Lecture 10: Synchronous Motor Drives
ELEC-E8402 Control of Electric Drives and Power Converters
Marko Hinkkanen
Spring 2018
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Learning Outcomes
After this lecture and exercises you will be able to:
I Identify, based on the cross-section of the rotor, if the motor is magnetically
anisotropic
I Explain what is the reluctance torque
I Calculate operating points of synchronous motors and draw the
corresponding vector diagrams
I Derive and explain the MTPA control principle
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Common AC Motor Types
I Synchronous motors
I Surface-mounted permanent-magnet synchronous motor (SPM)
I Interior permanent-magnet synchronous motor (IPM)
I Synchronous reluctance motor (SyRM)
I Permanent-magnet-assisted SyRM (PM-SyRM)
I Excited-rotor synchronous motor
I Asynchronous motors
I Induction motor with squirrel-cage rotor
I Wound-rotor induction motor
I 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.
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Outline
Synchronous Motors
Model
Control Principles
MTPA and MTPV
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Surface-Mounted Permanent-Magnet Synchronous Motor (SPM)
I 3-phase stator winding
I Distributed sinusoidally along the air gap
I Produces rotating magnetic field
I Permanent magnets (NdFeB or SmCo)
mounted at the rotor surface
I Benefits
I Very high efficiency (or power density)
I No magnetising supply needed
I Drawbacks
I Price of the magnets and manufacturing
I Limited field-weakening range
In SPMs, a concentrated stator winding is also possible instead of a distributed winding.
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Operating Principle
β
I Current distribution produced by the 3-phase q
winding is illustrated in the figure
I Torque is constant only if the supply d
frequency equals the electrical rotor speed F
ωm = dϑm /dt ϑm
I For controlling the torque, the current α
distribution has to be properly placed in
relation to the rotor F
I Rotor position has to be measured
or estimated
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Number of Pole Pairs p
ϑM = ϑm
ϑM = ϑm /2
2 poles (p = 1) 4 poles (p = 2)
Electrical angular speed ωm = p ωM and electrical angle ϑm = p ϑM
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Interior Permanent-Magnet Synchronous Motor (IPM)
q q
d d
SPM (Ls = Ld = Lq ) IPM (Ld < Lq )
Permeability of the magnets is almost the same as for air (µr ≈ 1.05)
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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/
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Synchronous Reluctance Motor (SyRM)
is is
Two poles (p = 1) Four poles (p = 2)
Note: no-load condition is illustrated in the figures for simplicity
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Structure and Operating Principle
I Distributed 3-phase stator winding
I Rotating magnetic field produced by the
stator currents
I Torque-production principle:
Rotor tries to find its way to the position that
minimizes the magnetic field energy
I More efficient than induction motors
I Cheaper than permanent-magnet motors
I Pump and fan applications
Figure: ABB
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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
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Example of Magnetic Saturation: 6.7-kW SyRM
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Permanent-Magnet SyRM (PM-SyRM)
I SyRM designs can be improved by
placing permanent magnets inside is
the flux barriers of the rotor
I Resulting motor is basically an IPM
having high reluctance torque
I These kind of motors are often
called permanent-magnet SyRMs
(PM-SyRMs) or hybrid synchronous
motors (HSMs)
I What is the reluctance torque in the
figure?
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I Compared to the SyRM, the permanent
magnets improve the power factor and
contribute to the torque
I Low-cost ferrite magnets can be used
I Good field-weakening properties
I Minor risk of overvoltages due to the low
back-emf induced by the permanent
magnets
Figure: http://www.abb.com/cawp/seitp202/ad26393b09a61275c1257caf00217a16.aspx
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Example PM-SyRM: Brusa HSM1-10.18.22
I For truck and bus applications
I Low magnetic material
I Speed: 4 400 rpm (nom), 12 000 rpm (max)
I Torque: 270 Nm (S1), 460 Nm (max)
I Power: 145 kW (S1), 220 kW (max)
I DC-bus voltage: 400 V (also 750 V available)
I Weight: 76 kg
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Example PM-SyRM: Brusa HSM1-10.18.22
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Example PM-SyRM: BMW i3
I Speed: 4 500 rpm (nom), 11 400
rpm (max)
I Torque: 250 Nm (max)
I Poles: 12
I Voltage: 250. . . 400 V
I Weight: 65 kg
Figure: J. Merwerth (2014) (http://hybridfordonscentrum.se/wp-content/uploads/2014/05/20140404 BMW.pdf)
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Design Parameter Plane: Optimal Field-Weakening Performance
Optimal design line
Saliency ratio Lq /Ld
ψf = Ld iN
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.
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Outline
Synchronous Motors
Model
Control Principles
MTPA and MTPV
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Review: Single-Phase Machine
ψaf ia
ψf
ϑm
ϑm
La dψa
dt
0 π/2 π 3π/2 2π ϑm
ψa = La ia + ψaf
h i
La = L0 − L2 cos(2ϑm ) TM = p L2 sin(2ϑm )ia2 − ψf sin(ϑm )ia
ψaf = ψf cos(ϑm )
Notice that the constant ψf is the maximum value of the stator flux linkage due to the rotor PMs. In Lecture 9, the flux linkage of the rotor field
winding was denoted by this same symbol.
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3-Phase Distributed Winding
b b
a ia a ia
b ib b ib
a a
c ic c ic
c c
Example of a 3-phase distributed winding Simplified representation
(Y or D connection)
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αβ Transformation
I Instantaneous 3-phase quantities can be transformed to the αβ components
ia
iα 2 1 √ −1/2 −1/2 √ ib
=
iβ 3 0 3/2 − 3/2
ic
where the currents are used as an example
I Equivalently, the space vector transformation could be used
2
i s = iα + jiβ = ia + ib ej2π/3 + ic ej4π/3
3
which gives the same components iα and iβ
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3-Phase Synchronous Machine
β
I Flux linkages
q d
iα
ψα Lαα Lαβ iα ψ
= + αf
ψβ Lβα Lββ iβ ψβf ϑm
Lαα = L0 − L2 cos(2ϑm ) dψα
dt α
Lββ = L0 + L2 cos(2ϑm )
Lαβ = Lβα = −L2 sin(2ϑm )
ψαf = ψf cos(ϑm ) ψβf = ψf sin(ϑm )
I Induced voltages iβ
dψα dψβ dψβ
eα = eβ = dt
dt dt
Torque could be derived using the approach described in Lecture 9, but transforming the machine model to rotor coordinates allows us to use a
shortcut, as shown in the following slides.
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Transformation to Rotor Coordinates
I αβ components can be transformed to the dq components
id cos(ϑm ) sin(ϑm ) iα
=
iq − sin(ϑm ) cos(ϑm ) iβ
I Equivalent to the transformation for complex space vectors
id + jiq = i s = e−jϑm i ss
= [cos(ϑm ) − j sin(ϑm )](iα + jiβ )
= cos(ϑm )iα + sin(ϑm )iβ + j[− sin(ϑm )iα + cos(ϑm )iβ ]
I Inverse transformation is obtained similarly
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Model in Rotor Coordinates
q
I Flux linkages β
ωm ψq
id
ψd L d 0 id ψ
= + f
ψq 0 Lq iq 0
I Inductances become constant dψd
ed
dt d
Ld = L0 − L2
ϑm
Lq = L0 + L2
α
I Induced voltages
dψq
dψd ωm ψd
ed = − ωm ψq dt
dt
dψq iq
eq = + ωm ψd eq
dt
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Model in Rotor Coordinates
I Model can be expressed using space vectors
I Stator flux linkage
ψ s = Ld id + jLq iq + ψf
where ψf is the stator flux linkage due to the PMs (ideally constant)
I If Ld = Lq = Ls , the model reduces to the SPM model
I If ψf = 0, the model reduces to the SyRM model
I Stator voltage
dψ s
u s = Ri s + + jωm ψ s
dt
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Power Balance
dψ s
3 3 3 ωm
Re {u s i ∗s } = R|i s |2 + Re i ∗s + TM
2 2 2 dt p
I Electromagnetic torque
3p n o 3p
TM = Im i s ψ ∗s = [ψf + (Ld − Lq )id ] iq
2 2
I Rate of change of the magnetic field energy
dψ s ∗
d 1 2 1 2
Re i = Ld i + Lq i
dt s dt 2 d 2 q
is zero in steady state
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Outline
Synchronous Motors
Model
Control Principles
MTPA and MTPV
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Typical Control Goals
I To produce the required torque quickly and accurately at all speeds with
minimum overall losses
I To maximize the torque for the given stator current limit and the DC-bus
voltage
I Robustness against parameter variations
I Simple or automatic controller tuning
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Torque
I Torque expression
3p
TM = [ψf + (Ld − Lq )id ] iq
2
I Reluctance torque term is useful if Ld − Lq is large
I Negative id can be used to increase the torque (i.e. minimize losses)
I Same torque can be produced with various current vectors
I How to choose the current vector?
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Vector Control: Simplified Block Diagram
ωM,ref
Speed TM,ref Current i s,ref
controller reference Current u s,ref dq
controller PWM
abc
is dq ia , ib , ic
abc
ωM ωm d ϑm ϑM
1/p p M
dt
I Fast current-control loop
I Rotor position ϑm is measured (or estimated)
I Current reference i s,ref is calculated in rotor coordinates
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Constant Torque Loci in id –iq Plane
I Torque iq
TM = 2TN
3p
TM = [ψf + (Ld − Lq )id ] iq
2 TM = TN
I Magnetic saturation is omitted in the TM = 0.5TN
following examples, but in practice it
should be taken into account (at id
least for SyRMs and PM-SyRMs)
I Example per-unit parameters
Ld = 0.58 Lq = 0.97 ψf = 0.68
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Maximum Current and Maximum Voltage
iq
I Maximum current ψs = 1 p.u. is = 1.5 p.u.
q
is = id2 + iq2 ≤ imax is = 1 p.u.
ψs = 0.3 p.u.
I Maximum flux linkage
id
umax
q
ψs = (ψf + Ld id )2 + (Lq iq )2 ≤
|ωm |
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Control Principles
I Speeds below the base speed
I Maximum torque per ampere (MTPA)
I Equals minimum-loss operation (omitting the core losses)
I Higher speeds
I MTPA not possible due to the limited voltage
I Maximum stator flux linkage depends on umax and ωm
q
ψs = (ψf + Ld id )2 + (Lq iq )2 ≤ umax /|ωm |
I To reach higher speeds, ψs has to be reduced by negative id
I Maximum torque per volt (MTPV) limit has to be taken into account
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Outline
Synchronous Motors
Model
Control Principles
MTPA and MTPV
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Maximum Torque per Ampere (MTPA)
q
I Current magnitude is = id2 + iq2
I Torque is represented as MTPA iq
3p
q TM = 0.5TN
TM = [ψf + (Ld − Lq )id ] is2 − id2
2 TM = TN
I Maximum torque at ∂TM /∂id = 0 is = 1 p.u.
ψf id
id2 + id − iq2 = 0
Ld − Lq
I Special cases
I id = 0 for nonsalient PMSMs (Ld = Lq )
I |id | = |iq | for SyRMs (ψf = 0)
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Maximum Torque per Volt (MTPV)
I Flux magnitude q
ψs = (ψf + Ld id )2 + (Lq iq )2
I MTPV condition can be derived similarly as the MTPA condition
Lq
(ψf + Ld id )2 + ψ (ψ + Ld id ) − (Lq iq )2 = 0
Ld − Lq f f
I Special cases
I id = −ψf /Ls for nonsalient PMSMs (Ld = Lq = Ls )
I |ψd | = |ψq | for SyRMs (ψf = 0)
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MTPV Current Locus
MTPA iq
MTPV
is = 1 p.u.
ψs = 0.3 p.u. id
ψs = 1 p.u.
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Feasible Operating Area, imax = 1.5 p.u.
MTPA iq
MTPV
is = 1.5 p.u.
id
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Example: Current Locus as the Torque Varies at the Base Speed
MTPA iq
MTPV
is = 1 p.u.
id
ψs = 1 p.u.
I Limitation due to maximum current is not shown
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Example: Acceleration Loci for imax = 1 p.u. and imax = 1.5 p.u.
iq (p.u.) TM /TN
ωm = 0.77 p.u. 1.5
1.5
ωm = 1 p.u.
1
1
0.5 0.5
ωm = 1.92 p.u.
0
−1.5 −1 −0.5 0 id (p.u.) 0 1 2 ωm (p.u.)
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TM /TN PM /PN
us (p.u.)
PM (overload)
1.5 1.5 PM (is = 1 p.u.)
us
1 1
0.5 0.5
0 0
0 1 2 ωm (p.u.) 0 1 2 ωm (p.u.)
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Current References for MTPA, MTPV, and Field Weakening
Field weakening
Udc 1 umax ψs,max
√ 2D look-up tables
3 ψs,ref id,ref
min
ωm |ωm |
ψs,MTPA id = id (ψs , TM )
iq = iq (ψs , TM )
TM,MTPV
TM,ref |TM,ref | iq,ref
min
1D look-up tables
sign(TM,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.
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Further Reading
I 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.
I W.L. Soong and T.J.E. Miller, “Field-weakening performance of brushless
synchronous AC motor drives,” IEE Proc. EPA, vol. 141, 1994.
I 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.
I 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.
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