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

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

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

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. 203-210 3

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 τ1 3 + 1 [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. 48-56 4

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 1 2 3 4 5 6 y y y y y y a1 τ 1 a2 τ2 a3 τ3 Llr lr1 lr2 lr3 lr4 ] Y r 5

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

Experimental Measurements - I Fundamental frequency impedance fz, k Z qs Control Algorithm [ 0.1 10] N fz 10 80 = 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

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

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

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

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

Impedance Errors Input data output data Impedance Errors AQDM 12

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

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

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

18 Evolution Process Best fitness ( N P = 1000 ) Best-fitness 12 s 6 16.4 7.87 based on based on f f fz fz/ ssfr 0 500 1000 Generation 16

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 0.0599 0.3219 0.3313 0.3718 0.4785 θ AQDM = θ fz/ssfr 0.0625 0.1026 0.0389 0.0325 0.0803 17

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

Quality of Fit In terms of fundamental frequency impedance 45 40 35 based on based on f f fz fz/ ssfr E k = % of PTS 30 25 20 15 10 5 0 0 5 10 15 20 25 E k 19

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

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

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

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

Dependency on population size N P = 1000,500,2000,5000, and 10000 Best-fitness Generation 24

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 7.86 0.063 0.103 0.039 0.033 0.080 500 7.95 0.063 0.101 0.037 0.034 0.077 2000 7.77 0.063 0.100 0.035 0.035 0.088 5000 7.96 0.063 0.103 0.037 0.033 0.076 10000 7.98 0.063 0.102 0.037 0.033 0.075 25

Dependency on population size In terms of Fundamental frequency % of data points 50 40 30 20 10 AQDM with fz/ ssfr( P N = 1000) P N = 500 P N = P N = 5000 2000 P N = 10000 fz k Zqs Zˆ Ek = 100 fz, k Z, fz, k qs qs 0 0 5 10 15 20 25 E k 26

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

Consistency in repeated applications 100 repeated applications with N P =500 µ σ f 7.834 0.0955 E fz 0.0628 0.00045 E k 69.70 5% 1.253 µ σ 5A Essfr 0.1003 0.00178 0.0358 10A E ssfr 0.00173 15A E ssfr 0.0355 0.00146 22A E ssfr 0.0841 0.00642 28

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

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

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

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

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

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

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

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

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)

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

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

MTPA Control based AQDM Curve Fitting s ω vs T e I s 2 3 4 s c0 c1 Te c2 Te c3 Te c4 Te ω = + + + + θ = { c1 c2 c3 c4 c5} T e 40

Validation II MTPA design ω ( ) ( ) 0.0177 0.0799 s e = 0.109 e 17.0 e + 18.5 e I T T T T ω AQDM with θ= θ 3 6 2 s Te = 1.4 2.4 10 Te + 176 10 Te 9 3 9 4 933 10 Te + 1.74 10 Te AQDM with θ= θ ( ) ( ) 0.0110 0.152 s e = 0.102 e 6.41 e + 7.79 e fz fz/ssfr I T T T T 3 6 2 s Te = 1.3+7 10 Te + 25.7 10 Te 9 3 12 4 Te Te 63.1 10 + 42.1 10 I s ω s T e 41

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

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

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

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

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

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

Variation of stator resistance Off-line Multi meter measurement 48

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

No load test : Variation of inductance 50

Variation of inductance 51

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

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 0.176 L lrz Z ( jω ) = r + jω L ( jω ) r s rz s lrz s ω s 53

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

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

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

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

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

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

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

( ) AMTPA control strategy 0.0110 0.152 s e = 0.102 e 6.41 e + 7.79 e I T T T T I s T e 61

AMTPA control strategy ( ) 0.9998 1.00 1.15 s Te, rrz 7.22 rrz 0.025 rrz Te ω = + ω s T e r rz 62

Derivation AQDM based rr estimator Estimate of rotor resistance 63

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

[ 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 = 0.0318sec = 0.0080sec = 0.005 Ω/s = 0.005 Ω/s r r rz,max rz,min = 0.35Ω = 0.09Ω 65

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

Validation - AMTPA 67

Validation - AMTPA One operating condition 68

Validation - AMTPA 69

Validation - AMTPA Changing operating conditions 70

Validation - AMTPA 71

Validation AQDM based rr estimator One operating conditions 72

Validation AQDM based rr estimator 73

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

Validation AQDM based rr estimator at 180 rpm 75

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

Validation AQDM based rr estimator Changing operating conditions 77