V5 and V6 can decrease the iqs . Similarly the suitablevoltage vectors can be selected for other sectors. V3 (010) V2 (110) Sector I V4 (011) V1 (100) V0 (000) V7 (111) V5 (001) V6 (101) Fig. 3 Inverter voltage space vectors with 6-sector division Table 1. Optimum voltage Switching vector look up table with 6-sectors N 1 2 3 4 5 6 Sq = 1 110 010 011 001 101 100 Sd = 1 Sq = 0 111 000 111 000 111 000 Sq = -1 101 100 110 010 011 001 Sq = 1 010 011 001 101 100 110 Sd = 0 Sq = 0 000 111 000 111 000 111 Sq = -1 001 101 100 110 010 011The proposed vector controlled induction motor drive block diagram s shown in fig.4 175
    • Computer Engineering and Intelligent Systems www.iiste.orgISSN 2222-1719 (Paper) ISSN 2222-2863 (Online)Vol 2, No.3 V dc w* r * Te iqs  iqs + PI + ST - Calculation - Optimal Look-up wr Sd Table *  ids r i ds + - Calculation Sector Estimation i qs  , Reference i ds frame angle and i ds , i qs estimation Motor Signals IM Fig. 4 Block diagram of proposed vector controlled induction motor drive As in conventional vector control, the proposed vector control algorithm generates d- and q- axescommands. Then as in DTC, the proposed algorithm uses hysteresis current controllers and switching table.Thus, the proposed algorithm eliminates time consuming PWM procedure. The generated d and q axiscurrent commands are compared with their actual current values obtained from the measured phasecurrents. The current errors are used to produce d and q flags as inputs to the switching table. A third inputto the table determines the sector through which the current vector is passing. It is produced by having the dand q axis currents and the rotor position. The switching table provides the proper voltage vectors bydeciding on the status of the inverter switches. In field oriented control, the current decoupling network is afeed forward (indirect) method to produce flux orientation. In proposed control system, Current decouplingmeans to determine the reference current space phasor ids , iqs , based on reference rotor flux  r and * * *torque Te* . Based on the outputs of hysteresis controllers and position of the stator current vector, theoptimum switching table will be constructed. This gives the optimum selection of the switching voltagespace vectors for all the possible stator current vector positions. As in DTC, the stator flux linkage andtorque errors are restricted within their respective hysteresis bands, which are 2ids and 2iqsrespectively. For the current control strategy it is enough to analyze only signs of voltage vectorcomponents V sd and V sq . In order to utilize all six active states per sector the stator flux locus isdivided into twelve sectors instead of six. This novel stator flux locus is introduced in Fig. 5. However, it isnecessary to define small and large variations. It is observed that V1 will produce a large increase in fluxand a small increase in torque in sectorS12. In contrast to this,V2 will increase the torque in largeproportion and the flux in a small one. The hysteresis block should consist of four levels so that the torqueerror can be divided in the number of intervals that are measured later. The look up table for 12-sector isshown in Table.2 176
    • Computer Engineering and Intelligent Systems www.iiste.org ISSN 2222-1719 (Paper) ISSN 2222-2863 (Online) Vol 2, No.3 V3 V2 4 3 5 2 6 1 V4 V1 7 12 8 11 V5 9 10 V6 Fig. 5 Inverter voltage space vectors divided into 12-sectors Table 2 Optimum voltage switching vector lookup tableSector 1 2 3 4 5 6 7 8 9 10 11 12 F TFI TI V2 V3 V3 V4 V4 V5 V5 V6 V6 V1 V1 V2FI TsI *V2 V2 *V3 V3 *V4 V4 *V5 V5 *V6 V6 *V1 V1FI TsD V1 *V1 V2 *V2 V3 *V3 V4 *V4 V5 *V5 V6 *V6FI TI V6 V1 V1 V2 V2 V3 V3 V4 V4 V5 V5 V6FD TI V3 V4 V4 V5 V5 V6 V6 V1 V1 V2 V2 V3FD TsI V4 *V4 V5 *V5 V6 *V6 V1 *V1 V2 *V2 V3 *V3FD TsD V7 V5 V0 V6 V7 V0 V0 V2 V7 V3 V0 V4FD TI V5 V6 V6 V1 V1 V2 V2 V3 V3 V4 V4 V5 5. Simulation Results and discussions To verify the proposed algorithm, a numerical simulation has been carried out using MATLAB- Simulink. The induction motor parameters are: Rs = 4.1Ω, Rr = 2.5 Ω, Ls = 0.545 H, Lr = 0.542 H, Lm = 0.51 H, number of poles = 4 and J = 0.04 Kg-m2. The results of conventional vector control and proposed vector 177
    • Computer Engineering and Intelligent Systems www.iiste.orgISSN 2222-1719 (Paper) ISSN 2222-2863 (Online)Vol 2, No.3control algorithms are presented and compared. The simulation studies have been carried for variousconditions such as starting, steady state, load change and speed reversal with a PI type speed controller.The results of conventional vector control algorithm are given in Fig. 7 – Fig. 12 and the results ofproposed algorithm for 6-sectors are given in Fig.13–Fig.18 andfor12-sectorsaregiveninFig.19–Fig.24 178
    • Computer Engineering and Intelligent Systems www.iiste.orgISSN 2222-1719 (Paper) ISSN 2222-2863 (Online)Vol 2, No.3 Fig.9 transients during load change inFig.7 starting transients in conventional vector conventional vector control algorithmcontrol algorithmFig.8 steady state plots in conventional vector Fig.10 transients during speed reversal (speed iscontrol changed from +1000 rpm to -1000 rpm)algorithm 179
    • Computer Engineering and Intelligent Systems www.iiste.orgISSN 2222-1719 (Paper) ISSN 2222-2863 (Online)Vol 2, No.3Fig.11 transients during speed reversal (speed ischanged from -1000 rpm to +1000 rpm) 0.25 THD= 2.52% Mag (% of Fundamental) 0.2 0.15 0.1 0.05 0 0 5000 10000 15000 20000 Frequency (Hz)Fig.12 Harmonic distortion of stator current inconventional vector control algorithm Fig15 .during the load variation with 6- sectors Fig.13 Motor speed, stator current andtorque during the starting period with 6-sectors Fig.16 transients during speed reversal (speed is changed from +1000 rpm to -1000 rpm) with 6- sectors Fig.14 Motor speed, stator current and torqueduring the steady state period with 6-sectors 180
    • Computer Engineering and Intelligent Systems www.iiste.orgISSN 2222-1719 (Paper) ISSN 2222-2863 (Online)Vol 2, No.3Fig.17 transients during speed reversal (speed is Fig.19 starting transients in proposed vectorchanged from -1000 rpm to +1000 rpm) with 6- control algorithm with 12-sectorssectors 1020 1010 Speed (rpm) 1000 990 980 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 Time (s) Fundamental (16.6667Hz) = 1.537 , THD= 2.68% 2 Stator currents (A) 0.1 1 Mag (% of Fundamental) 0 0.08 -1 0.06 -2 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.04 Time (s) 0.02 0.2 Torque (N-m) 0 0.1 0 5000 10000 15000 20000 0 Frequency (Hz) -0.1 -0.2 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 Time (s)Fig.18 Harmonic distortion of stator current inproposed algorithm with 6-sectors Fig.20 steady state plots in proposed vector control algorithm with 12-sectors 1000 Speed (rpm) 500 0 0 0.05 0.1 0.15 0.2 0.25 0.3 Time (s) 20 Stator currents (A) 10 0 -10 -20 0 0.05 0.1 0.15 0.2 0.25 0.3 Time (s) 15 Torque (N-m) 10 5 0 0 0.05 0.1 0.15 0.2 0.25 0.3 Time (s) 181
    • Computer Engineering and Intelligent Systems www.iiste.orgISSN 2222-1719 (Paper) ISSN 2222-2863 (Online)Vol 2, No.3 1005 1000 Speed (rpm) 500 Speed (rpm) 1000 0 995 -500 -1000 990 0.9 1 1.1 1.2 1.3 1.4 1.5 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 Time (s) Time (s) 5 Stator currents (A) 5 Stator currents (A) 0 0 -5 0.9 1 1.1 1.2 1.3 1.4 1.5 -5 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 Time (s) Time (s) 0 10 Torque (N-m) Torque (N-m) -5 5 -10 0 0.9 1 1.1 1.2 1.3 1.4 1.5 Time (s) 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 Time (s) Fig.22 transients during speed reversal (speed isFig.21 transients during load change in proposed changed from +1000 rpm to -1000 rpm) with 12-vector control algorithm with 12-sectors sectors Fundamental (16.6667Hz) = 1.537 , THD= 2.14% 1000 0.25 Speed (rpm) 500 Mag (% of Fundamental) 0 0.2 -500 -1000 0.15 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2 Time (s) 0.1 Stator currents (A) 5 0.05 0 0 0 5000 10000 15000 20000 -5 Frequency (Hz) 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2 Time (s) Fig.24 Harmonic distortion of stator current in proposed algorithm with 12-sectors Torque (N-m) 10 5 0 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2 Time (s)Fig.23 transients during speed reversal (speed ischanged from -1000 rpm to +1000 rpm) with 12-sectors 182
    • Computer Engineering and Intelligent Systems www.iiste.orgISSN 2222-1719 (Paper) ISSN 2222-2863 (Online)Vol 2, No.31. From the results shown, it can be observed that for all 3 cases of conventional control and usinglook up tables with 6 sectors and 12 sectors. The starting period is considered from time t = 0 – 0.3 sec.Initially speed increases linearly till 0.17 sec., and goes to steady state after overcoming the rotor inertia.The stator current is initially high and decreases slowly. The torque linearly increases and rapidly reachesto maximum point at 0.02 sec till 0.17 sec., and then decreases to zero and remains same. But the startingtransients are reduced in stator currents using look up tables compared with that of conventional control.2. The steady state period is considered from time t = 0.3 to 0.5 seconds and in all the 3 cases, themotor speed, stator current and electro magnetic torque are maintained constant. The main advantage ofusing look up table is that the torque ripples are reduced especially with 12-sectors which are found to behigh in conventional control.3. The case of load variation is considered from t = 0.5 – 0.9 sec. The step load is applied at t = 0.6sec., and removed at 0.8 seconds. During this period, the speed decreases, the stator current and torqueincreases as they are directly prop. To each other but speed is inversely proportional to load. After 0.8 sec.,all parameters came to original state. In conventional control, the stator current decreases and came tooriginal state but using look up table with both 6 & 12 sectors the stator current directly comes to originalstate with any change.4. In case of speed reversal from positive to negative during t = 0.9 – 1.5 seconds. The speed variesfrom positive to negative during t = 1 – 1.33 sec., the stator current increases but torque decreases. But thevalue of current Ia during the period is higher in case of proposed algorithm with 6 sectors and 12 sectorsand the current Ib remains in steady state for more time than in conventional vector control.5. The case of speed reversal from negative to positive at t = 1.5 – 2 sec. During t=1.6 – 1.93 sec., thespeed varies from negative to positive, the sector current and torque increases. The current I a. is small incase of proposed algorithm with 6 sectors and 12 sectors and the current I c remains in steady state for lesstime than in conventional vector control.6. It is observed that with the proposed 12-sectors, the harmonic distortion in stator current isconsiderably reduced compared with6-sectors.THD=2.68 for 6-sectors and THD=2.14 for 12-sectors 6. Conclusions A novel vector control algorithm is presented in this paper for the VSI-fed induction motor drive. Theproposed algorithm combines the basic principles of vector control and direct torque control algorithms. Ituses the instantaneous errors in d-and q axes stator currents and sector information to select the suitablevoltage vector. Hence, the proposed algorithm uses a predetermined look-up table instead of a much moretime consuming PWM procedure in conventional vector control algorithm. The proposed algorithm isvalidated through simulation results. From the results, it can be concluded that the proposed method issimple and gives good transient performance with slightly increased steady state ripple in stator current.References: 1. Peter Vas, “Sensorless vector and direct torque control” Oxford university press, New York, 1998. 2. F. Blaschke “The principle of field orientation as applied to the new transvector closed loop control system for rotating-field machines," Siemens Review, 1972, pp 217-220. 3. W. Leonhard, “30 years of space vectors, 20 years of field orientation, 10 years of digital signal processing with controlled AC-drives, a review (Part1)". EPE Journal, No. 1, July 1991, pages 13- 20. 4. W. Leonhard, “30 years of space vectors, 20 years of field orientation, 10 years of digital signal processing with controlled AC-drives, a review (Part 2)". EPE Journal, No. 2, Oct, 1991, pages 89-102. 183
    • Computer Engineering and Intelligent Systems www.iiste.orgISSN 2222-1719 (Paper) ISSN 2222-2863 (Online)Vol 2, No.3 5. E. D. Mitronikas, A. N. Safacas, and E. C. Tatakis, “A new stator resistance tuning method for stator-flux-oriented vector-controlled induction motor drive,” IEEE Trans. Ind. Electron., vol. 48, no. 6, pp.1148–1157, Dec. 2001. 6. J. A. Santisteban, and R. M. Stephan, “Vector control methods for induction machines: an overview,” IEEE Trans. On Education, vol. 44, no. 2, pp. 170-175, May 2001. 7. Isao Takahashi and Toshihiko Noguchi, “A new quick-response and high-efficiency control strategy of an induction motor,” IEEE Trans. Ind. Applicat., vol. IA-22, no.5, Sep/Oct 1986, pp. 820-827. 8. Domenico Casadei, Francesco Profumo, Giovanni Serra, and Angelo Tani, “FOC and DTC: Two Viable Schemes for Induction Motors Torque Control” IEEE Trans. Power Electron., vol. 17, no.5, Sep, 2002, pp. 779-787. 9. Marian P. Kaimierkowski, Maciej A. Dzieniakowski, and Waldemar Sulkowski, “Novel Space Vector Based Current Controllers for PWM-Inverters” IEEE Trans. Power Electronics, vol.6, no.1, Jan, 1991, pp. 158-166. 184