AN EFFICIENT I'HH 'IKClINlQUE FOR S P L I T PHASE INDUCTION HOTOR
OPERATION USING DUAL VOLTAGE SOURCE INVERTERS
K. Gopakumar
Scientific Officer
CEDT
V .T . Rqngana than
Assoc. Professor
Dept. of Elect.Engg.
S . R . Bhat
Asst. Professor
CEDT
Indjan Institute of Science
Bangalore 560 012, INDIA
ABSTRACT
Split phase induction motor operation from dual
PWM voltage source inverters offers the advantage of
reduced voltage rating for the inverter devices. In
addition, a total of 4 9 different locations are
possible for the resultant stator voltage space
phasor. The outermost locations form a twelve sided
polygon. By space phasor PWM generation based on the
vertices of the twelve sided polygon, a higher range
of fundamental motor voltage is possible in the
modulation range, up to 0.643 VD , where VEC is the
DC link voltage for an equivalen$ 3 phase inverter,
as compared to 0.577 VDc for the three phase motor.
This is brought about by the presence of 5th and 7th
harmonics in the average poler voltage waveform.
These harmonics get eliminated in the air gap mmf
because of the winding disposition.
However, they
cause stator Currents to flow and these currents are
limited Only by the stator leakage impedance. At low
speeds, these currents can be very high.
In this
paper a PWM strategy is proposed for a split phase
induction motor drive, wherein at IOW speeds each of
the inverters is operated with conventional three
phase space phasor modulation, thereby avoiding 5th
and 7th harmonics in the motor voltage. At the
higher end of the speed range a voltage space phasor
modulation based on the twelve sided polygonal
vertices is used, so that the benefit of a higher
speed in the modulation range is retained.
A
technique for achieving the transition to that range
without current transients is proposed. The scheme
is verified through computer simulation, using a
space phasor based model of the split phase motor.
Details of a practical control circuit for voltage
space phasor based PWM pulse generation are presented
and the results from an experimental drive are
highlighted.
1.
FIG.la
S P L I T PHASE I M D R I V E
[Fig. 11 are independent of each other a total Of 4 9
different voltage space phasor locations result for
the split phase drive ( ~ i g .2 ) . The switching states
of t h e i n v e r t e r f o r e a c h voltage s p a c e phaSor
location, are indicated in Fig. 3. The voltage space
phasors f r o m the i n d i v i d u a l l i n v e r t e r s f o r m a
B
.A
INTRODUCTION
When the phase belts of a 3 phase induction
motor are split into two equal halves, a split phase
induction motor results with two sets of stator coils
with their axes separated by thirty electrical
degrees. Such a machine can be operated from dual.
voltage source inverters (Fig. 1 ) . The voltage
ratinas for the inverter devices are, in this case,
C
/
I
'C
c 4.35
(4#4')
FIG.2
I N T E R I O R SPACE PHASOR COMBINATIONS
One possible PWM technique is to operate each of
the i n v e r t e r s i n d e p e n d e n t l y w i t h s p a c e phasor
modulation [2]. Each inverter will then generate the
vertices of the corresponding hexagon. The resultant
space phasor of motor voltage is then obtained by
vector addition of the space phasors generated by the
individual inverters. If the same voltage reference
is given to both the PWM generators, then the two
individual voltage space phasors will be separated by
30 electrical degrees. However, if the reference for
the lagging phase group ( A ' B ' C ' - Fig. 1) is delayed
by 30 electrical degrees, the individual voltage
space phasors will be in the same direction and will
add directly.
By this means, a maximum value of
0.89655 VDc can be achieved for the resultant voltage
space phasor. This corresponds to an equivalent
three phase peak fundamental phase voltage of 0.5977
V c, as compared to 0.577 V D for a conventional 3
ptase drive [1,2]. Since ea& inverter is operated
with conventional three phase space phasor based PWH,
using the hexagonal vertices, the average pole
voltage waveforms contain only the third harmonic in
addition to the fundamental.
In the absence of
neutral, the third harmonic voltages do not result in
any current flow t1.21.
An alternative PWM technique is possible for the
split-phase machine based on the vertices of the 12sided polygon [Fig. 31. In this method PWW patterns
for the two inverters are generated by switching
between the vertices of each of the 12 sectors of the
polygon as appropriate [l].
The maximum resultant
voltage space phascr that can be generated by this
method is 0.9659 VDc.
This corresponds t o an
equivalent three phase peak fundamental phase voltage
of 0.643 V
for the motor.
The extra boot in
voltage is Dostained because of the introduction of
the 5th, 7th, 17th. 19th, etc. harmonic components in
the average pole voltage waveform [ l ] . The stator
mmfs due to these components cancel out in the air
g a p , b e c a u s e of the winding d i s p o s i t i o n , and
therefore will not contribute to torque ripple.
However, the corresponding components are present in
the stator currents and their amplitude is only
limited by the stator impedances. Therefore if the
PWM technique is used down to the low speed range,
the current stress on the inverter devices at low
frequencies may be objectionable.
In this paper a PWM strategy is proposed for the
split phase drive, wherein the first technique
described above (using the hexagonal vertices) is
used in the low speed range and the technique based
on the 12 sided polygon is used in the high speed
range. By this means the advantage of higher motor
voltage in the modulation range is retained while
avoiding high currents at low frequencies.
Section 2 and 3 give the principle of P W M
g e n e r a t i o n f o r t h e a b o v e mentioned technique.
Section 4 describes the hardware details of the PWM
pattern generation. This includes the circuit for
s m o o t h t r a n s i t i o n b e t w e e n t h e two techniques.
S e c t i o n 5 p r e s e n t s the s i m u l a t i o n a s well a s
experimental results.
The simulation is based on
space phasor equations of the machine, the details of
which are given in Section-6.
t
FIG.4
583
SAMPLED REFERENCE VECTOR I N A SECTOR
2. GENERATIO$ OE' CIRCULAR TRAJECTORY FOR TNE VOLTAGE
SPACE Pli.ZLOit U S i N G IIEXAGONAL VERTlCES
A r e f e r e n c e s p a c e phasor with a c o n s t a n t
amplj.tude along a circular trajectory can be
approximated, in a sector, by switching between the
vertices of the corresponding sector and the zero
vector state (Fig. 4 ) [1,2].
Fig. 4 shows a sampled
reference vector (V_ ) in a sector; Y1 and y2 are the
start and end vertfces. for a sector. The sampled
vector 41 during T, (T,-sampling period) is generated
by switchng between y1 (for a period T1) and
(for
a period T2) and the zero vector (for the remaining
period To) such that the volt seconds produced by the
Y2 and the zero vector along the axis-a and axisb (Fig. 4 ) will be equal to the volt seconds produced
by the V vector along 'a' and 'b' axes [1,2,3]. The
switchi;;
states appropriate for all the sectors are
shown in Fig.3. The equations for T1, T2 and To are
as shown in eq.(l) [l]
T, = sampling period
(3)
OSWtC30'
VAO
(AVERAGE)
30 5 Ut C 90"
VA AVERAGEz%SIN(Wtt
43-
v2
vl,
FIG.5
T1 =
-k
T, sin (60 - a)
- THREE PHASE MOTOR
13
The averaqe pole voltage variation for phase A
using the 12 sided polygonal vertices is shown in
Fig. 6 111. A harmonic analysis of the pole voltage
waveforms shows that apart from fundammtal (V
x
cos15 x 2/3), it contains harmonics of the ordrr t'th,
7th, 17th, 19th, 29th, etc. [l].
Since these
harmonics will not contribute to the air-gap mmf due
to the split phase motor configuration, the current
produced by these harmonic voltages are limited by
the stator impedance only. In the proposed scheme,
the 12 sided polygonal vertices are used only in the
upper frequency range (i.e. from 0.8965 VDc t o 0.9659
V D c ) ; the harmonic current amplitudes due to these
harmonics are limited when compared to a scheme [l],
where the 12 sided polygonal vertices are used for
t h e e n t i r e f r e q u e n c y range. T h u s by using t h e
hexagonal structure for the lower frequency range and
the 1 2 sided p o l y g o n a l v e r t i c e s in the upper
f r e q u e n c y r a n g e for the voltage s p a c e phasor
generation, an efficient PWM strategy results.
1.
T2
= -
I: T, s i n
a
13
where 0 k I0.866
T, = sampling period.
The average pole voltage variation for phase-A
in a sector-1 can be computed using the following
equation [21
vA0 (average)
=
'r
~ -t2T~ +
2
To
T~ -
AVERAGE POLE VOLTAGE V A R I A T I O N
'DC
-I
~-
2
2 cos 15
x -
12)
TS
Here the zero state interval To is divided equally
between the two zero states ( + + + I and ( - - - ) and is
located at the start and end of a sampling period
[3].
Eqn. ( 1 ) can be substituted in eqn. (2) for
v a r i o u s s e c t o r s and the a v e r a g e p o l e voltage
variation can be determined and is shown in Fig. 5
[21. H e r e the average p o l e v o l t a g e v a r i a t i o n
consists of 3 fundamental [(2/3) (VDC/2cos15) x cos
30) and a third harmonic component. Since the third
harmonic will cancel out in a three phase system
without neutral, a sinusoidal average variation for
the motor phase voltage can be obtained using the
hexagonal vertices for the voltage space phasor for
the individual inverters. In the proposed scheme the
two individual inverters are switched with a 30'
phase shift, s o that the scalar addition of the
resultant voltage space phasors is possible. So with
this, the maximum amplitude of the resultant voltage
s p a c e phasor for a c i r c u l a r t r a j e c t o r y is
[(VDc/(2cos15)) x cos301 x 2 = 0.8965 VDc.
3 . VOLTAGE SPACE PEASOR GENERATION U S I N G 1 2 - S I D E D
POLYGON VERTICES [11
As in the case of hexagonal vertices for the
voltage space phasor, the periods TI, T2 and To for
the 12 sided polygonal vertices can also be computed
and is shown in Eqn. ( 3 ) [l].
T1 = 2 kTs sin (30-a)
T2 = 2 kT, sin a
T = T - (T t T2)
O o ( k 7 0.96&9
c
V
I
FIG.6
AVERAGE POLE VOLTAGE V A R I A T T O N
- S P L I T PHASE MOTOR
4.
PWlI PATTERN GENERATION
A simple V/f control is used for the present
scheme and is shc?wn in Fig. 7. The speed reference
signal gives the control signal for the output
voltage and 9iitput frequency. The speed reference
signal is converted into a 6 bit ADC output (V,) and
The
is connected to the higher address of EPROII-1.
VCO output is passed through a divide by twelve
counter, the lower 4 bits of which address (a) the
next lower address of the EPROM-1. The lowest 5 bits
of EPROM-1 are addressed by a 5 bit up-down counter
(This divides a sampling interval T in to 32 parts)
with a frequency of 64 kHz. EPR0I.I-9 stores the time
intervals T1, T2 and To for each Ts interval (500
psec) with a resolution of 32 samples per sampling
interval Ts. These are computed using eqn. ( 3 ) (for
the 12 s i p d polygonal vertices) f o r 16 different a
values ( 2
and 6 4 (26) different xS values in a
sector. It can be seen that the time duration for
T1, T2 and To are the same for all 12 sectors for the
same a and
This requires an EPROm with 1 5
address lines or 32K memory.
In EPROM-1, the
(for Yl
duration for T0/2 (initial zero state),
state), T2 (for 4 state) and T0/2 (for 7inal zero
state) are stored as bit patterns 00, 01, 10 and 11
respectively for a particular a and E, in a sector
[1,3].
In EPROM-2 the switching patterns are stored
according to each of 12 sectors for each of the above
bit patterns. EPROM-2 is addressed by the output of
EPROM-I and the sector information from the counter.
The output of EPROM-2 is used for the inverter gating
signals.
FROM SPEEO
REFERENCE
I
Vs
DATA
6BIE
MS8.
A/O
vco
vs.
J
BliS
SECTOR
a
P W M PATTERNS USING
HEXAGONAL VERTICES
Since the hexagonal structure is used for the
lower frequency range (up to an output maximum
circular voltage space phasor amplitude of 0 . 8 9 6 5
VDc) only 5 bits are used for the reference vector
E,. For the hexagonal vertices the span of ‘ a ’ in a
sector is 6 0 ’ .
So 5 bits are used for the a span and
3 bits are used for the sector (6-sector).
This
e n s u r e s the equal d i v i s i o n o f a s p a n for the
hexagonal as well as the 12 sided polygonal space
phasor structure. For the hexagonal structure the
address of EPROM-3 (periods T1, T2 and To for the ABC
phase group) for the a position is incremented by 30’
by the phase shifter in Fig. 7 . EPROM-4 stores the
inverter switching pattern for the ABC phase group.
In EPROM-5 the switching periods for the A’B’C’ phase
group are stored and EPROM-6 gives the switching
pattern f o r the A‘B‘C‘ phase group. The switching
intervals T1,T and To for the hexagonal vertices are
stored as in tie case of 12 sided polygonal structure
using the eqn. (1). From Fig. 7 , it can be seen that
the same speed reference signal addresses the EPROMS
for the 1 2 sided polygonal voltage-space phasor
operation as well as the hexagonal structure. The
switching pattern for the hexagonal structure is used
up to a certain frequency range, i . e . , upto 40 Hz,
above which (up t o 5 0 tiz) the 12 sided polygonal
structure is used.
This is decided by t h e final
selector block of Fig. 7 . Uhen the speed exceeds a
threshold l e v e l (example 4 0 Hz) the selector
immediately notices this using a comparator and it
waits for the next immediate zero states for all the
inverters to switch over to the 12 sided polygonal
structure.
5.
6 BITS
L
A
d
I
t
I
(A’8C.I
FIG.7
PWM PATTERN GENERATION
BXPBRIHENTAL VERIFICATION
An experimental model of the proposed scheme is
tested with a 2.5 KW split-phase motor.
fig. 8a
shows the motor phase currents of the split-phase
group A and A ‘ . The sinusoidal nature of the current
is because the hexagonal structure is used for the
voltage space phasor PWH generation.
The computer
simulation of the same is shown in Fig. 8b in TUTSIM
[21. The theoretical model developed for the motor
is explained in a lat,er section. The experimental
setup is driven using the 12 sided polygonal vectors
for the voltage space phasor FWM generation. Fig. 9a
shows the motor phase current and its harmonic
spectrum under no load operation. Fig. Ya shows the
presence of 5th and 7th harmonic currents i n t h e
motor phase. As these currents will n o t contribute
to the air-gap flux, the impedance seen by these
harmonic currents are due to the stator impedance
only. H e n c e the larger a m p l i t u d e s for these
harmonics at lower speeds. The computer simulation
of this is shown in Fig. 9b.
FIG.8a
PHASE-A AND A ’ CURRENTS - EXPERIMENTAL
RESULT ( P W M U S I N G HEXAGONAL V E R T I C E S )
585
The motor configuration is simulated for the
hexagonal structure as well as 12 sided polygoiial
structure and the transition between these two stages
under no load operation is shown in Fig. 10. The
system is operated under no load with simple V/f
control without any speed feedback. It can be noted
that there is a slight oscillation in the speed.
This can be corrected with a simple feedback loop.
Fig. 11 shows the transition under full load. Thus
with a simple speed feedback loop, the split phase
motor under voltage space phasor PWM operation can be
implemented for the full frequency range without any
current and torque transients. Thus this scheme
H:Hz
V:MRG
2 . OOKHz
0.00
FIG.8b
PHASE-A
AND A '
( S I M U L A T E D RESULTS
-
CURRENTS AND VOLTAGES
PWM U S I N G HEXAGONAL
VERTICES)
offers much bettei performance regarding voltage
range as compared to conventional 3-phase scheme,
still being in pulse width modulation.
6. S P L I T PHASE HOTOR M O D E L
COORDINATES
1
FIG.9a
I N S P A C E PIIASOR
PHASE-A
12-SIDED
CURRENT SPECTRUM
-
PWM U S I N G
POLYGONAL V E R T I C E S
In this section an equivalent motor model for
the split phase induction motor is derived. The
voltages and currents for the split phase groups are
derived in space phasor form.
The voltage and
current equations for each phase group is derived
with respect to its own reference axis; the reference
axes for each are phase shifted by 30'
(Fig. 12).
For the rotor equation the conventional three-phase
axis is used.
TUTSUIM
Stator-2 (ABC-phase group)
is1
eJ30~
(5)
Rotor
-
defined with respect to rotor axis
Eqn. (6) can be written in terms of the rotor c u r r e n t
referred to the lhxee-phase (Fig. 1 2 ) stationary axes
as :
FIG.9b
12
PHASE-A
CURRENT SIMULATED
S I D E D POLYGONAL V E R T I C E S
USING
where
R, - six-phase stator resistance per phase
;ss - six-phase stator self inductance per phase
- rotor resistance per phase
LRR - rotor self inductance per phase
L
- rotor t o six-phase stator mutual inductance
(HR-olz)Lss i s the mutual i n d u c t a n c e c o u p l i n g
coefficient term between the six-phase stator group
including the leakage coupling coefficient.
E - Rotor axis position with respect to 3 phase axis.
FIG.10
T h e s e e q u a t i o n s a r e used for the s i m u l a t i o n s
presented in the paper. From the above equations the
steady state equivalent circuit can be obtained and
is shown in Fig. 13.
--
L
T R A N S I T I O N FROM HEXAGONAL V E R T I C E S
TO 1 2 S I D E D POLYGONAL V E R T I C E S AT 4 0 H Z
(UNDER NO LOAD O P E R A T I O N 1
586
&ED
AX'S
\L
REFERENCE A X I S \ ' \
I
FIG.ll
I
I
I
I
I
I
CONVENTIONAL
, / 3 - PHASE AXIS
l-i
A' B Y
1
E
'. I
1
REFERENCE AXIS FOR
A B C PHASE GROUP
I
T R A N S I T I O N UNDER F U L L LOAD
FIG.12
SPACE PHASOR REFERENCE A X I S
( T R A N S I T I O N FROM HEXAGONAL STRUCTURE TO
1 2 S I D E D POLYGONAL STRUCTURE AT 4 0 H z )
7. CONCLUSION
An efficj.ent voltage space phasor based PWM
strategy for the split phase motor is developed.
This scheme offers a wide speed range within the
modulation range, more than that of a conventional
scheme. T h e n e c e s s a r y P V M s c h e m e developed i s
explained. An appropriate model for the split phase
mootor i s developed and used i n the computer
simulation.
REFERENCES
K. Gopakumar, et al., 'Split phase induction motor
operation from PWM voltage source inverter'. IEEE,
IAS Conf. Sept. 1991.
H.W. V a n d e r B r o e c k , et al., ' A n a l y s i s and
realisation of a pulse width modulator based on
voltage space phasors', IEEE Trans. IA, Vol. I A 2 4 , No. 1, Jan-Feb. 1988.
Holtz, J., et al., 'High speed drive system with
ultrasonic MOSFET PHI( inverter and single-chip
microprocessor control', IEEE TRans. IA, Vol. I A 2 3 , No. 6, Nov.-2ec. 1987.
c
j 15
VSlC
LSS
RS
=
=
RX
LXX
LSR
C l 2
=
=
=
=
0.4H
1 . 7 3 ohm
1 . 2 7 2 ohm
1.4927 H
0.746 H
0.00425
415
VsZe
Rr
FIG.13
SPACE PHASOR BASED E Q U I V A L E N T C I R C U I T FOR S P L I T PHASE
MOTOR
587