The slip is an important value to know before starting the steady-state calculations using the equivalent circuit of an induction motor. The slip is defined using following equation :

If we have no measurement of the motor speed, how can we estimate the slip for the equivalent circuit ?

The steady-state speed of an induction motor is a function of the stator voltage amplitude, the stator voltage frequency and the mechanical loading (here assuming that the motor has no speed control).

Here is a procedure for estimating a good slip value :

- First we must find the
**full-load slip**that produces rated power output (at rated voltage and frequency) when inserted in our equivalent circuit for the motor.

Be advised that nameplate full-load speed is an approximative value (its tolerance is 20 % of full-load slip speed). Because of this tolerance, the nameplate full-load speed should not be used in calculations with the equivalent circuit. For the same reason nameplate full-load speed should not be used in mechanical loading measurements.

We should always verify our full-load slip value before moving to step 2. For example : If we insert our full-load slip in our equivalent and calculate a 44 HP power output for a 50 HP machine, it means our initial error is 12 %. - Full-load slip of step 1 must be multiplied by the estimated mechanical loading (measured at a specific voltage). The loading is expressed in percentage of motor rated power.
- Slip of step 2 must be adjusted if our voltage for the equivalent circuit differs from the voltage of step 2.

Lower voltage means lower motor speed (and higher slip) but it is not easy to do a good estimate of the slip deviation.

SimPhase Interface takes care of step 1. The IMC program does steps 2 and 3.

Is step 3 necessary ? Next section does a little study.

### Study of the effects of stator voltage amplitude deviation on the slip

Two simulations are done here using SimPhase IMC program.

The same 50 HP 460 Volts 1500 RPM 50 Hz three-phase induction motor is used in both simulations. We have the equivalent circuit for the motor.

Mechanical loading is estimated to be 100% when measured at rated voltage amplitude. Load torque is here constant at all speed. Mechanical loading is the same in both simulations.

In both simulations the motor has no speed control.

In the first simulation stator voltage amplitude equals 100 % of motor rated voltage. Figure 1 presents the results.

In the second simulation, voltage amplitude equals 90 % of motor rated voltage. Figure 2 presents the results.

Here are some of the values in Figure 1 and 2 :

Simulation | Amplitude (%) | Speed (RPM) | Slip (%) |
---|---|---|---|

First | 100 | 1428.2 | 4.79 |

Second | 90 | 1409.9 | 6.01 |

The torque-speed characteristic of a motor for a 90 % voltage differs from the characteristic at 100 % voltage. This is why the slip for the 90 % voltage is greater than the slip for the 100 % voltage.

### What if we neglect the stator voltage amplitude deviation when estimating the slip ?

Using the results of the previous section, let’s intentionally use the wrong slip value in our calculations (using the slip of the first simulation with the voltage of the second simulation). This is like neglecting step 3 in the procedure mentioned earlier.

The load torque is constant. This means that the calculated motor torque output should be the same at both voltages.

What error would we make in our calculations with the wrong slip value ?

From induction motor theory we know that the torque output of a motor is proportional to the slip. We can use this to estimate our error.

Using the wrong slip, the calculated motor torque output approximately equals 79.7 % of the value that it should have (4.79 / 6.01 x 100 = 79.7 %). A 20.3 % error. This error on the torque output would have an important impact on the real power flow throughout the motor.

Neglecting the voltage amplitude deviation when estimating the slip, when the load torque is constant, is probably not a good idea.

Using SimPhase software suite you could do a similar study for a variable load torque.

### Conclusion

All 3 steps of the procedure are important.

I hope this helps you in your calculations.

Pierre Lacasse

September 2020