621.313.362
The Institution of Electrical Engineers
Monograph No. 260 U
Oct. 1957
SOME TESTS ON A STATOR-FED POLYPHASE SHUNT COMMUTATOR MOTOR
By C. S. JHA, B.Sc, Graduate.
(The paper was first received 28th May, and in revised form 29th July, 1957. // was published as an INSTITUTION MONOGRAPH
in October, 1957.)
SUMMARY
Based on theory developed in earlier papers, equivalent circuits are
established for a stator-fed 3-phase shunt commutator motor available
for tests. Details are given of methods used in the measurement of
equivalent-circuit parameters. The measurement and separation of
motor no-load losses are discussed. Test results obtained in no-load
and load tests are shown to give fairly good agreement with calculated
behaviour.
(1) INTRODUCTION
Polyphase shunt commutator machines were developed to
meet the need of alternating-current drives with induction motor
characteristics but with provision for speed regulation and powerfactor control. The basic principle of speed regulation and
power-factor improvement of an induction machine lies in the
injection of a suitable electromotive force into its secondary
circuit at slip frequency. In the stator-fed machine, the main
winding is on the stator, while the rotor carries a commutator
winding. The e.m.f. injected in the rotor circuit is usually
obtained at supply frequency from the combination of a double
induction regulator and an auxiliary winding on the motor stator,
and is converted into slip frequency by the commutator and
fixed brushes.
The theory of the double induction regulator and of the statorfed motor with regulator have been discussed in References 6
and 7, respectively. The present paper deals with some tests
carried out in experimental verification of the theory proposed
in Reference 7.
LIST OF PRINCIPAL SYMBOLS
a = Electrical angle by which the regulator shaft is
rotated from its neutral position, electrical
degrees.
6 = Brush shift angle, against the direction of rotation, electrical degrees.
y = Angle by which the auxiliary winding e.m.f.
lags the stator e.m.f. (neglecting transformer
effect).
a = Pairs of parallel paths in the armature.
'i> in h — Currents in the motor primary, machine secondary, and regulator primary circuits, respec(2) THE TEST MACHINE
tively.
The machine whose behaviour was tested has a simple
k — Effective turns ratio (secondary/primary) of the (unbiased) double regulator for speed regulation and an auxiliary
component single regulators of the double stator winding displaced 120° electrically from the main winding
regulator.
for power-factor improvement. A patented commutating
km, kx = Effective turns ratios, motor-secondary/motor- winding in the rotor slots is in parallel with the main rotor windprimary and motor-auxiliary/motor-primary, ing to ease commutation troubles. The brushes are diametrical
respectively.
and two terminals per phase are brought out on the terminal
Pu P2 = Wattmeter readings in the two-wattmeter method board. The regulator is the same as that used in tests described
of measuring power.
in Reference 6. The manufacturer's rating for the machine is
Rb = Carbon brush contact resistance for each brush as follows:
set on the motor, also effective per phase value
Motor: 5-5/0-55h.p.; 2200/220r.p.m.; 400 volts 50c/s 3-phase
for the test-motor brush contact resistance.
P-otw ^11 = Loss component of the mutual and self- 4-pole.
Regulator: 2-pole 3-phase. Input, 400 volts 9amp; output,
impedances of the primary winding, respec4 13kVA 30-6 volts, 45 amp.
tively.
Rsi, Rrl, RS3 — Resistances of the motor primary, secondary and The test machine connections are shown in Fig. 1.
auxiliary windings, respectively.
(3) THE IMPEDANCE TENSOR AND THE EQUIVALENT
s = Slip.
CIRCUITS OF THE TEST MACHINE
*si> xru xsi = Leakage reactances of the motor primary, seconUsing
Reference
7, the final impedance tensor for the test
dary and auxiliary windings, respectively.
Xunv X\ 1 = Reactive components of the mutual and self- machine can be shown to be
impedances, respectively.
fM\v
ZOnv> Z\ i = Mutual and self-impedances, respectively, of the
motor primary winding.
1
Zom(kme~*-kxe*)
Zn
zn = Leakage impedance of the motor primary
winding.
Zom(kmse*-kxe-Jf)
—kZ0 cos a
Zn
Zo, Zs = Mutual and self-impedances, respectively, of the
component single regulator primary windings.
—kZo cos a
Zs\2
zr, zs — Leakage impedances of the component single
regulator secondary and primary windings,
• • • • (1)
respectively.
All resistances, reactances and impedances are effective per- where Zn = Rsl + jxsl + Zom
phase values unless otherwise stated.
and Z,r = Rrl + jsxn + Rs3
Correspondence on Monographs is invited for consideration with a view to
publication.
The author was formerly at the Heriot-Watt College, Edinburgh, and is now with
the English Electric Co. Ltd.
r
+ 2zr + 2k2(Z0/Zs)zs + 2k2{Z2olZs) cos2 a . (2)
JHA: SOME TESTS ON A STATOR-FED POLYPHASE SHUNT COMMUTATOR MOTOR
118
(4.2) The Resistance Measurements
The measurement of primary and auxiliary winding resistances
is straightforward, but that of the secondary resistance is complicated by the presence of carbon brushes. The carbon brush
contact resistance forms a major part of the total secondary
resistance, and its non-linearity makes it necessary for the
resistance to be measured at different current densities. Moreover, the measured resistances must be converted to effective perphase values.
Fig. 1.—General connections of test machine.
(4.2.1) Separation of Winding and Contact Resistances.
In a 2-pole 3-phase armature with a commutator winding, as
shown in Fig. 4, if a direct voltage is applied to any pair (1-2) of
diametric brushes, such that the current entering and leaving
the brushes is /, then a current 7/2 will flow through each conductor. If r is the resistance of all conductors in the armature
connected in series, the resistance measured across 1-2 is given
by 2Rb + r/4, where Rb is the contact resistance of each brush
set. If, instead of a 2-pole armature, there are a pairs of parallel
paths, the resistance across 1-2 will be
* 12 = VnH = 2Rb\a + r/4a2 . . . .
Fig. 2.—Orthodox equivalent circuit for test machine.
(3)
If the current is passed as shown in Fig. 4, and voltages across
rt k^-iV; k2 = kmS-lQ - k*+K; fcj = 2/c cos o.
VOLTAGE 1 : K,'
CURRENT k 2 = 1
VOLTAGE K 3 : 1
CURRENT 1 •• K'3
Fig. 3.—Exact practical equivalent circuit of test machine.
Jfcj - 2k(ZJZ,) cos a;
Z\ - Zn - k[k'2Zu -
k'32Z,l2.
The orthodox and the exact practical equivalent circuits representing eqn. (1) are shown in Figs. 2 and 3, respectively. Iron
losses in the machine have been included by considering the
mutual-impedance terms Znm and Zn to include resistive
components.
Fig. 4.—Two-pole armature with commutator fed across one pair of
diametric brushes.
3-4 and across 5-6 are measured, V34 and F 56 , since they do not
include contact drops, will be given by
V34 = V56 = (I/2a)(rl6a)
Hence
V3JI = r/Ha2
(4)
From eqns. (3) and (4), Rb and r can be easily separated.
(4) MEASUREMENT OF PARAMETERS
In addition to the regulator parameters, the measurement of
which has been discussed in detail in Reference 6, the following
motor parameters must be known to enable theoretical calculation of machine performance:
(a) Effective turns ratios, km and kx.
(b)
(c)
(d)
(e)
(/)
Brush shift angle 6 and auxiliary winding displacement angle y.
Resistances Rs\, Rr\, and RS3.
Leakage reactances xsi, xr\, and xs3.
Reactive component of mutual impedance, Xom.
Loss component of mutual impedance, Rom.
(4.1) Effective Turns Ratios and the Displacement Angle
When design details of the motor windings and the configuration of the fixed brushes are available, the values of km, kx, 6
and y can be easily and accurately determined. In absence of
these details the normal open-circuit test is used. Comparison
of the magnitudes and the phase displacements of the secondary
and auxiliary induced voltages with those of the primary supply
voltage determines these four constants.
(4.2.2) Conversion of Measured Values to Effective Per-Phase Values.
Consider a 2-pole 3-phase armature with diametric brushes
being fed by a balanced 3-phase supply, and let the phase currents
be Jj, I2, and 73. The armature shown in Fig. 5 is divided into
six sections a, b, c, d, e and /. The current flowing in any of
these winding sections at any moment can be determined by
adding the separate effects of the three currents. It can be seen
that every section of the winding, and hence every conductor,
takes a current equal in magnitude to the phase currents. If
there are a parallel paths on the armature, the current in every
conductor will be J/a, where / is the magnitude of the phase
currents.
Hence,
Total loss in the rotor winding = (Jla)2r . . (5)
If the brushes are included, the total loss becomes
Qlafir + 6aRb)
since the number of brushes is 6a.
119
JHA: SOME TESTS ON A STATOR-FED POLYPHASE SHUNT COMMUTATOR MOTOR
Fig. 5.—Two-pole armature with commutator fed from a 3-phase
supply.
Total currents in the winding sections:
a, -h; b, +/i; c, -h; d, +/ 3 ; e, —h; and f, +/ 2 .
15
Therefore
Loss per phase = (//a)2(r/3 + 2aRb)
(6)
20
25
CURRENT. AMP
30
35
40
Fig. 6.—Variation of carbon-contact resistance with current and with
temperature.
(Related to the B-phase of the test motor.)
from which '
Effective resistance per phase = (r/3a2 -f 2RJa) .
(7)
2
O °: 1 3
In the test motor, a — 2, giving
rl
= r/12
(8)
Since the carbon contact resistance is non-linear, Rb was measured
for a series of values of /. Because Rb is very susceptible to
outside influences such as temperature, humidity, etc., any exact
reproduction of results over a long period is impossible, and
the values of Rb used for calculation of characteristics were
the means of numerous values obtained over a long period.
An investigation was carried out with a pair of carbon brushes
mounted on a copper slip-ring to find if there was any difference
between the a.c. and d.c. values of the contact resistances. It
was shown that for all practical purposes the d.c. value measured
across the brushes (i.e. the sum of the positive and negative
polarity contact resistances in series) was equal to the a.c. value
(two contact resistances in series).
Since the resistance is a function of temperature, the measurements should be carried out while the machine is hot and the
hot values used in the calculation of machine characteristics.
Copper resistances in the machine increase with temperature,
but the carbon contact resistance has a negative temperature coefficient. The curves for Rb obtained on the test motor
(B-phase) when cold and hot are shown in Fig. 6. On the
test machine, Rb for the three different phases showed a difference
of up to 20 %. The mean hot value for the three phases is shown
in Fig. 7, and this was used for performance calculation.
(4.3) Leakage Reactance Measurements
In separating primary and secondary leakage reactances in
induction machines an approximation is usually made that the
reactances referred to the same voltage base are equal. However, in any machine where an auxiliary winding either on the
stator or on the rotor is present, the individual leakage reactances
of the three windings can easily be measured. The method
involved is the same as that used in the determination of leakage
reactances in 3-winding transformers. This method, with
transformers, gives simultaneously the leakage reactances of the
three windings and their effective a.c. resistances. In the case
of the stator-fed motor, however, the presence of losses in shortcircuited coils makes the resistances measured in the test very
•different from actual values.
LJ*
z 0-12
<
\
>
0-11
< 0-10
'009
\
\
V
20
CURRENT. AMP
30
"1
Fig. 7.—Average hot values of carbon-contact resistance per phase
plotted against currentflowingthrough the contact.
The leakage reactances of the primary and auxiliary windings
on the stator-fed motor are independent of the speed of the rotor.
For normal induction machines the rotor leakage reactance is
proportional to the slip of the rotor. But the leakage reactance
of an armature with a commutator winding, measured across
fixed brushes, is known to have a slip-independent portion in
addition to the slip-dependent one. This necessitates the replacement of sxri in eqn. (1) by sx'rl + x'r\. The behaviour of the
secondary leakage reactance of a stator-fed commutator motor
is of considerable interest, and the determination of the slipindependent component x'r\ is essential for correct performance
calculation.
(4.3.1) Determination of the Slip-independent Portion of the Secondary
Leakage Reactance.
Let the motor be fed through the brushes, the primary kept
on short-circuit and the auxiliary on open-circuit. The voltage
equations for the primary and secondary circuits are then
0 = i^Rsi +jxsi + Zom) + irkmZomE-JQ
(9)
Vr = ifinsZtofi+J* + ir(Rrl + sx'rl + xr\
From which, on simplification, the short-circuit impedance is
.
. (10)
120
where
JHA: SOME TESTS ON A STATOR-FED POLYPHASE SHUNT COMMUTATOR MOTOR
R = Rrl + kmcsRsl
x = x'r\ + s(x'rl +
. . .
(11)
and
c being assumed approximately real.
If the rotor is driven in the direction of rotation of the field by
an auxiliary drive, both R and x will vary linearly with speed and
the value of x at synchronous speed will give x'r\. In actual
test, Vr\ir can be measured over the entire speed range quite
easily by noting the applied phase voltage and the phase current
at different speeds. If the power lost per phase, P, is also
recorded, x can be calculated from the relation
4-002;
x = V[(Klir)2 - (P//2)2]
-006
(12)
I O-IO
(a)
/
Curve (a) in Fig. 8 shows the values of x for the test motor
obtained by this method, and at first sight suggests that the slip\
independent portion of the armature leakage reactance changes
sign as the rotor is driven through synchronism. If this were so,
a study of the voltage and current oscillograms should show a
\
sudden change of phase of the secondary current as the rotor
0
1000
2000
3000
is driven through synchronism. No such sudden change was,
ARMATURE SPEED, R.P.M.
however, observed. The current was shown to be considerably
lagging the voltage when the rotor was at standstill (s = 1), and, Fig. 8.—Variation of secondary short-circuit reactance with armature
speed.
as the rotor speed was increased, the phase angle became gradually
Curve (a) calculated from eqn. (12).
smaller and smaller, until near synchronous speed (approxiCurve (b) calculated from eqn. (14).
mately 5 = 0) no phase difference between the current and
voltage waves could be ordinarily detected; and at speeds above carried out to study the variation of the secondary self-reactance
synchronism the current started leading the voltage. It therefore with speed. Results showed that in this experiment again
became obvious that the measurement of x by eqn. (12) is Pj = P 2 at a speed slightly less than synchronous. Since the
erroneous.
slip-independent value of the secondary leakage reactance is
The above method will give an accurate value of reactance JC equal to the secondary self-reactance at zero slip, this test conat the fundamental frequency, only if both the current and firmed that x'r\ for the test motor should be negative.
voltage in the test are sinusoidal. Under test conditions,
There seems to be no explanation for this result, which is so
although the current flowing could be kept sinusoidal and hence contrary to the general idea3 that the slip-independent portion
approximately free from harmonics, the voltage appearing at is about a quarter of the standstill value of the secondary leakage
the brushes, Vr, usually contains higher harmonics (mainly due reactance. Since x'r' is in any case very small, it has been
to commutation), the percentage of which becomes quite high assumed to be negligible in the subsequent calculation of
near synchronous speeds.
characteristics.
Richter2 has shown that in the case when either the voltage
or the current is free from harmonics, the phase angle cf> between
(4.4) Measurement of Xom
the fundamental components of voltage and current can be
The self-impedance Z, x of the primary winding can be easily
easily measured from the relation
measured in an open-circuit test, with the secondary and
auxiliary on open-circuit. The measurement of power loss in
-P2)
(13) the test enables Z n to be split into resistive and reactive comtan 0 =
ponents. The mutual impedance Zom is then obtained by
Curve (b) in Fig. 8 shows the variation of x with speed when subtracting the primary leakage impedance zn (~Rsi + jxs])
from Zn, i.e.
x is calculated from the relation
Zom = ^ n - *n = a + jb (say)
s i n <f>
(14)
Although this method of measuring x is more accurate than the
previous one, the effect of harmonics is not altogether eliminated,
since Vr contains harmonic components. The best method of
finding the slip-independent portion of the leakage reactance is
to find the speed at which P, = P 2 , giving tan 0 = 0 and hence
x = 0. A straight line is then drawn joining this point (x = 0)
on the speed axis with the value of x at zero speed, where the
effect of harmonics is practically negligible. The ordinate of this
straight line at synchronous speed (s = 0) gives x'r\.
From Fig. 8 it is seen that for the test motor Px = P 2 at a
speed slightly below synchronism, thus giving a very small
negative value for x'r\. It seemed unusual that x'r\ was negative;
its magnitude was, however, so small that experimental errors
may have been responsible for this.
An open-circuit test with the secondary connected to normalfrequency supply (primary and auxiliary open-circuited) was
If, in the magnetizing branch of the equivalent circuit, the
resistive and reactive components are in parallel, Xom is given
by (a2 + b2)/b. The test should be carried out at the operating
voltage to make the measured value approximate to the value
under normal working conditions.
(4.5) Measurement of Rom
The no-load mechanical losses (i.e. windage and friction) are
usually omitted from machine equivalent circuits, these losses
being considered to be part of the machine output. The electrical
no-load losses, on the other hand, are lumped together and
shown as part of the mutual-impedance branch of the primary
winding. This lumping together of the losses is not quite
justifiable as the losses occur in different parts of the machine,
but experience over a number of years has shown that no serious
errors are involved.
121
JHA: SOME TESTS ON A STATOR-FED POLYPHASE SHUNT COMMUTATOR MOTOR
In the stator-fed motor, the no-load electrical losses are a
complicated function of the motor speed and may vary within
very wide limits. Rom in the equivalent circuit must therefore
be represented by a variable resistance expressed as a function
of the slip of .the machine.7 One way of estimating Rom is to
record the total power lost in the no-load run of the motor with
regulator and then to subtract from it the mechanical losses, the
calculable I2R losses in the different circuits of the machine, and
the regulator iron losses. Neglecting the voltage drop across the
primary leakage impedance, Rom is then obtained by K2/loss-perphase. Loss per phase being a function of speed, Rom is thus
expressed as an experimentally determined function of the
machine slip.
In the test motor the no-load electrical losses measured in this
way were very different from the estimated values of normalfrequency iron losses. An attempt was therefore made to
separate the constituent no-load losses of the motor; this is
discussed in the next Section.
Test B
The same experiment is repeated with the brushes on the test
motor lifted off the commutator surface,
From tests A and B, six sets of readings for power at different
speeds are obtained, giving six curves plotted against speed.
Fig. 9 shows the results obtained on the test motor. D.C.I
1000
800
£600
400
(4.6) Measurement and Separation of No-load Losses
Apart from the calculable I2R losses and easily determinate
iron losses in the regulator, the no-load losses in the machine
include the following:
(a) Brush friction loss, Pb(b) Bearing friction and windage loss, P/.
(c) Fundamental-frequency stator iron losses (hysteresis and eddycurrent losses), Pel + Phiid) Rotor hysteresis loss, Phi(e) Rotor eddy-current loss, Pe2(/) Surface and pulsation losses (including all losses due to the
presence of stator and rotor slot openings), Pp.
(g) Losses in the coils short-circuited by the brushes, PscExcept for (g), these losses have the same nature as in any
polyphase induction machine.4 In induction machines, however,
the speed is more or less fixed, hence the variation of constituent
no-load losses with speed is of no particular importance. The
stator-fed commutator motor, on the other hand, has a wide
speed range and the variation of losses with speed is thus of
considerable interest from both design and operational points
of view.
The method used for separating the losses of this machine is
an extension of that used by Alger and Eksergian1 for separating
the iron losses of wound-rotor induction machines. If a constant
voltage and frequency are applied to the stator and the rotor is
driven by another motor at different speeds, the power taken
from the line decreases and that taken by the driving motor
increases abruptly when the rotor passes synchronous speed.
This discontinuity in the power curves at synchronous speed,
being due to the reversal of the rotor hysteretic torque as the
rotor is driven through synchronism, is equal in magnitude to
twice the standstill value of rotor hysteresis loss, Ph2If a driving motor is available and the brushes on the commutator can be easily lifted or removed, all the losses of the
test motor can be separated by means of the following two tests:
Test A
In this test the commutator motor, with the brushes in their
normal position, is driven by a d.c. driving motor in the direction of its normal rotation. Normal supply is connected to the
stator terminals of the test motor, while the auxiliary and
secondary windings are kept open-circuited. The power needed
for the driving motor to drive the combination with the test
motor unexcited is recorded for different speeds. The test motor
is then excited and the power input to the driving motor and to
the test motor at different speeds is recorded.
200
400
800
1200
1600
ARMATURE SPEED, R.P.M.
2000
2400
Fig. 9.—Separation of test motor no-load losses.
and D.C.2 represent the curves for the driving motor inputs
(corrected for copper losses in the driving motor) with the test
motor unexcited; D.C.I' and D.C.2', the driving motor inputs
(corrected for copper losses) with the test motor excited; and
A.C.I and A.C.2 the total inputs to the test motor (corrected for
copper losses in primary winding) in the two tests A and B,
respectively.
From these six curves all the test motor losses can be separated
and their variation with speed determined, as shown below:
(a) The brush friction loss, Pb, is given directly from the
difference of the two curves D.C.I and D.C.2.
(b) The bearing friction and windage loss, Pf, is given by subtracting P/, and the driving motor no-load losses from D.C.I.
(c) The stator iron loss, PeX + PhX, is independent of the
speed of the rotor and is given by the average value of the A.C.I
or A.C.2 curve at synchronous speed (i.e. midpoint of the
discontinuity).
(d) The standstill value of the rotor hysteresis loss, Ph2, is
given by half the amount of discontinuity in the A.C. curves at
synchronous speed. The magnitude of this loss at any particular
speed is obtained from the assumption that the loss is directly
proportional to the rotor slip. It is to be remembered, however, that the loss is always positive even when the slip is negative.
(e) In test B, owing to the absence of parasitic brush losses,
the ordinate of the A.C.2 curve at standstill represents the sum
of the standstill values of stator and rotor eddy-current and
hysteresis losses. Since the stator iron losses and the rotor
hysteresis loss have been obtained from (c) and (d) above, Pel
is easily determined. Using the assumption that the eddycurrent loss in the rotor, Pe2, is directly proportional to the
square of the rotor slip, the value of this loss at any motor speed
can be obtained.
(/) In test B, the total input to the driving motor and test
motor combination corrected for I2R losses is dissipated in the
form of the driving motor no-load losses, the windage and
friction losses in the test motor, the stator and rotor eddy-current
JHA: SOME TESTS ON A STATOR-FED POLYPHASE SHUNT COMMUTATOR MOTOR
122
and hysteresis losses and the surface and pulsation losses in the
test machine Hence Pp is obtained from
sPh2)
- (s2P
e2
. . . .
(15)
(g) The difference between the A.C.I and A.C.2 curves gives
the electrical input to the short-circuited coils. Part of this
input comes back as useful torque in driving the motor. The
direction of the torque is reversed at super-synchronous speeds.
This part which does work is given by
(16)
Pm —
Hence,
(17)
It is thus seen that the two tests A and B are sufficient for
measuring and separating the no-load losses of the test motor
at all speeds. Though a d.c. drive was used in the test, any other
drive may be used, provided that the no-load losses of the driving
motor do not vary appreciably with small changes of load. The
d.c. motor used in the test was separately excited and the field
current was kept constant throughout, the variation of speed
being obtained by varying the armature voltage. The variation
of armature currents relating to the four curves D.C.I, D.C.I',
D.C.2 and D.C.2' at any particular speed was small enough to
enable the effect of armature reaction to be ignored. Accurate
metering is essential for the success of the test.
a predominant part of the parasitic brush current circuit. Since
the contact resistance is high at low current densities and hence
low slips, and low at high current densities and hence high slips,
the parasitic-current circuit losses will vary apparently as a
power higher than the square of the slip.
The losses in the coils short-circuited by the brushes therefore
represent predominantly a contact loss. When the machine is
running normally there are two currents flowing through the
contact, the main secondary current ir and the current in the
short-circuited coils ib. The currents at the two ends of the
contact are therefore ir + ib and ir — ib. This non-uniform
distribution of current across the contact, which has a non-linear
resistance, makes it difficult to estimate an average value of the
contact resistance. The losses Psc have been measured in the
tests described above when ir — 0. The presence of ir in normal
machine operation not only affects the contact resistance, and
hence Psc, but also increases the magnitude of ib to some extent
(owing to the introduction of the reactance voltage due to commutation in the short-circuited coils). In this paper it has been
assumed that the two currents can be treated separately: the
main current ir produces the usual contact loss i}Rb, where
Rb depends only on /„ and the parasitic brush current ib produces
a loss which is independent of ir. This assumption, though
theoretically unjustifiable, does not introduce any serious error
in practice.
Table 1
Loss
Separation of no-load losses of test motor
Driving
motor
no-load
losses
Pi
P/
Pel + Phi
r.p.m.
watts
watts
watts
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
watts
0
9
17
25
34
42
51
62
75
90
105
126
150
0
15
27
42
58
71
88
110
134
162
190
223
260
0
8
16
23
30
42
51
63
78
102
135
189
260
160
160
160
160
160
160160
160
160
160
160
160
160
Armature
speed
SEPARATION TABLE
Pel
Pp
Pm
watts
watts
watts
watts
watts
25
21-6
18-3
15
11-7
8-3
50
1-7
1-7
5-0
8-3
11-7
150
91
68
49
33
20
10
3-6
0-4
0-4
3-6
10
20
33
0
13-4
24-7
34
48-3
65-7
77-4
91-9
114-9
138-4
169-7
225
312
0
15-5
18
13
13
4
174
84-5
30
12
3
2
Ph2
The separated values of the constituent no-load losses for the
test motor are shown in Table 1. In spite of best efforts the
ill-conditioning of eqn. (16) makes the measurement of Pm not
very accurate. To check that all the no-load losses have been
located, the values of total no-load losses, obtained by synthesizing the separated losses, are compared with those obtained
from a normal no-load run of the motor with regulator. The
comparison is given in the last two columns of Table 1 and shows
good agreement.
One surprising result obtained in the test is the apparent
evidence that the losses in short-circuited coils varied very nearly
as the fourth power of the slip. Since the parasitic brush losses
are directly proportional to the square of the commutator segment voltage and the latter is a linear function of slip, the
parasitic losses should be proportional to the square of the slip.
It is difficult to believe that experimental inaccuracies would
be responsible for such a wide divergence from theoretical
relationship. The test result can, however, be explained if we
consider the non-linearity of the contact resistance which forms
-4
-8
-13
P.c
2
3
12
Test motor
no-load
losses from
Total no-load no-load run
losses
watts
watts
450
370-5
325
319
331
359
385
427
489
571
675
832
1052
350
345
340
340
400
440
490
580
690
850
1070
(4.7) Measurement of Parameters of the Exact Equivalent Circuit
The principle of the measurement of parameters of the practical circuit (Fig. 3) has been discussed in Reference 7. In
practice the measurement is slightly modified by separating the
motor and regulator parameters, as shown in Fig. 10. The
regulator being a static piece of equipment, its parameters can
VOLTAGE 1 ••
CURRENT K2 • 1
VOLTAGE K 3 : 1
CURRENT 1 : K 3 '
Fig. 10.—Splitting of equivalent circuit of Fig. 3 into motor and
regulator constituents.
X,3)
Zlm
Zlr
+ {k2ms
zr + 2kKZ0IZ.)z,
JHA: SOME TESTS ON A STATOR-FED POLYPHASE SHUNT COMMUTATOR MOTOR
be measured with great accuracy and such measurement has
been discussed in Reference 6. The remaining motor parameters
to be measured are
(a) Zn
(b)
(c)
id)Zm
The open-circuit and short-circuit tests for the measurement
of the above parameters are now discussed.
Open-circuit test.
In this test the motor primary is connected to a normalvoltage normal-frequency supply, .while the secondary and auxiliary windings are kept open-circuited with the rotor locked.
The following symbols are used in the test:
V = Supply voltage, volts per phase.
I'I = Supply current, amperes per phase.
Vr = Induced voltage across the secondary, volts per phase,
and Vx — Induced voltage across the auxiliary, volts per phase.
Zn = V\ix ohms
Then
123
To eliminate the effect of non-linearity of contact resistance the
secondary current in the short-circuit test is kept at a fixed value
both at standstill and at the speed where Pj = P 2 . Corrections
for parasitic and iron losses at these points are made by measuring
these losses at the same input voltages in an open-circuit test
(primary open-circuited). From the corrected values of resistance
obtained at standstill and at a speed where Pj = P 2 , Rim is
easily expressed as Rb + sR + R', with Rb remaining in the
circuit as a non-linear parameter. Both for this test and for
characteristics calculation the variation of Rb with the secondary
current must be known (Fig. 7).
(4.8) Summarized Values of Motor Parameters
The values of parameters for the test motor as measured in the
preceding Sections are summarized below.
(a) For the orthodox equivalent circuit:
km = 0137, kx = 0-0181, 0 = 5°, y = 60°, Rsl = 2 0 ohms,
Rrl = Rb + 0015 ohm, Rs3 = 0008 5 ohm, xsl = 4-13 ohms,
xrl = 0-091 ohm, xs3 = 0 0065 ohm, xom (parallel branch) =
78-3ohms;andP*o/M (parallelbranch) = 53-3/(90 - 75* + 125*2)
kilohms.
(b) For the practical equivalent circuit:
m
Voltage
transformation
ratio = (0 130* - 0-008 5) +
n
7(0-011 3* + 0-0148); current transformation ratio = 0-121 5 y0-0261; Ru = 53-3/(106 - 75* + 125s2) kilohms; Xn = 83-2
ohms; ZUn = (Rb + 0-028 + 0 027*) + y-(0 161*) ohms.
Hence
kms~t
= SVJV - VJV
The above parameters and the variation of Rb with secondary
current, together with the regulator parameters, are sufficient to
The phases of iu Vr and Vx with respect to Fmust be measured enable calculation of characteristics for the test motor to be
to express the parameters in complex forms.
carried out.
Since ZomfZx j can be regarded as approximately real,
The parameters of the practical equivalent circuit can also be
calculated from the known values of parameters of the orthodox
= (VrlV)* - (VJV)*
circuit. Comparison of these calculated values with those
obtained by tests shows very slight expected differences, the
where (Vr/V)* and (VJV)* are complex conjugates of Vr\V
major difference being in the values of Z /m , as can be seen from
and VJV, respectively.
the following:
Xu, the reactive part of Zn, is a constant at constant voltage,
but the loss component as discussed earlier is a function of speed. Calculated. Zlm = (Rb + 0-013 + 0043*)
+ 7(0 • 156* + 0 • 008) ohms . (19)
If the total no-load losses (electrical) in the motor, including the
copper losses in the primary winding, are f(*), then Rn, the loss Test. Zlm = (Rb + 0 • 028 + 0 • 027*) + y(0 161*) ohms . (20)
component of Z n when Rn and Xn are in parallel, is given by
In the actual test for measuring i?/OT no correction was
RU = v2lf(s)
(18) made for iron losses at the speed where Pj = P 2 , these being
Short-circuit test.
considered to be small. This may be why the slip-indeIn this test the auxiliary and secondary are connected in pendent portion of R/m in eqn. (20) is higher and the slipseries (as in normal operation) and further connected to a dependent portion lower than the corresponding quantities in
normal-frequency supply, the primary terminals being on short- eqn. (19). The slip-independent portion of xlm in eqn. (19) is
circuit. The supply voltage is so adjusted as to allow full-load small compared with the slip-dependent portion, and its absence
current to flow in the primary winding. The leakage impedance in eqn. (20) may be due to experimental inaccuracies in measureterm Zlm is then given by the input impedance measured in the ment. In performance calculations eqn. (19) has been used.
test. To find its dependence on slip, the input impedance is
(4.9) Measured Values of Regulator Parameters
measured at at least two speeds, the rotor being driven by an
The values of regulator parameters taken from Reference 6
auxiliary drive. To avoid effects of harmonics, the impedance
was measured at standstill where the voltage and current waves are:
were nearly sinusoidal, and then the rotor was driven to the (a) Orthodox circuit:
speed where Pi = P 2 , P\ and P 2 being the wattmeter readings
k = 0068, Z o = 12-53 +y"6703 ohms, zs = 1-47 +71-85
in the two-wattmeter method of measuring power (see Section 9).
and zr = 00178 +70-0083 ohm.
ohms
This speed was noted. At this speed the circuit is purely resistive,
and hence xlm, the reactive portion of z/m, must be zero. From (b) Practical circuit:
the knowledge of x /m at standstill and the speed at which it is
ZJ2 = 7 + 7 3 4 - 4 4 ohms, 2k(Z0/Zs) = 0-132 and
zero, its slip-dependent and slip-independent parts are easily
Zlr = 0 049 +70-033 ohm.
evaluated.
Determination of /? /m , the resistive portion of Zlm, and its (5) CHARACTERISTICS CALCULATION AND COMPARISON
WITH TEST RESULTS
dependence on slip present considerable difficulty owing to the
presence of the non-linear contact resistance, the iron losses in
Once the parameters are evaluated, either of the circuits of
the test and the losses in the coils short-circuited by the brushes. Fig. 2 or 3 or the tensor equations i = Z~' V can be used to
z
JHA: SOME TESTS ON A STATOR-FED POLYPHASE SHUNT COMMUTATOR MOTOR
124
calculate the behaviour of the test motor under steady-state
conditions. The orthodox and practical circuits given identical
performance equations since both are exact representations of
the impedance tensor [eqn. (1)]. Owing to the various approximations made in measurement of parameters, the two circuits
using measured values as shown in Sections 4.8 and 4.9 give
slightly different results under the same operating conditions.
The difference, however, is usually small, as is illustrated by a
sample below.
the loss component of current representing the no-load losses in
the motor [eqns. (21a) and (22a)]. The difference is due to the
approximation made in the orthodox circuit by neglecting the
voltage drop across the primary leakage impedance in determining Rom. For all practical purposes the two circuits can be
considered identical and hence, in subsequent calculation, only
the practical circuit has been used. It will be appreciated that
the practical circuit is easier to handle for numerical solutions.
Operating conditions', cos a = 0-707; slip = 0-673; supply
voltage = 231 volts per phase.
(a) From the orthodox circuit on calculation:
/j = (0-44 -72-77) + (0-12 -y*00264)/ r . . . .
(21a)
ir = 231(- 00146 +j00226)lRb + 0-091 + 7*0-146 (21b)
i2 = (I.33 -y*6-45) -0-0932/,.
(21c)
(b) From the exact practical circuit:
11 = (0-48 -7*2-77) + (01215 -j0026)i,
. . . (22a)
i, = 231(- 0-0142 + j00224)/Rb + 0-091 + 7*0-146 (22b)
12 = (I.33 -76-45) -0-0932/ r
(22c)
On comparison it is seen that ir and i2 in eqns. (21) and (22)
are almost identical. There is, however, a slight difference in
Using the equivalent circuit, the supply current and individual
currents in the motor primary, regulator primary and the rotor
circuit can be calculated for given values of cos a and slip. In
experimental verification of the theory a number of no-load and
load tests were carried out on the test machine. Calculated and
observed values of currents in the test are shown in Tables
2 and 3.
The temperature and other ambient conditions affect the
current in the rotor circuit considerably. Variation in rotorcircuit current in its turn affects, though to a lesser degree, the
motor and regulator primary currents. Precautions were taken
to allow the machine to run for a considerable time before any
readings were taken, to ensure that the brush contacts had reached
a steady temperature. In spite of this, there were variations of
(5.1) No-Load and Load Tests
Table 2
COMPARISON OF NO-LOAD TEST RESULTS WITH CALCULATIONS FROM THE EQUIVALENT CIRCUIT
I'V!
cos a
0-707
0-582
0-442
0-291
0131
-0033
-0196
-0-354
-0-50
-0-635
-0-707
Slip
Calculated
0-673
0-574
0-446
0-314
0173
0-0133
- 0 140
-0-286
-0-427
-0-568
-0-640
Observed
amp
amp
26-8
25-8
25-2
240
230
22-4
20-6
18-6
16-4
28
26
25
23-5
21
19-5
18
16
14
12
10
130
110
Calculated
Observed
Calculated
amp
amp
amp
1-61 +70-33
1-64+70-2
1-57 +70-13
1-59 -70-02
1-61 —70-18
1-34-70-17
119 -70-30
1-20 -70-57
1-17 -7'0-8
0-92 - y i - 1 4
0-92 -71-41
/ = h + i2
h
'l
Observed
0-95 + 7*0-2 1 0 -7*8-93
0-95 +7*0-2 0-99 -7*8-4
1-05+70-2 1-09 -77-91
1-15-77-36
1-06 +7O
105 -7'0-2 1-24 -7*6-84
0-95 -7*0-4 1-34-76-35
1 0 -7'0-6 1-36 -75-92
0-97 -y0-8 1-38 -7*5-59
0-95 -70-9 1-36-75-35
0-98 -7*1-2 1-16-75-36
1 0 —yi-3 1-14 -7*5-35
Calculated
Observed
amp
amp
amp
1-75-79-2
1-63-78-8
1-52-78-5
1-50-77-8
1-45 -7*7-3
1-35 -7*6-4
1-40 - 7 6 O
1-55 -7*5-6
1-65 -75-2
1-67-75-1
1-68 - 7 5 0
2-61 -78-6
2-63 -78-2
2-66-77-78
2-74-77-38
2-85 — 77-02
2-68 -7*6-52
2-55 -76-22
2-58 - 7 6 I 6
2-53 - 7 6 1 5
2-08 -7*6-50
2 0 6 -76-76
2-7 - 7 9 0
2-58-78-6
2-57-7*8-3
2-56-77-8
2-5.0 -77-5
2-30-770
2-40 -76-6
2-52 - 7 6 - 4
2-6 - 7 6 I
2-65 -76-3
2-68 -76-3
Table 3
COMPARISON OF LOAD TEST RESULTS WITH CALCULATIONS FROM THE EQUIVALENT CIRCUIT
r
C O S Ot
Calculated Observed
amp
0-707
(subsynchronous)
0-673
0-69
0-72
0-76
0-80
-0033
(near
synchronous)
00133
005
010
013
016
-0-5
(supersynchronous)
/=
2
'1
ii
+ h
Slip
-0-427
-0-40
-0-38
-0-36
-0-34
-0-32
26-8
25-8
24
22-4
22-2
22-4
22-8
26
29-8
33-2
amp
28
26
24
22-5
22
19-5
21
24
27
30
16-4
19-5
14
24
22
25
27-4
30-2
37-2
16-5
28
33
Calculated
Observed
Calculated
amp
-7*8-6
-7*8-65
-7*8-81
-7*9-03
-7*9-22
2-71
2-72
2-8
2-9
-790
-7*9-0
-7*9-2
-7*9-3
-7*6-35
-7*6-36
-7*6-38
-7*6-39
-7*6-4
1-35
1-4
1-45
1-46
1-49
-7"6-4
-7*6-4
-7*6-4
-7*6-4
-7*6-4
2-68
3-58
4-71
5-37
5-98
-7*6-52
-7*6-94
-7*7-6
-78-03
-7*8-47
2-30
3 10
4-25
5-16
5-69
-7*7-0
-7*7-2
-7*7-7
-7*8-2
-7*8-6
-7*5-35
-7*5-24
-7*5-15
-7*5-05
-7*5-0
-7*4-95
1 -65
2-2
2-4
2-4
2-7
3-3
-7*5-2
-7*5-2
-7*5-0
-7*5-1
-7*5-1
-7*5-1
2-53 -7*6-15
3-64 -7*5-95
4-56 — 7*5-76
5-75 -7*5-68
6-48 -7*5-67
2-6
3-8
4-7
5-8
6-6
8-5
-7*6-1
-7*6-0
-7*5-7
-7*5-8
-7*5-8
-7*6-0
10
0-82
0-52
014
-0-2
amp
-7*8-93
-78-8
-78-52
-7*8-18
-77-86
1-34
1-37
1-42
1-44
1-47
1-36
1-74
205
2-47
2-72
3-29
+70-15
-7*0-4
-7IO
2-82 -7-1-5
1-34
2-21
3-29
3-93
4-51
-7'0-17
-70-58
-71-22
-71-64
-72-07
0-95 -7*0-4
1 1 7 -70-8
1-9 -70-71
0-95 - y O - 9
2-51 - 7 O 6 I
3-28 -70-63
3-76 -7*0-67
4-82 -70-77
1-8
2-3
1-7
2-8
3-7
4-2
1-6
2-3
3-4
3-9
5-2
-7O8
-71-3
-7l-8
-72-2
-7'0-8
-70-7
-7*0-7
-7*0-7
-7*0-9
Observed
2 61
2-62
2-62
2-68
2-72
amp
0-95 +7'0-2
1-4 +70
-70-29
2-54 -70-85
2-92 -71-36
Calculated
simp
1-75 -7*9-2
1 -31 -7*9-0
0-92 - 7 8 6
0-5 - 7 * 8 - 2
0 0 8 -7*7-8
amp
1 -61 +70-33
1-8
21
Observed
8 1 1 -7*5-72
amp
2-7 -7*9-0
JHA: SOME TESTS ON A STATOR-FED POLYPHASE SHUNT COMMUTATOR MOTOR
about 10-15 % from day to day. The observed values for currents
shown in Tables 2 and 3 are an average of numerous readings
taken over a long period.
The small size of the machine and the loading generator
(3 • 1 kW) limited the tests to a small range of loads, which is a
serious disadvantage in any experimental verification of theory.
In view of the inherent limitations of the theory, the dependence
of some of the parameters supposed constant on the operating
conditions (e.g. leakage reactances on current, mutual reactances
on voltage, etc.) and many difficulties experienced in the measurement of parameters, the agreement between calculated and
observed values shown in Tables 2 and 3 is very encouraging.
The supply currents seem to agree best, but their division into
motor and regulator currents shows considerable divergence in
the calculated and observed values, particularly at subsynchronous speeds. The divergence is in the loss components of
the currents, the quadrature components agreeing reasonably
well, more power being supplied through the regulator and less
through the motor than calculated. This is thought to be due
to the regulator supplying part of the surface and parasitic losses
in the motor at subsynchronous speeds.
Some tests were made on the machine with the auxiliary
winding disconnected from the main machine circuit. The
agreement reached between calculated behaviour and test results
was of about the same order as in tests with the auxiliary
winding in.
(6) CONCLUSION
The evidence of fairly good agreement between experimental
and theoretical results justifies the belief that not only is the
theory within its inherent limitations basically sound but also
that the methods used for measurement of machine parameters
are fairly accurate. It is hoped that the information contained
in this paper and in two earlier related papers6'7 will prove
useful to those interested in the design and operation of the
stator-fed 3-phase shunt commutator motor with induction
regulator control.
(7) ACKNOWLEDGMENTS
The investigation was part of a thesis study,5 and the author is
obliged to the Principal of the Heriot-Watt College, Edinburgh,
for permission to publish this paper. Thanks are also due to
Mr. E. O. Taylor, Assistant Professor of Electrical Engineering,
and other members of the laboratory staff of the Heriot-Watt
College for help received during the investigation.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8) REFERENCES*
P. L., and EKSERGIAN, R.: 'Iron Losses in Induction
Motors', Journal of the American I.E.E., 1920, 39, p. 906.
RICHTER, R.: 'Elektrische Maschinen' (Springer-Verlag,
Berlin, 1950), Vol. 5.
ADKINS, B., and GIBBS, W. J.: 'Polyphase Commutator
Machines' (Cambridge University Press, 1951).
SAY, M. G.: 'The Performance and Design of Alternating
Current Machines' (Pitman, 1952).
JHA, C. S.: 'Tensor Analysis of the Steady-State Behaviour
of the Stator-Fed Polyphase Shunt Commutator Motor',
Thesis for Fellowship, Heriot-Watt College, June, 1955.
JHA, C. S.: "Theory and Equivalent Circuits of the Double
Induction Regulator', Proceedings I.E.E., Monograph No.
197 U, September, 1956 (104 C, p. 96).
JHA, C. S.: 'Theory and Equivalent Circuits of the Stator-Fed
Polyphase Shunt Commutator Motor', ibid., Monograph
No. 220 U, February, 1957 (104 C, p. 305).
125
(9) APPENDIX: SPECIAL APPLICATION OF THE TWO
WATTMETER METHOD OF MEASURING POWER AND
THE PHASE ANGLE BETWEEN VOLTAGE AND CURRENT
VECTORS IN A THREE-PHASE CIRCUIT
(9.1) Three-phase Three-wire System
The two-wattmeter method of measuring power in a 3-phase
3-wire circuit is well known. If Px and P2 be the two wattmeter
readings,
Total power = Px + P2 . . . . (23)
The phase angle <f> between voltage and current vectors is given
by the relation
V3CP, - P 2 )
t a n <f> —
(24)
P1+P2
(9.2) When the Load is in the form of a Commutator Winding with
Two Brushes per Phase
In this case, assuming a 3-phase 6-wire supply available, the
wattmeter connections for measuring power and tan <f> are as
shown in Fig. 11. For balanced conditions, the following
relations can be easily derived:
Total power = 2{PX + P2)
and
.
.
.
.
-Pi)
t a n (f> =
(25)
(26)
Fig. 11.—The two-wattmeter method when the load is in the form of
a commutator winding with two brushes per phase.
ALGER,
* For a comprehensive Bibliography see Reference 7.
Fig. 12.—The two-wattmeter method when the load is in the form of
a commutator winding with two brushes per phase and an extra
balanced load connected to each phase.
(9.3) When, in addition to the Commutator Winding with Two
Brushes per Phase, extra Balanced Loads are present in
each Phase
In this case, the measurement is slightly modified, the wattmeter connections being as shown in Fig. 12. It can be shown
that for balanced conditions
Total power = 3(Pt + P2)
t a n <f> =
Pi
-Pi
+ Pi)
•
(27)
.
(28)