USING A VARIABLE FREQUENCY AND VOLTAGE INVERTER TO REGULATE INDUCTION MOTOR SPEED

8.1 Objective

In this exercise, we will work with a speed variation process based on the most used industrial drive for asynchronous machine.
We will study how an induction motor's speed-torque changes when we fed the stator with a control law of variable voltage and frequency that allows us to maintain a constant flux.

The asynchronous machine's is energized in this exercise by an IGBT-based, battery-fed, three-phase PWM inverter which provides variable frequency and voltage.

8.2 Initialization of the Setup

When the simulator is started up, the initial settings on screen are as follows:

• DC voltage supplies SC1, SC2 set to 0 V.
• AC voltage supply SA1, in the “AC Grid” tab, set to 0 V.
• Switches K1, K2, K3 are open: asynchronous machine stator windings are in open-circuit. See Table 4.
• Switch K6 is disabled: the asynchronous machine rotor is driven by the DC motor. See Table 4.
• Switches K4 and K5 are disabled: asynchronous machine rotor windings are short-circuited. See Table 4.
• Trigger switches K10 and K11, in the oscilloscope tabs, are enabled. Triggers are active for oscilloscope groups oscilloscopes1 and oscilloscopes2. See Table 4.

8.3 Setup Diagram

Figure 11: Electrical diagram setup for exercise 5

In this exercise the asynchronous machine's is powered by a three-phase PWM inverter that provides variable frequency and voltage.

A frequency-voltage control law that allows a constant flux is implemented in the inverter command system.
It specifies that for each fs value specified by the user in the “Inverter” tab, the RMS voltage U_s provided by the inverter is:

Rotor windings are short-circuited by switch K4.
The asynchronous machine is operating in motor mode, driving a DC generator that is discharging on its fixed load resistance R_ch.
Use SC2 to vary the current I_f. DC voltage source SC1 is set to 0 V for this exercise and does not appear in the diagram when the DC machine is operating in generator mode because it has unidirectional voltage and current (it has a serial diode not shown here).

In this exercise, we will study how the motor torque-speed characteristic changes when we modify voltage and frequency at the asynchronous machine’s stator. This allows us to identify the resistant torque-speed characteristic for several inverter frequency values.

8.4 Exercise

1. Restore the setup to its initial conditions, as described in Section 8.2; by resetting sources SC3, SC1, SC2 and SA1 and setting all switches to their initial states.
2. Select the “Inverter” tab. Set the Inverter frequency f_s to 0 Hz. Close switch K2 to connect the asynchronous machine’s stator windings to the PWM inverter.
3. Slowly increase the inverter frequency f_s to 60 Hz to start the asynchronous machine.
   Make sure not to exceed the asynchronous machine’s nominal current value I_sn by increasing f_s proportionate to the motor speed increase, otherwise asynchronous machine stator winding fuses F_i1, F_i2 and F_i3 may be blown, and the drive will stop.
   If this happens, wait until speed is null and return to initial settings (see Section 8.2).
   Then, and only then can we simulate replacing fuses by resetting the protection system using push-button K8.
4. Once the steady state is reached and speed is stable, note the (i) active power P absorbed by the induction motor, (ii) RMS line-line voltage U_s at stator, (iii) RMS line current I_s at stator, (iv) torque T_u and (v) rotation speed N.
5. Vary the DC generator’s resisting speed-torque characteristic slope k(I_f) by adjusting the current I_f using SC2.
   This will define a new operating point for the induction motor's speed-torque for frequency f_s= 60 Hz.
   Take note of 10 points from this characteristic by increasing the DC generator's inductor current l_f using source SC2.
   For each steady state operating point, identify (i) the active power P absorbed by the induction motor, (ii) RMS line-line voltage U_s at the stator, (iii) RMS line current I_s at the stator, torque T_u, and (iv) rotation speed N.
   Do not exceed the asynchronous machine’s nominal current I_sn or the DC generator’s nominal armature I_an, otherwise, fuses will be blown, and the drive will stop.
   If this happens, wait until speed is null and return to initial settings (see Section 8.2).
   Then, and only then can we simulate replacing fuses by resetting the protection system using push-button K8.
   Restart the exercise.
6. Set the inverter frequency f_s to 40 Hz and repeat steps 3 to 5.
7. Set the inverter frequency f_s to 20 Hz and repeat steps 3 to 5.

8.5 Lab Report

1. Present the results from Section 8.4 in tables (with units in SI).
2. Using the results of the exercise, plot the three characteristics for the induction motor torque-speed T_u-N with frequency values f_s =60 Hz, f_s=40 Hz, f_s=20 Hz.
3. Observe how the characteristics for the induction motor torque-speed T_u-N change with frequency f_s.
   Can we then assume that the process of using variable voltage to vary speed can be used to drive an elevator with a constant resistant torque (resistant torque-speed characteristic Tr-Ω = constant, regardless of Ω)?
   Would this be a safe solution?
   Could it be used to drive a cooling fan propeller that has a characteristic type Tr-Ω = m Ω² (resistant torque proportional to the square of the speed)? Discuss.
4. Compare the induction motor’s torque-speed characteristics T_u-N obtained through the exercises 3-5 with different speed variation procedures: (i) variable voltage, fixed frequency in the machine’s stator (ii) fixed voltage and frequency in the machine’s stator, variable rotor resistors and (iii) variable voltage and frequency in the machine’s stator.
   Show how the variable voltage and frequency speed variation procedure combines the advantages of the two others.
5. Calculate the induction motor cosφ power factor for each operating point in Section 8.4. Plot all three cosφ-N characteristics with the frequency values f_s=60 Hz, f_s= 40Hz, f_s= 20Hz.
   Explain the results.
6. Plot the three current-speed characteristics I_s-N with the frequency values f_s=60 Hz, f_s=40 Hz, f_s=20Hz.
   Explain the results.
7. We could also theoretically predict the induction motor’s speed-torque without the load tests run in Section 8.4 by using a steady state asynchronous machine model.
   All it requires is using a theoretical expression of the induction motor torque T_{em ^(Note1)} to implement the circuit parameters identified using the low power tests in exercise 2.
   Calculate the theoretical electromagnetic torque characteristics T_em-speed N(rpm) for the induction motor in Section 8.4, using this simplified expression:
   
   V_s is the stator RMS line-neutral determined by the inverter’s constant flux command law
   
   
   p is the number of pair poles for the induction motor and ω_s is the angular speed.
   s is the motor slip when it turns at speed N: 
   
   N_s is the motor synchronous speed corresponding to f_s.
   
   

   Important note: reactances also vary with power frequency f_s, which must be considered in the previous expression.
   
   

8. Superimpose the 3 theoretical motor speed-torque characteristics for the induction motor T_em-N and the three characteristics T_u-N from step 2 on the same graph.
   Compare theoretical and measured characteristics and discuss the differences.