Comparison of carrier signal based approaches for
sensorless wound rotor synchronous machines
Alexander Rambetius, and Bernhard Piepenbreier, Senior Member, IEEE
Chair of Electrical Drives and Machines, University of Erlangen-Nuremberg, Germany
Email: [email protected]
Abstract—Wound rotor synchronous machines enable a large
variety of approaches for carrier signal based sensorless control
since the rotor voltage serves as an additional input to the system
and the rotor current as an additional, easy to measure, state
variable. Consequently it is possible to use the rotor winding
either as the transmitter or as the receiver of a carrier signal. In
these cases the mutual inductance between the d-axis and the
rotor winding is of major importance. Moreover a rotor saliency
can be evaluated if the stator is used as the transmitter and as the
receiver of the carrier signal. If voltage injection is used, the
rotor winding acts like a damper winding for the carrier signal
and consequently the evaluated saliency differs from the saliency
which is utilized for sensorless control of permanent magnet syn-
chronous machines. Carrier current control on the other hand
offers the possibility to evaluate a magnetic saliency regarding
the inductances in the d- and q-axis. This work provides a de-
tailed review of the aforementioned approaches and analyses the
prerequisites. In addition to this the different approaches are
made comparable in terms of signal-to-noise ratio and cross
saturation. This is done by introducing suitable intensity terms.
With the help of identified parameters the most promising
approach for the investigated machine is found. Experimental
results confirm the validity of the comparison.
Keywords—wound rotor synchronous machine, wound field
synchronous machine, electrically excited synchronous machine,
sensorless control, high frequency injection, traction motor
I. INTRODUCTION
Wound rotor synchronous machines (WRSM) are synchro-
nous machines (SM), in which the rotor flux is generated by an
electrical winding. Besides WRSM, other notations are used in
the literature as well. Some of the most common ones are:
• Wound rotor [1-6] or wound field SM [7-9]
• Electrically excited [10-12] or energized SM [13]
• Externally excited SM [14]
• DC-excited SM [15]
In the following the term WRSM will be used. WRSMs feature
certain characteristics that suite the needs of automotive
traction applications very well [1], [14-15]. If field oriented
current control is applied to a WRSM, information about the
rotor position is required. This information is usually obtained
by a motion sensor (incremental encoder, resolver, etc.).
Leaving out this sensor reduces cost and may increase the
reliability of the whole drive system. Therefore sensorless
control is highly desirable in automotive traction [15]. At high
speed the rotor position can be obtained by evaluating the
motional electromotive force (EMF) [4], [15]. These methods
however fail at standstill and low speed. A common approach
to overcome this limitation is the injection of a carrier signal.
This carrier signal usually has got a higher frequency than the
fundamental wave and is therefore often referred to as high-
frequency (HF) signal. The conventional approaches for
permanent magnet synchronous machines (PMSM) inject
continuous HF-voltages into the stator and evaluate the
resulting current response. In contrast to PMSMs WRSMs
allow to use the rotor winding as the transmitter or as the
receiver of the carrier signal, which results in the following
possibilities for the transmission:
• Stator Stator [7], [10], [16]
• Rotor Stator [2], [5-6], [8-9], [12-13], [17-20]
• Stator Rotor [10], [21]
Furthermore it is possible to use the rotor as the transmitter and
as the receiver. In this case the stator slots represent a position
dependent saliency which can be evaluated. The stator teeth
however saturate very quickly and consequently the rotor
position estimation becomes complex. Therefore this approach
is not addressed in this paper. A method to estimate the rotor
speed by evaluating stator slotting harmonics in the rotor
current can be found in [4].
The most intuitive approach of the aforementioned methods
is to emulate a resolver by using the rotor as the transmitter and
the stator as the receiver of the HF-signal. Since the rotor self-
inductance is usually quite large this is not necessarily the
approach to be favored since large rotor voltages might be
necessary to create detectable stator currents [2]. If a rotating
diode rectifier is used to inductively transmit the rotor power,
the pulsation of this rectifier can be used as a carrier signal.
The resulting current response can either be evaluated in the
stator [5-6], [8] or in the rotor [22].
If the stator is used as the transmitter and as the receiver of
the carrier signal (like for PMSM [23-25]) the rotor winding
acts like a damper winding for the HF-signal and consequently
the required saliency differs from the saliency which is
necessary for sensorless control of PMSMs [10].
Recently HF-current control has been applied to PMSMs
instead of HF-voltage injection [26-30]. If this approach is
applied to WRSMs, the prerequisites chance compared to HF-
voltage injection: Since the HF-current in the rotor can be
controlled to zero, the rotor winding does not act like a damper
winding anymore. Consequently a differential magnetic sali-
ency regarding the inductances in the d- and q-axis is
evaluated.
The aim of this paper is to make the aforementioned
approaches comparable in terms of signal-to-noise ratio and
978-1-4799-4749-2/14/$31.00 ©2014 IEEE
2014
International Symposium on Power Electronics,
Electrical Drives, Automation and Motion
1152
cross saturation. For this purpose the prerequisites for the
different approaches are analyzed and suitable intensity terms
are introduced. With the help of identified parameters the most
promising approach for the investigated machine is found. The
validity of the comparison is confirmed by experimental
results.
II. MACHINE MODELING
The rotor fixed fundamental wave model derived in [11]
will be used throughout the paper. Moreover it is assumed that
the HF-analysis and the fundamental wave analysis can be
carried out separately from each other. Using complex phasor
notation for ac steady state signals, the voltage equations for
the HF-analysis at standstill are given by:
,
,
,
,
, ,
,
,
,
(1)
With ,,, the impedances in (1) are given by:
(2)
(3)
denotes the self-inductance of the i-axis, the mutual
inductance between the i-axis and the j-axis. Apart from the
actual magnetic coupling , cross saturation effects are
considered by the mutual inductances and [2-3], [10-
11], [13]. The machine model is depicted in Fig 1. If HF-
voltage injection is used, the current response is of interest and
consequently the admittance matrix, which is the inverse of the
impedance matrix, is required:
,
,
,
,,
,
,
,
(4)
III. HF-VOLTAGE INJECTION BASED SENSORLESS CONTROL
HF-voltage injection (HF-VI) is the most common ap-
proach for carrier signal based sensorless control. If secondary
saliencies are neglected, WRSMs enable three transmission
directions. Furthermore it is possible to distinguish between
direct and indirect methods. Direct methods directly compute
the rotor position, while indirect methods rely on the mini-
mization of an error angle. Whether a method is direct or
indirect depends on the injection (either rotating or alternating
carrier signal) and on the evaluation (either evaluation in stator
fixed αβ-coordinates or in rotor fixed dq-coordinates). Table I
summarizes all the possible approaches. In the following only
the indirect methods are investigated in detail because they
seem to be more popular. The direct methods are addressed
briefly in Subsection D. For the indirect methods, it is assumed
that the estimated dq-reference frame is misaligned. The
difference between the estimated rotor position and the actual
rotor position is denoted by ∆. Furthermore the error angle
is assumed to be small and therefore a linearization is carried
out around small error angles in the following [2], [10].
Fig. 1. Machine model: the d-axis and the field winding are magnetically
coupled by . The coupling between the d-axis and the q-axis and
between the q-axis and the field winding is caused by saturation effects.
TABLE I. APPROACHES FOR HF-VI BASED SENSORLESS CONROL
Stator Transmitter
=> Stator Receiver
Rotor Transmitter
=> Stator Receiver
Stator Transmitter
=> Rotor Receiver
Indirect
• Alternating carrier
• Evaluation in dq
• PMSM [22-23]
• EESM [7], [10]
• Fig. 2
• Alternating carrier
• Evaluation in dq
• [2], [6], [13]
• Fig. 3
• Alternating carrier
• Evaluation in dq
• [10], [21]
• Fig. 4
Direct
• Rotating carrier
• Evaluation in αβ
• PMSM [24]
• EESM [16]
• Alternating carrier
• Evaluation in αβ
• [2], [5], [8-9], [12],
[17-20]
• Rotating carrier
• Evaluation in dq
• Section III.D
Fig. 2 – Fig. 4 depict the basic structure of the possible indirect
methods if HF-voltage injection is applied. The injection is
marked in red, the evaluation in blue. CC stands for current
control, EST for rotor position estimator.
A. Stator Transmitter – Stator Receiver (Method 1, see Fig. 2)
This method is well known from PMSMs [22-23] and has
been applied to WRSMs as well [7], [10]. The most common
approach uses an alternating carrier signal and is depicted in
Fig. 2. To derive the underlying prerequisite, it is assumed that
a HF-voltage is injected in the estimated -reference frame:
,
, 00
(5)
Transforming this excitation to actual -reference frame and
inserting it into (4) the HF-current response can be calculated.
This current response is then transformed back to the estimated
reference frame. The required transformation matrices are
given in [10]. Linearizing the result around small error angles,
the current response in the estimated -axis is given by:
,∆,
(6)
As can be seen in (6) the current response contains information
about the rotor position if there is a saliency regarding the
admittances in the d- and q-axis. Due to the inversion of the
impedance matrix in (1) the admittances include resistive and
inductive parts. However in general the inductive voltage drop
is dominant for HF-excitation. To extract a meaningful
prerequisite, the resistive voltage drops as well as cross
saturation is neglected in the following.
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Fig. 2. : HF-VI: The Stator is the transmitter and
the receiver (Method 1)
Fig. 3. HF-VI: The rotor is the transmitter and the
stator the receiver (Method 2)
Fig. 4. HF-VI: The stator is the transmitter and
the rotor the receiver (Method 3)
In this case the current response in (6) can be written as:
, ,
∆
(7)
denotes the effective HF-inductance of the d-axis for a
short circuited field winding and is given by (8) [2], [10].
(8)
It can be seen that apart from the actual HF-inductance of the
d-axis, the coupling between the d-axis and the field winding is
of importance. For the HF-analysis the field winding can be
regarded as short-circuited and therefore acts like a damper
winding. Consequently the HF-flux in the d-axis is weakened
which leads to a drop in the effective HF-inductance of the d-
axis. As a result no actual magnetic saliency is necessary like
for PMSMs. Instead a saliency regarding the effective HF-
inductance of the d- and q-axis is required:
0
(9)
This effect is also used in [31-33] to increase the saliency of a
PMSM by adding a short circuited winding to the rotor.
Analyzing (6), it can be concluded that an estimation error is
introduced by cross saturation. This estimation error is given
by: ∆
/
(10)
B. Rotor Transmitter – Stator Receiver (Method 2, see Fig. 3)
This intuitive approach is based on the principle of a
resolver and is depicted in Fig. 3. Concerning the injection, the
power transmission to the rotating field winding is of major
importance. The transmission is either done via slip rings [10],
[13-15], or brushless using inductive coupling and a rotating
diode rectifier [5-6], [8]. Moreover capacitive power trans-
mission has been suggested recently [34]. The easiest way to
perform the injection is to superimpose the HF-voltage to the
fundamental wave DC-voltage using the rotor converter [13].
This approach might not be feasibly for every machine, since
the voltage reserve for the field current controller is reduced
significantly. In certain cases the available DC-link voltage
might even be insufficient to create detectable stator currents
[2]. If a rotating diode rectifier is used, it is possible to
overcome this problem by using the pulsation of the rectifier as
a carrier signal [5-6], [8]. If a rotor chopper is used to create the
field voltage, the switching of this chopper can be utilized as a
carrier signal [2], [9], [12]. A drawback of this injection tech-
nique is that the amplitude and the phase of the carrier signal
vary depending on the duty cycle of the rotor chopper [2]. In
the following it is assumed that a cosine-shaped HF-voltage is
superimposed to the DC field voltage:
,
00
,
(11)
Calculating the HF-current response due to this excitation and
transforming it to the estimated -reference frame, one yields:
, ∆,
(12)
From (12) it can be concluded that the HF-current response in
the estimated q-axis contains information about the rotor
position. If resistive voltage drops and cross saturation are
neglected (12) can be simplified, which results in:
, ,
∆
(13)
It can be deduced that the d-axis and the field winding have to
be coupled magnetically. Apart from the inductance ratio
in (14) is of major importance.
/
(14)
Moreover (12) shows that an error is introduced due to cross
saturation which is given by:
∆
/
(15)
C. Stator Transmitter – Rotor Receiver (Method 3, see Fig. 4)
This approach is successfully applied to a WRSM in [10]
and is depicted in Fig. 4. An advantage of this approach is that
the measurement range of the field current is small compared
to the one of the stator currents. Therefore even small signal
amplitudes are detectable. The HF-injection for this approach is
done in the q-axis of the estimated -reference frame:
,
0
, 0
(16)
Transforming this excitation to the actual -reference frame
and calculating the resulting HF-current response in the field
winding, one yields:
,
∆,
(17)
Comparing (17) to (12), it becomes apparent that both current
responses differ only by the scalar 3/2 and by the excitation.
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Consequently the prerequisite for this approach is the same like
in Subsection B and the estimation error due to cross saturation
is given by (18). ∆
∆
(18)
D. Direct methods
If the stator is used as the transmitter and as the receiver of
the carrier signal, the absolute rotor position can be estimated
by injecting a rotating HF-voltage and evaluating the resulting
HF-current response in the stator in stator fixed αβ-coordinates.
Possible implementations for this approach can be found in
[16] and [24].
If the rotor is used as the transmitter of the carrier signal, an
estimate of the absolute rotor position can be obtained by
evaluating the resulting HF-current response in the stator in
stator fixed αβ-coordinates. Possible implementations can be
found in [2], [5], [8-9], [12], [17-20].
If the rotor is used as the receiver of the carrier signal, an
estimate of the absolute rotor position can be obtained by
injection of a rotating carrier signal. Since this approach is not
properly addressed yet in the literature, the basic idea is briefly
discussed. The rotating carrier signal in stator fixed coordinates
is given by: ,
, , 0
(19)
Resistances and cross saturation are neglected in the following.
The HF-current response in the field winding resulting from
the excitation in (19) can then be written as:
, 3
21
sin
,
(20)
The absolute rotor position can now be calculated by separat-
ing the real and the imaginary part in (20):
arctan,/,
(21)
IV. HF-CURRENT INJECTION BASED SENSORLESS CONTROL
Recently, HF-current injection (HF-CI) has been applied in-
stead of HF-voltage injection (HF-VI) [26-30]. In order to
inject the HF-currents with zero steady state control error
advanced control techniques have to be applied. [26] for
instance uses resonant controllers in combination with a
flatness based feed forward control. Fig. 5 depicts the basic
structure for an indirect carrier signal based approach, if the
stator is used as the transmitter and as the receiver. In this
scheme CC stands for a current controller, which is suitable for
fundamental wave current control as well as for HF-current
control. It can be seen that the output of the current controllers
is used to estimate the rotor position.
A. Stator Transmitter – Stator Receiver (Fig. 5)
Like suggested in [26-28] an alternating HF-current is
injected into the estimated d-axis. The HF-currents in the
estimated q-axis and in the field winding are controlled to zero.
The HF-excitation in estimated rotor fixed coordinates is
consequently given by (22).
,
, 00
(22)
The superscript * denotes set point values. (22) is now
transformed to the actual dq-reference frame. Cross saturation
is neglected in the following. If the HF-current control injects
the set point in (22) with zero steady state error, the output of
the HF-current controller in the estimated -axis is given by
(23) and contains information about the rotor position.
, ,∆
(23)
In contrast to (6) a saliency regarding the impedances in the d-
and q-axis is a prerequisite for this approach. Inserting (2) in
(23), one yields:
,
,∆
(24)
It can be seen that either a resistive saliency or an inductive
saliency can be evaluated. The inductive saliency however
appears to be more frequently used. Furthermore it can be
deduced that, since the HF-current in the field winding is
controlled to zero, the damping effect described in Section
III.A does not appear anymore. Consequently an actual
magnetic saliency regarding the inductances in the d- and q-
axis is required for this approach.
B. Rotor Transmitter or Receiver
If an alternating HF-current is injected into the field winding
the output of the HF-current controller of the estimated -axis
contains information about the rotor position. If an alternating
HF-current is injected into the estimated -axis, the output of
the HF-current controller of the field winding contains
information about the rotor position. Compared to HF-voltage
injection the prerequisites do not change: The d-axis and the
field winding have to be coupled magnetically. Therefore these
approaches are not addressed in detail.
V. PARAMETER IDENTIFICATION
The differential HF-inductances are identified using the HF-
current injection based technique suggested in [29-30]. The
investigated drive system is summarized in Table II. The
identification is carried out while the machine is rotating at 2.5
rpm and the results are averaged over one electrical period. The
alternating carrier signal used for the identification has got a
frequency of 1 kHz. To reduce the number of dependencies a
new fictive magnetization in the d-axis is defined:
(25)
Fig. 5. HF-CI: The Stator is the transmitter and the receiver of an alternating
carrier signal. The evaluation is done in the dq-reference frame
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Fig. 6. Self-inductances of the d- and of the q-
axis
Fig. 7. Self-inductance of the field winding Fig. 8. Mutual inductance between the d-axis and
the field winding
Fig. 9. Effective HF-self-inductance of the d-axis
and self-inductance of the q-axis
Fig. 10. Mutual inductance between the d-axis and
the q-axis due to cross saturation
Fig. 11. Mutual inductance between the q-axis and
the field winding due to cross saturation
is a transmission ratio, which makes the currents and
magnetically comparable, such that:
,00,
(26)
denotes the stator flux linkage of the d-axis. Fig. 6 depicts
the self-inductance of the d- and q-axis. It can be seen that for
an unmagnetized d-axis a large saliency is present due to the
salient rotor. This saliency however vanishes for large magnet-
ization currents in the d-axis. The reason is that the air-gap,
which has got linear magnetic characteristics, is relatively large
in the q-axis and therefore the self-inductance of the q-axis is
comparatively constant. The d-axis on the other hand saturates
quickly due to the small air gap of the d-axis. Consequently the
HF-CI based approach in Section IV.A is not applicable for
large magnetization currents and is therefore not further ana-
lyzed. The effective HF-inductance of the d-axis for HF-VI is
given by (8) and is identified by turning off the HF-current
controller of the field winding during the identification process.
The identification results are depicted in Fig. 9. Since the field
winding damps the HF-flux in the d-axis, the inductance
is smaller than the self-inductance of the q-axis. It can be seen
that the investigated machine features a large saliency regard-
ing the effective HF-inductances of the stator if HF-VI is
applied. This saliency is present for all operating points. Fig. 7
depicts the self-inductance of the field winding, Fig. 8 the
mutual inductance between the field winding and the d-axis. It
can be seen that saturation effects manifest themselves in a
similar manner for both inductances. Therefore, the inductance
ratio in (14) does not change significantly for different
operating point. Fig. 10 and Fig. 11 depict the two mutual cross
saturation inductances. It can be seen that cross saturation only
appears for a q-current unequal to zero [29-30].
TABLE II. SUMMARY OF THE INVESTIGATED DRIVE SYSTEM
Wound Rotor Synchronous Machine
Stator 3-phase distributed winding
Rotor Salient pole with slip rings
Number of pole pairs 3
Rated power/Rated Speed 12 /3325
Rated/Maximum stator current (rms) 250
/ 320
Rated phase voltage (rms) 18.3
Rated/Maximum field current 16
Power Electronics (3-phase VSI Stator, 2-phase VSI Rotor)
DC-link voltage 45
Switching frequency stator/rotor
, 16 /
, 8
VI. COMPARISON
The Comparison is carried out for the indirect HF-VI
approaches described in Section III. HF-CI is not addressed
since the investigated WRSM does not feature the necessary
saliency if the stator is used as the transmitter and as the
receiver. If the rotor is used either as the transmitter or as the
receiver, the magnetic coupling between the d-axis and the
field winding is utilized for both HF-VI and HF-CI. The three
HF-VI based approaches are compared in terms of signal-to-
noise ratio and estimation errors due to cross saturation. In the
following it will be assumed that only the imaginary part of the
current responses in (6), (12) and (17) is evaluated which
means that the imaginary part of the admittances (susceptance)
in (4) is of importance. Consequently mainly, but not solely,
inductive effects are evaluated.
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