Speed Sensorless Rotor Flux Estimation in Vector Controlled Induction Motor Drive

Transcription

1 25 WSEAS Int. Conf. on DYNAMICAL SYSTEMS and CONTROL, Venice, Italy, Novembe 2-4, 25 (pp49-414) Speed Sensoless Roto Flux Estimation in Vecto Contolled Induction Moto Dive J. S. THONGAM and M.OUHROUCHE Electical Machines Identification and Contol Laboatoy (EMICLab) Depatment of Applied Sciences, Univesity of Quebec at Chicoutimi 555, Boulevad de l Univesite, Chicoutimi, QC G7h 2B1 CANADA Abstact: - This pape pesents a speed sensoless oto flux estimation algoithm in a vecto contolled induction moto dive. The poposed method is based on obseving a newly defined state which eplaces the unknown tems containing oto flux and speed on ight hand side of the state equation of the moto. A new mathematical model of the moto is deived afte intoducing the above mentioned sate. Roto flux estimation is achieved using a modified Blaschke equation obtained afte intoducing the new state into the Blaschke equation. Roto speed is computed using a simple equation deived using the newly defined state. Key-wods: Induction moto, vecto contol, flux estimation, speed estimation, educed ode obseve. 1 Intoduction Vecto Contol (VC) [1, 2] has evolutionised the use of induction motos in high pefomance dive applications. Conventional VC dive uses speed senso such as a shaft encode fo speed contol. Howeve, a speed senso can not be mounted in cetain applications such as a moto dive in hostile envionment o a high speed dive etc. It also equies caeful cabling aangement with pope attention to electical noise. Moeove, it makes the dive system moe bulky and expensive. Theefoe, a lot of eseach ae undeway to develop good speed estimation methods. Recently seveal speed sensoless vecto contol schemes have been poposed [3-12]. Induction machines do not allow oto flux to be easily measued, theefoe, fo vecto contol one has to esot to flux estimation. The cuent model (CM) and the voltage model (VM) ae the taditional solutions, and thei benefits and dawbacks ae well known [13]. Vaious obseves fo flux estimation wee analyzed in the pioneeing wok by Veghese and Sandes [14]. Ove the yeas seveal othe have been pesented, many of which include speed estimation [6-12, 15]. In [6] extended kalman filte was used fo estimating the oto flux and speed using a full ode model of the moto assuming that oto speed is a constant. A speed adaptive flux obseve was poposed in [7] fo estimating oto flux and speed. In [8] Gopinath style educed ode obseve was used fo estimating the oto flux while the speed was computed using an equation deived fom the moto model. Tajima et al [9] poposed MRAS [3] with novel pole allocation method fo speed estimation while oto flux estimation was done using Gopinath s obseve. Yan et al [1] poposed a flux and speed estimato based on the slidingmode contol methodology. Ohtani et al [11] used the voltage model fo flux estimation ovecoming the poblem associated with integato and low pass filte while speed was computed by subtacting slip speed fom the synchonous speed. In [12] voltage model was used fo oto flux estimation [11] and speed estimation was achieved based on a educed ode obseve which estimates a new quantity that is used along with oto flux in computing the speed. In this pape we pesent a speed sensoless oto flux estimation algoithm in a vecto contolled induction moto dive. The poposed method is based on obseving a newly defined state [12] which is a function of oto flux and speed. Availability of this state makes the speed sensoless oto flux estimation possible. Roto flux estimation poposed in this wok is achieved using a modified Blaschke equation obtained afte intoduction of the quantity into the moto model. Roto speed is computed using a simple equation which is deived using the newly defined state [12].

2 25 WSEAS Int. Conf. on DYNAMICAL SYSTEMS and CONTROL, Venice, Italy, Novembe 2-4, 25 (pp49-414) 2 Induction Moto Model The induction moto model in stationay stato efeence fame α-β is given by: dψ = A11Ψ + A12 (1) dis = A21Ψ + A22 is + A23v s (2) Whee = R / L + ω A11 ( ) I J, 12 = ( LmR / L ) A21 = L m / ( σ LsL ){( R / L) I ωj } A I, { Rs ( σls) RL 2 m ( σlsl 2 )} A22 = / + / I, ( σ ) A23 = 1 / Ls I, Ψ = Ψα Ψβ, T 1 1 = isα isβ, I = 1 and J = 1 3 Roto Flux and Speed Estimation We intoduce a new state into the moto model which when intoduced will make the ight hand side of the (1) and (2) independent of the unknowns the oto flux and speed. Let s define the new state as: Z =A Ψ (3) 11 A new moto model is obtained afte intoduction of the new state as given below: dψ = A12is + A14 Z (4) dis = A22is + A23vs + A24 Z (5) dz = A32is + A34 Z (6) A I, = L ( σ L L ) whee 14 = T { } m s A I, 24 / 2 2 ( LmR L ) ( LmR L ) A32 = / I ω / J and A = A It can be seen fom (3) and (4) that speed and oto flux can be estimated if Z is known. A Gopinath s educed ode obseve [16] is constucted using (5) and (6) fo estimating Z. The Z obseve equation is as given below [12]: dz dis di s = A32is + A34 Z + G (7) g1 g2 whee G = g2 g is the obseve gain. 1 di Using equation (6) fo s the obseve equation becomes: dz 32 s 34 = A i + A Z dis + G A22 is A23vs A24 Z (8) The obseve poles can be placed at the desied locations in the stable egion of the complex plane by popely choosing the values of the elements of the G matix. In ode to avoid deivative of the stato cuent in the algoithm we intoduce anothe new quantity: F = Z Gi (9) s Finally, the obseve is of the following fom: d ( ) + ( ) F = A + A G GA GA G i GA v s 23 s A34 GA24 F (1) Z = F + Gi (11) s Assuming no paamete vaiation and no speed eo, the equation fo eo dynamics is given by: ( ) ( ) d d Z = Z Z = A A G Z (12) Eigenvalues of ( A ) 34 A24G ae the obseve poles which ae as given below: R L m obs1,2 = + g1 L σ LsL P Lm ± j ω σ LL s g2 (13) It is to be noted hee that the model of the moto used in implementing the obseve algoithm has been developed assuming that the deivative of the oto speed is zeo. It is valid to make such an assumption since the dynamics of oto speed is

3 25 WSEAS Int. Conf. on DYNAMICAL SYSTEMS and CONTROL, Venice, Italy, Novembe 2-4, 25 (pp49-414) much slowe than that of electical states. Moeove, such an assumption allows estimation without equiing the knowledge of mechanical quantities of the dive such as load toque, inetia etc. 3.1 Roto Flux Estimation Roto flux may be obtained fom the modified Blaschke equation (4) which is obtained afte intoduction of the new state Z. Howeve, oto flux computation by pue integation suffes fom dc offset and dift poblems. To ovecome the above poblems a low pass filte is used instead of pue integato and the phase eo due to low pass filteing is appoximately compensated by adding low pass filteed efeence flux with the same time constant as used above [11]. The equation of the poposed oto flux estimato is as given below: e axis ζ ζ τ s τ 1 + τ s {( L / Lm) } e τ s axis τ 1 Ψ = ( A12is + A14 Z) + Ψ (14) 1+ τs 1+ τs whee τ is the LPF time constant. The command oto flux Ψ is obtained as follows: Ψ α Ψ cos ρ Ψ = = (15) Ψ β Ψ sin ρ whee Ψ = Lmisd and angle is as given by: ω s ρ the command oto flux ρ = (16) ω s the command oto flux speed is computed as given below: s sl ω = ω + ω (17) The command slip speed ω sl is given by: Ri qs ω sl = (18) Lds i We know that the equation of the back emf is given by: Lm dψ Lm e = = ( A12is + A14 Z ) (19) L L Fig. 1. Obtaining of estimated oto flux Now, equation (14) may also be witten as: τ L 1 Ψ = e + Ψ (2) 1+ τs Lm 1+ τs Fig. 1. explains how estimated flux is obtained using equation (2). 3.2 Speed Estimation Pefoming matix multiplication of equation (3) we have: 2 2 ( ) α β β α α β Ψ T J with Z Ψ Z Ψ = Ψ + Ψ ω (21) This simple equation is used fo computing speed by eplacing the actual values of Z and flux by estimated ones as given below [12]: Z Ψ Z Ψ ω = α β β α 2 2 Ψ α + Ψ β (22) The block diagam of the flux and speed estimato is shown in Fig. 1.

4 25 WSEAS Int. Conf. on DYNAMICAL SYSTEMS and CONTROL, Venice, Italy, Novembe 2-4, 25 (pp49-414) v s Z Estimation Ẑ Ψ Roto Flux Estimation Ψ Speed Computation Fig. 2. Block diagam of oto flux and speed estimato. ω 4 Real-Time Digital Simulation The poposed estimation algoithm is incopoated into a vecto contolled induction moto dive system. The block diagam of the sensoless dive system is shown in Fig. 3. A pc cluste based fully digital eal-time simulation is caied out using RT- Lab softwae package [17] in ode to analyze the pefomance of the poposed scheme. ω + q + v sq v sa + V dc Ψ + Ψ q d q + d dq v sd abc dq abc ρ v sb v sc INVERTER FLUX VECTOR GENERATION Ψ ω ROTOR FLUX & SPEED ESTIMATOR v s IM Fig. 3. Block diagam of sensoless VC induction moto dive. Speed [ ad/s ] Speed estimation eo [ ad/s ] Actual ψ β ( a ).5 Refeence speed Actual speed Estimated speed Actual ψ α ( c ) Flux Flux estimation eo Estimated ψ β ( b ).5 Actual flux Estimated flux Estimated ψ α ( d ) Fig. 4. Acceleation and speed evesal at no-load; (a) efeence ( ω ), actual (ω )and estimated ( ω ) speed, and speed estimation eo; (b) actual ( Ψ ) and estimated ( Ψ ) oto flux, and oto flux estimation eo ( Ψ Ψ ); (c) locus of actual flux ( Ψ β vs. Ψ α ); (d) locus of estimated flux ( Ψ β vs. Ψ α ).

5 25 WSEAS Int. Conf. on DYNAMICAL SYSTEMS and CONTROL, Venice, Italy, Novembe 2-4, 25 (pp49-414) Fist, acceleation and speed evesal at no load is pefomed. A speed command of 15 ad/s at.5 s is given to the dive system which was initially at est, and then the speed is evesed at 3 s. The esponse of the dive is shown in Fig. 4. Fig. 4 (a) shows efeence ( ω ), actual (ω ), estimated ( ω ) speed, and speed estimation eo ( ω ω ). The module of the actual ( Ψ ), estimated ( Ψ ) oto flux, and oto flux estimation eo ( Ψ Ψ ) ae shown in Fig. 4 (b). Fig. 4 (c) and (d) shows espectively the locus of the actual and estimated oto flux. Speed [ ad/s ] Speed estimation eo [ ad/s ] 15 Refeence speed 1 Actual speed Estimated speed ( a ) Flux Flux estimation eo Actual flux Estimated flux ( b ) Actual ψ β Actual ψ α Estimated ψ β Estimated ψ α ( c ) ( d ) Fig. 5. No-load opeation with step incease in speeds; (a) efeence ( ω ), actual (ω )and estimated ( ω ) speed, and speed estimation eo; (b) actual ( Ψ ) and estimated ( Ψ ) oto flux, and oto flux estimation eo ( Ψ Ψ ); (c) locus of actual flux ( Ψ β vs. Ψ α ); (d) locus of estimated flux ( Ψ β vs. Ψ α ). Speed [ ad/s ] Speed estimation eo [ ad/s ] Refeence speed Actual speed Estimated speed ( a ) Flux Flux estimation eo Actual flux Estimated flux ( b ) Actual ψ β Actual ψ α Estimatedl ψ β Estimatedl ψ α ( c ) ( d ) Fig. 6 Opeation at full load at vaious speeds; (a) efeence ( ω ), actual (ω )and estimated ( ω ) speed, and speed estimation eo; (b) actual ( Ψ ) and estimated ( Ψ ) oto flux, and oto flux estimation eo ( Ψ Ψ ); (c) locus of actual flux ( Ψ β vs. Ψ α ); (d) locus of estimated flux ( Ψ β vs. Ψ α ).

6 25 WSEAS Int. Conf. on DYNAMICAL SYSTEMS and CONTROL, Venice, Italy, Novembe 2-4, 25 (pp49-414) Then, the dive is subjected to step incease in speed unde no load condition. It is acceleated fom est to 1 ad/s at.5 s, then acceleated futhe to 5 ad/s, 1 ad/s and 15 ad/s at 1.5 s, 3 s and 4.5 s espectively. Fig. 5 shows the estimation of oto flux and speed, and the esponse of the sensoless dive system. Futhe, the pefomance of the estimato is veified unde loaded conditions at vaious opeating speeds. The fully loaded dive is acceleated to 15 ad/s at.5 s and then deceleated in steps to 1 ad/s, 5 ad/s and 1 ad/s at 1.5 s, 3 s and 4.5 s espectively. Fig. 6 shows the estimation esults and esponse of the loaded dive system. 5 Conclusion A speed sensoless oto flux estimation algoithm in vecto contolled induction moto dive has been poposed. The oto flux estimation was achieved using a modified Blaschke equation obtained afte intoducing a newly defined state. The oto speed was computed using a simple equation obtained using the newly defined state. Accuate estimations of oto flux and speed wee achieved unde both tansient and steady state conditions, and the esponse of the sensoless vecto contolled induction moto dive was found to be satisfactoy. Refeences: [1] F. Blaschke, The Pinciple of Field Oientation as Applied to the New TRANSVEKTOR Closed-loop Contol System fo Rotating Field Machines, Siemens Review XXXIX, No. 5, 1972, pp [2] K. Hasse, On the Dynamics of Speed Contol of a Static AC Dive with a Squiel-cage induction machine, PhD dissetation, Tech. Hochsch. Damsta, [3] C. Schaude, Adaptive Speed Identification fo Vecto Contol of Induction Motos without Rotational Tansduces, IEEE Tans. Ind. Appl., Vol. 28, No. 5, Sept./Oct. 1992, pp [4] F. Z. Peng and T. Fukao, Robust Speed Identification fo Speed Sensoless Vecto Contol of Induction Moto, IEEE Tans. Ind. Appl.., Vol. 3, No. 5, Sept./Oct. 1994, pp [5] S. H. Kim, T. S. Pak, J. Y. Yoo and G. T. Pak, Speed-Sensoless Vecto Contol of an Induction Moto Using Neual Netwok Speed Estimation, IEEE Tans. Ind. Electon.,Vol. 48, No. 3, June 21, pp [6] Y. R. Kim, S. K. Sul and M. H. Pak, Speed Sensoless Vecto Contol of Induction Moto Using Extended Kalman Filte, IEEE Tans. Ind. Appl., Vol. 3, No. 5, Sept./Oct. 1994, pp [7] H. Kubota, K. Matsuse and T. Nakano, DSP- Based Speed Adaptative Flux Obseve of Induction Moto, IEEE Tans. Ind. Appl., Vol. 29, No. 2, Mach/Apil 1993, pp [8] S. Sathiakuma, Dynamic Flux Obseve fo Induction Moto Speed Contol, Poc. Austalian Univesities Powe Engineeing Conf. AUPEC 2, Bisbane, Austalia, Sept. 2, pp [9] H. Tajima and Y. Hoi, Speed Sensoless Field Oientation Contol of the Induction Machine, IEEE Tans. Ind. Appl., Vol. 29, No. 1, Jan/Feb. 1993, pp [1] Z. Yan, C. Jin and V. I. Utkin, Sensoless Sliding-Mode Contol of Induction Motos, IEEE Tans. Ind. Elec., Vol. 47, No. 6, Dec. 2, pp [11] T. Ohtani, N. Takada and K. Tanaka, Vecto Contol of Induction Moto Without Shaft Encode, IEEE Tans. Ind. Appl., Vol. 28, No. 1, Jan./Feb. 1992, pp [12] J. S. Thongam and M. Ouhouche, A New Speed Estimation Algoithm in Roto Flux Oiented Contolled Induction Moto Dive, WSEAS Tansactions on Systems, Issue 5, Vol. 4, May 25, pp [13] B. K. Bose, Powe Electonics and Vaiable Fequency Dives, Piscataway, NJ: IEEE Pess, [14] G. C. Geghese and S. R. Sandes, Obseves fo Flux Estimation in Induction Machines, IEEE Tans. Ind. Elec., Vol. 35, No. 1, Feb. 1988, pp [15] P. L. Jansen and R. D. Loenz, A Physically Insightful Appoach to the Design and Accuacy Assessment of Flux Obseves fo Field Oiented Induction Machine Dives, IEEE Tans. Ind. App., Vol. 3, No.1, Jan./Feb. 1994, pp [16] B. Gopinath, On the Contol of Linea Multiple Input-Output Systems, Bell Sys. Tech. J., Vol. 5, Mach [17] Opal RT Technologies, RT Lab 7.1 Use s Manual.