A modified load angle based DTC-SVM scheme for three-phase induction motors

Transcription

1 Joé L. AZCUE-PUMA 1, Helio GAZIOLLA 2, Alfeu J. SGUAREZI FILHO 2, Erneto RUPPERT 1 Univeridade Etadual de Campina (1), Univeridade Federal do ABC (2) A modified load angle baed DTC-SVM cheme for three-phae induction motor Abtract. Thi work propoe a direct torque control with pace vector modulation baed on load angle uing PI controller. Thi controller calculate dynamically the load angle between tator and rotor flux vector uing a PI controller. A reference of tator flux on tationary reference frame i calculated by uing the load angle, rotor poition and the tator flux magnitude. Another PI controller calculate the tator voltage to be upplied to the induction motor baed on tator flux error. Thu, the electromagnetic torque neceary to upply the motor load i achieved. Thi trategy i eay to implement and experimental reult are preented to validate the propoed trategy. Strezczenie. W artykule opiano bezpośrednie terowanie momentem z przetrzenną modulacja wektora bazującąnak acie obciażenia i regulatorze PI. Sterownik dynamicznie oblicza kat między wektorami trumienia tojana i wirnika. Ta trategia jet łatwa do zatoowania co potwierdziły wyniki ekperymentu. (Bezpośrednie terowanie momentem trójfazowego ilnika indukcyjnego bazujace na obliczaniu kata obciażenia) Keyword: Direct Torque Control, PI Controller, Load Angle, Induction Motor. Słowa kluczowe: bezpośrednie terowani momentem DTC, ilnik indukcyjny. Introduction The three-phae induction motor (IM) are widely ued in indutrial application today due to it low cot, imple contruction, reliability and robutne. In the lat year direct torque control (DTC) trategy ha become a popular technique for three-phae IM drive a it provide a fat dynamic torque repone and robutne under machine parameter variation without the ue of current regulator. The induction machine high dynamic performance can be achieved by uing a DTC trategy. Thee trategie can baed on, e.g., voltage-vector election uing witching table [1], direct elf-control [2]. An alternative approach to reduce the torque ripple i baed on pace vector modulation (SVM) technique [3], [4]. An alternative olution for variable witching frequency problem, DTC trategie operating at contant witching frequency are propoed by uing PI [5], deadbeat [6], lide mode [7] and predictive [8, 9], Fuzzy [10, 11] controller. The controller calculate the required tator voltage vector, averaged over a ampling period. Thee trategie have atifactory flux and torque repone although they do not preent low peed operation reult. A DTC trategy that ha imple one tep tator flux control algorithm which avoid coordinate rotation and predictive controller i preented in [13]. However, thi cheme ha a teady tate error in the flux repone. An intereting trategy baed on load angle etimation i preented in [12]. To overcome the teady tate error in the flux repone in [13], thi paper propoe a DTC trategy that allow a null teady tate error in flux repone uing PI controller. Thi controller calculate dynamically the load angle between tator and rotor flux vector uing a PI controller. A reference of tator flux on tationary reference frame i calculated by uing the calculated load angle, rotor poition and the tator flux magnitude. Another PI controller calculate the tator voltage to be upplied to the induction motor baed on tator flux error. Thu, the electromagnetic torque neceary to upply the motor load i achieved. Thi trategy i eay to implement and experimental reult are preented to validate the trategy operation. Dynamical Equation of the Three-Phae Induction Motor By utilizing the definition of the fluxe, current and voltage pace vector, the dynamical equation of the threephae IM in tationary reference frame can be put into the following mathematical form [14]: (1) (2) (3) (4) u = R i d ψ dt 0 = R r i r d ψ r dt jω rψ r ψ = L i L m i r ψ r = L r i r L m i Where u i the tator voltage pace vector, i and i r are the tator and rotor current pace vector, repectively, ψ and ψ r are the tator and rotor flux pace vector, i the rotor angular peed, R and R r are the tator and rotor reitance, L, L r and L m are the tator, rotor and mutual inductance, repectively. The electromagnetic torque i expreed in term of the cro product of the tator and the rotor flux pace vector. = 3 2 P L m (5) ψ L r L σ r ψ = 3 2 P L m ψ L r L σ r ψ (6) in(γ) Where γ i the load angle between tator and rotor flux pace vector, P i a number of pole pair and σ =1 L 2 m /(L L r ) i the diperion factor. Three-phae Induction Motor Direct Torque Control If the ample time i hort enough, uch that the tator voltage pace vector i impoed to the motor keeping the tator flux contant at the reference value. The rotor flux will become contant becaue it change lower than the tator flux. The electromagnetic torque (6) can be quickly changed by changing the angle γ in the deired direction. Thi angle γ can be eaily changed when chooing the appropriate tator voltage pace vector. For implicity, let u aume that the tator phae ohmic drop could be neglected in (1). Therefore d ψ /dt = u. During a hort time Δt, when the voltage pace vector i applied it ha: (7) Δ ψ u Δt Thu the tator flux pace vector move by Δ ψ in the direction of the tator voltage pace vector at a peed which i PRZEGLAD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 89 NR 9/

2 γ t em PI ψ ψ Δψ u Flux reference calculator PI SVM SW DC link Voltage calculation ABC d-q i b ψ r ψ Torque and flux etimator u i Fig. 1. Direct torque control with pace vector modulation and PI controller. proportional to the magnitude of the tator voltage pace vector. By electing tep-by-tep the appropriate tator voltage vector, it i poible to change the tator flux in the required direction. Direct Torque Control Baed on Load Angle and PI controller In Fig. 1, we how the block diagram of the propoed DTC-SVM cheme with PI controller. Thi cheme i an alternative to the claical DTC cheme [1], [2] and [3]. In thi cheme, the load angle γ i not prefixed but it i calculated by a PI controller. Equation (6) how that the angle γ determine the electromagnetic torque which i neceary to upply the load. The PI controller determine thi angle from the torque error. Detail about thi controller i going to be preented in the next ection. In Fig. 2, we can ee the cheme of the power electronic drive ued in our imulation. The control ignal for three-phae, two-level inverter i generated by the DTC-SVM block hown in Fig. 1. A B C P N Three-Phae diode rectifier V L V L V V Braking chopper Link DC Fig. 2. Scheme of power electronic drive. Three-Phae Inverter Control ignal Induction motor Stator Flux Reference Calculation A hown in Fig. 3, in tationary reference frame, the tator flux reference ψ can be decompoed in two perpendicular component ψd and ψ q. The addition of the angle determinate γ, which i the output of the PI controller, to the etimated rotor flux angle ψ r permit to etimate the next angle of the tator flux reference. In thi paper, the magnitude of tator flux reference i conidered contant. We ue the relation, preented in (8), to calculate the tator flux reference vector. q ψ q = ψ in( ψr γ ) γ ψ γ ψ r ψ ψ d = ψ co( ψ r γ ) Fig. 3. Load angle γ between tator flux reference ψ and rotor flux ψ r in tationary reference frame. (8) ψ = ψ co(γ ψ r )j ψ in(γ ψ r ) With the application of the tator voltage u during a hort time Δt it i poible to reproduce a flux variation Δ ψ. Notice that the tator flux variation i nearly proportional to the tator voltage pace vector a een in the equation (7). Stator Voltage Calculation The input for the tator voltage calculator block in Fig. 1 are the DC link voltage U dc and the inverter witch tate (S a, S b, S c ). The tator voltage vector u i determined a: (9) u = 2 3 [ ψ r (S a S ] b S c 3 )j 2 2 (S b S c ) U dc Electromagnetic Torque and Flux Etimation The tator flux pace vector etimation depend of the back electromotive force (emf), it i: d 310 PRZEGLAD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 89 NR 9/2013

3 (10) ψ = ψ = ( u R i )dt ( emf)dt ψ 2 q emf γ ψ 1 d when the tator flux i calculate with equation (10) it ha problem aociated with a pure integrator. With the aim to olve thi problem i ued the integrator with an adaptive compenation method propoed in [15]. Thi method can be ued to accurately etimate the motor flux including it magnitude and phae angle over a wide peed range. Fig. 4 how a block diagram of thi method. The main idea of thi method i the fact that the motor tator flux pace vector i orthogonal to it back emf. The quadrature detector detect if the orthogonality between the etimated tator flux pace vector and emf i maintained. The operating principle of thi method i explained by uing a vector diagram hown in Fig. 5. The etimated tator flux pace vector i a um of two vector, a feedforward vector ψ 1 which i the output of the Low Pa (LP) filter (ψ d1 and ψ q1 ) and a feedback vector ψ 2 which i compoed of ψ d2 and ψ q2. Ideally, the tator flux pace vector ψ hould be orthogonal to the emf, and the output of the quadrature detector i zero. When an initial value or dc drift i introduced to the integrator, the above orthogonal relation i lot, and the phae angle between the flux and emf vector i no longer 90, which yield an error ignal defined by (11) Δ e = ψ emf/ ψ Δ e = (ψ q emf q ψ d emf d )/ ψ Δ e = emf co(γ) Auming that the magnitude of the feedback vector ψ 2 i increaed to ψ 2 a hown in Fig. 5 due to a dc offet or initial value problem, the phae angle γ will be greater that 90. The quadrature detector will generate a negative error ignal. The output of the PI regulator ψ cmp i reduced and o i the feedback vector. A a reult, the tator flux pace vector ψ move toward the original poition of 90 until the orthogonal relationhip between ψ and emf i reetablihed. If γ i le than 90 for ome reaon, an oppoite proce will occur, which bring γ back to 90. Therefore, the modified integrator with the adaptive control can adjut the flux compenation level ψ cmp automatically to an optimal value uch that the initial value and dc drift problem are eentially eliminated. emf q emf d 1 ψ q1 ω c 1 ω c ψ d1 ψ q2 ψ d2 ω c ω c Polar PI ω c ω c to Carteian ψ cmp quadrature detector ψ q emf q ψ d emf d Δe ϕ ψ Carteian to Fig. 4. Block diagram of the adaptive compenation method. On the other hand, the rotor flux depend on the etimated tator flux and tator current pace vector. From the equation (3) and (4) we etimate the rotor flux pace vector: Polar ψ q ψ d ψ 2 ψ ψ Δγ : offet angle Fig. 5. Vector diagram howing the emf and flux linkage relationhip. (12) ψr = L r ψ L L r σ i L m L m With the component of ψ r we can obtain the angle of the rotor flux: (13) ψ r =tan 1 ( ψ qr ψ dr ) With equation (10) and (12) in (5) it i poible to etimate the electromagnetic torque, it i: (14) = 3 2 P L m L r L σ (ψ drψ q ψ qr ψ d ) Stator Voltage Reference Calculation The propoed DTC trategy ue a PI controller to generate a tator flux vector reference baed on calculated load angle (8). Thu, the PI controller will proce the error between the calculated tator flux vector and it reference and it will calculate the tator voltage reference to be applied to the motor. Thi controller will allow that the torque and flux will reach the deired value with no teady tate error. The expreion that calculate the tator voltage reference are done by: (15) u d = (16) u q = ( K p K ) i (ψd ψ d ) ( K p1 K ) i1 (ψ q ψ ) q Where d/dt and the tator flux reference are calculated by uing (8) (17) ψ d = ψ co(γ ψ r ) and (18) ψ q = ψ in(γ ψ r ) and K p, K i, K p1 and K i1 are the gain of the PI controller. Thu, if the gain wa corrected adjuted the torque and flux loop will have null teady tate error. PRZEGLAD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 89 NR 9/

4 Experimental Reult The DTC trategy were implemented uing a Texa Intrument DSP TMS320F28335 platform. The ytem conit of a three-phae voltage ource inverter with inulatedgate bipolar tranitor (IGBT) and the three-phae induction motor hown in the appendix. The tator voltage command are modulated by uing ymmetrical pace vector PWM with witching frequency equal to 10 khz. The DC link voltage of the inverter i 350 V and a conventional PI controller generate a torque reference by uing the peed error. The flux and torque etimation, the DTC trategy and peed controller have the ame ampling frequency of 10 khz. The encoder reolution i 3600 pule per revolution. The experimental etup i hown in Figure 6. C1 Fig. 8. Step of peed reference, torque and phae a current (C1,: 1 pu/div; : 10 N.m/div; : 5 A/div; 2 /div). ω r Fig. 6. Experimental etup. Three tet are made and in all tet the reference of tator flux i 1pu. In the firt no-load tet a tep of peed reference from 0pu to 0.5pu i applied to the peed controller. The tet i hown in Fig. 7. Thi reult confirm the atifactory performance of the DTC load angle controller due to the fact that the peed reache the reference. In the econd no-load tet, the peed reference i changed from 0.5pu to -0.5pu and again to 0.5pu i applied to the peed controller and it i hown in Fig. 8. Again, the atifactory performance of the DTC load angle controller can be een due to the fact that the peed reache the reference in everal peed condition. Fig. 9. Load tet - peed reference, torque and phae a current (: 10 N.m/div; : 0.5 pu/div; : 5 A/div; 5 /div). ψ Fig. 7. Step of peed reference, torque and phae a current (: 0.2 pu/div; : 10 N.m/div; : 5 A/div; 5 /div). A full load tet i the third. In thi cae, the peed reference i contant at 0.5pu and a 1pu of load toque i applied to the motor. The reult are hown in Figure 9 and 10. Again, the atifactory performance of the DTC load angle controller can be een due to the fact that the peed reache the reference in everal condition. Fig. 10. load tet - tator flux magnitude, torque and phae a current (: 10 N.m/div; : 0.2 Wb/div; : 5 A/div; 5 /div). The ame full load tet wa made uing the DTC trategy preented in [13]. The peed reference i contant at 0.5pu anda1pu of load toque i applied to the motor. The reult of the load tet i preented in Fig. 11. It can be een that the trategy ha a flux error of 9% in teady tate with and without load. So the motor will operate at weaking flux region. So, the machine can drive the full load but the loe will increae and efficient will decreae. Nowaday high efficient i very deirable and thi type of operation at full load i not good. In thi work the propoed DTC trategy allow a null error flux a can be een comparing Figure 10 and 11. Concluion In thi paper a DTC trategy baed on load angle ha been propoed to be an alternative olution for correct the flux error in tead tate operation a preented in DTC trat- 312 PRZEGLAD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 89 NR 9/2013

5 ψ Fig. 11. Load tet of DTC propoed by [13] (: 10 N.m/div; : 0.2 Wb/div; : 5 A/div; 5 /div). egy [13]. The trategy ue only PI controller and mitigated the mentioned flux error. The trategy ha imple implementation. The experimental reult preented the atifactory performance of the DTC controller due to the fact the torque, tator flux and peed reach the reference. Although the gain of PI controller have to be correctly deign for the good performance of the controller. Hence, the propoed DTC trategy become an intereting tool for implementation IM drive. Acknowledgement The author are grateful to CAPES and FAPESP for the financial upport for thi reearch. xx, no., pp., January 2012 [10] Lin Chen; Kang-Ling Fang; Zi-Fan Hu, "A cheme of fuzzy direct torque control for induction machine," Machine Learning and Cybernetic, Proceeding of 2005 International Conference on, vol.2, no., pp Vol. 2, Aug [11] Koutogianni, Z.; Adamidi, G.; Fyntanaki, A., "Direct torque control uing pace vector modulation and dynamic performance of the drive, via a fuzzy logic controller for peed regulation," Power Electronic and Application, 2007 European Conference on, vol., no., pp.1-10, 2-5 Sept [12] Abu-Rub, H.; Guzinki, J.; Krzeminki, Z.; Toliyat, H.A., "Advanced control of induction motor baed on load angle etimation," Indutrial Electronic, IEEE Tranaction on, vol.51, no.1, pp. 5-14, Feb [13] J. Rodriguez, J. Pontt, C. Silva, S. Kouro and H. Miranda, "A Novel Direct Torque Control Scheme for Induction Machine with Space Vector Modulation," 35th Annual IEEE Power Electronic Specialit Conference, [14] P. Va, "Senorle vector and Direct Torque Control", Oxford Univerity Pre, [15] Jun Hu; Bin Wu, "New integration algorithm for etimating motor flux over a wide peed range," Power Electronic, IEEE Tranaction on, vol.13, no.5, pp.969,977, Sep Author: Dr. Joé L. Azcue-Puma, Prof. Dr. Erneto Ruppert, DSCE/FEEC/UNICAMP, Campina - SP, Brazil, azcue@ieee.org, ruppert@fee.unicamp.br, Prof. Dr. Alfeu J. Sguarezi Filho, Mr. Helio Gaziolla, CECS/UFABC, Santo André - Sao Paulo - Brazil, helio.gaziolla; alfeu.guarezi@ufabc.edu.br Appendix The three-phae induction motor ha the rated value P N =1.1 kw, f N =60Hz, U N = 220 V, T N =6.1 N.m, ω N = rad/, P =2pole pair and the parameter R =5.56Ω, R r =4.25Ω, L = L r =0.309 H, L m = H and J = K g m 2. REFERENCES [1] Takahahi, Iao; Noguchi, Tohihiko, "A New Quick-Repone and High-Efficiency Control Strategy of an Induction Motor," Indutry Application, IEEE Tranaction on, vol.ia-22, no.5, pp , Sept [2] Depenbrock, M., "Direct elf-control (DSC) of inverter-fed induction machine," Power Electronic, IEEE Tranaction on, vol.3, no.4, pp , Oct 1988 [3] Habetler, T.G.; Profumo, F.; Patorelli, M.; Tolbert, L.M., "Direct torque control of induction machine uing pace vector modulation," Indutry Application, IEEE Tranaction on, vol.28, no.5, pp , Sep/Oct 1992 [4] Jun-Koo Kang, Seung-Ki Sul,"New Direct Torque Control of Induction Motor for Minimum Torque Ripple and Contant Switching Frequency", Indutry Application, IEEE Tranaction on, vol. 35, no. 5, pp , Sep/Oct [5] Stojic, D. M.; N. Vukoavic, Slobodan, "A New Induction Motor Drive Baed on the Flux Vector Acceleration Method", Indutry Application, IEEE Tranaction on,vol. 20, no.1, pp , March 2005 [6] Lee, J. H.; Kim, C. G.; Youn, M. J., "A deadbeat type digital controller for the direct torque control of an induction motor", Power Electronic, IEEE Tranaction on,vol. 17, no.1, pp , September 2002 [7] Lacu, C. ; Boldea, I.; Blaabjerg,F., "Direct torque control of enorle induction motor drive: a liding mode approach", Indutry Application, IEEE Tranaction on, vol. 40, no.2, pp , March 2004 [8] Beerten, Jef ; Verveckken, Jan ; Drieen, Johan L J, "Predictive Direct Torque Control for Flux and Torque Ripple Reduction", Indutrial Electronic, IEEE Tranaction on, vol. 57, no.1, pp , January 2010 [9] Thoma, Jean; Hanon, Ander, "Speed Tracking of a Linear Induction Motor-Enumerative Nonlinear Model Predictive Control",Control Sytem Technology, IEEE Tranaction on, vol. PRZEGLAD ELEKTROTECHNICZNY (Electrical Review), ISSN , R. 89 NR 9/