The motor parameters of Induction Motors are crucial when the Field Oriented Control Close loop torque/speed control is needed. More specifically, the rotor’s flux absolute position is determined mathematically using known speed, voltage and current, and a model representation of the motor’s main parameters. This blog shows how to determine these parameters.

The motor parameters of Induction Motors are crucial when the Field Oriented Control Close loop torque/speed control is needed. More specifically, the rotor’s flux absolute position is determined mathematically using known speed, voltage and current, and a model representation of the motor’s main parameters shown in the figure below.

These parameters include per phase rotor resistance ‘R_r’, rotor leakage inductance ‘L_lr’, mutual inductance ‘L_m’ and rotor leakage inductance ‘L_lr’ (core losses R_c are neglected). Furthermore, in order to set the FOC (Flux and Torque) PID gains, the Stator Resistance (R_s) and Stator Inductance (L_ls) needed, according to the method as described in chapter “FOC Gains Tuning” - Section 8 of Roboteq controllers User Manual v2.0. The most common ways, to manually estimate induction motor parameters through the controller, are to test induction motor under no-load and locked rotor conditions.

The no-load test, like the open circuit test on a transformer, gives information about exciting flux I_d current, the magnetizing inductance L_m and rotational losses. The test is performed by applying balanced rated voltage on the stator windings at the rated frequency. The small power provided to the motor is due to core losses, friction and winding loses. The motor will consume the necessary flux I_d current in order to establish the appropriate magnetic field. Motor will rotate at almost a synchronous speed, which makes slip nearly zero (s≈0). Therefore, the motor equivalent circuit is expressed as follows:

Assuming that the R_s (Ω), L_s(Η) are much lower than the magnetizing inductance L_m (H), the following equation can be extracted:

where V_s (V) is the phase stator voltage applied (RMS value), f_s (Hz) is the stator frequency and I (A) is the RMS  motor amps.

In order to implement the above mentioned no load test with RoboteQ induction motor controllers, please follow these steps:

• Set the operating mode to “Volts per Hertz” mode. encoder feedback action needed.
• Configure the Volt per Hertz setting according to motor nominal voltage (peak value of stator voltage according to manufacturer) and frequency.
• Run the motor without load up to the maximum available voltage (Command=1000), utilizing small acceleration/deceleration value. Be sure that the configured volt per hertz is correct, by checking the “Stator speed RPM” to be approximately equal to manufacturer’s synchronous rated speed.
• Calculate the applied V_s by the following equation:
  
  where m_a is the output PWM level (%1000) applied which is equal to Motor Power output measurement in Roborun+ utility (-1000 to 1000 range) and V_dc is the battery volts (V). In the considered no-load test the ma is 1000, therefore the applied voltage can be calculated as 
• Measure the motor RMS current from the utility (Motor Amps). Furthermore, the peak amps value should be configured as “Rotor Flux current” in the configuration tab.
• Calculate the magnetizing inductance for the no load test according to equation (1).

Example:

The following data have been given from the induction motor manufacturer:

P = 400 W (nominal power)

I_N = 23 A (nominal stator current)

V_dc = 24 V (Input dc voltage at controller)

f_s = 90 Hz (Nominal stator frequency)

n_s = 2700 rpm (Synchronous speed)

p= 2 (pole pairs)

Therefore, the Volts per Hertz ratio introduced in configuration tab is 

Then the motor run volts per Hertz and the respective results from Roborun+ utility are illustrated below.

From the above results, it can been observed that the stator speed is close to the synchronous speed (2700 rpm), while the slip is very small due to the no-load operation.

Therefore, by applying equation (1) the magnetizing inductance is: 

Furthermore, the rotor “Rotor Flux current” should be set in the configuration as 

The locked rotor test, like short circuit test on a transformer, provides the information about leakage impedances and rotor resistance. Rotor is at the stand still, while low voltage is applied to stator windings up to rated current. Due to the fact that the magnetizing inductance L_m is much higher that leakage phase inductances L_ls, L_lr, it can be assumed that there is no current is floating to L_m parallel branch. Typically, leakage inductances L_ls, L_lr should be around 2-10% of the magnetizing inductance L_m. Since there is no rotation slip (rotor at standstill) s=1, which gives us the following equivalent circuit.

Therefore, the phase L_ls (H) , L_lr (H), R_s (Ω), R_r (Ω) motor parameters are calculated as follows:

where P_s (W) is the input phase motor power, V_s (V) is the phase stator voltage applied (peak value), f_s (Hz) is the stator frequency, cosφ is the power factor, I (A) is the motor current (RMS value), Z (Ω) is the equivalent phase impedance at locked rotor test.

According to equations (7) and (8), it is assumed that rotor resistance is equal to the stator resistance, as well as rotor leakage inductance is equal to stator leakage inductance.

In order to implement the above mentioned locked rotor test with induction motor controllers, please follow these steps:

• Set the operating mode to “Volts per Hertz” mode. Encoder feedback action needed.
• Configure the Volt per Hertz setting according to five times lower the motor nominal voltage (peak value of stator voltage according to manufacturer) and frequency (1/5 of nominal V/f). The reason for configuring lower V/f ratio than in no-load test is to appropriately weaken the induced field and reduce the produced torque at startup, in order to be easier to lock the rotor for the test.
• Lock the rotor by appropriate tool/device and increase the command up reaching the 80% of the rated motor current. If the produced torque is high and the rotor cannot be locked, then reduce appropriately the Volt per Hertz at configuration and repeat the test.
• Calculate the applied V_s by utilizing equation (2).
• Calculate the input phase motor power P_s by utilizing the following equation: 

  where V_dc (V) is the battery dc volts, I_dc (A) is the battery dc current, η is the controller efficiency (assume 0.95 efficiency for RoboteQ controllers). Battery volts and amps can be measured from Roborun+ utility.

  • Measure the I_q (A) current from the Roborun+ utility (FOC Torque Amps).
  • Calculate the L_ls, L_lr , R_s, R_r motor parameters by applying the equations (3) - (8).

Example:

For the same induction motor at no load test example, the Volts per Hertz ratio is set 5 times lower than the nominal, that is 0.053. The respective results taken from Roborun+ utility are shown below:

Therefore, the input phase motor power P_s is equal to 

The power factor is  

, while the equivalent phase impedance is Z = 0.081 Ω according to equation (4).

Therefore, the motor stator and rotor resistances are R_s = R_r = 24 mΩ according to equations (5) and (7) and the leakage inductances according to equation (6) are:  

It is noted that the synchronous frequency in locked rotor test is different to the synchronous frequency in no-load test. Finally, the L_ls = L_lr = 76 uH according to equation (8).

After estimating L_m, L_ls, L_lr , R_s, R_r motor parameters from no-load and locked-rotor tests, the optimal slip where the motor produces the maximum torque s_maxT can be estimated as follows:

Next, in order to apply at configuration tab the optimal slip in Hz, the following transformation needed:

Example:

For the calculated L_m = 754 uH, motor leakage inductances L_ls = L_lr = 76 uH and resistance R_s = R_r = 24 mΩ, the optimal slip is calculated equal to s = 5.1 Hz at rated motor speed.