The Control of a Continuously Operated PoleChanging Induction Machine J.W. Kelly Electrical and Computer Engineering Michigan State University East Lansing, MI 48824 28 February 2002 MD Lab 1/0202 1
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
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
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
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
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
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 4 180 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
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
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
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 1/0202 10
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 1/0202 11
Transformation Matrix from original six dimensional space to 2 3dimensional subspaces q 4 d 4 q T = 2 = 1 d 2 3 0 4 0 2 1 1 1 1 1 1 2 2 2 2 0 0 3 3 3 3 2 2 2 2 1 1 1 1 1 1 2 2 2 2 0 0 3 3 3 3 2 2 2 2 1 2 1 2 1 2 1 2 1 2 1 2 1 1 1 2 1 2 1 1 2 2 2 2 (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 ) 1 2 1 2 1 2 1 2 1 2 1 2 1 1 1 2 1 2 1 1 2 2 2 2 (13) MD Lab 1/0202 12
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 1/0202 13
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 1/0202 14
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 1/0202 15
3phase4pole vs 9phase4pole MMF MMF 9 phase for one complete electrical cycle 150 100 50 200 0 0 200 400 50 300 100 200 80 150 0 10 20 30 40 50 60 70 slots degrees 100 0 0 20 40 slots 60 MMF 3 phase for one complete electrical cycle 150 200 100 0 50 50 100 0 150 0 10 20 30 40 50 60 70 slots 200 400 350 300 250 200 150 100 degrees 50 0 0 20 slots 40 60 80 MD Lab 1/0202 16
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 1/0202 17
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 1 0 1 0 0 0 0 0 0 3 f bs 0 0 0 cos(α 2π 9 ) sin(α 2π 9 ) 1 0 0 0 f d3 fcs 0 0 0 0 0 0 cos(α 4π f 9 ) sin(α 4π 9 ) 1 f o ds fes = 3 cos(α 6π 9 ) sin(α 6π 3 9 ) 1 0 0 0 0 0 0 f q 0 0 0 cos(α 2 8π 9 ) sin(α 8π 3 9 ) 1 0 0 0 f d3 f fs 0 0 0 0 0 0 cos(α 10π ) sin(α 10π 9 9 ) 1 f o fgs cos(α 12π 3 ) sin(α 12π 9 9 ) 1 0 0 0 0 0 0 f q f hs 0 0 0 cos(α 14π ) sin(α 14π 9 9 ) 1 0 0 0 3 f d3 f is 0 0 0 0 0 0 cos(α 16π ) sin(α 16π 9 9 ) 1 f o 3 (25) MD Lab 1/0202 18
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 o1 1 0 0 1 0 0 1 0 f 2 2 2 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 o2 0 1 0 0 1 0 0 1 2 2 2 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 o3 0 0 1 0 0 1 0 0 2 2 (26) MD Lab 1/0202 19
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 0 0.2 Vdc 0.6 Vdc 0.4 Vdc MD Lab 1/0202 20
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 1/0202 21
A new SVPWM for n > 3 nphase Systems The Minimum Voltage Difference SVPWM Technique 110111111 000000010 111011111 000000001 00000110 100011111 000000010 000000110 110011111 110111111 110111111 110011111 000000110 000000010 00000011 000001111 000000111 000001111 100001111 100011111 100011111 100001111 000001111 000000110 000000111 000000111 100011111 110011111 110011111 100011111 000000111 100000111 000000111 100001111 000000110 110001111 000000011 110001111 000000111 100001111 110001111 110011111 100000111 110011111 000000111 000000010 110001111 000000011 000000111 110011111 000000011 111011111 111011111 110011111 100000011 000000011 100000111 000000011 000000010 110000111 100000011 000000001 110001111 110001111 000000011 110001111 111001111 111001111 110000111 111001111 111011111 110001111 100000111 111011111 100000011 111001111 100000011 000000011 000000011 111001111000000001 100000011 110000111 110011111 00000111 100001111 110001111 100000111 MD Lab 1/0202 22
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 1/0202 23
Comparison of 4 pole and 12 pole Stator Current Densities 4 pole Stator Current Density 0 12 pole Stator Current Density 0 1 2 3 4 5 6 7 radians: Stators Circumference MD Lab 1/0202 24
MD Lab 1/0202 25 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 0 1 2 3 4 5 6 7 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 0 0 1 2 3 4 5 6 7 radians
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 1/0202 26
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 1/0202 27
Speedtorque curves for the 12 pole and 4 pole configurations 45 40 35 30 3phase 12pole Motor Nm 25 20 15 9phase 4pole Motor 10 5 0 0 100 200 300 400 500 600 700 800 rpm Figure 1: Speedtorque curves for 12 pole and 4 pole configurations MD Lab 1/0202 28
Speed control: 3phase12pole Induction motor Space Vector Field Orientation Control 3phase SVPWM 700 600 500 400 rpms 300 200 100 0 0 50 100 150 seconds Figure 2: Speedtorque curves for 12 pole and 4 pole configurations MD Lab 1/0202 29
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 1/0202 30