Electric Power / Controls
Courseware Sample
85822-F0
A
ELECTRIC POWER / CONTROLS
COURSEWARE SAMPLE
by
the Staff
of
Lab-Volt Ltd.
Copyright © 2009 Lab-Volt Ltd.
All rights reserved. No part of this publication may be reproduced,
in any form or by any means, without the prior written permission
of Lab-Volt Ltd.
Printed in Canada
October 2009
Table of Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V
Courseware Outline
Asynchronous and Doubly-Fed Generators . . . . . . . . . . . . . . . . . . . . . . . . VII
Sample Exercise Extracted from Asynchronous and Doubly-Fed Generators
Exercise 3-9
The Boost Chopper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Instructor Guide Sample Exercise Extracted from Asynchronous and
Doubly-Fed Generators
Exercise 3-11
The Four-Quadrant Chopper . . . . . . . . . . . . . . . . . . . . . . . 17
Bibliography
III
IV
Introduction
The Lab-Volt Asynchronous and Doubly-Fed Generators system, model 8052-1,
introduces the principles of electrical power generation and control in the field of wind
turbines.
Known as the standard for technical training systems in use across virtually every
industry and around the globe, Lab-Volt is now using its expertise to facilitate the
development, production, installation, and maintenance of the widest variety of
Alternative and Renewable Energy Power Training Systems.
While most power generation requires the creation, management, and conversion
of heat energy into motion—with most variations simply involving the way heat is
produced—alternative and renewable sources are far more varied.
Many take advantage of the motion already found in nature; others harness nature’s
own renewable forms of heat and energy. Capturing and converting that motion or
energy often requires very non-traditional methods.
Accustomed to breaking down processes and procedures into elemental blocks,
Lab-Volt’s new training systems take the esoteric and theoretical out of the
laboratory and translate it into apparatus that introduce practical, understandable
teaching methods.
Regardless of the operational scale of the alternative energy sources , Lab-Volt has
distilled the essential elements of the process down to safe, hands-on classroom
applications, developing each training product and process to yield realistic,
repeatable, and logical results.
V
VI
Courseware Outline
ASYNCHRONOUS AND DOUBLY-FED GENERATORS
Unit 1 Fundamentals for Rotating Machines
Introduction to rotating machines. Work, speed, torque, and power.
Operation of the Prime Mover / Dynamometer module.
Ex. 1-1 Prime Mover Operation
Familiarization with the Prime Mover / Dynamometer module
operating in the Prime Mover mode. Prime mover speed versus
voltage. Friction torque versus speed. Measurement of the opposition torque caused by the machine driven by the Prime Mover.
Unit 2 AC Induction Motors
The principles of electromagnetic induction. Rotating magnetic field and
synchronous speed. Demonstrating the operation and characteristics of
AC induction motors.
Ex. 2-1 The Three-Phase Squirrel-Cage Induction Motor
Creating a rotating magnetic field in a three-phase squirrel-cage
induction motor. Synchronous speed. Description and operation of
the Three-Phase Squirrel-Cage Induction Motor. Torque versus
speed characteristic. Reactive power required for creating the
rotating magnetic field.
Ex. 2-2 Eddy-Current Brake and Asynchronous Generator
Description and operation of the eddy-current brake. Operating a
three-phase squirrel-cage induction motor as an asynchronous
generator. Demonstrating that an asynchronous generator can
supply active power to the AC power network. Demonstrating that
asynchronous generator operation requires reactive power.
Ex. 2-3 Effect of Voltage on the Characteristics
of Induction Motors
Saturation in induction motors. Nominal voltage of a squirrel-cage
induction motor. Demonstrating the effect of the motor voltage on
the torque versus speed characteristic of a squirrel-cage induction
motor.
Unit 3 Power Electronics Fundamentals
Introduction to Reversible DC Power Supply, Rectifiers, Choppers,
Inverters, High-Speed Power Switching, and Effect of Frequency in
Magnetic Circuits.
VII
Courseware Outline
ASYNCHRONOUS AND DOUBLY-FED GENERATORS
Ex. 3-1 Familiarization with the Reversible DC Power Supply
The reversible DC power supply. Implementing a reversible
DC power supply using a separately-excited DC motor/generator
and a synchronous or asynchronous motor/generator. Operation
of a reversible DC power supply implemented with a separatelyexcited DC motor/generator and a three-phase squirrel-cage
induction motor/generator (asynchronous motor/generator).
Ex. 3-2 Power Diode Single-Phase and Two-Phase Rectifiers
Operating principles of the diode. Half-wave rectifier. Rectifier with
free-wheeling diode. Battery charger circuit. Single-phase bridge
rectifier. Two-phase half-wave rectifier.
Ex. 3-3 Power Diode Three-Phase Rectifiers
Three-phase, three-pulse rectifier. Three-phase, six-pulse rectifier.
Ex. 3-4 Familiarization with the Chopper / Inverter
Control Unit (Chopper Modes)
Description of the controls, connectors, and indicators of the
Chopper / Inverter Control Unit. Operation and use of the
Chopper / Inverter Control Unit in a PWM-control chopper and a
two-step neutral-zone (bang-bang) control chopper. Examples of
various types of choppers built with IGBTs.
Ex. 3-5 Familiarization with the Chopper / Inverter
Control Unit (Inverter Modes)
Operation and use of the Chopper / Inverter Control Unit in various
two-phase and three-phase inverters. Introduction to the 120E-,
180E-, and programmed-waveform modulations. Use of synchronous pulse-width modulation (PWM) to obtain a constant V/f ratio
three-phase inverter. Examples of inverters built with electronic
switches.
Ex. 3-6 Familiarization with the
IGBT Chopper / Inverter Module
Description of the IGBT Chopper / Inverter. Operation of the IGBT
Chopper / Inverter module used as a buck chopper. Effect of the
duty cycle on the power delivered.
Ex. 3-7 Introduction to High-Speed Power Switching
Voltage-type circuit. Current-type circuit. Free-wheeling diodes.
Use of a capacitor to obtain a voltage-type source. Interconnecting
voltage- and current-type circuits.
VIII
Courseware Outline
ASYNCHRONOUS AND DOUBLY-FED GENERATORS
Ex. 3-8
The Buck Chopper
Operation of a buck chopper in a simple circuit with a
resistive/inductive load. Power flow. Voltage transfer ratio versus
the duty cycle. Effect of frequency on the output voltage and
current. Power efficiency.
Ex. 3-9
The Boost Chopper
Operation of a boost chopper in a simple circuit with a resistive
load. Power flow. Voltage transfer ratio versus the duty cycle.
Effect of frequency on the output voltage and current. Power
efficiency.
Ex. 3-10 The Buck / Boost Chopper
Operation of a buck/boost chopper in a simple circuit with two
DC power supplies. Power flow. Voltage transfer ratio versus duty
cycle.
Ex. 3-11 The Four-Quadrant Chopper
Operation of a four-quadrant chopper in a simple circuit with a
resistive load. Voltage transfer ratio versus the duty cycle. Power
flow. Observing four-quadrant operation on an oscilloscope.
Ex. 3-12 The Single-Phase Inverter
Using a four-quadrant chopper as a single-phase inverter with
variable voltage and frequency (variable voltage and frequency
single-phase ac network). A simple dual-polarity DC power
supply. Operation of a single-phase inverter built with a
dual-polarity DC power supply and two electronic switches, and
using either pulse-width modulation (PWM) or 180E-modulation.
Ex. 3-13 Saturation and Effect of Frequency
in Magnetic Circuits
The phenomenon of saturation in magnetic circuits. Saturation
curve of magnetic circuits. Effect of frequency in magnetic circuits.
Unit 4 Wound-Rotor Induction Machines
Familiarization with the operation and characteristics of wound-rotor
induction motor and doubly-fed induction generator.
IX
Courseware Outline
ASYNCHRONOUS AND DOUBLY-FED GENERATORS
Ex. 4-1
Wound-Rotor Induction Motor
To examine the construction of the Three-Phase Wound-Rotor
Induction Motor. To understand exciting current, synchronous
speed and slip in a wound-rotor induction motor. To observe the
effect of the revolving field and rotor speed upon the voltage
induced in the rotor.
Ex. 4-2
Wound-Rotor Induction Motor with Short-Circuited
Rotor
To observe the starting characteristics of the Three-Phase
Wound-Rotor Induction Motor having short-circuited rotor
windings. You will also show the rotor and stator currents at
different motor speeds.
Ex. 4-3
Wound-Rotor Induction Motor with Variable Rotor
Resistors
To observe speed control using external variable resistors
connected in series with the rotor windings.
Ex. 4-4
Wound-Rotor Frequency Conversion Principles
To observe no-load and full-load characteristics of a rotary
frequency converter.
Ex. 4-5
Speed Control of a Wound-Rotor Generator
Using Rotor Resistors
To demonstrate how the speed of a wound-rotor generator can be
controlled by varying the resistance of the rotor windings.
Ex. 4-6
Variable Speed Doubly-Fed Induction Generator
Using Rotor Frequency Injection
To demonstrate how to synchronize a generator to an AC power
network, demonstrate how a doubly-fed induction generator can
produce output power at various speeds, how to control the
output power level, and how to control the power factor of a
generator.
Appendices A
B
C
D
E
F
G
X
Circuit Diagram Symbols
Impedance Tables
Equipment Utilization Chart
Reversible DC Power Supply
New Terms and Words
Configuration Files
Saving a Window in WordPad
Sample Exercise
Extracted from
Asynchronous and
Doubly-Fed Generators
Exercise
3-9
The Boost Chopper
EXERCISE OBJECTIVE
When you have completed this exercise, you will be familiar with the operation of a
boost chopper.
DISCUSSION
The Boost Chopper
As discussed in the previous exercise of this manual, transformers allow AC voltage
and current levels to be converted. For example, a step-up transformer is normally
used to convert an AC voltage into a higher AC voltage. With DC power, a similar
conversion can be performed using a boost chopper.
Figure 3-66 shows a boost chopper built with an electronic switch (Q) and a
diode (D), and some waveforms related to this circuit. When electronic switch Q
switches on, the voltage across its terminals becomes virtually null, the DC power
supply voltage (EI) is applied to the inductor (L), and the current flowing in inductor L
(IL) starts to increase. Simultaneously, diode D switches off since it becomes
reverse-biased. At this moment, capacitor C starts to discharge into the load and
both the output current (IO) and voltage (EO) start to decrease.
3
The Boost Chopper
Figure 3-66. Operation of a boost chopper.
When electronic switch Q switches off, the voltage across its terminals increases
very rapidly until it reaches approximately EO + 0.7 V (due to inductor L). This applies
a forward-bias voltage of approximately 0.7 V to diode D, which therefore switches
4
The Boost Chopper
on. At this moment, a current equal to IL ! IO starts to charge up capacitor C, and
both EO and IO start to increase.
The DC voltage at the boost chopper output (EO) is proportional to the DC voltage
at the boost chopper input (EI) and the time the electronic switch is on during each
cycle. This time, which is referred to as the on-time (tON), is in turn proportional to the
duty cycle α of the switching control signal applied to the control signal input of
electronic switch Q. The equation relating voltages EO and EI is given by the
expression:
Thus, voltage EO can be varied by varying the duty cycle α. This equation indicates
that voltage EO can range between voltage EI and an infinite voltage when the duty
cycle α varies between 0 and 100%. In practice, however, the duty cycle α only
approaches 0 and 100%. Therefore, voltage EO can vary between a voltage a little
higher than voltage EI and many times voltage EI. In certain circuits, however, the
maximum value of the duty cycle α must be limited to limit the maximum voltage the
boost chopper can produce.
Varying the frequency of the switching control signal while maintaining the duty
cycle α constant does not vary the DC voltage and current at the boost chopper
output (EO and IO). However, the ripple on the output voltage decreases as the
frequency of the switching control signal increases.
The power which the boost chopper delivers at its output (PO) is equal to the power
it receives at its input (PI) minus the power dissipated in the electronic switch and the
inductor. The power dissipated in the electronic switch and the inductor is usually
small compared to the power PO. The power efficiency of boost choppers, thus, often
exceeds 80%. Notice that the power efficiency is the ratio of the output power on the
input power times 100%, as stated in the following equation:
Procedure summary
In the first part of this exercise, you will set up the equipment required to perform this
exercise.
In the second part, you will use the circuit shown in Figure 3-67 to observe the
operation of a boost chopper. In this circuit, the boost chopper output is connected
to a resistive load consisting of resistors R2 and R3 connected in series.
You will vary the duty cycle of the switching control signal while observing the
DC voltage and current at the boost chopper output. This will allow you to verify the
relationship between the duty cycle and the DC voltage at the boost chopper input
and output, and to determine the direction of power flow.
In the third part, you will vary the frequency of the switching control signal while
observing the DC voltage and current, as well as the voltage waveform, at the boost
chopper output. This will allow you to verify the effect of frequency on these
parameters.
5
The Boost Chopper
In the fourth part, you will determine the power at the input and output of the boost
chopper. You will then compare the output power to the input power and determine
the power efficiency of the chopper.
EQUIPMENT REQUIRED
Refer to the Equipment Utilization Chart, in Appendix C of this manual, to obtain the
list of the equipment required to carry out this exercise.
PROCEDURE
CAUTION!
High voltages are present in this laboratory exercise! Do not make
or modify any banana jack connections with the power on unless
otherwise specified!
Setting up the Equipment
G
1. Install the Enclosure / Power Supply, Power Supply, Chopper / Inverter,
Smoothing Inductors, Resistive Load (2), and Data Acquisition Interface
modules in the Mobile Workstation.
Install the Chopper / Inverter Control Unit in the Enclosure / Power Supply.
Plug the Enclosure / Power Supply line cord into a wall receptacle. Set the
power switch of the Enclosure / Power Supply to I (on).
G
2. On the Power Supply, make sure that the main power switch is set to O (off)
and the voltage control knob to 0%.
Make sure that the Power Supply is connected to a three-phase power
source.
G
3. Make sure that the USB port cable from the computer is connected to the
DAI module.
Connect the Low Power Inputs of the DAI and Chopper / Inverter modules
to the 24-V ac output of the Power Supply.
On the Power Supply, set the 24-V ac power switch to I (on).
G
6
4. Open the LVDAM-EMS Oscilloscope window.
The Boost Chopper
Operation of the Boost Chopper
G
5. Set up the circuit shown in Figure 3-67.
Figure 3-67. Circuit used to observe the operation of a boost chopper.
Make the appropriate connections on the Smoothing Inductors module to
obtain an inductance of 0.2 H for L1.
7
The Boost Chopper
Note: Diode D1 is the power diode connected in parallel
with electronic switch Q1. Diode D4 (connected in parallel with
electronic switch Q4) and electronic switch Q1 are not shown in
the figure because they are not used in this circuit. Electronic
switch Q1 is forced to the off state by connecting SWITCHING
CONTROL INPUT 1 to the common point.
G
6. Make the following settings:
On the Chopper / Inverter Control Unit
MODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CHOP. PWM
On the Chopper / Inverter module
Switch S1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . lower position
In the Oscilloscope window
Display E1, E2, AI-1, and I2 on Ch1, Ch2, Ch3, and Ch4.
Ch1 Vertical Scale Setting . . . . . . . . 100 V/Div. (DC coupling)
Ch2 Vertical Scale Setting . . . . . . . . 100 V/Div. (DC coupling)
Ch3 Vertical Scale Setting . . . . . . . . . . 2 V/Div. (DC coupling)
Ch4 Vertical Scale Setting . . . . . . . . 0.1 A/Div. (DC coupling)
Time Base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 ms/div.
Trigger Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ext. Sync.
In the LVDAM-EMS application
Analog Output AO-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +10 V
Analog Output AO-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 V
G
7. Set the Resistive Load modules to obtain a resistance of 400 Ω for R2 and
R3 .
G
8. On the Power Supply, set the main power switch to I (on), then set the
voltage control knob to 20%.
Note: Select convenient vertical scale and position settings in the
Oscilloscope window to facilitate observation.
Set Analog Output AO-2 so that two complete cycles of the switching control
signal coincide as closely as possible with the full width of the Oscilloscope
window. This sets the period of the switching control signal to approximately
5 ms. Consequently, the operating frequency of the boost chopper is
approximately 200 Hz.
Set Analog Output AO-1 so that the duty cycle of the switching control signal
is approximately 80% while observing the DC voltage at the boost chopper
output in the AVG column of the Waveform Data box in the Oscilloscope
window.
8
The Boost Chopper
Note: Notice that the duty cycle of PWM control signals 2 and 4
varies linearly from 0.95 to 0.05 as the voltage applied to
CONTROL INPUT 1 varies from -10 to +10 V when the Chopper /
Inverter Control Unit in the CHOP. PWM mode.
G
9. Print or save the waveforms displayed in the Oscilloscope window
as OW391.
They represent the supply voltage (EI on Ch1), the voltage across the load
connected to the boost chopper output (EO on Ch2), the switching control
signal applied to electronic switch Q4 (Ch3), and the load current (IO on
Ch4).
G 10. Describe how the DC voltage at the boost chopper output varies when the
duty cycle of the switching control signal is increased.
G 11. Briefly explain why the boost chopper can produce output voltages which
are much higher than the voltage applied at its input.
G 12. Set Analog Output AO-1 so that the duty cycle of the switching control signal
is approximately 5% (minimum value).
Print or save the waveforms displayed in the Oscilloscope window
as OW392.
G 13. Compare the DC voltage at the boost chopper output (Ch2) with the
DC voltage provided to the boost chopper (Ch1) (shown in the AVG column
of the Waveform Data box).
Explain why this circuit is referred to as a boost chopper, knowing that the
duty cycle of the switching control signal is set to minimum.
9
The Boost Chopper
G 14. Compare the DC voltages at the boost chopper output for both duty cycle
values: 5 and 80%. Do your observations confirm that the DC voltage at the
boost chopper output increases as the duty cycle of the switching control
signal is increased?
G Yes
G No
G 15. Set Analog Output AO-1 so that the duty cycle of the switching control signal
increases from 5 to 80% while observing the load current (Ch4).
Does the polarity of the load current change as the duty cycle of the
switching control signal increases from 5 to 80%?
G Yes
G No
In which direction does the power flow?
G 16. Record the supply voltage (EI) shown in the AVG column (Ch1) of the
Waveform Data box.
Supply voltage EI =
G 17. Calculate the DC voltage which should appear at the output of the boost
chopper using the following equation (α = 80%):
G 18. Record the output voltage EO shown in the AVG column (Ch2) of the
Waveform Data box.
Measured output voltage EO =
Note: The difference between the calculated and measured value
is caused by the voltage drops in the inductor and in the
electronic switch.
10
The Boost Chopper
Observing the Effect of the Switching Control Signal Frequency
G 19. Make the following settings in the Oscilloscope window:
Display E1, E2, I1, and I2 on Ch1, Ch2, Ch3, and Ch4.
Ch1 Vertical Scale Setting . . . . . . . . . . 100 V/Div. (DC coupling)
Ch2 Vertical Scale Setting . . . . . . . . . . 100 V/Div. (DC coupling)
Ch3 Vertical Scale Setting . . . . . . . . . . . . 1 A/Div. (DC coupling)
Ch4 Vertical Scale Setting . . . . . . . . . . . . 1 A/Div. (DC coupling)
Time Base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 ms/div.
Trigger Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ext. Sync.
G 20. Make sure that the duty cycle of the switching control signal is set to 80%.
Make sure that the voltage control knob on the Power Supply is set to 20%.
Slowly vary the voltage applied to Control Input 2 from -10 to +10 V to vary
the frequency of the switching control signal, while observing the average
voltage and current at the buck chopper output (shown in the AVG column
(Ch2 and Ch4) of the Waveform Data box).
Does the frequency of the switching control signal have a significant effect
on the average voltage and current the buck chopper provides? If so,
describe this effect.
G 21. Set the voltage applied to Control Input 2 to obtain a minimum frequency of
the switching control signal.
Print or save the waveforms displayed in the Oscilloscope window
as OW393.
G 22. Slowly vary the voltage applied to Control Input 2 from -10 to +10 V to vary
the frequency of the switching control signal, while observing the waveform
of the current at the boost chopper input in the Oscilloscope window (Ch3).
Does the frequency of the switching control signal have a significant effect
on the ripple of the current at the boost chopper input? If so, describe this
effect.
11
The Boost Chopper
Set the voltage applied to Control Input 2 to obtain a maximum frequency
of the switching control signal.
Print or save the waveforms displayed in the Oscilloscope window
as OW394.
Output Power Versus Input Power
G 23. Set Analog Output AO-2 to +10 V.
Make sure that the duty cycle of the switching control signal is still set to
80%.
Using the DC voltage and current supplied by the variable-voltage
DC power supply to the buck chopper, calculate the power (PI) which is
supplied to the boost chopper. Record the resulting power in the following
blank space.
Power supplied to the boost chopper PI =
G 24. Using the DC voltage and current supplied by the buck chopper to the load,
calculate the power (PO) which is supplied to the load. Record the resulting
power in the following blank space.
PO =
G 25. Calculate the power efficiency of the boost chopper using the following
equation:
G 26. Is the power at the output of the boost chopper nearly equal to the power at
its input?
G Yes
G No
G 27. On the Power Supply, set the voltage control knob to 0%, then set the main
power switch and the 24-V ac power switch to O (off). Set the power switch
on the Enclosure / Power Supply to O (off). Remove all leads and cables.
CONCLUSION
In this exercise, you verified that the DC voltage at the boost chopper output
increases as the duty cycle of the switching control signal is increased. You found
that the minimum DC voltage that can be obtained at the boost chopper output is
slightly higher than the DC voltage at its input.
12
The Boost Chopper
You saw that power always flows in the same direction in a boost chopper. You
observed that the frequency of the switching control signal has no effect on the
DC voltage and current provided by the boost chopper. Nevertheless, you saw that
as the frequency of the switching control signal increases, the ripple on the input
current of the boost chopper decreases. You verified that the power at the boost
chopper output is approximately equal to the power at its input.
REVIEW QUESTIONS
1. Describe the effect the switching control signal frequency has on the output
voltage and current of a boost chopper.
2. A boost chopper is powered by a 12-V dc power supply. What is the output
voltage range of this chopper if the duty cycle can vary between 20 and 95%?
3. Briefly describe the operation of the boost chopper.
4. Explain why the maximum value of the duty cycle must be limited in certain
boost choppers.
5. Name the component operating with AC power which best compares to the
boost chopper.
13
Instructor Guide
Sample Exercise
Extracted from
Asynchronous and
Doubly-Fed Generators
Asynchronous and Doubly-Fed Generators
EXERCISE 3-11
THE FOUR-QUADRANT CHOPPER
ANSWERS TO PROCEDURE STEP QUESTIONS
G
8. Electronic switches Q1 and Q5 turn on at same time, and they are
complementary to electronic switches Q2 and Q4.
Figure OW3111.
Refer to the circuit shown in Figure 3-74.
Duty cycle = 70%.
Ch1 = AI-1 = switching control signal 1.
Ch2 = AI-2 = switching control signal 2.
Ch3 = AI-3 = switching control signal 4.
Ch4 = AI-4 = switching control signal 5.
G 11. Because the voltage switches from positive to negative and stays the same
time for each polarity.
G 12. DC voltage at the input of the four-quadrant chopper = 117 V.
17
Asynchronous and Doubly-Fed Generators
Figure OW3112.
Refer to the circuit shown in Figure 3-74.
Duty cycle = 50%.
Ch1 = AI-1 = switching control signal 1.
Ch2 = AI-2 = switching control signal 2.
Ch3 = E2 = output voltage of the four-quadrant chopper.
Ch4 = I2 = output current of the four-quadrant chopper.
Ch5 = E1 = supply voltage of the four-quadrant chopper.
G 13. When the duty cycle is minimum for Q1, EO is approximately equal to -EI.
When the duty cycle is maximum for Q1, EO is approximately equal to +EI.
Between the minimum and maximum duty cycles, EO varies.
G 14.
DUTY CYCLE
EO
(V)
IO
(A)
5%
-101
-1.2
95%
101
1.2
Table 3-11-1. DC voltage and current at the output of the four-quadrant chopper.
18
Asynchronous and Doubly-Fed Generators
G 15. The range of the four-quadrant chopper is -EI to +EI.
G 16. Yes.
G 17.
Figure OW3113.
Refer to the circuit shown in Figure 3-74.
Duty cycle = 80%.
Ch1 = AI-1 = switching control signal 1.
Ch2 = AI-2 = switching control signal 2.
Ch3 = E2 = output voltage of the four-quadrant chopper.
Ch4 = I2 = output current of the four-quadrant chopper.
G 18. Calculated EO = 71 V.
Yes.
G 19. No.
19
Asynchronous and Doubly-Fed Generators
G 26.
Figure G3111.
Refer to the circuit shown in Figure 3-75.
Ch1 = AI-1 = output current of the four-quadrant chopper.
Ch2 = AI-2 = output voltage of the four-quadrant chopper.
20
Asynchronous and Doubly-Fed Generators
G 30.
Figure G3112.
Refer to the circuit shown in Figure 3-75.
Ch1 = AI-1 = output current of the four-quadrant chopper.
Ch2 = AI-2 = output voltage of the four-quadrant chopper.
G 31. Because it is a reversible chopper in voltage and in current (it operates in
the four quadrants).
G 32. In quadrants 2 and 4.
ANSWERS TO REVIEW QUESTIONS
1. When electronic switches Q1 and Q5 are on, EI is applied to the load and when
Q2 and Q4 are on, -EI is applied to the load. If the duty cycle is greater than 50%
for Q1, the average output voltage will be positive and if the duty cycle is less
than 50%, the average output voltage will be negative.
2. Yes.
3. The four-quadrant operation can provide a positive or a negative DC voltage
regardless of the direction in which the current flows.
21
Asynchronous and Doubly-Fed Generators
4. The equation relating voltages EO and EI is EO = EI x (2αQ1 - 1).
So -24 = 200 x (2αQ1 - 1) = 56%.
5. The output voltage is reversible.
22
Bibliography
Jackson, Herbert W. Introduction to Electric Circuits, 5th edition,
New Jersey: Prentice Hall, 1981
ISBN 0-13-481432-0
Wildi, Theodore. Electrical Machines, Drives, and Power Systems, 2nd edition,
New Jersey: Prentice Hall, 1991.
ISBN 0-13-251547-4