Sensorless Control at High Starting Torque of a 4000 Nm
Traction Drive With Permanent Magnet Synchronous
Machine
F. Demmelmayr, M. Susic, M. Schroedl
VIENNA UNIVERSITY OF TECHNOLOGY
INSTITUTE OF ENERGY SYSTEMS AND ELECTRICAL DRIVES
Gusshausstrasse 25-29 / E370-2
Vienna, Austria
E-Mail: florian.demmelmayr@tuwien.ac.at
URL: http://www.ieam.tuwien.ac.at
Keywords
<<sensorless control>>, <<permanent magnet synchronous machine>>, <<electric drive>>
Abstract
This paper presents numerical torque simulations and sensorless control of a permanent magnet synchronous machine (PMSM). The machine was developed for a wheel-hub traction drive with a maximum
torque of 4000 Nm. The Indirect Flux detection by Online Reactance Measurement (INFORM) method
provides control at standstill and low speed without a rotor position sensor. A back electromotive force
(EMF) model handles the operation at higher speed. The structure of the control and the load behaviour
of INFORM are shown. The torque characteristic is calculated by numerical simulation and compared
with recorded values. An additional curve depicts the influence of the INFORM test signals on machine
torque.
Introduction
Direct traction drives with wheel-hub machines require high starting torque and wide speed range. High
dynamic space vector control of permanent magnet synchronous machines (PMSMs) fulfils these demands. Vector control requires the knowledge of the actual rotor angular position. The rotor angle can be
received by special sensors such as encoders or resolvers. But these sensors have some drawbacks: They
increase the total cost of electric machines and decrease the reliability. Sensorless techniques overcome
these weaknesses. The properties of sensorless control mostly depend on the machine speed. At high
speed, back electromotive force (EMF) methods are state-of-the-art [1], [2]. But they fail at standstill
or very low speed [3]. At this operating range, most methods base on tracking the position of magnetic
saliencies [4]. The presented Indirect Flux detection by Online Reactance Measurement (INFORM)
model estimates the rotor angular position by special test signals [5]. The control of the regarded PMSM
drive deals with two sensorless techniques. Below a rated engine speed of 10 % INFORM calculates the
rotor position. Above that speed, the back-EMF model is used.
Figure 1: Stator (left) and rotor (right) of the PMSM
The presented PMSM prototype was developed, constructed (fig. 1) and tested with the support of
our industrial partner Voith Turbo GmbH (St. Pölten, Austria). A numerical simulation calculates the
required starting torque. The result is compared with recorded values of two different control methods.
These methods present the torque behaviour with position estimation from encoder and from sensorless
control. The second method examines the influence of the test signals on torque characteristic.
Sensorless control of the PMSM
The machine speed usually influences the quality of sensorless control methods. At high speed, beyond
about 10 % of rated speed, back-EMF methods handle the position detection. They are based on the
induced voltage and appropriate models of the machine. The induced voltage decreases with reducing
rotor speed and vanishes at machine standstill. Therefore the back-EMF model becomes worse with
decreasing rotor speed. In this operation range the INFORM method supplies applicable position information.
The INFORM method
The implemented encoderless INFORM method for standstill and low speed utilizes varying magnetic
properties depending on the angular rotor position. These properties arise from saturation and/or reluctance effects [5].
INFORM uses test signals for position calculation. These voltage space phasor test pulses (us ) interrupt the inverter-fed current control of the machine at certain time slices. In the meantime, the resulting
current-change space phasors (∆is /∆τ) are measured. Both, the test signals and their results define incremental inductances“ (l inc ). These position-varying inductances are used for rotor angular determination.
”
l inc :=
us
∆is /∆τ
(1)
Following considerations are based on the inverse of these inductances
yINF :=
1
.
l inc
(2)
Reluctance and saturation effects have an electrical angular symmetry of 180◦ . Therefore also the complex quantity yINF displays this characteristic. It describes a circle in the Gaussian plane if the fundamental harmonic of the signal is considered only.
yINF := y0 + ∆y · e j(2 γINF −2 γU )
(3)
The function can be expressed by an offset y0 and the radius of the circle ∆y. The position on the circle
is a function of the angle of the test pulse stator voltage space phasor γU and the searched rotor position
γINF . Usually a three phase traction inverter offers voltage space phasors in six different directions
π
γU = k ,
3
k = 0, 1, 2...
(4)
The presented INFORM method uses test signals in all of these directions. Figure 2 sketches the voltage
und current behaviour of phase U during a U+, V+ and W+ test sequence. Current changes of the test
signals are measured in all three phases.
Each of the three complex current changes ∆i|u, ∆i|v and ∆i|w from figure 3 yield two different results,
one from its real and one from its imaginary part. Therefore six equations for the three unknown values
y0 , ∆y and 2 γINF are available. The components from equation (3) can be calculated by real or imaginary
part consideration.
Implementation of the sensorless control
The implemented sensorless control uses INFORM below a rated speed of about 10 % and the back-EMF
method at higher speed [10].
Uu
U
V
W
6
6
≈ 23 Udc
?
Iu
6∆iu |u
6
∆iu |v
6
?
. . . current measuring points
∆iu |w
6
?
?
-t
6
≈ 1 Udc
? 3
tsequence
-t
-
Figure 2: Voltage test signals Uu and current responses Iu during the INFORM measurement in phase u with three
cyclic voltage signals U, V and W [8]
Figure 3: Rotor position dependent current changes [9]
The Back-EMF model
Figure 4 shows the structure of the sensorless calculation. At the top left, the machine model for the
back-EMF estimation is depicted. The components of the stator voltage space phasor (uS,α , uS,β ) and
the stator current space phasor (iS,α , iS,β ) define the actual operating point. The complex stator voltage
equation of a PMSM in the αβ stator-oriented reference frame
uS,αβ = rS iS,αβ +
d ΨS,αβ
dτ
(5)
represents the model of the machine with the per unit stator resistance (rS ) and the time derivative of the
complex stator flux linkage (ΨS ). Equation 6 calculates the complex flux linkage due to the permanent
magnets (ΨM,αβ ) with the stator inductance lS .
ΨM,αβ = ΨS,αβ − lS iS,αβ
(6)
The argument of ΨM,αβ corresponds with the searched rotor position γEMF . The small feedback component KΨ (figure 4) stabilises the two digital integrators and prevents drift effects due to parameter
uncertainties and measuring errors.
iS,α
q
?
rs
uS,α
?
ls
z−1 ?
- j- ?
e
?
S,α
q Ψq j
ΨM,α
6
KΨ
tan−1
KΨ
?
ΨM,β
ΨM,α
?
- j
γEMF
z−1 - Kω - ?
e
6
uS,β
?
- j- e
6 6
rs
iS,β
q q j
ΨS,β
z−1 q
6
ω̂
?
6
a?
a
a
∆γ
creal
jc
imag
-
tan−1
-ω̂
tct
6
ls
back EMF method
iu - j
iv iw - j
q
q
?
ΨM,β
c
-
imag
creal
q
γ̂
switch
INFORM/ mechanical observer
EMF
2γINF
- j
6
q- Kγ
?
- j
∗
- z−1 q γ
?
- jq -
2
INFORM method
Figure 4: Structure of the sensorless INFORM/EMF estimation
The INFORM method
The INFORM method is pictured at the bottom left of figure 4. The changes of the phase currents (iU , iV
and iW ) during the test signals define a complex function cINF with its real (creal ) and imaginary (cimag )
part
cINF = ∆y · e j 2 γINF = creal + j cimag
(7)
This function is called Characteristic INFORM curve. Its argument (2γINF ) is twice the searched rotor
position.
Switch between back EMF and INFORM method
A speed-dependent switch decides which sensorless method (2γINF or γEMF ) will be used. It has a small
hysteresis to prevent unwanted toggle.
Observer structure
A mechanical observer improves the sensorless position information and determines the actual rotor
speed (ω̂). The input of the observer (∆γ) is the difference between sensorless estimation (γEMF or 2γINF )
and the actual observed rotor position (γ∗ or 2γ∗ ),
EMF method: ∆γ = γEMF − γ∗
(8)
INFORM method: ∆γ = 2γINF − 2γ∗ .
(9)
or
This value affects the outcome of the speed and the angle calculation with the two constants Kω and Kγ .
The constants quantify the values from sensorless estimation and the observer.
The whole structure from figure 4 is implemented by using the microcontroller of the drive inverter. Each
software task of the controller calculates a new position value. The actual rotor speed (ω̂) influences the
angle estimation of the next task. The normalized dead time tct considers the time between two tasks of
the used controller. Equations 10 and 11 describe the oberserver structure in the discrete z-domain.
γ̂ = Kγ · ∆γ + z−1 · (ω̂ · tct + γ̂)
(10)
ω̂ = Kω · ∆γ + z−1 · ω̂
(11)
Control structure of the traction drive
The control structure of the traction drive is depicted in figure 5 [11]. The torque and field weakening
controller determines the reference stator current components (id,ref and iq,ref ). The two components
depend on the reference torque (tref ) from a tramway cab, the actual rotor speed (ω̂) and the components
of the voltage space phasor (uα and uβ ). The current controller works with two separated PI structures in
direct and quadrature direction. Current and voltage space phasors are transformed from stator oriented
to rotor oriented reference frame and vice versa using the estimated rotor angle (γ̂).
torque
and
field
weakening
controller
dq - current controller
∆id
- m
id,ref
- u
-+
Sα
- inverter uSβ
- u vw
α
q u- d, q
uβ
- α, β q PWM
6
γ̂
6
q
- m ∆i-
iq,ref
bUDC b
transformation - dq/αβ
reference frame
6
tref 6
uβ 6
uα 6
ω̂ 6
id,meas
u,v,w 6
d, q
iq,meas
q
q
phase current measurement PMSM
γ̂
ω̂
iv ?
iw ?
iu ?
uSα
uSβ
sensorless position estimation - INFORM/EMF Figure 5: Control structure
Numerical torque calculation
Numerical simulation with the finite element method (FEM) provides appropriate results of the produced
torque of the PMSM. The presented calculation expects vector oriented control, with a quadrature current
component only.
The Maxwell stress (−~n · p) can be expressed by the magnetic flux density (~B) along the cylindrical
air-gap between stator and rotor of the machine [6], [7].
1 ~ ~ 1 ~ ~ −~n · p =
~n · B B −
B · B ~n
(12)
µ0
2
Analizing the Maxwell stress yields to an electromagnetic torque vector (~T ) on a cylindrical surface (∂V )
in the air-gap with the radius r and the normal vector ~n.
I
1 ~ ~ ~T = ~r × 1
~
~
~n · B B −
B · B ~n dΓ
(13)
µ0
2
∂V
The calculation assumes constant flux density along the active iron length (lfe ) and therefore a twodimensional design (Bz = 0). Cylindrical coordinates (r, ϕ) with the normal unit vectors (~er and ~eϕ ) are
used. dΓ denotes the surface element of the integral.
~n = −~er ,
~B = Br~er + Bϕ~eϕ ,
r2 lfe
Tz = −
µ0
Z2π
dΓ = rlfe dϕ
Br (r, ϕ)Bϕ (r, ϕ) dϕ
(14)
(15)
0
The flux density (Br , Bϕ ) in the air-gap is evaluated using the software tool Ansys V12.1. The resulting
torque (eq. 15) over quadrature stator current magnitude is shown in figure 7.
(a) iq = 0
(b) iq = 1
(c) iq = 2
(d) iq = 3
Figure 6: Flux lines of the magnetic field from FEM calculation at different quadrature stator current (iq )
Figure 6 depicts the magnetic flux lines of a 60◦ anti-periodic section of the PMSM at different quadrature
stator currents (iq ). The section of the PMSM represents the whole machine due to its specific symmetry.
The coloured lines represent isolines of the magnetic vector potential. Two adjacent flux lines represent
a magnetic flux of 0.84 mWb. The torque is derived from results of the magnetic flux density from the
FEM.
Measurements and Results
Torque characteristic
Figure 7 illustrates the torque over the normalized stator current. The top curve describes the result of the
numerical simulation. Below, two measured graphs are displayed. The encoder control graph shows the
produced torque of the drive, using a position sensor. It is compared to the encoderless INFORM control
which includes short interruptions of the pulse width modulation (PWM) for the active test pulses. The
sensorless method has only little influence. The numerical simulation provides a good agreement with
the recorded values.
The figure also depicts the Characteristic INFORM curves (eq. (7)) at no-load, iq = 1, iq = 2 and iq =
3. The size of the loci and therefore the signal to noise ratio of the rotor position calculation increase
with rising stator current up to twice current magnitude. The curves are similar to triangles instead of
estimated circles because of higher harmonics [9].
Machine efficiency curve
The machine efficiency curve (Fig. 8) shows the produced torque over machine speed. Each point is
recorded at steady state. The colour fields represent various efficiency values of the fundamental wave.
The figure includes the reluctance torque, produced by a negative direct current component besides the
main current component in quadrature axis. Also the lines of constant power are plotted from 5 kW to
140 kW mechanical output power. The machine provides high efficiency over a wide operation range
and wide field weakening range.
INFORM is used below a rated machine speed of 10 %. In this operation range the machine efficiency is
not significant. Therefore this paper does not regard the influence of the INFORM test sequence on the
efficiency.
Figure 7: Torque over stator current magnitude with Characteristic INFORM curves at selected operation points
at ω = 5%
Figure 8: Machine efficiency curve of the PMSM
Conclusion
The presented PMSM drive reaches high starting torque up to 4000 Nm. Measurements and numerical
simulations of produced torque show a good agreement. The sensorless control operates from standstill
to maximum speed. It works with a combined INFORM/back-EMF model. The quality of the INFORM
calculation increases with rising load and works well up to high starting torque.
References
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R
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