The Control of a Continuously Operated Pole-Changing Induction Machine

Transcription

1 The Control of a Continuously Operated PoleChanging Induction Machine J.W. Kelly Electrical and Computer Engineering Michigan State University East Lansing, MI February 2002 MD Lab 1/0202 1

2 Outline Pole Changing Techniques for Induction Machines Reconfigurable Stator Winding Multiple Stator Windings Experimental Induction Machine with a 3:1 Pole Ratio 3phase12pole Configuration 3phase4pole Configuration 9phase4pole Configuration PolePhase Variation MD Lab 1/0202 2

3 Nine Phase Operation Coordinate Transformation of Machine Variables 9 Phase PWM Techniques Continuous Operation of a Pole Changing Induction Machine Issues During the PoleChanging Transition Proposed Technique for Torque Regulation During PoleChanging Transient Experimental Setup Conclusions MD Lab 1/0202 3

4 Background 2:1 Polechanging using Reconfigurable Stator Winding Series connected phase coils resulting in 8 poles Mechanical Contactors phasebelt C 1 C 2 C 3 C 4 C 3 C 1 C 4 C 2 3phase Power supply MD Lab 1/0202 4

5 Seriesparallel connected phase coils resulting in 4 poles Mechanical Contactors phasebelt C 1 C 2 C 3 C 4 C 1 C 3 C 2 C 4 3phase Power supply MD Lab 1/0202 5

6 3:1 Polechanging using Reconfigurable Stator Winding Delta connected phase coils resulting in 2 poles 60 o Phase Belt phasebelt (Mechanical degrees) 60 o L 1 L 2 L 3 L 5 L 6 L 7 L 8 L 9 L 1 L 2 L 3 L 4 L 5 L 6 L 7 L 8 a a a c c c b b b a a a c c c b b b L 4 L 9 L 7 L 7 L 8 L 1 L 1 L2 L2 polepitch (Electrical degrees) 180 o L 9 L 8 L 9 L 3 L 3 MD Lab 1/0202 6

7 Wye connected phase coils resulting in 6 poles 60 o Phase Belt L 1 L 1 L 2 phasebelt (Mechanical degrees) 20 o L 3 L 4 L 5 L 6 L 7 L 8 L 9 L 1 L 2 L 3 L 4 L 5 L 6 L 7 L 8 L 9 a c b a c b a c b a c b a c b a c b L 1 L 7 L 7 L o polepitch (Electrical degrees) b L 9 L L 9 6 L L 6 3 L 3 a L 4 c L 8 L 8 L5 L 5 L 2 MD Lab 1/0202 7

8 Induction Machine with Dual Stator Windings: Lippo and Osama 4 pole configuration two 3phase inverters, 6 winding currents:[i a1,i b1,i c1,i a2,i b2,i c2 ] a aaabbbb b bbbcccc c c ccaaaaaaaabbbb b bbbcccc c c ccaaa a c c c c c c c c a a a a a a a a b b b b b b b b c c c c c c c c a a a a a a a a b b b b b b b b 2 pole configuration two 3phase inverters, 6 winding currents:[i a1,i b1,i c1, i a2, i c2, i b2 ] a aa a c c c c c c c c b b b b b b b b a a aa a aa a c c c c c c c c b b b b b b b b a a a a b b b b b b b b a a a a a a a a c c c c c c c c b b b b b b b b a aa a aa a a c c c c c c c c MD Lab 1/0202 8

9 Machine Variables Described in Six Dimensional Space Analysis in sixdimensional space too complex V 1 V 2 V 3 V 4 V 5 V 6 = [R][I] d [λ] (1) dt Transformation to Simplify Analysis: One 6D Machine mapped into Two independent machines in 3D V 2q V 2d V 4q V 4d V 02 V 04 = [T] V 1 V 2 V 3 V 4 V 5 V 6 (2) MD Lab 1/0202 9

10 Use Stator Winding MMF as basis for Transformation I 1 (φ) = I 2 (φ) = I 3 (φ) = I 4 (φ) = I 5 (φ) = I 6 (φ) = N sh cos (h(φ)i a (t)) (3) h=1,2,3... h=1,2,3... h=1,2,3... h=1,2,3... h=1,2,3... h=1,2,3... N sh cos (h(φ π)i a (t)) (4) N sh cos h(φ π 3 )i a(t) (5) N sh cos h(φ 2π 3 )i a(t) (6) N sh cos h(φ 2π 3 )i a(t) (7) N sh cos h(φ π 3 )i a(t) (8) (9) Total MMF of Dual Stator Machine I T otal = I 1 I 2 I 3 I 4 I 4 I 5 I 6 (10) MD Lab 1/

11 Total MMF Harmonic Composition (Fourier Series Expansion) I T otal = I fundalmental I 2 nd I 3 rd I 4 th I 5 th I 6 th (11) The 6D machine variables are transformed into two sets of 2D variables. One set is based the MMF fundamental component. These machines describe a 2 pole machine. The other set is based on MMF 2 nd harmonic component. These variables describe a 4 pole machine. The 3 rd harmonic component of the Total MMF defines the 1D zerosequence subspace for the 2 pole machine The 6 rd harmonic component of the Total MMF defines the 1D zerosequence subspace for the 4 pole machine MD Lab 1/

12 Transformation Matrix from original six dimensional space to 2 3dimensional subspaces q 4 d 4 q T = 2 = 1 d (12) Transformation Matrix for arbitrary reference frame rotating at θ m T (θm) = 1 3 cos(2θm) cos(2θm) cos(2θm 2π 3 ) cos(2θ m 2π 3 ) cos(2θ m 2π 3 ) cos(2θ m 2π 3 ) sin(2θm) sin(2θm) sin(2θm 2π 3 ) sin(2θ m 2π 3 ) sin(2θ m 2π 3 ) sin(2θ m 2π 3 ) cos(θm) cos(θm) cos(θm 2π 3 ) cos(θ m 2π 3 ) cos(θ m 2π 3 ) cos(θ m 2π 3 ) sin(θm) sin(θm) sin(θm 2π 3 ) sin(θ m 2π 3 ) sin(θ m 2π 3 ) sin(θ m 2π 3 ) (13) MD Lab 1/

13 Transformed Voltage and Flux Linkage Equations v q4s = r s i q4s λ q4s ω 4 λ d4s (14) v d4s = r s i d4s λ d4s ω 4 λ d4s (15) v q2s = r s i q2s λ q2s ω 2 λ d2s (16) v d2s = r s i d2s λ d2s ω 2 λ d2s (17) v 04s = r s i 04s λ 04s (18) v 02s = r s i 02s λ 02s (19) λ q4s = (L m4 L ls )i q4s L m4 i q4r (20) λ d4s = (L m4 L ls )i d4s L m4 i d4r (21) λ q2s = (L m2 L ls )i q2s L m2 i q2r (22) λ d2s = (L m2 L ls )i q2s L m2 i d2r (23) Transformed Torque Equation T e = 2(λ d4s i q4s λ q4s i d4s ) (λ d2s i q2s λ q2s i d2s ) (24) MD Lab 1/

14 Experimental 3:1 Pole Induction Machine Winding Diagram 9 Leg Inverter 12p 3phase i A1 i B2 i C3 i A4 i B5 i C6 i A7 i B8 i C9 4p i A1 i A2 i A3 i B4 i B5 i B6 i C7 i C8 i C9 3phase i A1 i B2 i C3 i D4 i E5 i F6 i G7 i H8 i I9 4p 9phase MD Lab 1/

15 3phase12pole Configuration phasebelt 10 o a c' b a' c b' a c' b a' c b' a c' b a' c b' a c' b a' c b' a c' b a' c b' a c' b a' c b' 0 o 60 o 120 o 180 o 240 o 300 o 0 o 60 o 120 o 180 o 240 o 300 o 0 o 60 o 120 o 180 o 240 o 300 o 0 o 60 o 120 o 180 o 240 o 300 o 0 o 60 o 120 o 180 o 240 o 300 o 0 o 60 o 120 o 180 o 240 o 300 o Ni 3phase4pole Configuration phasebelt 30 o a a' a c' c c' b b' b a' a a' c c' c b' b b' 0 o 180 o 0 o 60 o 240 o 60 o 120 o 300 o 120 o 180 o 0 o 180 o 240 o 60 o 240 o 300 o 120 o 120 o a a' a c' c c' b b' b a' a a' c c' c b' b b' 0 o 180 o 0 o 60 o 240 o 60 o 120 o 300 o 120 o 180 o 0 o 180 o 240 o 60 o 240 o 300 o 120 o 120 o Ni 9phase4pole Configuration phasebelt 10 o a f' b g' c h' d i' e a' f b' g c' h d' i e' 0 o 20 o 40 o 60 o 80 o 100 o 120 o 140 o 160 o 180 o 200 o 220 o 240 o 260 o 280 o 300 o 320 o 340 o a f' b g' c h' d i' e a' f b' g c' h d' i e' 0 o 20 o 40 o 60 o 80 o 100 o 120 o 140 o 160 o 180 o 200 o 220 o 240 o 260 o 280 o 300 o 320 o 340 o Ni MD Lab 1/

16 3phase4pole vs 9phase4pole MMF MMF 9 phase for one complete electrical cycle slots degrees slots 60 MMF 3 phase for one complete electrical cycle slots degrees slots MD Lab 1/

17 9 Phase Operation Coordinate Transformation 9 dimensional machine variables too complex, transform to 2D space (for conventional Field Orientation Control) Transformation from 9 to 2 dimensions is over defined Transformation from 2 to 9 dimensions is under defined Add Constraints in order to make transformation unique MD Lab 1/

18 Define a new 9D coordinate system consisting of three 3phase coordinate systems, rotated 40 o wrt to each other Map 1 3 of the 2D space vector into each 3phase system 2 to 9 transformation fq fas f bs cos(α 2π 9 ) sin(α 2π 9 ) f d3 fcs cos(α 4π f 9 ) sin(α 4π 9 ) 1 f o ds fes = 3 cos(α 6π 9 ) sin(α 6π 3 9 ) f q cos(α 2 8π 9 ) sin(α 8π 3 9 ) f d3 f fs cos(α 10π ) sin(α 10π 9 9 ) 1 f o fgs cos(α 12π 3 ) sin(α 12π 9 9 ) f q f hs cos(α 14π ) sin(α 14π 9 9 ) f d3 f is cos(α 16π ) sin(α 16π 9 9 ) 1 f o 3 (25) MD Lab 1/

19 9 to 2 transformation f q1 cos(α) 0 0 cos(α 2π 3 ) 0 0 cos(α 2π 3 ) 0 f d1 sin(α) 0 0 sin(α 2π 3 ) 0 0 sin(α 2π 3 ) 0 f o f q2 f d2 = 2 0 cos(α 2π 9 ) 0 0 cos(α 8π 9 ) 0 0 cos(α 8π 9 ) 0 sin(α 9 2π 9 ) 0 0 sin(α 8π 9 ) 0 0 sin(α 8π 9 ) f o f q3 0 0 cos(α 4π ) 0 0 cos(α 10π 9 9 ) 0 0 cos(α f d3 0 0 sin(α 4π ) 0 0 sin(α 10π 9 9 ) 0 0 sin(α f o (26) MD Lab 1/

20 Realization of a 9D Space Vector Voltage Command Via Pulse Width Modulation (PWM) 512 possible space vectors from a 9leg inverter NinephaseVoltage Space Vectors j0.6 Vdc j0.4 Vdc j0.2 Vdc 0 j0.2 Vdc j0.4 Vdc j0.6 Vdc 0.6 Vdc 0.4 Vdc 0.2 Vdc Vdc 0.6 Vdc 0.4 Vdc MD Lab 1/

21 Extending 3phase Space Vector PWM algorithm for 9phase Space Vector PWM Only 72 space vectors are used V n, offset = max V 1 V dc... V n V dc min V 1 V dc... V n V dc (27) {V45 max} {V36 max} {V27 max} {V18 max} MD Lab 1/

22 A new SVPWM for n > 3 nphase Systems The Minimum Voltage Difference SVPWM Technique MD Lab 1/

23 Proposal: The Control of a Continuously Operated PoleChanging Induction Machine Goals: Decrease the Torque reduction during the polechanging transition Preserve Control during the polechanging transition MD Lab 1/

24 Comparison of 4 pole and 12 pole Stator Current Densities 4 pole Stator Current Density 0 12 pole Stator Current Density radians: Stators Circumference MD Lab 1/

25 MD Lab 1/ Interaction between the Stator Current Density and airgap flux results in a tangential force on the rotor df dθ = B gk s (t, θ) (28) 4 pole steady state operation Tangential Force K s B grotor 0 K s stator current B g airgap flux from rotor currents radians Transition from 12 poles to 4 poles Tangential Force K s B grotor K s stator current B g airgap flux from rotor currents radians

26 Approach: Via a coordinate transformation, decouple the machine into two (possibly three) independent machines Regulate the two independent torques in order to pole change Control each machine separately MD Lab 1/

27 Experimental Setup: A/D quadature Inputs position sensor Control Program i a PIII 600MHz RTLinux 3.0 FPGA I/O board 9Leg Inverter torque sensor Dynamometer SVPWM & Communication i i 9 Winding IM MD Lab 1/

28 Speedtorque curves for the 12 pole and 4 pole configurations phase 12pole Motor Nm phase 4pole Motor rpm Figure 1: Speedtorque curves for 12 pole and 4 pole configurations MD Lab 1/

29 Speed control: 3phase12pole Induction motor Space Vector Field Orientation Control 3phase SVPWM rpms seconds Figure 2: Speedtorque curves for 12 pole and 4 pole configurations MD Lab 1/

30 Conclusions: A variety of pole changing technique exists There are no techniques for regulating torque during the polechanging transition Issues during the polechanging transition: reduction in torque flux and torque tracking) Requirements for a method to decrease torque reduction during the polechanging transition and preserve control: New PWM scheme Modelling the machine as two independent machines Develop method to analyze a polechanging machine in terms of Field Orientation Transformation MD Lab 1/