Saliency Tracking-Based Sensorless Control of AC Drives. F. Briz, 6/2010 Saliency Tracking-based Sensorless Control of AC Drives 1

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1 Saliency Tracking-Baed Senorle Control of AC Drive F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 1

2 High Frequency Signal Injection Baed Senorle Method Senorle control of AC drive: Motivation ω* ω λ * Speed (torque) regulator ^ λ Flux reg. e iq * e iqd * e id * Current reg. e iqd vqd vqd Inverter vqd (PWM) Coord. tranf. ^ λ ρ^ * oberver iqd machine ω Poition/ velocity enor Velocity/poition etimation i normally needed for two different purpoe: Flux angle etimation for flux and torque control. Motion control (velocity/poition regulation). Incremental encoder i currently the mot commonly ued enor. Elimination of the poition enor (and cabling) ha advantage in term of 1) cot, 2) robutne and 3) pace. Senorle control ha been a major field of reearch for the lat two decade. F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 2

3 High Frequency Signal Injection Baed Senorle Method Senorle control of AC drive ω* ω λ * e Speed (torque) iq * regulator iqd e * Flux reg. e id * ^ λ vqd Current vqd e* vqd * Inverter reg. Coord. (PWM) e tranf. iqd iqd ρ^ ρ^ ^ λ oberver machine ω Poition/ velocity enor Elimination of the poition enor (and cabling) ha advantage in term of: Cot. Robutne. Space. Elimination of the poition enor require the ue of ome form of oberver, it input normally being already available electric quantitie. Two different approache: model baed method and aliency tracking baed method. F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 3

4 High Frequency Signal Injection Baed Senorle Method Model baed enorle method Induction machine model (complex vector notation, tationary reference frame) pi qd = 1 L σ (v qd R ω br = R r L r j ω r i qd L m Lr pλ qdr= L m Lr R r i qd ω br λ qdr, L σ = L L2 m, L r ω br λ qdr) Lm 2 R = R L r Rr Thee method ue (in different form) the back emf induced in the tator winding. Stator current are normally (and eaily) meaured. ^ λ qdr Stator voltage are not normally meaured, but etimated from the voltage command to the inverter. The model uffer from a ignificant parameter enitivity. ω^ r model ^ R r, ^ R L ^ m, L^ r, L^ vqd * Inverter (PWM) Accurate peed (and flux) etimation can be obtained in the medium and high peed range. Significant problem arie in the low peed range, mainly coming from error in the tator reitance etimation and in the voltage meaurement. Poition control i not poible (no back emf exit at zero peed). vqd iqd machine F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 4

5 High Frequency Signal Injection Baed Senorle Method High frequency ignal injection baed enorle method Thee method track patial aliencie (aymmetrie) contructively aociated to the rotor. No parameter enitivity to the electrical parameter of the machine (ideally). Independent of the fundamental excitation (i.e. electrical/mechanical peed, flux and torque level, ideally). Can work at very low and zero peed, alo allowing poition control. Often complicated ignal proceing. May require modification of the machine deign. Require the injection of high frequency ignal or modification of the PWM pattern, what can reult in unwanted effect (vibration, noie, additional loe, reduction of the voltage available for the fundamental operation of the machine, ). May require additional enor (voltage enor, di/dt enor, ). F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 5

6 High Frequency Signal Injection Baed Senorle Method High frequency model of induction machine Conventional Steady-State Equivalent Circuit (ωe ωr ) i qd v qd R jω e L l jω L jω e L m e lr R r ω e ω ω e r c a b High Frequency Circuit (ωc>>ωr ) i qd_c v qd_c R jω c L l jω L jω c L m c lr R r ω c ω ω c r b a c High Frequency Equivalent Circuit i qd_c v qd_c jω c L σ Saliency tracking-baed enorle method require that the tator tranient inductance varie with the rotor poition (through the rotor leakage inductance) F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 6

7 High Frequency Signal Injection Baed Senorle Method Spatial aliencie in induction machine Modulation of the rotor lot width Rotor tator lotting Stator lot Modulation of the rotor lot width implie a modification of the manufacturing proce, or pot-manufacturing machining. Rotor-tator lotting can be preent in tandard machine with open or emi-open rotor lot (depend on the number of rotor and tator lot, and number of pole), the rotor kew angle trongly influencing. Rotor lot F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 7

8 High Frequency Signal Injection Baed Senorle Method Spatial aliencie in permanent magnet machine S Radial flux, interior permanent magnet machine N d N S N q S S Radial flux, urface permanent magnet machine N d S N q Tangential flux, interior permanent magnet machine d N N d S S q S N N S N S S S N N Saturation can help F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 8

9 High Frequency Signal Injection Baed Senorle Method Form of high frequency excitation and reulting high frequency ignal V dc/2 V dc/2 Inverter i a i b i c v an v bn v cn Induction machine v n Continuou/dicontinuou excitation Carrier ignal PWM harmonic Rotating vector Pulating vector Carrier current Zero equence voltage* di/dt Zero equence voltage * Zero equence current for delta-connected machine F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 9

10 Introduction to Complex Vector Spatial phaor FEM Simulation of a two-pole Induction Machine a 3 A/mm 2 c b b c a -3 A/mm 2 Flux denity Flux line Current denity There are three tator winding eparated 12 electrical degree from each other. However, electromagnetic variable involved in the electro-mechanical power converion that take place within the machine have a quai-inuoidal patial ditribution with a period equal to 36 electrical degree. All electromagnetic quantitie can be repreented by a complex vector (patial phaor). F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 1

11 Introduction to Complex Vector The current heet and the current complex vector 3 A/mm 2 Stator Rotor Current denity -3 A/mm 2 The current heet ha a quai-inuoidal patial ditribution. The current complex vector i orthogonal to the current heet, it magnitude being proportional to the total current. Similarly, flux and voltage complex vector can alo be defined. F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 11

12 Introduction to Complex Vector The tator current heet and the tator current complex vector b c a a c b b c Im The tator current complex vector i obtained uing the meaured phae current and the knowledge of the tator winding patial poition. The rotor current complex vector could be obtained in a imilar fahion. Thi i not poible however for the cae of quirrel cage induction machine. a Re Im i a i b i c i qd = 2 (iaib e j2π/3 ice j4π/3 ) 3 i c i qd i a i b Re i = d j i q Im i qd time Re F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 12

13 Introduction to Complex Vector The tator current heet and the tator current complex vector i a i b i c Im i qd time Re i d i q time Im Re i qd = 2 (iaib e j2π/3 ice j4π/3 ) 3 i = d j i q F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 13

14 Introduction to Complex Vector The Fourier Tranform of a complex ignal tiempo () i qd tiempo () i qd 1 5 Im Re 1 5 Im Rel magnitude Spectrum i qd magnitude frequency (Hz) frequency (Hz) The Fourier Tranform of a complex vector ignal decompoe the ignal in individual rotating complex vector. Complex vector can rotate both forward and backward the frequency pectrum will contain both of poitive and negative frequencie. F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 14

15 Introduction to Complex Vector The Fourier Tranform of a complex ignal Balanced three-phae ytem i a, i b, i c i q, i d i qd Im balanced imbalanced Re time () Imbalanced three-phae ytem i a, i b, i c i q, i d time () Negative equence current magnitude magnitude 5 Poitive equence current -5 5 frequency (Hz) Spectrum i a Spectrum i qd F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 15

16 High Frequency Signal Injection Baed Senorle Method Rotating carrier voltage vector excitation Im vqd_c =V c e jω c t Re vqd vqd_c Inverter (PWM) va vb vc Induction machine vd = Vc co(ω c) vd = Vc co(ω c π 2 ) c a b va = Vc co(ω c) vb = Vc co(ω c 2π ) 3 vc = Vc co(ω c 4π 3 ) b a c F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 16

17 High Frequency Signal Injection Baed Senorle Method Amplitude modulated carrier voltage vector excitation Im vqd_c = Vc co(ω c) e jρt ρ=º Re vqd vqd_c Inverter (PWM) va vb vc Induction machine vd vd = Vc co(ω ) c co(ρ) = Vc co(ω ) c in(ρ) c a ρ=º b va = Vc co(ω ) c co(ρ) vb = Vc co(ω c) co(ρ 2π 3 ) vc = Vc co(ω c) co(ρ 4π 3 ) b a c F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 17

18 High Frequency Signal Injection Baed Senorle Method Amplitude modulated carrier voltage vector excitation Im vqd_c = Vc co(ω c) e jρt ρ=2º Re vqd vqd_c Inverter (PWM) va vb vc Induction machine vd vd = Vc co(ω ) c co(ρ) = Vc co(ω ) c in(ρ) c a ρ=2º b va = Vc co(ω ) c co(ρ) vb = Vc co(ω c) co(ρ 2π 3 ) vc = Vc co(ω c) co(ρ 4π 3 ) b a c F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 18

19 High Frequency Signal Injection Baed Senorle Method PWM harmonic baed high frequency excitation Make ue of the fat PWM tranition. V dc/2 V dc/2 Modification of th normal PWM pattern i needed to obtain uitable information. Different variable can be meaured to detect the aliency poition: Zero equence voltage. Require an additional enor and acce to the terminal box. Strongly influenced by paraitic phenomena (cable length, cable hielding, ). di/dt (current derivative). Though the current derivative could initially be derived from two current meaurement, di/dt enor normally need to be ued in practice (e.g. Rogowki coil). Acquiition of ignal i complicated, a need to be ynchronized with PWM tranition. Inverter v a v b v c b c i a i b i c a Induction machine v an v bn v cn a c b v n F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 19

20 High Frequency Signal Injection Baed Senorle Method PWM harmonic baed high frequency excitation v a v b V dc/2 V dc/2 Inverter v a v b v c i a i b i c Induction machine v an v bn v cn v n v c Zero-equence voltage v n v 3 v 2 v 3 v 2 v 3 v 2 v 4 v 1 v 4 v 1 v 4 v 1 v 5 v 6 v 5 V 6 v 5 v 6 v a i a di/dt vσa vσb vσc vσ = van vbn vcn 3 v qdσ = 2 vσa v σb e j2π/3 vσc e j4π/3 3 ( ) F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 2

21 High Frequency Signal Injection Baed Senorle Method c q a b Rotating carrier voltage vector excitation: The carrier ignal current and the zero equence carrier ignal voltage d Symmetric machine - The carrier current trajectory i a circle. b - There i no zero equence carrier ignal voltage. c a v qd q v qd i qd i qd d v = (v anvbnvcn) 3 v F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 21

22 High Frequency Signal Injection Baed Senorle Method q a Rotating carrier voltage vector excitation: The carrier ignal current and the zero equence carrier ignal voltage c Aymmetric machine b d - The carrier current trajectory i an ellipi, it orientation being function of the aliency phae angle. b c - A zero equence carrier ignal voltage exit, it phae angle being function of the aliency phae angle a v qd i qd q vqd i qd i qd d v = (v anvbnvcn) 3 v F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 22

23 High Frequency Signal Injection Baed Senorle Method q a Rotating carrier voltage vector excitation: The carrier ignal current and the zero equence carrier ignal voltage c Aymmetric machine b d - The carrier current trajectory i an ellipi, it eccentricity being function of the level of aymmetry. b c - A zero equence carrier ignal voltage exit, it magnitude being function of the level of aymmetry. a v qd i qd q v qd i qd i qd d v = (v anvbnvcn) 3 v F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 23

24 High Frequency Signal Injection Baed Senorle Method b c iqd_cp a q a c b Rotating carrier voltage vector excitation: The carrier ignal current and the zero equence carrier ignal voltage d vqd_c iqd_c = Vc e jω c t = j Icp e jω c t j I cn e j(hθ e ω c t) v c = V ch co (ω cthθ e ) V c2h co (ω c t 2hθ e ) : Poitive equence carrier ignal current. Reult from the ymmetric part of the machine, and doe not contain any aliency related information. iqd_cn: Negative equence carrier ignal current. Reult from the aymmetric part of the machine and contain information on the magnitude and patial poition of the aliency. v c : Zero equence carrier ignal voltage. Reult from the aymmetric part of the machine and contain information on the magnitude and patial poition of the aliency. vqd_c = iqd_cp iqd_cn q i qd_c iqd_cn iqd_cp d F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 24

25 Carrier Signal Meaurement and Proceing Meaurement of the carrier ignal: The carrier ignal current and the zero equence carrier ignal voltage vqd vqd_c Inverter (PWM) va vb vc i a i b i c v bn v an machine v cn i qd = 2 (iaib e j2π/3 ice j4π/3 ) 3 v = (v anvbnvcn) 3 - Complex vector ignal (at leat two enor are needed) - Current enor are normally preent for control/protection purpoe - Scalar ignal (one enor hould be enough) - Require acce to the terminal box - Require an additional enor F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 25

26 Carrier Signal Meaurement and Proceing Meaurement of the zero equence voltage Uing three voltage enor Inverter Induction machine ( = v an vbn vcn ) v 3 V dc/2 V dc /2 v b v c v a v an v bn v cn v n v n Uing an auxiliary reitor network and a ingle voltage enor V dc/2 V dc /2 Inverter Induction machine v n v n The auxiliary reitor network meaure (and decouple) the zero equence voltage generated by the inverter. v n _nr Voltage probe (galvanic iolation) v nr R R R Balanced reitor network F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 26

27 Carrier Signal Meaurement and Proceing Proceing of the carrier ignal current: Separation of the negative equence carrier ignal current iqd_c = j Icp e jω c t j I cn e j(2θ r ω c t) iqd_c e jω ct cn iqd_c LPF cn iqd_cn q a q i cn qd _ cn c b d d b a c F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 27

28 Carrier Signal Meaurement and Proceing Rotor poition etimation uing the tator and rotor lotting aliency vqd Vc e jω c t Inverter (PWM) va vb vc Induction machine Stator lot Rotor lot Requirement for rotor-tator lotting aliencie to couple with the tator winding and produce meaurable ignal: R S = n p R, S, p number of rotor, tator lot and pole n = 1,2,4,5,7,8, Induction Motor Parameter 1.1 kw, p=4 S=36, R=28, kewed The aliency rotate at a frequency R ω rm R S The reulting component rotate at a frequency R ω rm F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 28

29 Carrier Signal Meaurement and Proceing Proceing of the carrier ignal current: Separation of the negative equence carrier ignal current iqd_c = j Icp e jω c t j I cn e j(8θ r ω ct) iqd_c e jω ct cn iqd_c LPF cn iqd_cn q a q i cn qd _ cn c b d d b a c F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 29

30 Carrier Signal Meaurement and Proceing Secondary aliencie: Saturation induced aliencie IPMSM, no load Injection of fundamental current during the normal operation of the machine reult in additional aliencie (aymmetrie). Thee aliencie are caued (and therefore related) to the fundamental fluxe, acting like a diturbance to the rotor poition dependent aliency. Saturation reult in: Shift of the aliency angle. Variation of the aliency ratio. Secondary patial harmonic of the aliency (i.e. aliencie with a non-inuoidal patial ditribution). IPMSM, rated torque Decoupling of econdary aliencie i practically alway mandatory to obtain adequate accuracy, and very often table operation. F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 3

31 Carrier Signal Meaurement and Proceing Secondary aliencie: Saturation induced aliencie High frequency excitation Stator current heet vqd Vc e jω c t Inverter (PWM) va vb vc Induction machine V f V f FFT vqd V c Stator lot Rotor lot I f I f FFT iqd I cn I cp ω c ω c F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 31

32 Carrier Signal Meaurement and Proceing Secondary aliencie: Saturation induced aliencie High frequency excitation Stator current heet Vc = Vc = 2 2 V (peak) (peak) ωc = ωc = 5 5 Hz Hz vqd Vc e jω c t Inverter (PWM) va vb vc Induction machine 1 FFT iqd (A).1.1 Stator lot Rotor lot (ma) 4 2ω e 14ω r frequency (Hz) (A) frequency (Hz) frequency (Hz) F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 32

33 Carrier Signal Meaurement and Proceing Secondary aliencie: Saturation induced aliencie High frequency excitation Stator current heet Vc = Vc = 2 2 V (peak) (peak) ωc = ωc = 5 5 Hz Hz vqd Vc e jω c t Inverter (PWM) va vb vc Induction machine (ma) FFT iqd 4 2ω e 14ω r frequency (Hz) Stator lot Rotor lot Saturation-induced aliencie produce additional component of the negative equence carrier ignal current. Accurate rotor poition etimation require thee aturationinduced aliencie be compenated for. They are meaured during an off-line commiioning proce, then compenated during the regular enorle operation of the drive. F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 33

34 Carrier Signal Meaurement and Proceing iqd_c Modeling and compenation of aturation induced aliencie e jω ct cn iqd_c LPF cn iqd_cn i cn qd_14ωr Poition etimation ω^ r θ ^ r iqd Look-up table & interpolation c iqd_2ω e (A) 5-5 iq, i d (ma) 2-2 cn iq_c cn, i d_c (ma) (ma) F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive time () cn i q _2ωe, i cn d_2ωe cn iq_14ωr, i cn d_14ωr

35 Senorle Control Senorle poition control: Secondary aliencie decoupling (deg.) (mech. deg.) ^ θrf ^ θr e iq Carrier Carrier voltage: voltage: ωc=375 ωc=375 Hz, Hz, Vc=15 Vc=15 V (peak) (peak) (carrier (carrier current current 1% 1% rated rated current). current). Machine Machine operated operated at at rated rated flux, flux, 8% 8% rated rated load. load. Look-up table & interpolation cn iqd _2ωe cn iqd _4ωe cn iqd _4ωe i cn qd _c _ 14ωr Tracking oberver ω^ r θ ^ r (mech. deg.) 2-2 θr ^ θr 2ωe component compenated (mech. deg.) time ().8 θr ^ θr 2ωe, 4ωe and 2ωe 14ωr component compenated F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 35

36 Ongoing and future reearch line Machine deign (epecially IPMSM): No deterioration of the fundamental operation of the machine. Minimization of econdary aliencie Improvement of the ignal to noie ratio. Wide range of operation. Secondary aliencie decoupling: Self-commiioning method. Adaptive method (e.g. with temperature). Dynamic operation. Better undertanding of the effect due to the non-ideal behavior of the inverter and their compenation. Form of high frequency excitation. Signal acquiition and proceing. What the limit of the method are? F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 36

37 Publication Some 2 IEEE Tranaction paper. Some 3 international conference paper F. Briz, 6/21 Saliency Tracking-baed Senorle Control of AC Drive 37