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.

MethodologyDuring 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 conditionIf 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 LRTThe 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 calculationsMany 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 2If 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 - UK = ----------- [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 Abs. Current Ik Torque Tk 575 V 32.6 A 14.7 Nm961 V 55.8 A 49.1 Nm1529 V 90.4 A 147.2 NmTable 1

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 currentTk1,2 = 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 Nm360 V (experiment) 344,9 A 313 Nm987 V(test validation)

1288 A 3847 Nm

Table 2

The results of LRT parameter estimations obtained by using different methods with corresponding errors, are.

Ikn [Amps] Tkn [Nm] NotesMethod 1 958 2415 No saturation

consideredMethod 2U= 80 V

1133 3379 Quadratic estimation

Method 3Logarithmic

1202 3817 Zi = 1.24Zt = 2.48

Test data @ 987 Volts

1288 3847Validation test

Errors of method 3

- 6,7 % - 0,8 % Validated estimation

Errors of method 1

- 25,6 % - 37,2 % Poor estimationNon-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 validationAccurate 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, 2nd Edition, New York [2] M.G.Say: “Performance and design of alternating current machines”, Isaac Pitman & Sons, 3rd Edition, London[3] H d Swart: “Locked rotor test explained”, Vector, Nov/Dec 2004[4] P.L.Alger: ”Induction Machines” Gordon&Breach Science Publishers, 2nd 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, danpit@femco.co.za