In the three examples that follow we use the same 25 hp, 460 Volts, 50 Hz, 1500 RPM three-phase induction motor. The electrical parameters of motor equivalent circuit are assumed to be known (the interface can calculate them).

The mechanical load is 80 % of motor rated power when measured at 102 % of motor rated voltage at rated frequency (the motor had no speed control when the load was measured). The load torque is assumed to be proportional to the square of the speed *.

* How the load torque varies with the speed is an important characteristic of a mechanical load.

**Example 1** : What are the steady-state running conditions of the motor when the terminal voltage amplitude equals 102 % of motor rating and the terminal voltage frequency equals the rated frequency (the motor has no speed control) ** ?

** These are the conditions that we had when the 80 % mechanical load was measured. By definition the motor power output should equal 80% of motor rated power (80% of 25 hp).

The speed and the slip are unknown before the calculations.

Solution :

Option 4 of the IMC program does not require to know the speed or the slip before the calculations.

Here are the conditions calculated by option 4 :

Option 4 calculated a 79.95 % motor power output. We expected 80 %. That is pretty good.

**Example 2** : Same motor. Same mechanical load. No speed control. What are the conditions if the voltage amplitude falls to 90 % of motor rated voltage and the stator voltage frequency falls to 49.75 Hz ?

Solution :

The speed of an induction motor changes when the voltage or when the frequency changes. Therefore we know that the speed here has changed. But we do not know the new values for the speed and for the slip.

Option 4 of the IMC program calculates the new steady-state conditions :

The speed is now 1445.7 RPM (it was1463.4 in example 1).

**Example 3** : Same motor. Same mechanical load. What are motor conditions if we add a variable frequency drive (VFD) speed control and set the speed equal to 1000 RPM ?

Solution :

We know the speed before the calculations but we do not know the voltage amplitude and the voltage frequency (because both are modified by the VFD speed control).

In SimPhase Software Suite, each VFD is assumed to be the combination of a three-phase diode rectifier and a three-phase PWM Voltage Source Inverter.

Option 4 easily does the calculations. Here are the results :

Following table compares some of the values calculated in the 3 examples.

Motor Calculated Value | Example 1 | Example 2 | Example 3 |
---|---|---|---|

Speed in RPM | 1463.4 | 1445.7 | 1000.0 |

Real Power Input in kW | 16.93 | 16.61 | 5.74 |

Reactive power Input in kvar | 7.97 | 7.18 | 1.17 |

Power Factor in % | 90.46 | 91.78 | 98.0 (approx) |

Efficiency in % | 88.06 | 86.53 | 82.99 |

Rotor Resistive Losses in % of full-load value | 59.65 | 74.52 | 15.09 |

Stator Current in % of full-load value | 79.0 | 86.58 | 45.11 |

Conclusion

With option 4 of SimPhase IMC program we do not need to know the speed or the slip before starting the calculations of motor steady-state conditions.

Option 4 can be used to verify our field measurement of the mechanical loading (as in example 1).

It can estimate the effects of voltage amplitude variations and voltage frequency variations (as in example 2).

It can estimate the conditions of a motor after adding a variable frequency drive (VFD) speed control (as in example 3).

Pierre Lacasse