Question 1 The armature of a separately excited (fixed field) DC motor with the parameters given below is to be driven from a single switch DC Chopper.

i) Draw the circuit diagram for the circuit and sketch the waveforms for the motor voltage and current.

ii) Derive the equation for the average voltage seen by the motor as a function of the on-time of the power electronic switch.

iii) Show that in the steady-state the average voltage applied to the motor must equal the sum of the motor EMF and the average voltage across the armature resistance.

The motor is to be operated at 50% base speed and at 20% rated torque.

iv) Calculate the duty cycle of the chopper circuit for this condition.

v) Estimate the current ripple for the duty cycle calculated in part v.

Motor Data:

Base Speed: 1000rpm

Rated Voltage: 500V

Rated Current 200A

Armature Resistance: 0.2?

Armature Inductance: 5mH

Chopper Data:

DC supply Voltage: 600V

Switching Frequency: 4kHz

Question 2. The figure below shows a feed back system applied to separately excited DC motor.

The figure below shows a feed back system applied to separately excited DC motor.

DC Motor Parameters
Va(Rated)=500V
Ia (Rated)=400A
Rotor Circuit: 4mH, 0.1Ohm
Base Speed: 1000rpm
Machine constant km=4.4Nm/A
Moment of Inertia: 406kgm2

i) Briefly explain how feed back may be applied to regulate the torque and speed of an electrical machine.

ii) Derive an expression for the steady-state speed in terms of the following parameters.

Speed Error Gain: Ke
Feed back Gain: Kf
Machine Constant: Km
Electrical Torque: T
Armature Resistance: Ra
Demand signal : Vd

iii) Calculate the error signal (Ve) required to give apply 500V to the armature of the motor.

iv) Estimate the steady-state speed for a demand of Vd=10 for the following conditions.

a. No load T≈0

b. Rated Electrical Torque.

v) The system is initially operated under no load with demand signal Vd=10, the load torque is then increased to is rate value. Explain how the feed back system responds to this change and sketch waveforms of motor speed (ω), Motor current (Ia) and speed error to show the response of the system.

Question 1. The following question refers to a three phase, pulse width modulated inverter.

1. Draw the circuit for a three phase (IGBT) based inverter.

2. Explain how pulse width modulation may be used to give a controlled fundamental from the three phase inverter.

3. Summarise the advantages and disadvantages of high frequency PWM in power electronic systems.

4. Estimate the DC supply voltage required if a three phase inverter is operated with sinusoidal PWM to give balanced line output voltage of 415V rms.

Question 2. An induction machine is to be controlled using a variable frequency three phase inverter.

1 Explain why the magnitude of the applied voltage is reduced as speed is reduced.

2 Derive an expression for the motor torque when constant voltage:frequency ratio (V_s/f= constant). is used to control the motor speed.

Question 3. A 2 pole induction motor designed for operation from a three phase 415 V (rms) 50 Hz supply has the following parameters at rated frequency: Xs = 0.75
Rs is assumed to be negligible.
Xr = 0.7
Rr = 0.7
L_m is assumed to be large.

The motor is to be operated at variable speed from a three phase inverter which operates in open loop with constant voltage: frequency ratio (V_s/f = constant).

1. Calculate the motor torque and current when operating at a slip of 0.2, with a supply frequency of half the rated value.

2. If the supply frequency is rapidly increased to the rated value, calculate the values of motor torque and current immediately after the step change in frequency.

3. How may the behaviour seen in part 2) be improved