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Machine design and control strategy for wide-speed-range PMSG systems
Article in COMPEL International Journal of Computations and Mathematics in Electrical · January 2015
DOI: 10.1108/COMPEL-03-2014-0054
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Zhejiang University
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COMPEL: The International Journal for Computation and
Mathematics in Electrical and Electronic Engineering
Machine design and control strategy for wide-speed-range PMSG systems
Jianxin Shen Dong-Min Miao
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Article information:
To cite this document:
Jianxin Shen Dong-Min Miao , (2015),"Machine design and control strategy for wide-speed-range
PMSG systems", COMPEL: The International Journal for Computation and Mathematics in Electrical
and Electronic Engineering, Vol. 34 Iss 1 pp. 92 - 109
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COMPEL
34,1
Machine design and control
strategy for wide-speed-range
PMSG systems
92
Jian-Xin Shen and Dong-Min Miao
Department of Electrical Engineering, Zhejiang University, Hangzhou, China
Abstract
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Purpose – The purpose of this paper is to focus on the machine design and control strategy of the
permanent magnet synchronous generator (PMSG) system, especially utilized in variable speed
applications, in order to stabilize the output voltage on the dc link over a wide speed range.
Design/methodology/approach – Different ac/dc power converter topologies are comparatively
studied, each with an accordingly designed PMSG, so as to investigate the influence of the armature
winding inductance as well as the relationship between the PMSG and power converter topologies.
Findings – Pulse width modulation (PWM) rectifier is preferable for the said application due to its
good performance and controllability. Moreover, by employing the PWM rectifier, relatively large
inductance of the PMSG is considered for both short-circuit current reduction and field regulation.
Originality/value – Field-regulating control is realized with a space vector PWM (SVPWM) rectifier,
which can weaken the PMSG magnetic field during high-speed operation, while even properly enhance
the field at low speed, ensuring a small change of the PMSG output voltage and a stable dc voltage.
Keywords Field-regulating, Permanent magnet synchronous generator, Power converter topology,
PWM rectifier, Space vector pulse width modulation, Wide speed range
Paper type Research paper
COMPEL: The International
Journal for Computation and
Mathematics in Electrical and
Electronic Engineering
Vol. 34 No. 1, 2015
pp. 92-109
r Emerald Group Publishing Limited
0332-1649
DOI 10.1108/COMPEL-03-2014-0054
1. Introduction
Permanent magnet synchronous generator (PMSG) systems are gaining extensive
applications. A PMSG is often connected to an ac/dc power converter, and the obtained
dc power is then directly utilized by a dc load, or further converted to ac power
with a dc/ac converter (note, hereafter the dc/ac converter is also regarded as a special
dc load).
The PMSG is often driven by a variable-speed power plant, for example, when it is
applied for wind energy (Chan and Lai, 2007), aircraft generator (Ning et al., 2012),
vehicle alternator (Xia et al., 2011), and so on. In all these cases, the output voltage of
the dc power (after the ac/dc converter) and/or the ac power (after the dc/ac converter)
should be stable.
However, in a PMSG, the permanent magnets excite a constant airgap field, thus
the induced electromotive force (EMF) is proportional to the rotor speed. It is desirable
to regulate the field with some techniques in order to stabilize the output of
the variable-speed PMSG. In recent years, a variety of mechanical methods for
field-regulating have been proposed (Capponi et al., 2009; Javadi and Mirsalim, 2008;
Shen and Miao, 2013). Also, electromagnetic methods have been studied, using hybrid
(electric and permanent magnet) excitation (Chau et al., 2006), or, injecting an extra
field-regulating current into the PMSG armature windings with an individual inverter
(Wu et al., 2006).
This work was supported by the Natural Science Foundation of China (51377140, 51077116) and
the National Basic Research Program of China (2013CB035604, 2011CB707204).
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On the other hand, in the permanent magnet synchronous motor (PMSM)
applications, field-weakening control, a type of field-regulation, has been widely used
in order to extend the motor speed range under the restriction of a constant dc power
supply. However, until now, few papers have concerned the field-regulating control in
the PMSG systems. Although back-to-back power converter topology is proposed
in the large-scale wind power PMSG, and field-weakening at the extended speed is
mentioned, no detailed approaches have been addressed.
This paper focusses on the variable-speed PMSG system, concerning the ac/dc
power converter topologies as well as the machine designs. Both simulation and
experimental verifications are presented.
Machine
design and
control
strategy
93
2. Ac/dc power converter topologies and machine designs
There are three categories of ac/dc power converter topologies for the variable-speed
PMSG, viz., the diode rectifier with a dc/dc converter, the thyrister rectifier, and the
pulse width modulation (PWM) rectifier. According to the characteristics of each ac/dc
converter, specific machine should be designed so that it can properly cooperate with
the ac/dc converter.
To illustrate the system design considerations, an aircraft PMSG system is taken as
an example. Its dc output voltage is 270 V over a wide rotor speed range of
800B8,000 rpm. The rated dc power is 1.5 kW, thus, the PMSG rated power is designed
as 1.65 kW by roughly considering the energy loss of the ac/dc converter. The outer
diameter of the PMSG armature core is restricted to 200 mm, and the stack length is
fixed at 100 mm.
A. Using diode rectifier and dc/dc converter
Figure 1 shows the PMSG system in which the dc/dc converter is used to boost or
reduce the rectified dc voltage to the demanded voltage on the dc load.
There are several types of dc/dc converters, such as the commonly used boost
converter, the buck converter, and the boost/buck converter, which are shown
in Figure 2.
(1) Using boost converter. The output voltage Uo of the boost converter is
always greater than the input voltage Ui, and, Ui is actually the output voltage
of the diode rectifier. The duty cycle a of the switching device (such as
MOSFET or IGBT) is given in (1), where ton is the turn-on time interval and T is
the switching cycle:
a¼
PMSG
ton
T
ð1Þ
dc/dc
converter
dc
load
Figure 1.
PMSG system with
diode rectifier and
dc/dc converter
COMPEL
34,1
(a)
Ui
switch
dc
load
Uo
dc
load
Uo
94
–
(b)
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switch
Ui
–
(c)
switch
dc
Uo
load
Ui
Figure 2.
Schematics
of common
dc/dc converters
–
Notes: (a) Boost converter; (b) Buck converter;
(c) Boost/buck converter
The relationship between the input and output voltages is:
Uo
T
1
¼
¼
Ui T ton 1 a
ð2Þ
In the studied system, the demanded Uo is 270 V, thus, the PMSG should be specifically
designed to ensure that Ui at 8,000 rpm under no-load condition is slightly lower than
270 V, and a is approaching 0. Consequently, Ui at 800 rpm under load condition
will be much lower than 270 V, and a must be rather approaching 100 percent. To
satisfy these, a PMSG is accordingly designed, denoted as PMSG-1. It employs shaped
permanent magnets on the rotor surface, as Figure 3 shows. Its armature inductances
and resistance are small, being L ¼ 0.138 mH, M ¼ 0.035 mH, and R ¼ 0.0055 ohm,
respectively.
(2) Using buck converter. In this case, Uo is always less than Ui, and their relation is
expressed in (3), assuming that the current in the inductor is continuous:
Uo ton
¼a
¼
Ui
T
ð3Þ
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95
Figure 3.
Cross-section
of PMSG
The PMSG should then be designed to ensure that Ui at 800 rpm under load condition
is slightly greater than 270 V with a approaching 100 percent. Thus, Ui at 8,000 rpm
under no-load condition will be much greater than 270 V, and a must be close to 0.
A machine (PMSG-2) is also accordingly designed, having the same stator core and the
same rotor as the PMSG-1, but much more turns and thinner wire gauge of the
armature windings (note, the PMSG-2 has the same slot-filling factor as the PMSG-1,
and also as the PMSG-3 and -4 which will be described hereafter). Its armature
inductances are L ¼ 28.3 mH and M ¼ 7.5 mH, and the resistance is R ¼ 1.0 ohm, all
are much greater than those of the PMSG-1.
(3) Using boost/buck converter. Figure 2(c) shows the basic schematic of a boost/
buck converter, in which the output is of the opposite polarity of the input. Here, Uo can
be either greater or less than Ui, and their relation is given in (4):
Uo
ton
a
ð4Þ
¼
¼
1a
Ui
toff
While using the same stator core and rotor as the PMSG-1, the PMSG-3 is specifically
designed to ensure that, around the moderate speed (2,500 rpm) and load, Ui is 270 V
with a being 0.5. Thus, at lower speed down to 800 rpm and under heavier load, the
dc/dc converter works as a booster with a40.5, while at higher speed up to 8,000 rpm
and under lighter load, the dc/dc converter works as a bucker with ao0.5. Compared
with the above-mentioned two systems, the duty cycle of the boost/buck converter will
not approach the extreme values of 100 percent or 0. Clearly, the design of PMSG-3 is
between those of PMSG-1 and PMSG-2, having L ¼ 1.96 mH, M ¼ 0.55 mH, and
R ¼ 0.071 O, respectively.
(4) Comparative study. The design parameters of the three PMSGs are listed
in Table I.
The amplitude value of the line-line no-load voltage (i.e. the open-circuit induced
EMF) of the PMSG at the maximum speed (8,000 rpm) is the maximum voltage
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96
Table I.
Design parameters
of studied PMSGs
Stator core outer diameter (mm)
Stator core inner diameter (mm)
Stator stack length (mm)
Rotor outer diameter (mm)
Magnet thickness (mm)
Magnet volume (cm3)
Rotor inner diameter (mm)
Number of stator slots
Number of coils per phase
Coils parallel branch
Coil pitch/slot pitch
Number of turns in series per phase
Copper wire gauge (mm)
PMSG-1
PMSG-2
PMSG-3
PMSG-4
200
124
100
120.2
6
159.1
35
24
4
1
5
18
f0.71 61
200
124
100
120.2
6
159.1
35
24
4
1
5
252
f0.63 6
200
124
100
120.2
6
159.1
35
24
4
1
5
68
f0.71 18
200
84
100
80
5
85.2
35
24
4
1
5
160
f0.71 13
imposed on the power devices; hence, it determines the device voltage rating. The
maximum voltages for the three PMSGs are listed in Table II. Clearly, the device
voltage rating for the PMSG-1 system can be 600 V only, and that for the PMSG-3
system should be at least 1,700 V. However, the maximum voltage (3,480 V) with the
PMSG-2 system is much greater than the demanded dc voltage (270 V), and, it is very
difficult to choose appropriate power devices with sufficient voltage rating. In practice,
five or even more devices with a voltage rating of 1,200 V should be connected in series
to perform as a single device. Further, the duty cycle a of the dc/dc converters at
the maximum speed with no load is also listed in Table II. It is seen that a for the
PMSG-1 and -2 systems is quite close to 0, hence, the dc/dc converters operation is
not sufficiently stable, and the current and output voltage usually contain remarkable
ripples. However, this is not the case for the PMSG-3 system with a boost/buck
power converter.
On the other hand, the line-line voltage at the minimum speed (800 rpm) with the
rated load for each PMSG is less than one-tenth of the above-mentioned maximum
voltage. Moreover, the phase angle of the armature current is uncontrollable by the
diode rectifier, hence, the PMSG power factor is usually low due to the winding
impedance. From this point of view, low self- and mutual-inductances of the armature
windings are desired.
When the PMSGs work at the minimum speed with the rated power, the machine
voltage and current as well as the dc voltage after the diode rectifier are all given
in Table III. The current rating of the power devices should be chosen according to
these currents, which can be 150, 10 and 40 A for the PMSG-1, -2 and -3 systems,
respectively. It is now seen that the power devices of the PMSG-3 system have both
Table II.
Specifications at
8,000 rpm with
no load
Machine
Maximum
voltage (V)
Power device voltage
rating (V)
Dc voltage after diode
rectifier (V)
Duty cycle of dc/dc
converter (%)
PMSG-1
PMSG-2
PMSG-3
PMSG-4
245
3,480
920
270
600
1,200*5
1,700
600
245
3,480
920
–
9.3
7.8
22.7
–
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moderate ratings of voltage and current, while those of the PMSG-1 system need
a very large current rating (generally speaking, meaning higher cost and lower
reliability), and those with the PMSG-2 system need an extraordinarily high voltage
rating. Furthermore, as can be seen from Table III, the duty cycle a of the dc/dc
converters for the PMSG-1 and -2 is very close to 100 percent, which may deteriorate
the performance and reliability. But a for the PMSG-3 system is, as preferred,
of a moderate value.
From the above analysis, it can be concluded that, by considering the device rating
of voltage (see Table II) or current (see Table III) as well as the duty cycle at the extreme
speeds (see Tables II and III), the PMSG system using the diode rectifier and the buck
or boost dc/dc converter is not really suitable for the wide-speed-range operation.
However, the boost/buck converter, which seems the best to cooperate with the diode
rectifier, is practically much more complicated than the schematic in Figure 2(c), hence,
is usually expensive and of bulky volume. Moreover, the voltage rating of the boost/
buck converter devices is still much higher than the demanded dc voltage, boosting the
cost and potentially reducing the reliability.
On the other hand, the short-circuit current is another important issue to consider.
Table IV gives the armature currents of the three PMSGs when they are short-circuited
at the minimum and maximum speeds, each being much greater than the rated
current. The short-circuit current is in direct proportion to the induced EMF, but is
restricted by the armature winding impedance, of which the reactance should be the
dominant part, since a low resistance is usually preferred so as to reduce the ohmic
loss. From Table IV, it can be seen that the short-circuit current is hardly influenced by
the machine speed because both the induced EMF and the winding reactance are in
direct proportion to the speed, while the winding resistance is much smaller than
the reactance.
Therefore, on one hand, a high inductance is essential to achieve a low short-circuit
current. And, on the other hand, as analyzed above, a low inductance is preferred to
reduce the voltage variation when the PMSG is loaded, so that the PMSG maximum
current at the minimum speed under the rated load is as low as possible. In conclusion,
it is critical to compromise these two aspects when designing the PMSG system.
Machine
Armature current
(RMS value) (A)
Power device
current rating (A)
Dc voltage after diode
rectifier (V)
Duty cycle of dc/dc
converter (%)
PMSG-1
PMSG-2
PMSG-3
PMSG-4
63.1
4.44
16.9
12.5
150
10
40
30
18.2
291
76.7
–
93.3
92.8
77.9
–
Machine
At 800 rpm (A)
At 8,000 rpm (A)
PMSG-1
PMSG-2
PMSG-3
PMSG-4
325
25.1
92.7
25.7
356
25.5
94.6
25.8
Machine
design and
control
strategy
97
Table III.
Specifications
at 800 rpm with
rated power
Table IV.
Comparison of
short-circuit
armature current
(RMS value)
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98
B. Using thyrister rectifier
Among all kinds of power switches, the thyrister has, in general, the greatest voltage
and current ratings, and is of low cost and high reliability. The thyrister rectifier can be
regarded as a combination of the diode rectifier and the buck dc/dc converter. However,
its dc output voltage is rich of ripple, especially when the triggering angle is large.
The relation between the thyrister rectifier dc output voltage Udc and the PMSG
line-line voltage amplitude Uab is as in (5):
3
Udc ¼ Uab cosat
p
ð5Þ
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where at is the triggering angle. Clearly, for the application of the above-mentioned
aircraft PMSG system, the generator should be designed as the same as the PMSG-2, or
similar to the PMSG-2 but with a slightly lower induced EMF. Therefore, at the
maximum speed of 8,000 rpm and with no load, the maximum voltage imposed on
the thyrister is extraordinary (up to 3,480 V), making it very difficult to choose the
thyristers with sufficient voltage rating.
C. Using PWM rectifier
The PWM rectifier is being extensively studied and applied. For most applications, it is
powered by ac mains supply, which has both constant frequency and stable
sine-wave voltage. Inductors are required between the mains power supply and the
PWM rectifier.
Here, the PWM rectifier is proposed to operate with a PMSG, as shown in Figure 4.
In this case, the PMSG winding inductances is used to replace the inductors, therefore,
they should be designed with an appropriate value. Moreover, the induced EMF vector
E of the PMSG is equivalent to the ac voltage vector of the mains supply, while
the terminal voltage vector U of the PMSG is equivalent to the voltage vector after the
inductors, which is directly applied on the PWM rectifier.
The PWM rectifier is a boost converter, say, its actual output dc voltage Udc is
always higher than the dc voltage when all the power switches are turned off (i.e. when
the PWM rectifier operates as a diode rectifier). From this point of view, the PMSG-1 is
suitable for the PWM rectifier. However, a PMSG with higher induced EMF is proposed
in this paper, as will be explained in Subsection 3-B.
DC
Load
PMSG
Figure 4.
PMSG system
with PWM rectifier
ω, θ
ia, ib, ic,
Controller
Udc
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The PMSG system shown in Figure 4 is similar to a traditional PMSM system, except
that in the PMSM system the power converter is a PWM inverter and the energy flows
from the dc bus to the ac motor, while in the PMSG system the power converter is a
PWM rectifier and the energy flows from the ac generator to the dc bus. For simplicity
of analysis and control, the PMSG system can be regarded as a special PMSM system
with a negative input power. Of course, the traditional space vector PWM (SVPWM)
can be employed for the field-oriented control and magnetic field regulation of the
PMSM and PMSG.
As long as the PWM rectifier outputs a stable dc voltage Udc, the amplitude of the
line-line voltage of the PMSG is always Udc, hence, the actual voltage imposed on
the power devices does not change even if the PMSG speed and the PWM duty cycle
vary. However, the PWM duty cycle changes the fundamental component of the PMSG
terminal voltage, where the fundamental component can be denoted as the vector U.
Large winding inductances are beneficial to lower the short-circuit current, but
also possibly lead to large voltage variation when the PMSG is loaded. However, with
PWM rectifier, this contradictory consideration is not really crucial, because the
current vector I becomes controllable, hence, the voltage vector U is also under control.
Thus, the inductances are actually designed to be large, in order to achieve good
field-regulating effect, which is going to be examined later. Moreover, the imposed
voltage on the power devices is proportional to the dc output voltage as long as the
controller is working properly, hence, the voltage rating of the power devices can be
determined according to the demanded dc voltage. For the abovementioned aircraft
PMSG system, the voltage rating of the PWM rectifier devices can be 600 V only,
since its actual imposed voltage is constantly 270 V even at the maximum speed with
no load, as listed in Table II.
For the wide-speed-range application, if the PMSG operates at high speed,
field-weakening control can be applied in order to obtain an expected stable dc
output voltage. However, at the very low speed, appropriate field-strengthening can
be considered. To realize field weakening or strengthening, it is not necessary to use
an additional power converter like what was proposed by (Wu et al., 2006). Instead, the
field-regulating current, viz., a negative d-axis current (id) for field-weakening or a
positive id for field-strengthening, can be easily injected into the PMSG armature
windings with the PWM rectifier. The effectiveness of such field regulation has been
verified in the previous work (Miao and Shen, 2012). The field regulation not only
helps to output a stable dc voltage, but also extends the operational speed range.
Nevertheless, demagnetization to the permanent magnets under field-weakening
or magnetic saturation under field-strengthening must be considered during the
machine design.
To describe the field-weakening capability of the permanent magnet machine,
a coefficient Km is defined as in (6), where cm is the flux linkage in the armature
windings which is generated by the magnets, Im is the amplitude of the rated
armature current, and Ld is the d-axis inductance:
Km ¼
cm
L d Im
ð6Þ
A smaller value of Km stands for a better field regulating capability if demagnetization
or saturation has been avoided by proper machine design. In order to design a smaller
Km, the PMSG magnetic load should be decreased while the electrical load should be
Machine
design and
control
strategy
99
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100
increased, by decreasing the rotor size and magnets volume, and enlarging the stator
size (e.g. reducing the stator inner diameter) to contain more turns of armature
windings. Again, a prototype machine is designed, denoted as PMSG-4. It has the same
structure as shown in Figure 4, and its parameters are listed in Table I. If its
armature windings are open-circuited, its maximum line-line voltage at 8,000 rpm is
1,030 V. However, when it cooperates with the PWM rectifier, its maximum voltage
is 270 V only, as already given in Table II (note, the PMSG-4 does not work together
with a dc/dc converter, while the PWM rectifier duty cycle changes dynamically,
hence, no duty cycle is listed in Table II). The inductances of the PMSG-4 are
L ¼ 11.5 mH and M ¼ 2.3 mH, respectively, and the resistance is R ¼ 0.217 ohm. Its
rated armature current (viz., that at the minimum speed of 800 rpm and under the
rated load) is 12.5 A, hence, the current rating of the power devices is 30 A only, as
listed in Table III. Moreover, the PMSG-4 has much better field-regulating capability
than all the other three machines, as illustrated in Table V. Especially, if the armature
current is fully utilized to weaken the field (i.e. id ¼ Im ¼ 17.7 A), finite element
analysis (FEA) shows that the permanent magnets are still safe from being
demagnetized. Moreover, the short-circuit currents of the PMSG-4 at the minimum and
maximum speeds are also listed in Table IV, which are just twice the rated current
and are usually acceptable. From this point of view, the PMSG-4 has better short-circuit
performance than the other three machines, too.
In summary, the PWM rectifier is the best option for the wide-speed-range PMSG
system, on account of the synthetic concerns of good field-regulating capability, low
short-circuit current and controllable voltage amplitude of the machine, as well as low
voltage and current ratings of the power devices. Moreover, the ripple in the output dc
voltage is minor. Therefore, the PMSG system with the PWM rectifier is further
investigated in the following sections.
3. Simulation study
A. PMSG modeling
A PM synchronous machine, no matter it is a motor or a generator, always satisfies the
voltage balancing equation as in (7):
U ¼ E þ R I þ joLq Iq þ joLd Id
ð7Þ
where E is the induced EMF vector which is always located on the q-axis with an
amplitude of ocm, while o is the electric angular speed, and o ¼ por, where p is the
number of pole pairs of the machine, and or is the mechanical angular speed. Id and Iq
are the d- and q-axis current vectors, namely, the two components of the stator current
vector I, while their amplitudes are id and iq, respectively. Generally, when the machine
operates as a motor, iq is positive and the machine input electric power is positive, too.
While, both iq and the input electric power are negative when the machine runs as a
Table V.
Comparison of
field-regulating
capability
Machine
cm (Wb)
Ld (mH)
Im (A)
Km
PMSG-1
PMSG-2
PMSG-3
PMSG-4
0.0844
1.199
0.317
0.498
0.176
35.8
2.46
13.8
89.2
6.28
23.9
17.7
5.38
5.33
5.39
2.04
generator. In many cases, the voltage drop on the winding resistance is neglected so as
to simplify the analysis, thus, the machine model can be expressed by the phasor
diagrams in Figure 5, where (a) is of the PMSM and (b) is of the PMSG. Moreover,
a positive value of id means that the armature current helps to strengthen the magnetic
(a)
Machine
design and
control
strategy
q
101
U
jωLdId
jωLqIq
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E
jωLdId
U
iq > 0
id < 0
iq > 0
Iq
I
I
id > 0
Id
Id
(b)
d
q
U
jωLdId
E
jωLqIq
jωLdId
U
Id
Id
d
iq < 0
iq < 0
id < 0
id > 0
I
Iq
I
Notes: (a) PMSM, solid lines showing field-strengthening
and dashed lines showing field-weakening; (b) PMSG, solid
lines showing field-strengthening and dashed lines showing
field-weakening
Figure 5.
Phasor diagrams
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102
field, and vice versa. Thus, a proper id can be injected by the inverter to the PMSM or
by the PWM rectifier to the PMSG in order to regulate the magnetic field. This further,
as can be seen from Figure 5, affects the terminal voltage U in both aspects of
amplitude and phase angle. For the PMSG system, U is also the fundamental
component of the input ac voltage of the PWM rectifier. It should be pointed out that the
actual PMSG terminal voltage is not of sine-wave, but contains pulses due to the PWM.
B. Control strategy
Figure 6 shows the system block diagram in the Matlab/Simulink environment. The
PWM signals are generated by a closed-loop control and SVPWM module, which is
detailed in Figure 7. The machine core saturation or the magnets demagnetization due
to the field regulation is neglected. The machine core loss is not considered, though it
actually reduces if field-weakening is applied. The power devices are considered as
ideal switches. By ignoring the power loss of the PWM rectifier, the system power
balancing can be expressed as (8):
3
ocm iq ¼ Udc Idc
ð8Þ
2
The left hand of (8) is the electromagnetic power of the PMSG when neglecting the
rotor saliency, which is the same as the machine output power if the winding resistance
PWM
Rectifier
[PWM]
Speed
+
w
PMSG
B
i
– +
– +
C
–
A
m
N
S
Figure 6.
Block diagram of
PMSG system
in Simulink
g
A
C
–
+
C
AC Current
Sensors
wm
p
[w]
thetam
p
[theta]
R
B
[Udc]
m
[iabc]
v +
–
DC Voltage
Sensor
Rotor Position and
Speed Measurement
Udc
id*
ω
Figure 7.
Block diagram of
closed-loop control
and SVPWM module
in Simulink
Udc*
ia
ib
ic
uα*
SVPWM
PI
U
iq*
–
Udc
ud* dq0
I
+
abc
dq0
uq*
αβ0 u *
β
id
iq
theta
PWM
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is neglected. The right hand is the dc link power. Clearly, the dc output voltage Udc is
influenced by the product of o and iq, and also by the load condition. Therefore, in
order to achieve the demanded Udc, iq should be adjusted dynamically with closed-loop
control, such as the conventional PI control in Figure 7. Moreover, it seems that id
should always be set to 0 since it is not related to Udc.
However, when the machine speed o is higher than a certain threshold othr, the
required q-axis current i*q should be extremely small. Nevertheless, the actual iq is out
of control, being greater than the required i*q. This is because, at high speed, the induced
EMF is also high, and, even if all the power devices are turned off, the diodes in the PWM
rectifier will form a diode rectifier and naturally convert the ac voltage to dc voltage which
is already higher than the demanded Udc. In other words, the high end of the speed range is
limited to the threshold othr. Note, for the PMSG-4, othr is designed as a moderate value
between the minimum (800 rpm) and the maximum (8,000 rpm) speed. However, this
problem can be solved by injecting a negative id into the armature windings, which
weakens the magnetic field inside the PMSG and reduce the amplitude of the terminal
voltage U. This extra id will, of course, increase the winding ohmic loss, but is beneficial to
extend the maximum operation speed, and also to reduce the machine core loss at high
speed. The required d-axis current i*d should be generated automatically according to the
machine model and the operation condition. When the actual speed is lower than othr, i*d is
fixed as 0. However, when the actual speed is greater than othr, a negative i*d is required to
restrict the amplitude of U vector to Udc/sqrt(3) (Liu et al., 2011). Thus, i*d can be
calculated as in (9) if the winding resistance is not considered, where i*q should be
determined in advance by the closed-loop control of Udc. In the simulation and experiment
hereafter, i*d is either manually set so as to investigate its influence, or automatically
determined as in (9):
8
< 0;
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ooothr
Udc 2
ð9Þ
id ¼
cm ðLq iq Þ2
3o2
:
;
oXo
thr
Ld
On the other hand, from (8) it is seen that at the very low speed, as long as iq is
large enough (of course the actual armature current should be limited below the
rated value), the required dc voltage Udc can always be achieved, while id seems
useless. However, in such a case, the duty cycle of the PWM rectifier usually
approaches 0 or 100 percent, making the turn-on or turn-off period very short.
This will deteriorate the rectifier operation condition and bring ripple to the dc voltage.
To solve this problem, it is proposed here to inject a positive id to the PMSG
armature windings, so as to strengthen the magnetic field in the PMSG and increase
the voltage U. A trade-off is that both the stator iron loss and winding ohmic
loss increase slightly. Nevertheless, such a trade-off is acceptable in practical
applications. The key issue is to determine the value of id automatically, according to
the machine parameters, speed and load condition. This will be discussed in detail
in a future paper.
When considering the winding resistance and rotor saliency of the PMSG, the
power balancing model should be refined from (8). Furthermore, in the salient PMSG, id
not only regulates the magnetic field but also contributes to the electromagnetic power.
Therefore, the determination of id and iq is rather complicated. However, the
determination for the non-salient PMSG can still be used, since the inaccuracy in
the model (8) is located inside the Udc closed-loop, and the demanded Udc can still be
Machine
design and
control
strategy
103
COMPEL
34,1
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104
achieved. Of course, with this model simplification, the PMSG armature current may
become slightly higher.
C. Simulation results
The PMSG-4 and PWM rectifier system which uses the above control strategy is
analyzed with Simulink simulation. Figure 8 shows the maximum allowable speed
when the machine is fed with different field-weakening current id. Clearly, to achieve a
low dc voltage, the maximum operation speed is limited. Moreover, the lower the fieldweakening effect is, the lower the maximum speed. This agrees with the aboveaddressed analysis. Note, the maximum allowable speed with id ¼ 0 is actually the
threshold speed othr.
Figure 9 shows the dc output voltage when the PMSG-4 runs at different speeds
(800, 3,200, 5,600 and 8,000 rpm, respectively) with different i*d. When i*d is fixed at 0,
only at the low speed of 800 rpm the dc voltage of 270 V can be achieved, while the dc
voltage is out of control if the speed is 3,200 rpm or higher. However, when i*d is fixed
at 30 A, the dc voltage of 270 V can always be obtained over the full speed range.
This agrees with Figure 8. On the other hand, if i*d is dynamically determined by (9),
the dc voltage of 270 V can still be obtained, however, its armature current and ohmic
loss will be lower than those when i*d is fixed at 30 A. Therefore, a dynamic i*d is
preferable.
It should be pointed out that, in order to achieve the 1.5 kW and 270 V dc outputs
at the maximum speed of 8,000 rpm, i*q should be 1.2 A as derived from (8), and i*d
should be 30 A as seen from Figure 8. Hence, the armature current RMS value
will be 21.2 A, greater than the pre-determined value of 12.5 A which has been
listed in Table III. However, it is acceptable to enlarge the rated current of the
PMSG-4 from 12.5 A to 21.2 A, because the winding current density is still 4.1 A/mm2
only, and, as concluded from FEA (see Figure 10), the permanent magnets are
still safe from being demagnetized. However, the current rating of the PWM
rectifier devices should be increased to 50 A. Moreover, id does cause extra ohmic loss
in the windings.
4. Experimental investigation
A test bench, as shown in Figure 11, is built to experimentally verify the
PMSG and PWM rectifier system. Instead of the PMSG-4, an existing PMSG
8,000
Figure 8.
Relationship between
maximum operation
speed and
field-weakening
current
Maximum Speed (rpm)
7,000
Udc*= 270V
Udc*= 150V
Udc*= 100V
6,000
5,000
4,000
3,000
2,000
1,000
0
–30
–20
–10
Field-weakening Current id* (A)
0
Machine
design and
control
strategy
Rotating Speed
(rpm)
9,600
8,000
6,400
4,800
3,200
1,600
105
800
600
400
200
DC Voltage (V)
with id* = –30A
0
300
DC Voltage (V)
with Dynamic id*
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DC Voltage (V)
with id* = 0A
0
1,000
250
200
150
100
50
0
300
250
200
150
100
50
0
Figure 9.
Simulation results of
dc output voltage at
different speed with
different id
Time (0.1s/div)
B (T)
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
in the laboratory is used as an example. Its parameters include: Ld ¼ 1.41 mH,
L q ¼ 0.33 mH, R ¼ 0.3 ohm, cm ¼ 0.0215 Wb, p ¼ 5, and its speed range is
300B3,000 rpm. The PMSG is driven by an inverter-fed induction motor. A low
demanded dc voltage (5 V) is set so as to investigate the field-weakening effect
Figure 10.
Flux density in
magnetization
direction inside
magnet with
id ¼ 30 A and
iq ¼ 1.2 A
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Induction Motor
106
PMSG
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DC Load
Figure 11.
Test bench
Central Control Unit
PWM Rectifier
at a relatively low speed. Resistors are connected to the dc output of the PWM
rectifier as the load.
Both simulation and test results are presented in Figure 12(a). The step-changing
speed command is set into the inverter, while the actual speed of the induction motor
and the PMSG changes slowly due to the moment of inertia. i*d is determined with (9),
and the dc output voltage from experiment agrees well with that from simulation,
although improvement of the PI closed-loop control is expected to further
dynamically stabilize the dc voltage. Also, waveforms of the PMSG line-line voltage
and dc voltage, as well as that of the PMSG armature current, are all shown in
Figure 12(b). Clearly, the voltage amplitude on the power devices of the PWM
rectifier is the same as the dc voltage, but much lower than the induced EMF at the
maximum speed.
5. Conclusions
The PMSG systems have gained extensive applications, especially for the
variable-speed situations. Various power converter topologies utilized in the PMSG
systems, such as the diode rectifier with three different dc/dc converters, the thyrister
rectifier, and the PWM rectifier, are introduced, while the design considerations of the
corresponding PMSGs are addressed. It has been seen that the PMSG system with a
PWM rectifier is prior to use for the wide-speed-range applications, considering the
voltage change due to load, the short-circuit current, the voltage and current ratings of
the power devices, and the extension of the operation speed range. Performance of the
PMSG system with the field-regulation by the PWM rectifier is investigated by both
Matlab/Simulink simulation and experiment, validating the good workability and
controllability. More studies regarding the field-strengthening at low operation speed
and the determination of the d- and q-axis currents of the salient PMSG will be
reported in future papers.
d-axis Current
Reference id* (A)
Machine
design and
control
strategy
3,500
3,000
2,500
2,000
1,500
1,000
500
0
20
107
10
0
–10
–20
DC Voltage
by Experiment (V)
DC Voltage
by Simulation (V)
20
15
10
5
0
20
15
10
5
0
Time (20s/div)
Line-Line Voltage
and DC Voltage (V)
(b)
10
8
6
4
2
0
–2
–4
–6
–8
dc voltage
Line-Line voltage
20
Armature
Current (A)
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Rotating Speed
Command (rpm)
(a)
10
0
–10
–20
Time (0.001s/div)
Notes: (a) Performance over the full speed range; (b) Voltage
and current wavforms at 3,000 rpm
Figure 12.
Simulation and
test results
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108
References
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regulation for an ironless axial-flux PM automotive alternator with electromechanical
flux weakening”, IEEE Transactions on Industry Applications, Vol. 45 No. 5,
pp. 1785-1793.
Chan, T.F. and Lai, L.L. (2007), “An axial-flux permanent-magnet synchronous generator for a
direct-coupled wind-turbine system”, IEEE Transactions on Energy Conversion, Vol. 22
No. 1, pp. 86-94.
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Chau, K.T., Li, Y.B., Jiang, J.Z. and Niu, S.X. (2006), “Design and control of a PM brushless hybrid
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automotive applications”, IEEE Transactions on Magnetics, Vol. 44 No. 12,
pp. 4591-4598.
Liu, H.S., Zhu, Z.Q., Mohamed, E., Fu, Y.L. and Qi, X.Y. (2011), “Comparison of drive
performance of PM synchronous machine fed by inverters with different PWM
strategies in constant torque and constant power regions”, Conference Record of 2011
IEEE International Electric Machines and Drives Conference, Niagara Falls, Ontario,
pp. 1334-1339.
Miao, D.M. and Shen, J.X. (2012), “Simulation and analysis of a variable speed permanent
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hybrid excitation synchronous variable frequency aircraft generator”, Conference
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pp. 1-5.
Shen, J.X. and Miao, D.M. (2013), “Variable speed permanent magnet synchronous generator
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About the authors
Dr Jian-Xin Shen received the BS and MS degrees from the Xi’an Jiaotong
University, China in 1991 and 1994, respectively, and the PhD degree
from the Zhejiang University, China in 1997. He was with the Nanyang
Technological University, Singapore (1997-1999), the University of Sheffield,
UK (1999-2002), and IMRA Europe SAS, UK Research Centre, UK (2002-2004).
Since 2004 he has been a Professor of Electrical Engineering at the Zhejiang
University. His main research interests include design, control and applications of electrical
machines and drives, and renewable energies. Dr Jian-Xin Shen is the corresponding author and
can be contacted at: J_X_Shen@zju.edu.cn
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Dong-Min Miao received the BS degree in Electrical Engineering from the
Zhejiang University, China in 2011. She is currently pursuing the PhD
degree at the Zhejiang University. Her research interests include machine
design and control strategy of permanent magnet synchronous generator
system.
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