Determining Induction Machine Parameters
Three tests are needed to determine the parameters in an induction machine model. Detailed testing is quite involved and is specified in IEEE Standard 112.
DC Resistance Test
If a DC voltage is applied to the stator terminals, there will be no potential difference across any inductance and no induced voltage on the rotor. As a result, the per-phase circuit is reduced to the stator winding resistance. Applying a DC voltage across two motor terminals and measuring the current, the stator resistance can be found. Considering the figures below, it can be seen that the apparent impedance will depend on whether the machine is wye or delta connected.
Locked Rotor Test
In the locked rotor test, the rotor of the machine is prevented from rotating and the supply voltage gradually increased until rated current is reached. When the rotor is stationary , the slip, s = 1 and the equivalent circuit can be drawn as
Analysing the circuit:
Therfore, if the stator power, current and reactive power are measured, the resistance and leakage reactances can be found.
Ideally, the locked rotor test should be performed at a reduced frequency to account for skin depth and more accurately predict the rotor resistance under load conditions. Typically, this test is done at 1/4 rated frequency. With the value of stator resistance from the DC test, the rotor resistance referred to the stator can be found.
If the locked rotor test is done at reduced frequency, then the reactances (which are proportional to frequency) must be scaled to find the correct value at rated frequency:
At this point, only the total leakage reactance is known. The relative values of stator and rotor leakage must be found from experience and are summarised in the table below
Percentages of leakage reactance due to stator or rotor
No Load Test
During the no-load test, the machine is allowed to accelerate up to synchronous speed with no load applied. The machine will run close to synchronous speed, with s → 0 If slip approaches zero, the rotor current will fall to zero and the equivalent circuit can be drawn as shown below.
Remembering that this is a per-phase circuit we can write
where rotational losses are defined as
PF&W are friction and windage losses, Pcore are iron core losses and Pstray are stray load losses.
Again, measuring the stator current, power and reactive power, the remaining paramters can be found. Using the power, if stator resistance is known (from the DC test), the total rotational losses can be found
Using the value of X1 from the locked rotor test, the magnetising reactance, Xm, may be found from the no load reactive power.