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ES96Z0

MSc Examinations: Summer 2019

ELECTRICAL MACHINES AND DRIVES

3. A separately excited direct current motor has the rated power of 7 kW and the rated velocity of 2850 rpm. The ratio of the rated EMF and angular velocity is equal to 0.75 V/(rad/s). The ratio of the rated torque and armature current is 1.3 N m/A. Assume that the armature resistance is 0.34 Ω .

(a)  Compute the following parameters of the motor:

(i)   Rated angular velocity in rad/s.                                                                        (1 mark)

(ii)  Rated torque.                                                                                                     (1 mark)

(iii) Rated armature current.                                                                                     (1 mark)

(iv) Rated EMF.                                                                                                       (1 mark)

(v)  Rated voltage.                                                                                                   (1 mark)

(b)  The armature winding of the motor is connected to a DC voltage source. An additional resistor of 10 Ω is placed in series to the armature winding. The load torque applied to the motor shaft is active and equals to 10 N m. The magnetisation flux is rated and constant. The motor does not rotate.

(i)   Determine the value of the DC voltage applied to the armature winding. (2 marks)

(ii)  Compute the value of the velocity in rad/s after the magnetisation flux was reduced by 25%. (2 marks)

(iii) For case (ii), determine if the DC machine works as a motor or a generator. (1 mark)

(c)  For the motor’s angular velocity regulation, a two loop cascade control system is implemented according to Figure 3.1. The system utilizes a P-controller of the velocity and an I-controller of the armature current. The excitation voltage is rated and constant. The block diagram of the regulation system is depicted in Figure 3.2. Its parameters are explained in Table 3.1.

(i)   Define the variables labelled 1, 2 and 3 in Figure 3.2. (1 mark)

(ii)  The  parameters values are: c1Φr = 0.75 V/(rad/s), c2Φr = 1.3 N m/A, RaΣ = 1.1 Ω, ki =0.4 V/A, kω = 0.028 V/(rad/s). The angular velocity reference voltage is 5 V, the proportional gain of the velocity controller is 5, and the ammeter in Figure 3.1 shows 8 A. The system operates in a steady state. Compute the angular velocity of the motor and the value measured by the voltmeter. (3 marks)

(iii) For case (c)(ii), the load torque and the velocity reference voltage do not change. The excitation voltage (magnetic flux) is reduced by 25%. Determine the new steady state angular velocity of the motor. (3 marks)

(i)   Rated angular velocity in rad/s.                                                                       (1 mark)

(ii)  Rated slip.                                                                                                         (1 mark)

(iii) Rated torque.                                                                                                    (1 mark)

(iv) Rated stator current.                                                                                         (1 mark)

(v)  Number of pole pairs.                                                                                     (1 mark)

(b)  Assume the rated critical torque is 100 N m and the rated critical slip is 10%. A rated three-phase voltage is applied to the stator winding and the motor velocity is 1480 rpm. Compute the following values using simplified Kloss formula:

(i)   The slip of the motor and the motor load torque. (4 marks)

(ii)  The velocity in rad/s  of the motor when the  frequency is reduced to 45 Hz and

V/f=const control is implemented. The load torque remains the same. The equations for critical slip, critical torque and no load velocity are given below

(6 marks)

(c)  The block diagram of the vector control system of the motor’s angular velocity is shown in Figure 4.1. The d-q frame is aligned with the rotor flux linkage vector in the d axis. There are four controllers in the system: Angular Velocity P-Controller (AVC), rotor Flux Linkage I-Controller (FLC), two Current PI-Controllers (CC1 and CC2). The Flux Sensor (FS) and the Vector Computation block (VC) are used to determine the position and magnitude of the rotor flux linkage vector. At specific moment in time, the system is in a steady state and the components of the rotor flux linkage vector in a and b axes are 0.8 Wb and 0.2 Wb, respectively. The reference of the angular velocity is 100 rad/s, the gain of the AVC controller is 5, the instantaneous stator current values in U, V and Wphases are 4.34 A, 5.63 A and -9.97 A, respectively. For this moment in time:

(i)   Determine the angular position of the d-q reference frame with respect to the a axis. (2 marks)

(ii)  The output signal values of the FLC and AVC. (3 marks)

(iii) Calculate the angular velocity of the motor. (1 mark)

Assume that the i1d and i1q feedbacks were disconnected. The load torque was decreased by 20%, the reference velocity and the reference rotor flux linkage did not change. Compute the steady state angular velocity value and the d and q axes stator currents. (4 marks)

(Total 25 Marks)