EE595S : Class Lecture Notes Parameter Identification and Maximum Torque Per Amp Control Algorithm

Transcription

1 EE595S : Class Lecture Notes Parameter Identification and Maximum Torque Per Amp Control Algorithm

2 Outline GA based AQDM Characterization Procedure MTPA Control strategy AMTPA Control Strategy 2

3 Alternate QD IM Model (AQDM) [1] S ωe ωr = ω e Steady-State T-Equivalent Circuit [1] S. D. Sudhoff, D. C. Aliprantis, B. T. Kuhn, and P. L. Chapman, An Induction Machine Model for Predicting Inverter Machine Interaction, IEEE Transactions on Energy Conversion, Vol. 17, June 2002, pp

4 Specific Forms of AQDM parameters For practical use of AQDM L ls L lr Γ m () (const) () = l ls = l lr1 + () = m 1 m 2 λm l lr2 l ( l λ ) 4 lr 1+ lr3 m m3 ( λm m4 ) m5 ( λm m6 ) + e + e Y () s r = y ya1 ya2 ya + + s + 1 yτ 2s + 1 yτ 3s τ [2] S. D. Sudhoff, D. C. Aliprantis, B. T. Kuhn, and P. L. Chapman, Experimental Characterization Procedure for Use With and Advanced Induction Machine Model, IEEE Transactions on Energy Conversion, Vol. 18, No. 1, March 2003, pp

5 AQDM parameters Parameter vector to be identified is Coefficients of L, Γ, L, Y ls m lr r θ = [ Lls l s1 Γm m m m m m m y y y y y y a1 τ 1 a2 τ2 a3 τ3 Llr lr1 lr2 lr3 lr4 ] Y r 5

6 Experimental Measurements - I Fundamental frequency impedance test set-up 6

7 Experimental Measurements - I Fundamental frequency impedance fz, k Z qs Control Algorithm [ ] N fz = 0 = ω s e i qi e i di 900 rpm = Induction Machine Drive ~ k k k fz, k i qs ωe s Zqs ω input data output data 7

8 Experimental Measurements - I Analytical form of fundamental frequency impedance ˆ fz k Z, qs = 8

9 Experimental Measurements - II Stand Still Frequency Response impedances To extract high frequency phenomenon in inverter-machine interaction Current (A) time (sec) 9

10 Experimental Measurements - II SSFR impedance test set-up Z qs j ssfr, m, i m t + i m j m = { 05A 10A 15A 22A} v + m t v m j m 2 m m j iqm0 = it ω e, 3 ssfr, m Z qs, j output data input data 10

11 Experimental Measurements - II Analytical form of SSFR impedance m m for given input data i ω { qm0 e, i} ˆ ssfr, m Z qs, j = v i m j m j = r + sl λ ( m ) 0 s ls qm m 1 m ( λ 0 ) M0 r ( ) lr( λqm0) i 0 1 qs λ 1 m m r ( ) lr( λqm0) M0 ( ) ( ) L sl Y s + L s ls qm m + + Y s + L + L s where m, s = jω ei 11

12 Impedance Errors Input data output data Impedance Errors AQDM 12

13 Impedance Errors Fundamental frequency impedance error SSFR impedance error for each m=5,10,15,22 A 13

14 GA based Characterization Procedure Parameter Identification for AQDM Nonlinear Optimization Problem 14

15 GA based Optimization problem (OP) GA is employed to solve the OP Case I Case II 15

16 18 Evolution Process Best fitness ( N P = 1000 ) Best-fitness 12 s based on based on f f fz fz/ ssfr Generation 16

17 Quality of Fit In terms of impedance error E fz 5A E ssfr 10A E ssfr 15A E ssfr 22 A E ssfr AQDM θ = θ fz θ AQDM = θ fz/ssfr

18 Quality of Fit In terms of fundamental frequency impedance fz Z fz qs Z qs e i qi log10 s ω e i qi log10 ωs 18

19 Quality of Fit In terms of fundamental frequency impedance based on based on f f fz fz/ ssfr E k = % of PTS E k 19

20 Quality of Fit In terms of SSFR impedance i t = 05A ssfr Y qs ssfr Y qs log10 ω 20

21 Quality of Fit In terms of SSFR impedance i t = 10A ssfr Y qs ssfr Y qs log10 ω 21

22 Quality of Fit In terms of SSFR impedance i t = 15A ssfr Y qs ssfr Y qs log10 ω 22

23 Quality of Fit In terms of SSFR impedance i t = 22A ssfr Y qs ssfr Y qs log10 ω 23

24 Dependency on population size N P = 1000,500,2000,5000, and Best-fitness Generation 24

25 Dependency on population size In terms of impedance errors NP f E fz 5A E ssfr 10A Essfr 15A E ssfr 22A E ssfr θ fz/ssfr

26 Dependency on population size In terms of Fundamental frequency % of data points AQDM with fz/ ssfr( P N = 1000) P N = 500 P N = P N = P N = fz k Zqs Zˆ Ek = 100 fz, k Z, fz, k qs qs E k 26

27 Dependency on population size In terms of SSFR impedance at 15 A DC bias 27

28 Consistency in repeated applications 100 repeated applications with N P =500 µ σ f E fz E k % µ σ 5A Essfr A E ssfr A E ssfr A E ssfr

29 Validation I Time domain simulation 1790 rpm Comparison of c-phase current ripple Measurement of c-phase current IM was driven at a speed of 1790 rpm e i qi ω s = 55A and = 2.09 rad/sec Use of Oscilloscope with 20u sec data acquisition sampling time 29

30 Validation I Time domain simulation C-phase current waveform and its ripple θ = θ AQDM with fz AQDM with fz/ssfr Measured θ = θ 30

31 Validation I Time domain simulation C-phase current waveform and its ripple θ = θ AQDM with fz AQDM with fz/ssfr Measured θ = θ 31

32 Validation II Application to MTPA Structure MTPA Control Scheme Goal (Tracking) (MTPA condition) 32

33 MTPA Control based AQDM Derivation 3 P T = i i 22 ( e e e e λ λ ) e dm qs qm ds 33

34 34 ( ) ( ) = s s e s m ag s s e I I j Z P I T ω ω λ ω, Im 2 3, Derivation (cont) MTPA Control based AQDM

35 MTPA Control based AQDM How to calculate λ m Newton-Raphson method 35

36 MTPA Control based AQDM ω s Find optimal for a given and I s λm Optimal technique - Newton method 36

37 37 MTPA Control based AQDM ( ) ( ) = s s e s m ag s s e I I j Z P I T ω ω λ ω, Im 2 3, Newton Method (cont)

38 MTPA Control based AQDM Maximum Torque for given I s ( ω ) T,max = max T, I e ω e s s s fixed T e,1 ω s,1 Is,1 0A T ω ej, s, j I s, j T en, ω J s,n J I s, N I J s, rat 38

39 MTPA Control based AQDM Curve Fitting s I vs T e ω s b b s = 1 e + 2 e + 3 e I a T a T a T θ = 1 2 { a1 a2 a3 b1 b2} T e 39

40 MTPA Control based AQDM Curve Fitting s ω vs T e I s s c0 c1 Te c2 Te c3 Te c4 Te ω = θ = { c1 c2 c3 c4 c5} T e 40

41 Validation II MTPA design ω ( ) ( ) s e = e 17.0 e e I T T T T ω AQDM with θ= θ s Te = Te Te Te Te AQDM with θ= θ ( ) ( ) s e = e 6.41 e e fz fz/ssfr I T T T T s Te = Te Te Te Te I s ω s T e 41

42 Validation II MTPA design Question? How to show that MTPA condition is met at ω s 42

43 Validation II MTPA design Measured torque achieved in open loop torque mode using AQDM based MTPA control strategy AQDM with θ = θ fz T T e e T e 43

44 Validation II MTPA design AQDM with θ = θ fz/ssfr T T e e T e 44

45 MTPA performance at a temperature Torque achieved by MTPA in open loop torque mode at the temperature T C when IM was characterized s ( ) T e = 150 MTPA Control Strategy T e / T e I s ω s =25.1 =2.68 T e (Nm) 45

46 Thermal Effect on MTPA performance Torque achieved by MTPA in open loop torque mode ω s I =25.1 =2.68 s Torque at w s T e Surface temperature ( o C) 46

47 Thermal Effect on MTPA performance Torque at 3 different ω s T e Surface temperature ( o C) 47

48 Variation of stator resistance Off-line Multi meter measurement 48

49 Variation of stator resistance No dependence of MTPA control on stator resistance T e ( I, ω ) s Z ag s = jγ m ( λ ) m + ω s e jω L lr ( λ, ω ) 3 Z ag m s = P Im I s I s 2 jωe ω ( λ ) m s + Y r 1 ( jω ) s Newton-Raphson methond e m s ag ( λ ω ) ω λ = 2 I Z, m s 49

50 No load test : Variation of inductance 50

51 Variation of inductance 51

52 AQDM with r ( ) in explicit form jωs Steady-state equivalent circuit Z ( jω ) = r ( jω ) + jω L ( jω ) r s rz s s lrz s r ( jω ) = Re( Z ( jω )) rz s r s 1 Llrz( jωs) = Im( Zr( jωs)) ω s 52

53 Justification of r in AQDM for MTPA design rrz from 1 to 4 rad/sec of ω at s T(C) s Z ( jω ) = r ( jω ) + jω L ( jω ) r s rz s s lrz s r rz L lrz Z ( jω ) = r + jω L ( jω ) r s rz s lrz s ω s 53

54 Comparison between MTPA laws MTPA law based on AQDM with r rz =0.176 at T ( C) s Z r r jω + jω L ( ) rz s s lrz r + j ω L rz s lrz I s ω s T e T e 54

55 r Influence of on MTPA control law MTPA control laws based on AQDM with Z ( jω ) = r + jω L ( jω ) r s rz s lrz s where r rz vary from 0.01Ω to 0.21Ω in 5 steps I s T e 55

56 r Influence of on MTPA control law ω s T e 56

57 Structure AMTPA control strategy Goal MTPA Control Scheme (Tracking) (MTPA condition) 57

58 AMTPA control strategy T e ( I, ω, rˆ ) s s r 3 Z P Imag ( λ, ω, rˆ ) I ag m s r = I s s 2 jωe Maximum Torque for a given I, s rr T max e, max = e ωs ω s { T (, I, rˆ )} s r T e ω s I s r r (fixed) 58

59 AMTPA control strategy Maximum Torque for a given I s, r rz ( ω ) T,max = max T, I, r e ω e s s rz s fixed T e,1,1 ω e,1,1 0A s,1 I 0.01Ω r rz,1 T ejk,, ω ejk,, I s, j r rz, k T en, J, N ω K en, J, N I s, rat K s, N J I 0.21Ω r rz N, K 59

60 AMTPA control strategy s I vs T e ω s vs T e and r r Current command Slip frequency command Torque command Torque command Rotor resistance 60

61 ( ) AMTPA control strategy s e = e 6.41 e e I T T T T I s T e 61

62 AMTPA control strategy ( ) s Te, rrz 7.22 rrz rrz Te ω = + ω s T e r rz 62

63 Derivation AQDM based rr estimator Estimate of rotor resistance 63

64 Derivation (continue) AQDM based rr estimator Z qs rˆ rz = S Re Estimate of rotor resistance 64

65 [ AQDM based rr estimator v v abi bci e K s,v LPF 1 ( s + a 1) 2 v e qi j v e di 3 2 v~qs max SRL min LPF 1 ( s + rrz 1) r rz,max r rz,min r rz, est m estimate ~ vqs ( rs j Lls ) ~ i e qs e ~ 0 v (1 ) Z I ~ i (1 qs ) IsT qs qs st Z qs 1 j m( m) Re Z r j L e e s {[( qs s ls ( e 1 { r rz m r rz Equation i i ai bi e K s,i 1 ( s + a 1) LPF 2 i e qi ji e di 1 6 ~qs i ~qs i j0 e τ τ a α α rrz max min = sec = sec = Ω/s = Ω/s r r rz,max rz,min = 0.35Ω = 0.09Ω 65

66 AQDM based rr estimator α α = min( α v, α i ) where α v = v~ qs 1 V st if v~ qs = 0 else v~ > V qs st α i = ~ i qs 1 I st ~ if iqs = 0 ~ else i > I qs st 66

67 Validation - AMTPA 67

68 Validation - AMTPA One operating condition 68

69 Validation - AMTPA 69

70 Validation - AMTPA Changing operating conditions 70

71 Validation - AMTPA 71

72 Validation AQDM based rr estimator One operating conditions 72

73 Validation AQDM based rr estimator 73

74 Validation AQDM based rr estimator Changing operating conditions at 900 rpm 74

75 Validation AQDM based rr estimator at 180 rpm 75

76 Validation AQDM based rr estimator Comparison of the estimated rotor resistances One operating conditions 76

77 Validation AQDM based rr estimator Changing operating conditions 77