Proc. of Int. Conf. on Advances in Electrical & Electronics 2010
Two Phasing Method for Conducting Heat Run
Test of Three Phase Induction Motors
Harish Kumar Sahu
AGM(RVC), Bhilai Steel Plant/SAIL
Bhilai (Chhattisgarh), India-490001
Email: hksahu1958@yahoo.com
Abstract—This paper introduces a new method1 developed for
equivalent loading for conducting heat run test for measuring
full load temperature rise of three phase induction motors.
This method does not require mechanical load, auxiliary
machines or identical motor of similar rating. It simulates the
running conditions with normally available apparatus
avoiding laborious computations. The induction motor is run
on no load at rated voltages across two phases with third
phase open. The third phase is connected to a variable
inductance. The rated load currents in all the phases are
obtained by adjusting the third phase external inductance and
making a little difference in two voltages. The different
components of losses in new method are nearly same as the
losses during normal full load operation. Hence the rise above
ambient temperature can be determined accurately. The
experimental results on heat run tests with new method and
with conventional method show an excellent agreement with
each other, confirming the validity of the proposed method.
This method is very simple, cheap and reliable in comparison
to others.
With the ever increasing sizes of induction motor, it
becomes more and more difficult and costly to perform a
fully loaded heat run test at manufacturing works.
Therefore, methods have been developed to perform heat
run test without mechanically loading the machine. They
are:
1) Direct loading using coupled generator (1963)[3]
2) Reverse rotation test (1963)[3]
3) Back to back: floating stator bed plate (1966) [4],
motorized coupling (1967) [5] and floating gear
box (1967)[6]
4) Phantom loading (1972) [7]
5) Forward short circuit test (1988)[8]
6) Variable inertia test (1994) [9,10]
7) No load run at over input voltage (1993-2001)
[11,12,13,14].
8) Two frequency method: using motor generator set
(1970)[15,16,17,18]
9)Two frequency, Sweep Frequency and amplitude
modulated rotating magnetic field at constant
speed method: using microprocessor controlled
powered electronic.
(1993-2009) [10,19,20,21,22,23,24,25,26,27,28]
Index Terms—Equivalent loading, Two phasing method,
Induction motor, temperature rise test, heat run test.
I. INTRODUCTION
Problem is always faced in deciding the rating of the
electrical machineries, which is limited by the temperature
rise of machines on full load. The temperature rise
predicted using electrical & mechanical design data may
differ from the actual temperature rise on full load. This is
because many physical systems can't be defined and the
calculation uses empirical formula.
In all the testing methods mentioned above, either
additional machines as load or specially designed power
supply (to produce mixed frequency power) are required or
inaccurate results are given requiring laborious
computations.
The mixed frequency method can be applied to all type of
machines, as it does not require an extra identical machine
or mechanical load. But it requires specially designed power
supply source. Several adjustment of main and secondary
voltages may be needed to establish rated voltage and
current. The vibration of the machine was found abnormal
[10,29]. The vertical motors may need additional bracing to
prevent torsional vibrations [16]. Design issues of supply
sources of different frequency had yet to be clarified [18].
Core losses and copper losses were increased over full load
value due to high harmonics giving results of several
degrees high (upto 8°C). An important problem in artificial
loading was to obtain losses equivalent to those when a real
load was applied to the shaft [19]. Presently there is no way
of determining the individual loss components in the real
machine under synthetic loading and further simulations for
reduction of torque pulsations are to be developed [24].
Operating of machine at higher temperature, not only
decreases the efficiency but the life of the machine is also
shortened due to deterioration of insulation given by
where 'A' and 'B' are constants and T is absolute
temperature [1]. For each 10°C increase in the temperature
above the limiting value of 105°C, the expected insulation
life is roughly halved [2].
The temperature of a motor must be limited also because
of the differing thermal expansions of iron, copper and other
materials giving
rise to mechanical stresses and
displacements that causes progressive deterioration.
1
This method was developed for submission of thesis for ME
(Research) to Nagpur University in April,1989.
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© 2010 ACEEE
DOI: 02.AEE.2010.01.159
Proc. of Int. Conf. on Advances in Electrical & Electronics 2010
The another method, which can be applied to a free
standing motor is to run the induction motor at 120% of
rated voltage at no load. The negligible rotor copper and
iron losses at no load are compensated by increased stator
copper loss in small motors and by increased stator iron loss
in large size motors [14]. In normal full load run, rotor
losses provide significant contribution in temperature rise
of the machine[30]. With the absence of rotor components
from the thermal circuit, the efficiency of the cooling
medium will be always doubtful.
The present method of two phasing was developed to
simplify the heat run test by overcoming the problems
faced in equivalent loading for temperature rise.
θ1, θ2, θ3 - Trigonometric function defines the space
distribution varying
sinusoidally with time
'm' is a factor by which voltage across two phases differs
'k' is the ratio of current in open phase to current in other
two phases
'a' is the operator that causes a rotation of a phasor through
120° in
counter clockwise direction
II. PRINCIPAL OF TWO PHASED LOADING
A. Expression for Rotating Magnetic Fields
The operation of 3 phase induction motor under 2
phasing may be examined by analyzing the resultant field
III. TWO REVOLVING FIELD THEORY FOR TWO
PHASED LOADING
The new term 'two phasing' was used first time for a three
phase induction motor running with its two windings
connected across the two phases of a three 3 phase supply
system. The third phase remained open. This was obtained
by grounding the star point of the motor windings with one
phase open. [H. K. Sahu, 1989]. In case of star connected
windings, only star point is needed in addition to three leads
outside the motor, whilst in delta connected stator windings,
all the six leads are to be brought out of the motor.
However, it is common to bring out six leads in large
induction machines for metering and protection. Unlike the
single phasing of three phase induction motors, the phase
difference of 120° is maintained in input voltages across the
two running stator windings producing rotating magnetic
field to develop the starting torque.A voltage is generated
across the third open phase due to stator and rotor currents.
By loading the third phase with an external impedance and
making a little difference in voltage across two phases, the
current in all the phases may be increased equally to full
load rated current. Thus, the motor runs partially as self
excited single phase generator as shown in Figure 1.Based
on the above, the present method was developed for
in a similar way as given in ref. [1]. The general expression
for resultant mmf for three phase induction motor at any
time t and at any point θ under unbalanced two phasing can
be derived as given in ref. [31], where current in one of the
phases is 'k' times of current in other two phases:
when k = [ 1, 0, -1], the three phase induction motor
running under following conditions are described
respectively:
(a) Normal 3 phase balanced condition, with balanced
equal current producing resultant mmf as:
(b) Two phased no load condition, with zero current in an
open phase producing resultant mmf as:
(c) Two phased on load condition, with equal negative viz.
generating current in open phase by connecting an
external impedance as:
conducting an equivalent heat run test, which is equally
applicable to large induction machines as well as to small
induction machines.
Fig. 1. Three phase induction motor running under two phased condition
with open phase connected to an external impedance.
Thus the two mmf waves are produced by the excitation
of two phases of 3 phase distributed winding with 2 phase
sinusoidally varying current with phase displacement 120°:
Where,
L1, L2,L3 – Line Terminals , N - Neutral point
I1 , I2, I3- line currents, I-Maximum value of current
ZE - External impedance
a) having peak value equal to maximum amplitude of
pulsating mmf wave in one phase and argument is (θ - ωt)
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DOI: 02.AEE.2010.01.159
Proc. of Int. Conf. on Advances in Electrical & Electronics 2010
where Zp and ZN are impedances to positive and negative
phase sequence component of current.
A generalized equivalent circuit for three phase
induction motor running under two phased unbalanced
condition has been shown at Fig.2, which is in compliance
with the general expression for mmf "(1)" and voltage
current relationship "(5)". By putting the value of 'k' equal
to (1, 0, -1) in "(5)" the circuit is converted for the three
phase induction motor running under following conditions
as described in section III.
travels in forward direction of θ. It is 2/3 times or 66.77%
of the mmf produced by 3 phase balanced current.
b) having peak value half of the maximum amplitude of
pulsating mmf wave in one phase and argument is
(θ
+ ωt ) travels in backward direction of θ. It is 1/3 times or
33.3 % of the mmf produced by 3 phase balanced current.
Both the component describes a sinusoidal time varying
function of space angle θ and (θ+180° ), showing the
displacement of 180° between the positive peak of forward
and backward mmf in space.
(a). Normal 3 phase balanced condition
(b). Two phased no load condition and
B. Torque Speed Characteristic
(c). Two phased on load condition
Induction motor action is produced by both the
component mmf waves, but the corresponding torques are
in opposite direction. With the rotor at rest, due to
difference in magnitude of forward and backward air gap
flux waves created by the combined mmfs of stator and
rotor current, there will be a difference in forward and
backward torque, hence starting torque is produced.
The variation in current in two phases with change in
current in third phase is shown in Fig.3.
Thus, two rotating fields, one in forward and another in
backward direction are produced in air gap. Forward field
being double of the backward field, the motor is started and
run nearly at its normal no load speed in the forward
direction.
When the rotor is in motion the component rotor
currents induced by the backward field are greater than at
stand still or starting. Their mmf which opposes that of the
stator current, results in a reduction of backward flux wave.
As speed increases the forward flux wave increases, while
the backward flux wave decreases, their sum remaining
roughly constant since it induces the counter emf in stator,
which is approximately constant if the stator leakage
impedance drop is small. Hence with the rotor in motion,
the torque of the forward field is greater and that of the
backward field is less. In normal running region with small
value of slip, the forward field is several times greater than
the backward field, and the flux wave does not differ much
from the constant amplitude revolving field in the air gap
of a balanced polyphase motor. The torque speed
characteristic of a three phase induction motor under
normal running conditions and working under two phasing
condition do not differ much [1,32].
Fig. 2. Equivalent circuit of 3 phase induction motors
under two phased condition.
Where,
Z1 = impedance of stator winding, ZM = magnetizing
branch impedance, Z2' = impedance of rotor winding
referred to stator,
R1, X1 = resistance and reactance of stator winding,
R2', X2 ' = equivalent resistance and reactance of rotor
winding,
s = fractional slip
ZP, ZN = positive and negative sequence impedance of
motor
ZRP, ZRN = positive and negative sequence impedance of
rotor winding,
ZP = (R1 + jX1)+ (ZM-1 +ZRP-1)-1 ,
ZN = (R1 + jX1)+ (ZM-1
-1 -1
+ZRN )
ZRP = R2'/s + jX2',
ZRN = (R2'/(2-s) + jX2')
IV. EQUIVALENT CIRCUIT
A. Without an External Impedance Across Open Phase
A general expression showing the relation of current 'kI'
in one of the phases, with equal magnitude of current I in
other two phases for three phase induction motor can be
derived by symmetrical components as given in [ 31, 33]:
V = 1/3 (ZP – ZN) KI + 1/3 (2 ZP + ZN) I
(5)
B. With an External Impedance Across Open Phase
With star point grounded, the symmetrical components
were evaluated on phase basis assuming the phase
sequence of the line transferred to phases of motor. The
voltage across three stator windings shown in Fig.1 are
V1 = - I ZE, V2 = a2 V, V3 = (1 + m ) a V
(6)
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Proc. of Int. Conf. on Advances in Electrical & Electronics 2010
The equations for current in the three phases were
derived as given below [31]:
I1 =(V/3)[(2ZP-1 - ZN-1 - Z0-1) + m(ZP-1 + a2 ZN-1 + aZ0-1 )]
[1
+
(ZE/3)(ZP-1+
ZN-1
+
Z0-1]-1
(7)
I2 =(V/3)[(2a2 ZP-1- a ZN-1 -Z0-1)+m(a2ZP-1 + ZN-1 + aZ0-1 )3ZE {(√3ZP)-1 (jZN-1 + ∕30° Z0-1)+m(aZP-1 ZN-1 +ZP-1 Z0-1
+a2 ZN-1Z0-1 )}][1+(ZE/3) (ZP-1 + ZN-1 + Z0-1)]-1
(8)
I3=(V/3)[(2aZP-1 – a2 ZN-1 – Z0-1) + ma(ZP-1 + ZN-1 + Z0-1)3ZE {(√3ZP)-1 ( ZN-1 - ∕-30° Z0-1)+ma(ZP-1 ZN-1 + ZP-1 Z0-1
+ ZP-1 Z0-1 )}][1+(ZE/3) (ZP-1 + ZN-1+ Z0-1 )]-1
(9)
The change in three currents for different values of ZE
can be computed for different values of 'm' in steps of 0.01
till a condition is reached for a particular value of 'm' and
ZE, when the three currents are equal to rated full load
current.
iii) Copper losses taking place correspond to full load
copper losses of the motor since the current is set equal to
the full load value.
This may be concluded that by two phasing method,
heat run test may be conducted to certain approximation
without mechanically loading the motor.
VI. EXPERIMENTAL RESULTS
1. Experimental work
In order to make the proposition acceptable, the above
hypothesis was verified experimentally by carrying out the
experimental work on an induction motor having following
specifications:
1. Rated voltage - 440 V, 2. Power in shaft - 7.4 KW,
3. Stator line current - 13 A, 4. Rotor current - 24 A,
5. Potential between rotor rings at standstill - 194 V,
6. Power factor, Cos φ - 0.88, 7. (a) Synchronous
speed - 1500 rpm , (b) Rated load speed – 1430rpm,
8. Frequency - 50 Hz,
9. Stator winding resistance/ phase - 1.1 Ω,
Where, I0N is normal no load current.
Fig. 3. Current under normal and two phased conditions for 3-p I.M
10. Stator leakage reactance / phase - 1.75 Ω,
V. LOSSES UNDER TWO PHASED LOADING
11. Rotor winding resistance / phase - 0.21 Ω,
If the results of an equivalent load temperature test are to
be accurate, the losses must be close to the rated losses. It
was expected that the voltage applied across the two phases
will not differ by more than 5% to get the current in all the
phases equal to rated full load current. This will mean that:
12. Rotor leakage resistance / phase - 1.75 Ω,
13.Magnetizing reactance - 60 Ω.
A. Heat Run Test by Direct Loading:
i) Mechanical losses correspond very near to actual
mechanical losses (windage & bearing) when the motor is
operating at full load, since the motor runs nearly or
between at its normal no load and rated load speed.
Induction motor was run on 3 phase supply and loaded by
dc generator coupled to it. Rated full load current was
obtained by adjusting load resistance across the dc
generator. The motor was run for four hours on nearly full
load with rated voltage applied.
ii) Iron losses are also very near to the actual iron
losses which take place under normal running condition.
Under two phasing condition forward flux is several times
higher than backward flux ( more than 30 for large
induction motors). The stator iron losses remain nearly
same as operating at full load. Although the backward flux
cuts the rotor at nearly double the synchronous speed, the
iron losses still remain negligible in rotor.
B. Heat Run Test by Proposed Two Phasing Method:
The induction motor was run through two dimmerstats.
The motor was run on no load at rated voltages across two
phases with third phase open. The third open phase
was connected to a variable inductance. The rated full load
current in all the phases was obtained by adjusting the
external inductance and by making a little difference in two
voltages.
The experimental set up for the proposed
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DOI: 02.AEE.2010.01.159
Proc. of Int. Conf. on Advances in Electrical & Electronics 2010
method is shown in figure 4. The motor was run for four
hours on nearly full load current in all the phases with rated
voltage applied across two phases.
2. Experimental Analysis:
stator, which may do more than justify the conclusion
drawn from temperature rise test by two phasing method.
This is an area that could be explored in future
[34,35,36,37].The analytical and experimental approach
considering the following may be attempted;
During the heat run test the temperature of stator and
rotor winding was measured by the rise of resistances and
of body by thermometer. The resistance of windings were
measured by wheat-stone bridge. The rate of rise in
temperature of windings and body with time is almost same
in proposed method and the actual heat run. The heat run
was continued until thermal equilibrium between the motor
and the cooling medium was almost established. At the end
of equally long test period, thetemperature of stator body
and windings were measured, which resembled with the the
values reached under actual steady state loading. The table
I shows the comparison of test results with two methods.
i)
Computer based approach for prediction of value
of inductance required and voltage values for two
phases.
ii) Rigorous analysis based on generalized machine
theory.
iii) Possibility of use of this method for special
purpose motors ( like in an integrated process
industry, Bhilai Steel Plant/ SAIL.)
ACKNOWLEDGMENT
The author expresses his heartiest gratitude to
Shri
T. R. Subramanyam, Shri P. K. Kharbanda, Shri S.G.
Tarnekar, Shri A. S. Zadgaonkar and Shri P. R. Aldak for
their kind support at all the stages of the research work.
Author wishes to thank V.R.C.E., Nagpur and BSP for
granting permission to conduct experiments.
TABLE. 1 TEMPERATURE RISE ON FULL L OAD
S.
No.
Temperature
of
Parts
Coupled
Generator
Loading
Two Phase
Loading
1. Stator body
26°C
25.5°C
2. Stator winding
37.44°C
36.437°C
3. Rotor winding
14.205°C
13.408°C
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