Design and Control of an Hybrid Transmission with Electrical Power Splitting W. Hofmann
Design and Control of an Hybrid Transmission
with Electrical Power Splitting
W. Hofmann*, P. Tenberge**
* Chair of Electrical Machines and Drives, ** Chair of Machine Elements
University of Technology Chemnitz ; D-09126 Chemnitz, Germany
e-mail: [e-mail]
Phone:[phone], Fax.:[phone]
Acknowledgements:
We thank the  Deutsche Forschungsgemeinschaft which supports this project within its program
 Systemintegration elektrischer Antriebe
Keywords
Hybrid vehicles, permanent magnet motors, power transmission, ac machines
Abstract
A new kind of hybrid electric vehicle is described with power flow and distributing over an electric
train and mechanical drive. The electrical drive train consists of two motor/generators controlled by
inverters which are connected with a dc- link. One is connected with the combustion engine the other
with the sun wheel of the planetary gearing where both mechanical and electro-mechanical energy are
sumed again. The design of ac-drives, power electronics, and the total efficiency of the stepless po-
wer-distributed gear are discussed.
described in detail based on two equal-sized
Introduction
electrical machines of smaller power rates.
Certain merits of combustion engines and
Now for designing the main topics of the
electrical drives can be combined in hybrid
electrical components will be discussed.
vehicles carried out as serial or parallel power
transmission as reported in /1/. The junction
Transmission drive
between different drive types are given with
gears in switching or stepless modes. Further- The new hybrid concept is illustrated in fig.1
with two coupling shafts and a switching gear
more these gear boxes are necessary to adjust
the consumtion and power to optimal charac- for three driving ranges. This gear consists of
a planetary gearing III with bar as output shaft
teristics as shown in /2/ and /3/. Because the
power density of electric machines is reasona- and the distribution gear boxes I and II. The
energy splitting process can be described as
ble small, it can be better for the total petrol
consumption to use it in the gear box for ste- follows:
The drive shaft (an) is connected with the
pless transmission. Another way has been
hollow wheels of the planetary gearing steps I
propsed in /4/ with a new transmission based
and II and furthermore with the bar of the
on electrical power splitting. The first version
of practical realization became known recen- gearing step II. The so-called fast coupling
shaft is fixed to the sun wheel of step III. The
tly with the Toyota Hybrid System of PRIOS
/5/. This proposed special system is characte- hollow wheel can be combined with the gea-
ring package by the braking (B1). Three ope-
rized by a simple mechanical transmission part
but it is disadvantageous to use a higher po- ration ranges are possible. During the start
werful electrical machine and a smaller con- operation the fast coupling shaft (S) drives in
the switching gear. A high turning transmis-
trol machine with an higher total weight of the
sion to the output shaft (L) slow down.
vehicle. Therefore in /6/ an improved concept
with power splitting in three ranges has been
EPE '99 - Lausanne P. 1
Design and Control of an Hybrid Transmission with Electrical Power Splitting W. Hofmann
Design of the electric train
Depending on the definite hybrid system, the
power rating, and the speed operating ranges
different motor principles can be favorised.
An interesting special integrated double-stator
motor has been proposed for a series-hybrid
vehicle about 20 kW in /7/. A comparision for
using of high and low-speed transducers is
given in /8/ with different design results for a
parallel hybrid vehicle including an high po-
wer density electric drive of rating about
8 kW. Adapting for the principle with electric
Fig.1: Transmission principle (an: drive shaft
power splitting an electric drive in a medium
combustion engine; ab: off-drive shaft
speed range less than 6000/min is necessary.
wheels; LS: Power electronic, E1,E2:
Two types of ac-machines has been considered
electrical machines I,II,III: planetary
in the design process. These are the permanent
gearings; KV, K1, K2: couplings; S,L: fast
magnet synchronous machine (PSM) and the
and slow coupling shafts; B1: braking)
induction machine (IM). For both types a free
In the second operation range the regulating design has been made for a water cooled jack-
transmission is increased. The coupling (K3) et (VW = 5 l/h) than a normalized stator punch
can be closed during K2 is opened. and die set for an axis quantity of 132 has
The requirements for the electrical transmis- been chosen. The thermal rating is about
sion have been oriented on the normalized 1.7 kW therefore both types of ac-machines
drive cycles, the r.m.s. and peak torque values can be investigated in the given size. Conside-
could be determined by the simulation accor- ring a torque density limit value of 15 kN/m2
ding to fig.2. for operating time of 50 min determined for
water-cooled ac-machines at rated speed about

3000 min-1 the possible inner diameter and


length of the iron stack could be realized re-

garding to the desired size.



Synchronous motor

At first a non-salient pole machine with air-

gap permanent magnets has been intended

because the field-weakening range is not so
wide and the partial-load efficiency is higher

than known from induction motors. Because

of thermal stability and better corrosion resis-
Fig.2: Operating range of machine I and II
tance Sm2Co17 magnets has been used. Two
  r.m.s. torque,    peak torque
principal design variants for the PSM have
been studied:
The result shows a normal speed range up to
1) The motor is designed for this rated voltage
6000 /min for machine I. The requirements of
which is determined by the dc-voltage
the machine II is little smaller but the size
2) The motor is matched on a smaller rated
choosen is the same. Some different utilization
voltage as given from the available dc-
rates for both and a high peak torque value are
voltage for using the higher voltage reserve
important. Other solutions with pseudo-high
to impress the maximum torque
speed ranges are thinkable but it requires a
In case of 1) the dc-voltage determines the
modified construction of the mechanical
rated voltage. Because the maximum torque is
transmission part. The data from fig.2 are the
required near the rated speed the dimensioning
defaults for the machine design and power
of the machine has to be done that the concer-
electronics discussed in the next chapter.
ning q-axis current can be impressed.
EPE '99 - Lausanne P. 2
Design and Control of an Hybrid Transmission with Electrical Power Splitting W. Hofmann
&!S
From the voltage equations: 2
U1max 2 - (&!S LS Iq ) -U
PN
&!SN
(6)
(1) Id =
= - &!s Ls I q
U d
&!S LS
(2) These conditions have been considered for the
= &!s Ls I d + U P
U q
first design of a 4-pole PSM with surface ma-
considering of a standby voltage about 10%
gnets over a pole arc of 78% of one pole-pitch.
the acceptable synchronous inductivity for the
This gives the best results of the current har-
working point of peak torque desire is given
monics and also of the torque ripples. The
with:
field distribution is displayed in fig.3, where
some saturation areas near the pole edges and
(1 - ks)
2
2
(3)
= nN M N (0.9UN ) -UPN
M 1
in some teeths can be seen.
p &!N Ls
n I
1 N
where
: saturation coefficient
kS = / 2V´
"VFe½
½
: ratings
M , nN , IN
N
: pole pairs
p
: maximum power point values
M1, n1
4 Ä„
öÅ‚
: emf
sinëÅ‚Ä… ÷Å‚
= 2 Å"3p
U &! B k ìÅ‚
PN N ´ m à p
Ä„ 2
íÅ‚ Å‚Å‚
and then the magnetical air-gap is determined
with the synchronous inductance defined with:
3
(4)
µ0 1 li Di
= ( ¾l )2 k L + LÃ
L w
s
Ä„ p2 ´ m
where : inductivity factor.
kL
Fig.3: Induction of the 4-pole PSM at rated load
Because the windings are given with the
The exact design results have been summari-
m.m.f. and air gap induction required for tor-
zed in table 1.
que production, the main field voltage can be
In case of 2) the rated voltage is defined to a
limited if the right magnetic height is chosen
lower value as given with the constant dc-link
from:
voltage. If the maximum current for building
2
ëÅ‚
&!(wl¾l )liDi 3µ0 ÷Å‚
2
ìÅ‚
Uh = (2 2B´ ) + IS(wl¾l )öÅ‚ (5) the peak torque is required the control factor
ìÅ‚
of the pwm inverter is shorttime increased to
Ä„ p´m ÷Å‚
íÅ‚ Å‚Å‚
obtain the full output voltage on the motor
In general it follows a large magnetic height,
terminal. This corresponds with a very large
higher then given to keep the magnets from
voltage standby. The costs decreased on the
irreversible demagnetizing because it is not
motor side with a smaller magnet volume are
allowed to increase the synchronous inducti-
partially compensated through an higher di-
vity over 0.5 mH. Besides the higher costs for
mensioning of the dc-link and the inverter
magnet materials the current ripples are in-
blocking ability. Furthermore the voltage
creased and it is just as necessary to improve
range of the linked battery must be so enlarged
the switching frequency of both inverters.
that a serie-connected arrangement of partial
Another fact should be considered in the range
cells with a higher total volume will be neces-
of field weakening where a higher negative d-
sary. Besides one has to consider that a bad
axis current is required because of the small
voltage utilization is given because of the high
inductivity.
difference between the needed winding isola-
To keep constant the air gap power the q-axis
tion and the rated voltage. A further positive
current is changed with indirect proportiona-
effect is obtained for the smaller absolute d-
lity dependent on the frequency.
axis current needed in the field-weakening
From eqns. (1) and (2) considering the maxi-
range. It can be calculated with eqn. (6) where
mum voltage near rated point it follows the
the increased maximum voltage is inserted.
d-axis current above the rated frequency with
EPE '99 - Lausanne P. 3
Design and Control of an Hybrid Transmission with Electrical Power Splitting W. Hofmann
Special improvements are investigated in pa-
max. torque 85 Nm air gap 1 mm
rallel regard to the reduction of the rotor mass
with using of 6-pole machine and furthermore
3700 magnet
if the additional reluctance torque about 15% at max. speed 7.6 mm
min-1 height
will be utilized after reducing the magnet pole
total max. 6000 outer
arc and increasing the rotor bar to the air-gap.
206 mm
speed min-1 diameter
The expensive magnet materials and special
construction are the reasons to contemplate the
pole pairs 2 slot number 36
cheaper ones of the induction machine with
following results. To avoid the saturation ef-
fects the same iron stack as before in case of
power factor 0.7 slot depth 22 mm
4-pole variant has been used and the field
distribution shows a better result, see fig.4 and rated
0.938 slot width 6.6 mm
efficiency
/10/.
air gap
0.7 T pole arc 0.8
induction
dc-link
250 V
voltage
Design II
magnet 3/5/8
pole pairs 3
heights mm
rated dc-link
0.945 400 V
efficiency voltage
Table 1: Design parameters of the PSM
Induction motor
In this case the classical design steps for an ac-
Fig.4: Induction of the 6-pole PSM at rated load
machine can be used because the maximum
Furthermore the surface magnet has been con-
torque and the coresponded current is limited
figurated in a 3-level surface magnet over the
only from the leakage inductances and they
pole arc of 0.8 of one pole pitch. The different
are smaller then the synchronous inductivity
heights have been optimized at the working
of the PSM. After calculation of the estimated
point of peak torque regarding to the minimal
parameters a certain correcture of the air-gap
magnet volume with help of evolutionary
has to be done. Therefore the on-load current
strategies. For reducing the latching (dwell)
is a little bit higher then for normal ac-motors.
torque the stator iron stack has been skewed.
Because the maximum stator current has to be
Regarding the needed d-axis current in the
impressed on the basis of the choiced dc-link
field-weakening at the limited speed 6000 rpm
voltage the total leakage inductance should be
it is shown that the second design needs only
limited.
40% of the d-axis current compared to the
For improving the performance the change of
first motor version. The design results are put
the aluminium bars with a copper cage could
in table 1.
be done in future to reduce the rotor losses
about 20%. So far the same size as choiced for
Design I
PSM can be used.
inner
Power electronics
Rated voltage 112 V 128 mm
diameter
For converting the energy and adapting the
Rating 9 kW stack length 75 mm
torque and speed relations between both
electrical machines two pwm-inverters
3000
connected by a common dc-link has been
rated speed windings 48
min-1
used, see fig. 5.
EPE '99 - Lausanne P. 4
Design and Control of an Hybrid Transmission with Electrical Power Splitting W. Hofmann
Further points of view can be important for the the efficiency in the normal speed range. Only
inverter design. Some special remarks for in the field-weakening operation the relation
feeding of permanent synchronous machines between the d- and q-axis currents can be op-
have been given in /9/. Accordingly it is timally controlled. This requires to search an
possible to regenerating the energy on the dc- optimum going out from:
link should be taken into account if the signal
PV = PV Fe + PVCu
processing is broken down. This requires a
(7)
2
( + )2
voltage proof about 500 V. The maximum
= &! Ld I d ¨P +
R
Fe
output current should be 180 A of r.m.s
2
îÅ‚ Å‚Å‚
values to realize the peak torque desire.
ëÅ‚ &!( + )öÅ‚
L I ¨
d d P
2
+ R + ìÅ‚ + ÷Å‚ śł
ïÅ‚
I I
d q
ìÅ‚ ÷Å‚
Although the dc-link is connected with a
R
ïÅ‚ íÅ‚ Fe Å‚Å‚ śł
ðÅ‚ ûÅ‚
battery about 300 Wh, which is from NiMH-
type suitable for fast load cycles. An electro- and it obtains:
nic braking resistance is also inserted in the
&!Ld (R + RFe )¨P
(8)
= -
dc-link. All power modules are mounted on a I dopt
2
RRFe + &!2Ld (R + RFe )
common water cooled heat sink.
The optimal d-axis current is negative and
independent on the load current Iq. More im-
provements are possible if the construction of

the PSM is enlarged to a salient-pole machine.
Efficiency controlled IM
In this case an optimal efficiency-control has
got an higher effect because the most usual
operations appears at the non-field-weakening
operating range. From the power-losses:
= PVsCu + PVrCu + PVFe
P
V
2 (9)
ëÅ‚ öÅ‚
ëÅ‚ öÅ‚ (Lh Å" &!)
R R
Fe r
÷Å‚
= I 2 ìÅ‚ + ÷Å‚ + I 2 ìÅ‚ Rs +
R
sq s sd
ìÅ‚
+ Rr ÷Å‚ ìÅ‚ RFe + Rr ÷Å‚

R
íÅ‚ Fe Å‚Å‚
íÅ‚ Å‚Å‚

and considering the iron-losses resistance be-

cause of the higher stator-frequency the d-axis
Fig.5: DC-link pwm-inverters with battery
current can be minimized dependent on the
q-axis current:
Transmission efficiency
( + Rr ) + RFe Rr
R R
s Fe
(10)
=
The efficiency of the gear transmission is de- I sd I sq
( + Rr ) + ( &! Lh )2
Rs RFe
pendent on the quality of mechanical part at
first because a small quantity of average po-
where is:
wer is converted over the electrical transmis-
(11)
M = 3 p Lh I sd I sq
sion about 10-15%. Nevertheless high effi-
ciency of the electrical train is desired. The
The needed limit for further flux reduction is
frequently operations at partial load is usual
considered because of the dynamic perfor-
for this application. Therefore some control
mance from partial to full-load operations.
methods has been discussed concerning dif-
Efficiency of power electronics
ferent machine types in the respective opera-
tion ranges and the choice of the voltage rate
The losses of the power electronic devices are
considering the inverter losses.
determined by the switching and the on-state
power losses. The respective values have been
Efficiency controlled PSM
calculated for the efficiency quality of one
The calculation of the efficiency of PSM has
inverter and are shown in fig. 6.
been obtained in form of the so-called shell
From these results a rounded design of the
curves. PSM from the non-salient-pole type
control strategies is necessary. These require
can not be adapted by control for improving
EPE '99 - Lausanne P. 5
Design and Control of an Hybrid Transmission with Electrical Power Splitting W. Hofmann
to consider the power losses of the power de- ver the efficiency of the total transmission
vices in a common loss-model of pwm- including the mechanical and electrical parts
inverters including the forward power losses behaves about 92% because the partial power
of the IGB-transistor and the switching losses through the electrical train is lower than 15%.
of transistors and diodes based on a measured
·
specific loss-energy proposed in /10/ with:


PVinv = PVC (T ) + PVS (T ) + PVS (D)

(12)

îÅ‚
2 1
= ïÅ‚ ëÅ‚UCE + fc (ein(T)+eout(T) + eout(D))öÅ‚ Ia(eff)
ìÅ‚ ÷Å‚

Ä„ 2
íÅ‚ Å‚Å‚
ðÅ‚

1
+ rCE I 2 Å‚Å‚ Å"6
a(eff)
śł
2
ûÅ‚

In case of the IM it means that linear and qua-

dratic dependent terms of the r.m.s. output
current have to be considered, it follows a
numerical solution of the optimization pro-

blem. The power-losses arisen in power devi-


ces are more important if the switching fre-

quency fc is higher than 8 kHz and it operates
Fig.7: Total efficiency of electric transmission
at the partial-load region. Than the optimiza-
PSMI: inner pole type,
tion result has been inserted in the calculation
PSMA: outer pole,
tool for comparing the total efficiency of the
ASM: induction motor
electrical transmission obtained at different
ASMOPT: efficiency optimized IM
load-cycles. Fig.7 shows the result distinguis-
hed in several machine-types included the
Control of the drive train
respective inverter with consideration of effi-
ciency-optimized mode in the base speed The control strategy is harmonized with the
range. vehicle modes. Four different strategies have
been developed:

a) Inside of traction ranges: Load-control of



EM2 and cascaded speed control

b) Change of traction ranges: Speed control of


EM2 and pressure control of switching
elements
c) Storage operation: Load control of both

machines and cascaded speed control
d) Start-up and shunting: Speed control of
both machines and pressure control in the


starter element.
The regulation of the machines are based on
the rotor-oriented control scheme in that case


of using the PSM, shown in fig.8.


Fig.6: Power losses of inverter








Therefore the total efficiency is no greater





É ¨



than 80% because we have series-connected




machines E1 and E2 with assigned inverters






regarding to the energy-flow. Nevertheless the
best results have been obtained with using of
PSMs, on the other hand a fully optimized
Fig.8: Control structure of PSM
controlled IM with consideration of power
electronics shows comparable results. Howe- Further it was necessary to insert a special
EPE '99 - Lausanne P. 6
Design and Control of an Hybrid Transmission with Electrical Power Splitting W. Hofmann
limitation bloc for the stator current in the the interactions between the different control-
field-weakening range. The right d-axis cur- lers for EM1 and EM2 are shown in fig.10.
rent is given from an overlayed voltage limi-
tation control-loop.
Unlike a control method for hybrid vehicles
based on feedback linearization which was
described in /11/, in this case a dynamical
system linearized at the working point has
been provided. Therefore it is possible to use
simple controllers for decoupling and regula-
ting the desired power-flow through the
transmission trains. The control action after a
speed reference step of 100 rpm is given in
fig.9.
(a): Torque response of torque controlled motor I














(b): Rotor speed of torque controlled motor I


















(c): Torque response of speed controlled motor II
Fig.9: Step responses of speed and d,q-axis
currents
The drive and generator control consists of a
torque control-loop with optionally cascaded
speed control-loop so that the power-flow can
be continiuously guaranteed through both
converters with consideration of flow-
direction to the battery storage and back. The-
refore an auxillary control-loop of the dc-link
voltage is necessary as well. The machine
control itself is based on the rotor-position
oriented or field-oriented control principle for
(d): Speed response of speed controlled motor II
PSM or IM. Some simulation test results of
EPE '99 - Lausanne P. 7
Design and Control of an Hybrid Transmission with Electrical Power Splitting W. Hofmann
/3/ Dietrich, P.; Eberle, M.K.: Das ETH Hybrid
II Antriebskonzept. VDI-Berichte Nr.1225
(1995) S.27-43
/4/ Tenberge, P.; Hofmann, W.: Stufenloses
Fahrzeuggetriebe mit elektrischer Leistungs-
verzweigung. VDI-Berichte 1346 (1997)
S.83-114
/5/ Yaegashi, T.: Toyota Hybrid System THS.
Toyota Motor Corporation 1997
/6/ Tenberge, P.; Hofmann, W.: Mechanisch-
elektrische Fahrzeuggetriebe im Vergleich.
(e): Power responses of electrical train
VDI-Berichte 1393 (1998), S.551-576
Fig.10:Torque, speed and power step responses of
the electrical transmission
/7/ Bäckström, T. et.al.: Integrated Energy
Transducer Drive for Hybrid Electric Vehi-
In this simulation tool the complicate transfer
cles. EPE 97 p.4.721- 4.7261
function of the entire planetary gear box has
/8/ Krasser,B.; Lorenzen,W.: Comparision of
been modelled as a linear two-mass system.
Electromechanical Transducers for an Auto-
The pulse-frequency used of the inverters was
nomous Hybrid Vehicle. EPE 97 p.4727-
10 kHz. The obtained on-time of the torque is
4732
about 50 ms, what is usual for hybrid vehicle
/9/ Ackva,A.; Binder,A. et al.: Electric vehicle
applications in connection with the power
drive with surface-mounted magnets for wide
electronic devices. The power losses can be
field-weakening range. EPE 97. p. 1548-1553
seen in fig.10(e) as the power difference bet-
/10/ Bober, G.: Vergleichende Untersuchung
ween E1 and E2. Summarizing the simulated
schneller abschaltbarer Leistungshalbleiter für
and calculated results it can find out that the
ihre Anwendung in Pulswechselrichtern. Diss.
economy of this new transmission principle is
1994, Berlin
very good since a vehicle with a mass of
/11/ Mayer,T.; Schröder, D.: Simulation and
1475 kg and a TDI-motor of 66 kW needs
Hierarchical Controller Design for a Special
4l/100 km because the recuperating energy can
Hybrid Drivetrain. EPE 95 p.2.407-2.411
be reused.
/12/ Paul, M.: Studie zur Auslegung permanenter-
regter Synchronmaschinen. TU Chemnitz.
Conclusion
Mai 1999
A new efficient drive system for an hybrid
vehicle based on electrical power splitting
over a motor-generator system connected by
two inverters and dc-voltage link has been
described. Some design aspects for using of
permanent magnet synchronous or induction
motors have been discussed and simulated.
The performance of a good step response cha-
racteristic could be proofed. Further investi-
gations have been done to verify the advanta-
ges of this principle for a better economy and
drive conveniences.
References
/1/ Kahlen, H.; Maggetto, G.: Electric and Hy-
brid Vehicles. EPE 97 p.1.030-1.054
/2/ Vollmer, Th.; Höhn, B.: Der Autarke Hybrid:
Auslegung des Gesamtsystems. VDI-Berichte
Nr. 1225 (1995) S.9-26
EPE '99 - Lausanne P. 8