Download Performing locked rotor test on squirrel cage motors

Performing locked rotor test on squirrel cage motors
by CD Pitis, Femco Mining Motors, Brits
A locked rotor or short-circuit test (LRT) performed on squirrel cage motors is part of the routine
test series for such motors. The test is to confirm motor compliance with standard and customer
requirements. This article presents basics about estimation methods of parameters to be
evaluated when a LRT is performed.
The LRT gives information about leakage impedances required for equivalent circuit, motor circle
diagram and breakdown torque to ensure a reasonable margin for the motor’s overload capacity
and to allow for voltage variations. If not properly performed, the test can become dangerous for
the motor, leading to destruction. On the other hand, the LRT is compulsory in motor evaluation.
Methodology
During the test the rotor is blocked and the stator supplied with low voltage so as to avoid
excessive currents. Tests should be performed under the same conditions of rotor current and
frequency that will occur during normal operating conditions.
The IEEE recommends using 25 % of the rated frequency. This is because the rotor’s effective
resistance and leakage inductance at the reduced frequency may differ from their values at the
rated frequency. This will be particularly true for double cage or deep bar rotors and also for high
power motors [1].
However, because not many repairers have these facilities, we presume that the stator terminals
are supplied with balanced voltage at the rated frequency.
Fig. 1: Motor in STALL condition acting as a transformer @ 50 Hz rated frequency.
Motor in stall condition
If full voltage is to be applied to the motor terminals under stall conditions, the test becomes
analogous to an Abrupt Short-circuit Prototype Test of a transformer.
Consider a 570 kW, 3300 V, 115 A, 4 pole motor with “T” bars (186 mm²) fitted in the rotor. When
the rated voltage is applied to the stator terminals, the rotor bar current will be about 5 000 A.
Taking into account the “deep-bar” effect, the topside of the bar (23mm²) will have to cope with
about 150 A/mm² current densities.
For this example no voltage regulation been considered. It reveals that for some motors, if an
LRT is not performed properly, i.e. the motor is brought close to stall conditions, the rotor will act
as a fuse (Fig. 1)
Fig. 1: The broken starting cage of a 300 kW motor resulting from combined uneven thermal and
electrodynamic mechanical stresses generated in stall condition (the short-circuit ring is missing)
Performing an LRT
The stator is supplied with variable low voltage (Uk), which is raised in steps; monitoring
absorbed current (Ik); input power Pk), power factor (cos ) and torque (Tk); until the current
reaches the vicinity of twice rated value (In), supposing there is magnetic saturation effect of the
leakage paths.
If the position in which the rotor is clamped may affect the current, the variations are noted when
the rotor is locked in various positions and a mean position found.
Alternatively, the rotor may be allowed to rotate very slowly during the progress of the test [2].
Readings should be taken quickly to avoid overheating.
The winding temperatures should be observed before and after the test to minimise errors due to
changing resistance values.
Other details about how to perform LRT in [3]
Magnetic saturation effect and related calculations
Many repairers use the following relationships:
[Ikn / Ik] = [Un / Uk]
[1]
[Tkn / Tk] = [Un / Uk]
[2]
where “k” index stand for short-circuit test values and “n” index for rated values. This ‘formula
package’ is called Method 1. These conditions are likely to occur when the leakage flux does not
saturate the motor leakage paths or motor teeth; stator slot openings are open and no magnetic
wedges are fitted; rotor slot openings have relatively high values.
When no saturation of leakage paths occurs, the “short-circuit characteristic” Ik = f (Uk) is a
straight line.
Some manufacturers simulate the saturation effect by introducing “saturation coefficient - S” with
values of 1,05 – 1,2. This is a function of the motor design.
As a result the equation [2] can estimate more accurate locked rotor torques and other
parameters by using:
Tkn = Tk x [Un / Uk]² x S
[3]
When the stator has semi-closed or fully closed slots, i.e. magnetic wedges have been used, a
relatively small air gap value and small openings on the rotor slots, then the bridges covering the
slots (partially or totally) are rapidly saturated when applied voltage (Uk) reaches values between
30% and 50% of rated value (Un). At these values the saturated zone is extending rapidly,
starting from the teeth lips and extending toward the bottom of the teeth. As a result, some
authors recommended additional readings should be taken at half of full voltage to establish the
actual value of the starting current [4]. For this type of motors, the short-circuit characteristic Ik =
f(Uk) has a non-linear shape (see fig. 2).
Fig. 2: Characteristic LRT (Short-circuit) test graphs (in p.u.) revealing magnetic saturation.
Grapho-analytic method of evaluating short-circuit parameters (taking into account the magnetic
saturation effect) – Method 2
If the saturation effect is unknown, this method can provide the repairer with a relatively accurate
test result of LRT values.
By extending the linear portion of the Ik = f(Uk) graph, towards the abscise (where the “T” line will
cut the voltage line - abscise at the “M” point) a value OM = U is obtained. Then, the following
ratio should be calculated:
Un - U
K = ----------[4]
Uk - U
As a result the formulas [1] and [2] will become:
Ikn = Ik x K
[5]
Tkn = Tk x K
[6]
Example1: According to Table no. 1, a 800 kW, Un = 6600 V, In = 84 A, 4 pole motor [3] displays
the following LRT values:
Test voltage Uk
575 V
961 V
1529 V
Table 1
Abs. Current Ik
32.6 A
55.8 A
90.4 A
Torque Tk
14.7 Nm
49.1 Nm
147.2 Nm
If the calculation is done according to Method no. 1 [1], [2], it gives the following results:
Locked rotor current
Ikn = 390 A (4,64 p.u)
Locked rotor torque
Tkn = 2742 Nm (0,53 p.u.)
According to Method no. 2, by taking into account the magnetic saturation (see fig. 2) the
following steps need to be done:
Use the Ik = f (Uk) graph, and build the “T” line:
I – 90.4={[dI/dU]@(Uk=1529,Ik=90.4) x(U – 1529)}
From the “T” line intersection with the abscise line (I = 0), it results in the point “M” with U = 63 V.
According to [4] K = 6537 / 1466 = 4,46 and results in:
Locked rotor current
Ikn = 403 A (4,8 p.u)
Locked rotor torque
Tkn = 2930 Nm (0,573 p.u.)
If the test should be carried out in a region of double the rated current value, the saturation will be
more intense and the locked torque and current values should be estimated with greater
accuracy.
Mathematical estimation of locked torque parameters – Method no. 3.
In the formulas [2], [3] and [6], the exponent “2” has been used, as an estimated quadratic
variation of the torque function of the applied voltage. However, from experience, for some
motors, where the “skin effect” in the rotor bars is very intense, it has been found that a
logarithmic variation is a more accurate estimation and as a result the exponent has different
values (bigger than “2”):
Tkn = Tk x [Un / Uk] exp Zt
[7]
ln [Tk2 / Tk1]
Zt = ----------------------[8]
ln [Uk2 / Uk1]
Ikn = Ik x [Un / Uk] exp Zi
[9]
ln [Ik2 / Ik1]
Zi = ----------------------[10]
ln [Uk2 / Uk1]
Where Uk1,2 = two values of reduced test voltage
Ik1,2 = two corresponding values of current
Tk1,2 = two corresponding values of torque
Example2: According to Table 2, a 300 kW, Un = 1000 V, 4 pole motor [5] provides the following
LRT values:
Test voltage Uk
Abs. Current Ik Torque Tk
330 V (experiment)
309,6 A
253 Nm
360 V (experiment)
344,9 A
313 Nm
987 V(test
1288 A
3847 Nm
validation)
Table 2
The results of LRT parameter estimations obtained by using different methods with corresponding
errors, are.
Ikn [Amps] Tkn [Nm] Notes
Method 1
958
2415
No saturation
considered
Method 2
1133
3379
Quadratic
estimation
U= 80 V
Method 3
1202
3817
Zi = 1.24
Logarithmic
Zt = 2.48
Test data
Validation test
@ 987
1288
3847
Volts
Errors of
- 6,7 %
- 0,8 %
Validated
method 3
estimation
Errors of
- 25,6 %
- 37,2 %
Poor
method 1
estimation
Non-validated
Table 3
With reference to Example no. 1 and taking into account the voltage regulation when a motor
starts, estimations according to method no. 3 with current and torque exponents Zi = 1,244 and Zt
= 2,36 respectively, give:
Locked rotor current
Ikn = 489 A (5,82 p.u)
Locked rotor torque
Tkn = 3620 Nm (0,70 p.u.)
These values are estimating more accurate motor LRT performances, being very close to the real
site values.
Conclusions and results validation
Accurate tests and test data processing are of paramount importance in estimating motor
performance. A wrong estimation of the absorbed current at the start can influence voltage
regulation and cause a malfunction of the entire application.
The proposed methods offer an accurate mathematical model of estimating motor performance
by considering motor saturation and “skin effect”. The results were confirmed by direct tests at
close to full voltage. These methods ensure a consistent assessment of motor compliance with
standard and customer requirements.
References
[1] P.C. Sen: “Principles of Electric Machines and Power Electronics”, John Wiley & Sons, 2 nd
Edition, New York
[2] M.G.Say: “Performance and design of alternating current machines”, Isaac Pitman & Sons, 3 rd
Edition, London
[3] H d Swart: “Locked rotor test explained”, Vector, Nov/Dec 2004
[4] P.L.Alger: ”Induction Machines” Gordon&Breach Science Publishers, 2 nd Edition, New York
[5] VA Tech Hydro - Weiz HYDRO - WEIZ: “Test Report on asynchronous dPRW280/80-4KL
machine” Austria, Dec. 2002
Contact Constantin Pitis, Femco Mining Motors, Tel (011) 887-0953, [email protected]