Paper
Analysis of Stator-Fed AC Commutator
the Matrix Method
Member
Masahiko
Member
Iwao
Kamatani
Motor using
(Tokyo Metropolitan Institute of Technology)
Shibata
(Chiba Institute of Technology)
Characteristics analysis using the matrix method of stator-fed AC commutator motor are presented. Recently, many variable-speed AC motor drive systems with semiconductor switching devices
have been developed. However, the power supply systems suffer from higher harmonic currents
during switching. On the contrary, three-phase AC commutator motors have essentially no
detrimental influence on the power supply systems. Consequently, the motors are being reconsidered
for use in spite the fact that they need periodic maintenance for the replacement of commutators
and brushes.
So far, motor analysis was calculated using various vector methods : in this case complicated
calculations are required, with accurate solutions difficult to be obtained. We derive the fundamental equations using the matrix method which can be applied to the transient phenomenon. Also, we
obtained an agreement between calculations and experimental results of the steady-state characteristics.
Key words : AC commutator motor, Matrix method, Characteristics analysis
1.
Introduction
The
recent
been
supply
remarkable.
systems
suffer
rents
during
phase
AC commutator
detrimental
from
maintenance
and the brushes.
can be operated
at arbitrary
speeds,
AC
two types.
demonstrating
This
of comthis motor
or lower
with the primary
winding
called
motor
fed type with a stator
motors
is the
in the rotor,
and the other
as ordinary
on the analysis
rotor-fed
operation,
drive
of pumps
systems,
and agricultural
are
diagram
only
industrial
irrigations,
and so
motor
consists
regulator
porated
as one unit.
power
The rotor
armature
which is also
regulator
is a three-phase
is the stator-
induction
voltage
motor.
induction
using the matrix
rotor
70
winding
an induction
which
are incor-
is similar
is essentially
regulator
The
to that of
is the
T. IEE Japan,
to the
similar
induction
unit
and
regulator
which
in Fig. 1.
and is connected
of a DC motor.
voltage
and
control
Its stator
motor
motor
is shown
of a motor
for speed
induction
supply.
of the commutator
one phase
type
induction
power
to the
and sewage
voltage
a normal
commutator
One
services
for high
applications
A connection
they need
higher
we discuss
type AC commu-
on.
speed.
three-phase
We have reported
Futhermore,
is suitable
for the
water
no
systems.
for the replacement
than the synchronous
a Schrage
that
of the stator-fed
used in waterworks
are being recon-
of the fact
motor
mainly
three-
characteristics
In this paper,
motor.
This
cur-
essentially
supply
the use of the motors
for use in spite
into
have
tator
power
contrary,
the performance
motor""".
the characteristics
devices
the
harmonic
on the power
mutators
divided
higher
On the
periodic
The
switching
motors
influence
AC motor
However,
switching.
Consequently,
sidered
in variable-speed
with semiconductor
very
regarding
of the Schrage
progress
drive systems
has
method
having
to the
voltage
a
transformer
has
same
a
as
.
stator
an
single
The
and
ordinary
Vol. 111-D, No. 1,'91
固定子給電形整流子電動機の特性解析
①Motor
primary
②Motor
secondary
winding(stator)
winding(rotor)
③Transformer
(a)
④ Ｉnduction voltage reguiator
Fig.1.
Connection
of
commutator
Diagram
of an idealizedmotor.
motor.
wound-rotor induction motor. Its output voltage is
altered by regulating their mutual positions to control
motor speed. The primary winding of the induction
voltage regulator is connected to the supply, and the
secondary winding is supplied to the motor brushes.
As mentioned before, this motor is more complicated than other kinds of AC motors, and carbon
brushes used in the low-voltage circuit have non(b) Diagramof idealized
transformer
and induction
voltage
regulator.
linear voltage-current
characteristics.
For these
reasons, it was considered difficult to give the precise calculations on the characteristics, and mainly
the design depends on the experiment and experience.
So far, motor analysis has been reported by
Schwarz"', Yamaguchi and Nishimura"'.
However,
as in these types of literature, the analysis were
calculated using various vector methods : complicated calculatios are required, and it is difficult to
obtain accurate solutions.
More than the above,
when this motor is disconnected suddenly during
Fig.2.
results of the steady-state
obtained.
2.
Voltage
characteristics
equations
To derive voltage equations, let's consider a fundamental circuit as shown in Fig. 2 and make the
following assumptions :
(1)
All the windings
are symmetrical
(3)
Brushes used in the low-voltage
have linear voltage-current characteristics.
lation characteristics
can not be analyzed using the
vector method.
In this paper, we derived the fundamental equa-
Motor
v1 : primary winding induced voltage
i1 : primary current
ment between
電 学論D,
the calculations
111巻1号,平
成3年71
and experimental
three-
phase windings and star connections.
(2)
Core saturation andiron loss are negligible.
operation, the primary induced voltage may be
sustained or rise temporarily.
The condition causing such a self-excitation phenomenon and the oscil-
tions using the matrix method which is capable of
being applical transient phenomenon. Also, agree-
could be
circuit
v2 : secondary winding induced voltage
i2 : secondary current
R. l. L : resistance, leakage inductance
and
main
inductance
scripts
1 and
dary
windings,
M,z(=M21)
w
ƒÖr :
and
velocity
The
secon
winding
rotating
electrical
voltage
equation
Fig. 2 is expressed
derived
from
the circuit
in
as
inductance
secondary
of
primary
(1)
windings
rotating
field
of
the
of
the
where
angular
velocity
winding
voltage
vt1
and
mutual
primary
: angular
s : slip
winding(sub
primary
respectively)
secondary
Induction
each
for
: maximum
between
ƒÖ
of
2 stand
regulator
: transformer
primary
winding
primary
current
induced
volt-
age
it1 : transformer
Vt21
: transformer
secondary
winding
induced
secondary
winding
induced
voltage
vt22
: transformer
See
voltage
it21
: transformer
secondary
current
it22
: transformer
secondary
current
vr8
: induction
voltage
regulator
Appendix
As
currents
stator
about •kZ•l, •kZt•l
shown
in
have
Fig.
and •kZr•l.
1, the
been
following
relations
among
obtained:
winding
(2)
induced
vrr
voltage
: induction
voltage
induced
regulator
rotor
irs
: induction
voltage
regulator
stator
irr
: induction
voltage
regulator
rotor
R, l,
L
winding
Applying two-axis transformation
to Eq. (1) and
using the connection matrix which can be obtained
from Eq. (2) , we have
voltage
: resistance,
main
leakage
inductance
scripts
inductance
of
t1, t2, s,
and
primary
and
voltage
regulator
r
current
current
each
where
winding(sub-
stand
secondary
(3)
and
for
transformer
windings,
induction
See
stator
and
rotor
Appendix
Eq.
ings,
about •kZ'c•l.
wind(3)
is
equation.
Mtzu,
a
generalized
instantaneous
value
respectively)
M,212
: mutual
inductance
between
and
secondary
windings
of
steady-state
equation
can
be
priobtained
mary
The
the
by
p=jw
in •kZ'c•l
in
Eq.
(3).
Applying
transsymmetrical
coordinate
transformation
to
Eq.
(3)
former
we
Mt.
: mutual
inductance
winding
1 and
between
secondary
secondary
winding
2
of
(4)
the
where
transformer
M,M
: maximum
stator
mutual
winding
induction
a
voltage
position
are
inductance
and
: displacement
where
obtain
the
the
stator
between
winding
of
the
and subscripts
regulator
angle
of
rotor
from
regulator
and
rotor
the
(the
phase
11, 12, 21 and 22 stand for the pri
mary positive and negative-phase
component, the
secondary positive and negative-phase
component,
"neutral"
position
and subscript t stands
ments, respectively.
windings
coaxial)
72
for the transformer,'s
T. lEE Japan,
ele
Vol. 111-D, No. 1, '91
固定子給 電形整 流子電動機 の特性解析
See Appendix about V31,V32,R3,X3.
3.
Characteristic
equation
Eq. (5) gives torque tensor [G] such that
(7)
Therefore,
the torque-per-phase
is given
by
(8)
If the power
balanced,
source
voltage
and motor
winding
are
then
and therefore,
Eq. (9)
is rewritten
as
(9)
(10)
where
(5)
where
Primary and secondary currents, i. e., I1 and I2, are
derived from Eq. (6) and they are given by
(11)
(12)
Effective
values
1, and 12 are given
by
(13)
(14)
From Eq. (4), choosing the positive-phase compo
nents and eliminating It1 and It21, we have
Primary
and
cos ƒÓ2,
and
secondary
are
given
power
factor,
i. e.,
cos ƒÓ1
by
(15)
(6)
where V3is the output voltage of the voltage regula
(16)
tor, which is inserted to the secondary winding (V3
= V32+JV31).
電 学論D,111巻1号,平
成3年
Transformer
73
primary
current,
i. e., It, is given
by
(17)
where
(18)
(19)
4.
Comparison
between
culated
Rating
measured
and
cal
characteristics
and
constants
of
the
tested
motor
are
as
follows.
Fig. 3.
Ratings
output
: 5.5
poles
1.8
: 4 ; speed
quency
: 50
Constants
voltage
rpm
: 200
; fre-
V
:
L'1=0.0234
H
L'2=0.0019
H
H
:
Rt1=0.0530Ħ,
L't1=0.1837
Rt21=0.0104Ħ,
L't21=0.0167
H
Rt22=0.0086Ħ,
L't22=0.0088
H
M't211=0.0554
H,
M'tM=0.0121
Induction
H
M't212=0.0402
H
voltage
regulator
H
Rr=0.0870Ħ,
L'r=0.0088
H
M'rM=0.0087
and
measured
T(=3_??_)
Primary
current
Secondary
input
these
figures,
well
caused
due
to
for
current
Figs.
factor
cos ƒÓ0
it is shown
the
and
3
Fig. 5.
Secondary
5
to
: Fig.
6
7
with
by
:
4
12 : Fig.
power
are
3
1, : Fig.
: Fig.
agree
is
characteristics
:Fig.
current
Efficiency
From
current.
H
Torque
results
Primary
:
L's=0.0088
Calculated
Fig. 4.
H
Rs=0.0800Ħ,
Total
of
R2=0.1330Ħ,
Transformer
points
number
: R1=0.3045 Ħ,
M'12 =0.0065
tion
kW;
: 2,000-650
Hz;
(measured)
Motor
error
Torque.
:
the
secondary
rotor
7 are
that
the
measured
speed
from
calculated
ones.
The
resistance
varia
variations.
no-load
Test
to
125%
load.
74
T. IEE Japan,
current.
Vol. 111-D, No. 1, '91
固定子給電形整流子電動機の特性解析
Appendix
Fig. 6.
Power
Fig. 7.
5.
factor.
Efficiency.
[Z22], [Zt11],
[Zt22], [Zt23], [Zr11]and [Zr22] are
obtained by replacing subscript 1 in [Z11]by 2, t1, t21,
t22,s and r, respectively.
where
Conclusions
The fundamental
equations
method of the stator-fed
using
AC commutator
the matrix
motor are
presented, and the characteristic
equations of the
steady state such as, torque, current, power factor
and so on are derived.
From these fundamental
equations, it has been confirmed that the calculated
torque, current, power factor and efficiency of the
motor agree well with the measured values. The
accurate solution is obtained easier by this matrix
where
method than the vector method. The results can be
utilized to provide for design of the stator-fed AC
commutator motor. These fundamental equations
can be also applied to the transient
phenomenon.
(Manuscript received Apr. 9, 1990,
reviced July 25, 1990)
References
(1)
(2)
(3)
(4)
1.Shibata & b1. Kamatani : Trans. IEE Japan. 102-B.709
(Nov., 1982)(in Japanese).
b1. Kamatani & 1.Shibata : ibid.. 104-B. 305(May. 1984)
(in Japanese).
B. Schncarz : "The stator-fed AC commutator machine
with induction regulator control". Pstg. IEE(1949)
J. Yamaguchi & M. Nishimura : J: IEE Japan. 76. 108
(Feb.. 1956)(in Japanese)
電 学論D,111巻1号,平
成3年
75
Masahiko Kamatani
(Member)
He was born in Tottori, Japan,
on August 19, 1937. He received
the B. E. and M. E. degrees in
Electrical
Engineering
from
Tokyo Denki College, Tokyo, in 1963 and 1968,
respectively. From 1963 to 1971, he was with
Departmentof Electrical Engineeringof the Tokyo
MetropolitanTechnical College, and from 1971to
1985,with the Department of Electrical and Elec
tronic Engineeringof the Metropolitan College of
Technologyof Tokyo. In 1986,he joinedthe Depart
ment of ElectricalSystem Engineeringof the Tokyo
MetropolitanInstitute of Technology.
where
Iwao Shibata
(Member)
He was born in Tokyo, Japan,on
January 15, 1925. He received the
B. E. degree in Electrical Engineer
ing and the Dr. of Engineering
degrees 'from Tokyo Institute of Technology,
Tokyo, in 1949 and 1964,respectively. From 1949to
1971, he was employed by Toyo Denki Seizo Com
pany as a Research and Design Engineer. From
1971 to 1975, he was with Department of Electrical
and Electronic Engineering of the Metropolitan
College of Technology of Tokyo, as a Professor.
Since 1975, he has been Professor at Chiba Institute'
of Technology.
76
T. IEE Japan,
Vol. 111-D, No . 1, '91