Analysis of VSI-DTC Fed 6-phase Synchronous
Machines
Ibrahim Abuishmais*‡, Waqas M. Arshad*, Sami Kanerva†
*ABB Corporate Research, SE-72178 Västerås, Sweden
†ABB Oy, Machines, FI-00380 Helsinki, Finland
‡Norwegian University of Science and Technology O.S. Bragstadsplass 2E, 7491 Trondheim, Norway
Ibrahim.Abuishmais@elkraft.ntnu.no
+47 73594280
Abstract— High power drives with multiphase machine
utilizes paralleled legs converters to realize required power.
In addition to the reduced rating of the used semiconductor
devices, higher redundancy level could be achieved. Being a
relatively new technology for the combination of VSI-fed
operation and salient pole synchronous machines, a through
analysis is needed. This paper investigates 6-phase
synchronous machines with emphasis on redundancy, fault
conditions, the machine’s behavior under non-sinusoidal
voltage profiles and sensitivity of the design parameters. It is
shown that new design thinking is required when
considering converter-induced machine losses, especially
those on the rotor surface. Redundancy study shows the
possibility of operating the machine at half load when one
supply system is totally or partially lost without exceeding
machine’s total losses. When studying fault scenarios, the
worst case is found to be 4-phase short circuit (equivalent to
2-phase in a 3-phase machine) for the studied cases. Output
from sinus supply voltage study was utilized to understand
losses distribution inside the machine and establish an
effective comparison with different voltage profiles. A study
with square wave and DTC supplies shows higher losses in
damper bar, when compared to sinus supply. Voltage
profiles of two different DTC schemes are studied which
show that with particular well-thought control strategies
one can improve the machine losses specially those in the
damper bars.
performance advantages of a synchronous motor over an
induction motor and the DTC superiority over other
converter control schemes. The presented work looks at
some of the many aspects associated with this relatively
new concept of 6-phase salient-pole synchronous motors
fed with DTC-controlled voltage source converters. Issues
such as motor design parameters sensitivity, behavior
during normal, faulty and partially-faulty (redundancy)
operations are addressed by considering the interaction
between source’s time harmonics and machine’s space
harmonics and the relevant additional losses.
Keywords—Multiphase machines, synchronous machines
design, direct torque control.
Fig. 1. Schematic drawing of 6-phase machine stator windings, the two
winding sets are 30o displaced.
I. INTRODUCTION
Many industry segments today are increasingly asking
for medium-large motor solutions with traditional
demands of high efficiency, high power density, reliability
and superior control aspects for variable speed operations
along with a new demand of redundancy. Dual stator (or
6-phase) motors with 30 degrees displacement between
the two 3-phase windings sets (see Fig. 1), provides a
solution with this relatively new demand of redundancy. A
6-phase motor satisfies the reliability demands since one
of the systems provides a redundancy in case the other
fails. Powering the two sets by two different converters; i)
adds more redundancy level particularly if one supplying
system fails ii) reduces the size of semiconductor devices
used to built the converter making the size of large drive
system rating feasible and iii) increase the total system
efficiency. The choice of synchronous motors fed with
voltage source converters and employing direct torque
control (DTC) provides a very competitive solution due to
C
A
a
b
B
II. LITERATURE SURVEY-A HISTORICAL NOTE
The increase demand on high generation units in late
1920’s was restricted by the available circuit breaker
capacities at that time. In 1929, design engineers proposed
the dual stator windings generator as a solution of the high
rated current breaking ability [1] followed by the first
addressing of such kind of machines in AIEE in 1930 [2].
The generated voltage in the two windings of separate
systems was equal in phase which introduced several
discussion issues in generator connections and high
voltage switching until P. Robert et al [3] proposal to
displace the two windings by 300. This in addition to
solving the connection issues, also resulted in a reduction
in stray losses. In 1973, Fuchs and Rosenberg [4] modeled
the machine mathematically, using the orthogonal
transformation steady state model describing the machine
behavior. It is noticed that the used transformation matrix
ignores any mutual effect between the two winding sets.
In 1974, Nelson and Krause [5] presented a model of
multiphase induction machine. Although the proposed
882
c 2008 IEEE
978-1-4244-1742-1/08/$25.00 c
mathematical model can be useful to gain a better
understanding, the authors’ assumptions of uniform airgap
as well as ignoring the saturation and eddy current effects,
makes such model oversimplified to analyze a salient pole
machine. However, the authors highlighting of the
advantages of the dual stator configuration to achieve
higher reliability level and expanded overall drive system
availability rate, are valuable. Results of analytical and
experimental investigation for 6-phase voltage source
inverter driven induction machines were presented in
1983[6],[7]. 6-phase machine model with mutual leakage
coupling included was presented by Schiferl and Ong [8],
[9]. Back EMF voltage and input current harmonics are
also studied. Advantages of multiphase machines, in
general, are presented in [10],[4]. A review on multiphase
induction machine drives is recently reported in [11].
III. ANALYSIS OF 6-PHASE SYNCHRONOUS MACHINE
A. Harmonic Fields
The nature of synchronous machines and all AC
machine designs in general, e.g. rotor saliency and stator’s
slotting, imposes several deviations from the ideal targeted
sinusoidal harmonic free fields and smooth DC torque.
The investigation of these phenomena is interesting due to
its effect on machine performance and efficiency i.e. total
losses and output power.
To analyze harmonic field’s causes, analytical approach
can be applied. This approach depends on classical
analysis of the geometrical parameters of the machine and
to determine the resultant flux density. To elaborate more,
flux density can be obtained by multiplying permeance
waves which are function of stator slotting and rotor
saliency by MMF waves see (1) [12]. By applying this
approach, the harmonics behavior of the machine can be
studied analytically.
μ0 A 1
. MMF (θ , t )
δ (θ , t ) A
= Λ (θ , t ). MMF (θ ,t )
Β(θ , t ) =
(2)
These harmonics are stationary, in other words the
wave speed is zero with respect to the synchronous speed.
On the other hand, rotor permeance wave depends on pole
symmetry. Studied machine has a symmetrical pole pitch
geometry which means that permeance wave has
following harmonic orders:
j = 1, 2,3,...
±2 j
h S &R
υ S &R =
(3)
j = 1, 2, 3,...
(5)
nhx (θ ) = N h cos(hθ − ζ )
h = 1, 2,3...
(6)
Where x index refers to the six phases; A, B, C, a, b,
and c, the factor N h is the windings factor at different
harmonic order, while ζ is the phase shift between the
two supply systems. The winding functions for different
phases can be expressed as [13];
Nh
nh (θ ) = N h cos(hθ ) =
A
nh (θ ) = N h cos(h{θ −
B
Nh
=
2
(e
jh (θ −
2π
)
+e
3
− jh ( θ −
nh (θ ) = N h cos( h{θ +
C
Nh
2
(e
jh (θ +
2π
)
+e
3
− jh ( θ +
(e
2
2π
)
3
2π
3
)
− jhθ
(7)
)
(8)
) = α N h (e
h'
2π
3
+e
})
3
2π
jhθ
− jh '
) |h ' = ± h
})
(9)
) =α
−h '
N h (e
− jh '
) |h ' = ± h
2π
Where α = e 3 . The three remaining functions for the
other supply system can be derived in the same manner.
j
π
Introducing the operator β = e 6 , this indicates the
physical displacement between the two systems i.e. 30o in
the studied case. Winding function of second stator set can
be expressed as:
nha (θ ) = β h ' N h (e − jh ' ) |h '=± h
(10)
n (θ ) = α β N h (e
(11)
b
h
h'
h'
− jh '
) |h '=± h
nhc (θ ) = α − h ' β h ' N h (e − jh ' ) |h '=± h
(12)
The resultant magneto motive force is expressed as:
MMF S (θ , t ) =
¦
nhx (θ ) × ikx (t )
x = A , B ..
=
∞
∞
¦ ¦{
h '=−∞ k =1
Nh
2
((1 + β h ' β − k ) + α h 'α k (1 +β h ' β − k )
−h '
All of these harmonics pulsate with twice the
synchronous speed. Combined effect of rotor and stator
(4)
2) Stator and Rotor MMF
Stator MMF is a direct result of its winding, in case of
6-phase machines, windings arrangement is interesting as
it results in short circuiting some of machine space
harmonics for certain time harmonic orders. Windings as a
function of space can be expressed as:
j
i = 1,2,3,...
i, j = 1, 2,3,..
Rotating with speed
=
slots QS is given by QS = 12. p.qS . Where p is number
of pole pairs. Stator spatial harmonics due to slotting can
be expressed as
h R = 2. j
h S & R = 12.qS .i ± 2 j
(1)
1) Stator and Rotor Permeance Harmonics
Stator permeance harmonics result mainly due to
slotting. For a given number of slots per phase per pole
qS in 6-phase machine stator, total number of stator
h S = 12.q S .i
permeance results in a waveform with the following
harmonic contents:
−k
+ α α (1 + β β )) I k e
k
h'
j ( kwt − h 'θ )
}
(13)
Here k is the time harmonic order and the superscript
“S” indicates the stator MMF.
2008 13th International Power Electronics and Motion Control Conference (EPE-PEMC 2008)
883
Using (13), speeds of airgap space harmonics can be
predicted at any time harmonic “ k ” (k=1 for the
fundamental harmonic of supply current) and the space
harmonic h’=1,-5, 7,-11, 13 … etc. It can be noticed that
applying different sets of space and time harmonics,
results in several harmonics with zero speed, particularly
if h '− k = ±6n condition is satisfied, here n is an
integer. The common term in (13) i.e. (1 + β
be either 0 or 2:
h'
β −k )
will
Fig.2. Airgap fields for a sinus-fed 6-phase synchronous motor.
(14)
It is clear that harmonic suppression criterion depends
on the phase shift between the two different systems as
well as the order of the interacted harmonics.
On the other hand, rotor’s excitation creates MMF
wave containing harmonics rotate with the synchronous
speed and have the order
hmR = 1,3,5...
(15)
The situation for a 6-phase machine is provided in
TABLE I showing what harmonics are to be expected due
to the interaction between different MMFs and various
machine permeances. From this information, a
preliminary estimation of the machine behavior for a
selected design interacting with a certain converter can be
made. This increases machine controllability, knowing the
close relation between stator MMF harmonics and the
electrical phase shift between the two windings sets. To
identify field harmonics; an alternative approach is the
FEM analysis employing long time stepping solutions.
From the knowledge of fields; torques, losses and damper
bars currents developed in the machine can be derived.
Fig.2 shows main harmonic contents of the airgap flux
density during sinus operation. As can be seen, although
the 5th and 7th harmonics are present in the airgap (due to
rotor pole saliency) they have no impact on torque
pulsations.
Permeance
hm = 1, 3, 5... and
i , j = 1, 2, 3, ..
12.qS .i ± hm
Rotor saliency
2. j ± hm
Combined
stator
and rotor (+)
Combined
stator
and rotor (-)
2X
X
6
12
18
24
28
30
hmR
S
R
12.qS .i ± hm
S
R
2. j ± hm
12.q .i + 2. j ± h
S
12.q .i − 2. j ± h
S
S
m
S
m
12.q .i + 2. j ± h
R
12.q .i − 2. j ± h
R
S
S
m
m
qS is the number of slots per phase per pole.
Superscript “S and R” referred to stator and rotor,
respectively.
884
3X
R
i , j = 1, 2, 3, ..
Stator slotting
4X
Rotor MMF
and
hmS
5X
Harmonic order
hmS = 6 m + 1,
m = 0, ±2, ±4, ±6,...
Average
6X
0
TABLE I.
AIRGAP FLUX DENSITY HARMONICS
Stator MMF
B. Harmonic Torque and Speed
Torque components in synchronous machine are
produced mainly by the interaction of stator and rotor
fields. Besides the DC torque component that accelerates
the machine, pulsating torque components appear at the
shaft, these components can be divided into two types,
transient and persistent [15].
For persistent non-decaying pulsating components;
harmonic orders of developed torque at machine shaft can
be predicted utilizing flux linkage components or airgap
MMF since it differs only by scale from flux linkage
wave. Basically, the produced torque is an interaction
between two consecutive flux components resulting in
torque with frequency that equals the difference between
involved wave’s frequencies, taking into account the
direction of rotation. For example the 11th MMF
component rotates in negative direction with respect to
rotor flux rotating direction. It interacts with DC flux
component rotating at synchronous speed resulting in {1(-11)} 12th torque component and same order of the
induced damper bars current. See Fig. 3 .
Current [A]
­0 if n is odd
(1 + β h ' β − k ) = ®
¯2 if n is even
Fig. 3. Correlation between developed torque and damper bars current
harmonic spectrums.
In spite of existence of 5th and 7th (17th, 19th …etc)
harmonics in machine’s airgap, these harmonics do not
contribute in torque production. The same applies to
damper bars induced current.
2008 13th International Power Electronics and Motion Control Conference (EPE-PEMC 2008)
In 6-phase machine’s airgap the fact that the 5th and 7th
space harmonics order due to stator MMF are absent
results from the combined effect of physical displacement
between the two stator windings and electrical phase shift
between supplies voltages. It can be concluded that 6th
harmonic torque will not appear. Same applies to interpret
18th absence knowing that 17th and 19th MMF components
do not exist. On the other hand, airgap fluxes of 6-phase
machine contain the same 11th, 13th, 23rd and 25th
component’s magnitude compared to three-phase machine
which means torque pulsations at frequencies 12th and 24th
remain the same in the two different machines.
C. 5th, 7th, 17th, 19th Time Harmonics Behavior
The discussed 6-phase machine, differs with a 3-phase
machine in terms of its response to 5th, 7th, 17th, 19th,…
time harmonics. With 300 degree space shift between the
two winding sets and with the same electrical phase shift
between the supply voltages, certain harmonics disappear
from airgap fluxes. A generalized form of required
displacement is π / n for even sets number and 2π / n for
odd number of sets, where n is number of phases [5].
Analytically, analyzing the MMF wave and its interaction
with the different permeance functions explains the
phenomena. An alternative analytical way is presented by
M. Abbas et al. [6] and T. Jahns [14] using the generalized
two-phase real component transformation for n-phase
machine. The one can conclude that the excitation voltage
time harmonics such as 5th, 7th, 17th, 19th …etc. are
prevented from contribution to the airgap flux and torque
pulsations while they are contributing in the supply input
current. The reactance of these harmonics current paths
appears to be relatively small. To verify these analytical
conclusions flux paths inside the machine were studied
with Finite Element Method (FEM).
Applying an input supply containing only one harmonic
order e.g. 5th or 7th at a time, field maps and relative
permeability of the rotor region were in focus. Fig. 4
shows field maps in four different cases. 5th and 7th
harmonic in supply result in flux which is totally linked in
stator region only. This leads to same theoretical
conclusions that these components will not contribute in
torque pulsations or induce any damper bar currents. It
also shows that the stator linkage part of the reactance will
disappear making the total path reactance small. The same
observation can be noticed in case of 17th and 19th time
harmonic orders. On the other hand, 11th, 13th …etc
harmonic results in flux paths linked throughout the rotor
region.
Fig. 4. Field maps for different supply harmonics.
IV. DESIGN PARAMETERS
Sensitivity study for machine’s design parameters is
also studied, e.g., teeth dimensions, winding layout,
wedge material, damper bars and rotor pole shape. The
motivation behind this study is to establish a qualitative
comparison between the effects of different design
parameters on one of the main studied operating aspects,
e.g. machine’s harmonic fields. It is found that the
behavior is not much different to a 3-phase machine. One
important difference is to think about pole shape induced
5th, 7th, 17th, 19th etc. harmonics in airgap that induce
significant stator harmonic currents and thus affecting
machine performance. Such an optimization can be
combined with a decrease in the airgap length, which
results in a decrease in field windings copper loss at the
cost of an increase in damper bar losses.
V. REDUNDANCY ANALYSIS
Using machine with (n) winding systems makes it
possible to operate under faulty or partially faulty
conditions i.e. open phase or short circuit faults, if each
phase’s supply or group of phases is being fed from
independent supply, like independent inverters. The
investigation of the state of being supplied by (n-1)
systems is called redundancy analysis. One of the main
motivations behind using the 6-phase or double threephase stator design is to provide a high level of
redundancy. Redundancies modes include supply system
failure and internal machine faults. In former case losing
one supply system means that the machine is driven by
three phases out of six in the healthy case. Open phase
faults are also considered in this redundancy study.
The simulated cases are:
1. Supplying the 6-phase machine with only one
three-phase set, the other three phases are
blocked by introducing very high external
impedance.
2. Lowering the input current of one system by
25%.
3. Lowering the input current of one system by
65%.
2008 13th International Power Electronics and Motion Control Conference (EPE-PEMC 2008)
885
Simulation results for the first redundancy case are
provided in Fig. 5, for 50% load torque. Losing three
supply phases out of six but developing the same output
torque means that the connected phases have to deliver all
the required input power. As Fig. 5 shows the increase in
the current magnitudes is approximately 100%, it is also
noticeable that the waveforms are not identical i.e. they do
not contain same harmonic contents. Total harmonic
distortion of the input current decreases from 8.5% in case
of healthy six phases supply to 6.47% for the three phase
supply case. The most significant components are 5th and
7th with big difference in their magnitudes and phase
angles. The reason of less distorted input current is the
absence of harmonic low impedance paths, in particular
for 5th, 7th, 17th and 19th components. As the correspondent
counteracting harmonic MMFs which were generated by
the adjacent stator set are absent, these fields are able to
link through the rotor. Torque pulsations at 12th and 18th
are observed in output torque spectrum.
3Z
Current [A]
0
-3Z
0.3
0.4
0.5
0.7
0.8
0.9
1
Fig. 6. Input currents during redundancy case 2.
Pre-event
Post-event
3Z
92%
Post-event
65%
0
0
3Z
-Z
0.2
0.3
0.4
0.5
-2Z
0.3
Time [s]
0.4
0.5
Pre-event
Post-event
5Y
4Y
3Y
2Y
Y
0
0
0.7
0.8
0.9
1
0.6
0.1
0.2
0.3
Time [s]
0.4
0.5
0.6
Fig. 5. Input current (above) and developed torque during redundancy
event.
During these redundant conditions, input current was
limited by introducing a high external resistance. It is
found that the best machine behavior is obtained for case
1. Total machine losses are the lowest compared to the
other cases.
Input currents for the case 2 and 3 are shown in Fig. 6
and Fig. 7, respectively. for Case 2 where one of the two
supplies experiences a partial fault condition causes a
reduction of input current approximately by 25%, healthy
supply current increases by 68%. Similarly, current
reduction in Case 3 by 65% causes an increase in the
healthy supply current by 92%. This asymmetry in input
currents causes more loss to be dissipated in the two last
redundancy cases compared to Case 1. Moreover, torque
pulsations like 6th and 18th appear due to asymmetry. Bar
losses increase as well.
VI. FAULT ANALYSIS
Several different fault cases have been studied, namely;
2×three, 2×two and single phase faults. All short circuits
are simulated without introducing any fault impedance.
Short circuit currents as well as induced currents in the
field windings have been investigated. Results show that
the 2×2-phase short circuit results in the highest currents,
see Fig. 8. Investigation of flux densities during the
different fault conditions show that 2×2-phase case results
in the highest stator saturation i.e. lowest machine
inductances and hence highest short circuit currents.
During single phase faulted phase experiences an increase
in the magnitude as expected, but the adjacent phases also
experience such an increase.
(a)
6
Current P.U.
0.2
7Y
6Y
0.6
Time [s]
Fig. 7. Input currents during redundancy case 3.
0.1
0
-5
0
0.1
0.2
0.3
0.4
Time [s]
0.5
0.6
0.7
0
0.1
0.2
0.3
0.4
Time [s]
0.5
0.6
0.7
4
Current P.U.
-3Z
0
Torque [N.m]
0.6
Time [s]
Z
886
Post-event
25%
2Z
Current [A]
Pre-event
68%
Current [A]
Pre-event
3Z
3
1
0
2008 13th International Power Electronics and Motion Control Conference (EPE-PEMC 2008)
(b)
0
-2
0
0.1
0.2
0.3
0.4
Time [s]
0.5
0.6
0.7
Current P.U.
6
1
0
T
0.95T
0
0.1
0.2
0.3
0.4
Time [s]
0.5
0.6
0.7
Faulted phase
Current P.U.
1.05T
4
(c)
5
0
Adjacent phases
-5
0
0.1
0.2
0.3
0.4
Time [s]
0.5
0.6
0.7
0
0.1
0.2
0.3
0.4
Time [s]
0.5
0.6
0.7
4
Current P.U.
Normal Supply
Square-wave supply
1.1T
2
Torque [Nm]
Current P.U.
4
2
0
Fig. 8. Per unit phase (above) and field current (down) for: (a) 2×threephase fault, (b) 2×two phase-fault condition and (c) single phase fault.
VII. SUPPLY WAVEFORMS
Different supply voltage waveforms have been
simulated. The aim is to investigate the impact of supply
voltage waveform on harmonic fields, machine losses and
developed torque. The studied voltage waveforms are:
1. Sinusoidal voltage: the ideal supply waveform.
2. Square wave voltage: With π / 4 P.U. peak and
with 1 P.U. peak.
3. Voltage Source Inverter “VSI” waveforms:
DTC scheme.
Analyzing the machine under square wave supply
facilitate understanding of machine’s behavior avoiding
the complexity of simulating the stepped voltage
waveforms as in DTC case. However, both are presented
here. Motivation behind studying two different square
waves with different magnitudes is to show the effect of
increased voltages i.e. higher flux level, than that the
machine is designed for. It is found that the square wave
supply results in high magnitudes of THD in stator
currents and voltage supply (25-50% higher than sinus
cases) and about 5-20% higher losses in total.
Instantaneous developed torque in case of sinus and
square wave with fundamental component equaling rated
voltage (i.e. π / 4 P.U.) peak, are shown in Fig. 9. The
torques have same DC value, but higher frequency torque
pulsations arise for the later case. An increase of
approximately 340% in pulsating magnitude for 12th and
24th components was found.
0
0.05
0.1
0.15
0.2
0.25
0.3
Time [s]
0.35
0.4
0.45
0.5
Fig. 9. Developed torque versus time at sinus and square wave supply
voltages.
Direct torque control “DTC” scheme embeds the
control of the motor and supply inverter together.
Switching of inverter devices is dependant upon the
electromagnetic state inside the motor. Control signals are
produced after comparing reference torque and flux values
with real time values and error band limited by hysteresis
control method. Such scheme leads to stepped voltage
with high harmonic contents and variable switching
frequency. The DTC although can have high THD in
supply voltage, the magnitude in stator currents is
considerably lower and with almost the same total losses
as for the sinus case, showing the effectiveness of the
DTC solution as far as power density of the motor is
concerned. For input voltage and current waveforms see
[16] . TABLE II compares the three studied cases.
TABLE II. COMPARISON BETWEEN SINUS AND NON-SINUS VOLTAGE
WAVEFORM: THD, LOSSES AND MAIN TORQUE PULSATION.*
Sinus
Square wave
DTC
THDi
-
++
+
THDv
-
++
+
Ȉ Losses
+
++
-
Iron Loss
-
=
=
Field winding
loss
6th
torque
pulsation
+
++
-
=
+
=
* Here “-, +, ++” indicate an increase in magnitude
while “=” sign indicates fairly compared figures.
CONCLUSION
A through analysis of VSI-DTC fed synchronous
machines is presented in the paper. Such drive
arrangement has been proved to provide a competitive
alternative for high power drive systems that demand a
high reliability operating conditions. The sensitivity study
of design parameters showed the possibility to optimize
the machine gaining a higher efficiency level by reducing
some of the losses. Redundancy analysis showed the
possibility of operating the machine at half load when one
supply system is totally or partially lost without exceeding
machine’s total losses. Saturation level inside the machine
varies with fault type that affects fault current as well as
field windings induced current during the fault. One
natural continuation of this work is to do a multilevel
optimization modal where the machine and the converter
are optimized together.
2008 13th International Power Electronics and Motion Control Conference (EPE-PEMC 2008)
887
ACKNOWLEDGMENT
The authors would like to acknowledge the support
from Prof. Tore Undeland (NTNU, Norway), Sonja
Lundmark (Chalmers University of Technology, Sweden),
Heinz Lendenmann (ABB Corporate Research, Sweden)
and Fredrick Kieferndorf (ABB Corporate Research,
Switzerland).
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[6]
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2008 13th International Power Electronics and Motion Control Conference (EPE-PEMC 2008)