1 / 46 Lecture 7: Synchronous Motor Drives ELEC-E8402 Control of Electric Drives and Power Converters (5 ECTS) Marko Hinkkanen Spring 2017
2 / 46 Learning Outcomes After this lecture and exercises you will be able to: Identify, based on the cross-section of the rotor, if the motor is magnetically anisotropic Explain what is the reluctance torque Calculate operating points of synchronous motors and draw the corresponding vector diagrams Derive and explain the MTPA control principle
Common AC Motor Types Synchronous motors Surface-mounted permanent-magnet synchronous motor (SPM) Interior permanent-magnet synchronous motor (IPM) Synchronous reluctance motor (SyRM) Permanent-magnet-assisted SyRM (PM-SyRM) Excited-rotor synchronous motor Asynchronous motors Induction motor with squirrel-cage rotor Wound-rotor induction motor IPMs, SyRMs, and PM-SyRMs have magnetically anisotropic rotors Excited-rotor synchronous motors will be omitted in this course. SPMs are only briefly reviewed and considered as a special case of a more general IPM. 3 / 46
4 / 46 Outline Synchronous Motors Model Control Principles MTPA and MTPV
Surface-Mounted Permanent-Magnet Synchronous Motor (SPM) 3-phase stator winding Distributed sinusoidally along the air gap Produces rotating magnetic field Permanent magnets (NdFeB or SmCo) mounted at the rotor surface Benefits Very high efficiency (or power density) No magnetising supply needed Drawbacks Price of the magnets and manufacturing Limited field-weakening range In SPMs, a concentrated stator winding is also possible instead of a distributed winding. 5 / 46
6 / 46 Operating Principle Current distribution produced by the 3-phase winding is illustrated in the figure Torque is constant only if the supply frequency equals the electrical rotor speed ω m = dϑ m /dt For controlling the torque, the current distribution has to be properly placed in relation to the rotor Rotor position has to be measured or estimated F q β d ϑ m α F
ϑ M = ϑ m ϑ M = ϑ m /2 7 / 46 Number of Pole Pairs p 2 poles (p = 1) 4 poles (p = 2) Electrical angular speed ω m = p ω M and electrical angle ϑ m = p ϑ M
8 / 46 Interior Permanent-Magnet Synchronous Motor (IPM) q q d d SPM (L s = L d = L q ) IPM (L d < L q ) Permeability of the magnets is almost the same as for air (µ r 1.05)
Example IPM: GM High Voltage Hairpin (HVH) stator winding http://blog.caranddriver.com/we-build-the-chevy-spark-ev\ot1\textquoterights-ac-permanent-magnet-motor/ 9 / 46
10 / 46 Synchronous Reluctance Motor (SyRM) i s i s Two poles (p = 1) Four poles (p = 2) Note: no-load condition is illustrated in the figures for simplicity
Structure and Operating Principle Distributed 3-phase stator winding Rotating magnetic field produced by the stator currents Torque-production principle: Rotor tries to find its way to the position that minimizes the magnetic field energy More efficient than induction motors Cheaper than permanent-magnet motors Pump and fan applications Figure: ABB 11 / 46
Rotor Designs Conceptual rotor Axially laminated Transversally laminated Figure: T. Fukami et al., Steady-state analysis of a dual-winding reluctance generator with a multiple-barrier rotor, IEEE Trans. Energy Conv., 2008 12 / 46
Example of Magnetic Saturation: 6.7-kW SyRM 13 / 46
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15 / 46 Permanent-Magnet SyRM (PM-SyRM) SyRM designs can be improved by placing permanent magnets inside the flux barriers of the rotor Resulting motor is basically an IPM having high reluctance torque These kind of motors are often called permanent-magnet SyRMs (PM-SyRMs) or hybrid synchronous motors (HSMs) What is the reluctance torque in the figure? i s
Compared to the SyRM, the permanent magnets improve the power factor and contribute to the torque Low-cost ferrite magnets can be used Good field-weakening properties Minor risk of overvoltages due to the low back-emf induced by the permanent magnets Figure: http://www.abb.com/cawp/seitp202/ad26393b09a61275c1257caf00217a16.aspx 16 / 46
17 / 46 Example PM-SyRM: Brusa HSM1-10.18.22 For truck and bus applications Low magnetic material Speed: 4 400 rpm (nom), 12 000 rpm (max) Torque: 270 Nm (S1), 460 Nm (max) Power: 145 kw (S1), 220 kw (max) DC-bus voltage: 400 V (also 750 V available) Weight: 76 kg
Example PM-SyRM: Brusa HSM1-10.18.22 18 / 46
Example PM-SyRM: BMW i3 Speed: 4 500 rpm (nom), 11 400 rpm (max) Torque: 250 Nm (max) Poles: 12 Voltage: 250... 400 V Weight: 65 kg Figure: J. Merwerth (2014) (http://hybridfordonscentrum.se/wp-content/uploads/2014/05/20140404 BMW.pdf) 19 / 46
Design Parameter Plane: Optimal Field-Weakening Performance Saliency ratio Lq/Ld Optimal design line ψ f = L d i N Finite-speed drives Infinite-speed drives PM-flux linkage (p.u.) Figure (modified): Seminar presentation given by G. Pellegrino at Aalto University (2014). Further information: W.L. Soong and T.J.E. Miller, Field-weakening performance of brushless synchronous AC motor drives, IEE Proc. EPA, vol. 141, 1994. 20 / 46
21 / 46 Outline Synchronous Motors Model Control Principles MTPA and MTPV
Review: Single-Phase Machine ψ af ψ f i a ϑ m ϑ m L a dψ a dt 0 π/2 π 3π/2 2π ϑ m ψ a = L a i a + ψ af L a = L 0 L 2 cos(2ϑ m ) ψ af = ψ f cos(ϑ m ) ] T M = p [L 2 sin(2ϑ m )ia 2 ψ f sin(ϑ m )i a Notice that the constant ψ f is the maximum value of the stator flux linkage due to the rotor PMs. In Lecture 6, the flux linkage of the rotor field winding was denoted by this same symbol. 22 / 46
23 / 46 3-Phase Distributed Winding b b a i a a i a b c i b i c a b c i b i c a c c Example of a 3-phase distributed winding (Y or D connection) Simplified representation
24 / 46 αβ Transformation Instantaneous 3-phase quantities can be transformed to the αβ components [ iα i β ] = 2 3 [ 1 1/2 1/2 0 3/2 3/2 where the currents are used as an example ] a i i b i c Equivalently, the space vector transformation could be used i s = i α + ji β = 2 3 (i a + i b e j2π/3 + i c e j4π/3) which gives the same components i α and i β
3-Phase Synchronous Machine Flux linkages [ ] [ ] [ ] ψα Lαα L = αβ iα + ψ β L βα L ββ i β [ ψαf ψ βf ] i α q β d ϑ m L αα = L 0 L 2 cos(2ϑ m ) L ββ = L 0 + L 2 cos(2ϑ m ) L αβ = L βα = L 2 sin(2ϑ m ) ψ αf = ψ f cos(ϑ m ) ψ βf = ψ f sin(ϑ m ) dψ α dt α Induced voltages i β e α = dψ α dt e β = dψ β dt dψβ dt Torque could be derived using the approach described in Lecture 6, but transforming the machine model to rotor coordinates allows us to use a shortcut, as shown in the following slides. 25 / 46
26 / 46 Transformation to Rotor Coordinates αβ components can be transformed to the dq components [ ] [ ] [ ] id cos ϑm sin(ϑ = m ) iα sin ϑ m cos(ϑ m ) i q Equivalent to the transformation for complex space vectors i β i d + ji q = i s = e jϑm i s s = [cos(ϑ m ) j sin(ϑ m )](i α + ji β ) = cos(ϑ m )i α + sin(ϑ m )i β + j[ sin(ϑ m )i α + cos(ϑ m )i β ] Inverse transformation is obtained similarly
27 / 46 Model in Rotor Coordinates Flux linkages [ ] [ ] [ ] ψd Ld 0 id = + ψ q 0 L q i q [ ] ψf 0 i d ω m ψ q q β Inductances become constant L d = L 0 L 2 L q = L 0 + L 2 e d dψ d dt d ϑ m Induced voltages α e d = dψ d dt e q = dψ q dt ω m ψ q + ω m ψ d ω m ψ d i q dψ q dt e q
28 / 46 Model in Rotor Coordinates Model can be expressed using space vectors Stator flux linkage ψ s = L d i d + jl q i q + ψ f where ψ f is the stator flux linkage due to the PMs (ideally constant) If L d = L q = L s, the model reduces to the SPM model If ψ f = 0, the model reduces to the SyRM model Stator voltage u s = Ri s + dψ s dt + jω m ψ s
Power Balance Electromagnetic torque 3 2 Re {u s i s} = 3 2 R i s 2 + 3 { } dψs 2 Re i ω m s + T M dt p T M = 3p { } 2 Im i s ψ = 3p s 2 [ψ f + (L d L q )i d ] i q Rate of change of the magnetic field energy is zero in steady state { } dψs Re i s = d ( 1 dt dt 2 L did 2 + 1 ) 2 L qiq 2 29 / 46
30 / 46 Outline Synchronous Motors Model Control Principles MTPA and MTPV
31 / 46 Typical Control Goals To produce the required torque quickly and accurately at all speeds with minimum overall losses To maximize the torque for the given stator current limit and the DC-bus voltage Robustness against parameter variations Simple or automatic controller tuning
32 / 46 Torque Torque expression T M = 3p 2 [ψ f + (L d L q )i d ] i q Reluctance torque term is useful if L d L q is large Negative i d can be used to increase the torque (i.e. minimize losses) Same torque can be produced with various current vectors How to choose the current vector?
33 / 46 Vector Control: Simplified Block Diagram ω M,ref Speed controller T M,ref Current reference i s,ref Current controller u s,ref dq abc PWM i s dq abc i a, i b, i c ω M 1/p ω m d dt ϑ m p ϑ M M Fast current-control loop Rotor position ϑ m is measured (or estimated) Current reference i s,ref is calculated in rotor coordinates
34 / 46 Constant Torque Loci in i d i q Plane Torque T M = 3p 2 [ψ f + (L d L q )i d ] i q T M = 2T N i q Magnetic saturation is omitted in the following examples, but in practice it should be taken into account (at least for SyRMs and PM-SyRMs) T M = T N T M = 0.5T N i d Example per-unit parameters L d = 0.58 L q = 0.97 ψ f = 0.68
35 / 46 Maximum Current and Maximum Voltage i q Maximum current i s = id 2 + i2 q i max Maximum flux linkage ψ s = (ψ f + L d i d ) 2 + (L q i q ) 2 u max ω m ψ s = 1 p.u. ψ s = 0.3 p.u. i s = 1.5 p.u. i s = 1 p.u. i d
36 / 46 Control Principles Speeds below the base speed Maximum torque per ampere (MTPA) Equals minimum-loss operation (omitting the core losses) Higher speeds MTPA not possible due to the limited voltage Maximum stator flux linkage depends on umax and ω m ψ s = (ψ f + L d i d ) 2 + (L q i q ) 2 u max / ω m To reach higher speeds, ψs has to be reduced by negative i d Maximum torque per volt (MTPV) limit has to be taken into account
37 / 46 Outline Synchronous Motors Model Control Principles MTPA and MTPV
38 / 46 Maximum Torque per Ampere (MTPA) Current magnitude i s = Torque is represented as i 2 d + i2 q T M = 3p 2 [ψ f + (L d L q )i d ] is 2 id 2 Maximum torque at T M / i d = 0 T M = T N MTPA i q T M = 0.5T N i s = 1 p.u. Special cases ψ f id 2 + i d iq 2 = 0 L d L q i d = 0 for nonsalient PMSMs (L d = L q ) i d = i q for SyRMs (ψ f = 0) i d
39 / 46 Maximum Torque per Volt (MTPV) Flux magnitude ψ s = (ψ f + L d i d ) 2 + (L q i q ) 2 MTPV condition can be derived similarly as the MTPA condition Special cases (ψ f + L d i d ) 2 + L q L d L q ψ f (ψ f + L d i d ) (L q i q ) 2 = 0 id = ψ f /L s for nonsalient PMSMs (L d = L q = L s ) ψd = ψ q for SyRMs (ψ f = 0)
40 / 46 MTPV Current Locus MTPA i q MTPV i s = 1 p.u. ψ s = 0.3 p.u. i d ψ s = 1 p.u.
41 / 46 Feasible Operating Area, i max = 1.5 p.u. MTPA i q MTPV i s = 1.5 p.u. i d
42 / 46 Example: Current Locus as the Torque Varies at the Base Speed MTPA i q MTPV i s = 1 p.u. i d ψ s = 1 p.u. Limitation due to maximum current is not shown
43 / 46 Example: Acceleration Loci for i max = 1 p.u. and i max = 1.5 p.u. i q (p.u.) T M /T N ω m =0.77 p.u. ω m =1 p.u. 1.5 1 1.5 1 0.5 0.5 ω m =1.92 p.u. 0 1.5 1 0.5 0 i d (p.u.) 0 1 2 ω m (p.u.)
44 / 46 T M /T N 1.5 P M /P N u s (p.u.) 1.5 P M (overload) P M (i s = 1 p.u.) 1 1 u s 0.5 0.5 0 0 1 2 ω m (p.u.) 0 0 1 2 ω m (p.u.)
Current References for MTPA, MTPV, and Field Weakening Field weakening U dc 1 3 u max ψ s,max 2D look-up tables ω m ω m min ψ s,mtpa ψ s,ref i d = i d (ψ s, T M ) i d,ref T M,MTPV i q = i q (ψ s, T M ) T M,ref T M,ref min i q,ref 1D look-up tables sign(t M,ref ) This implementation example is based on the paper by M. Meyer and J. Böcker, Optimum control for interior permanent magnet synchronous motors (IPMSM) in constant torque and flux weakening range, in Proc. EPE-PEMC, 2006. Look-up tables are calculated off-line based on the motor saturation characteristics. Other control variables and control structures are also possible. 45 / 46
46 / 46 Further Reading S. Morimoto et al., Expansion of operating limits for permanent magnet motor by current vector control considering inverter capacity, IEEE Trans. Ind. Applicat., vol. 26, 1990. W.L. Soong and T.J.E. Miller, Field-weakening performance of brushless synchronous AC motor drives, IEE Proc. EPA, vol. 141, 1994. M. Meyer and J. Böcker, Optimum control for interior permanent magnet synchronous motors (IPMSM) in constant torque and flux weakening range, in Proc. EPE-PEMC, 2006. G. Pellegrino et al., Direct-flux vector control of IPM motor drives in the maximum torque per voltage speed range, IEEE Trans. Ind. Electron., vol. 59, 2012.