Download Chapter 9 – DC Motors and Generators

2/20/2013
EEE 118: Energy Conversion
Dr. Mongkol Konghirun
Department of Electrical Engineering
King Mongkut’s University of Technology Thonburi
Chapter 9
DC Motors and Generators
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9.1 Introduction to DC Motors
Introduction
The earliest power systems in US were dc systems, but by the 1890s
ac power systems were clearly winning out over dc systems.
However, the dc motors were still purchased until 1960s.
Reasons 1: dc power systems are still common in cars, trucks, and
aircraft.
Reasons 2: dc motors are easily used for speed control applications.
Nowadays, induction motors with solid-state drive packages are
preferred choice over dc motors for most speed control applications.
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Speed Regulation (SR)
DC motors are often compared by their speed regulation (SR).
The SR is a rough measure of shape of a motor’s torque-speed
characteristics.
The magnitude of SR tells approximately how steep the slope of the
torque-speed curve is.
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Types of DC Motors
There are five major types of dc
motors in general use:
1.The
2.The
3.The
4.The
5.The
separately excited dc motor
shunt dc motor
permanent-magnet dc motor
series dc motor
compounded dc motor
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9.2 The Equivalent Circuit of a DC
Motor
Equivalent Circuit of a DC
Motor
The entire rotor circuit includes rotor coils, interpoles, and
compensating windings, if present.
The brush voltage drop is represented by a small battery Vbrush
opposing the direction of current flow in the machine.
The Radj is an external resistor used to control the field current.
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Equivalent Circuit of a DC
Motor
The RF and Radj are lumped together. And Vbrush is often eliminated
due to its tiny fraction of the generated voltage.
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9.3 The Magnetization Curve of a
DC Machine
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Magnetization Curve of a DC
Machine
The field current produces a field magnetomotive force, mmf, ℑ =
NF IF .
This mmf produces a flux in the machine in accordance with its
magnetization curve as shown in Figure 9-3.
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Magnetization Curve of a DC
Machine
Since the EA is directly proportional to the flux, it is customary to
present the magnetization curve as a plot of EA versus IF for a given
speed ω0. See Figure 9-4.
Most motors and
generators are designed to
operate near saturation
point on the magnetization
curve.
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9.4 Separately Excited and Shunt
DC Motors
Equivalent Circuit of a Separately
Excited DC Motor & Shunt DC Motor
Separately excited dc motor
Shunt dc motor
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The Terminal Characteristic of
a Shunt DC Motor
The terminal characteristic of a motor is a plot of its output torque
versus speed.
How does a shunt dc motor respond to a load ?
1. Initially, τind = τload . The motor speed is constant.
2. Load torque, τload ↑,on the shaft is increased.
3. So, τload > τind. Then, the motor slows down ω↓.
4. Its internal generated voltage drops EA↓ = Kφω↓.
5. Armature current increases, IA ↑ = (VT – EA↓) / RA.
6. Induced torque increases τind ↑ = KφIA ↑ until τind = τload .
7. The motor speed is constant at a lower mechanical speed of
rotation.
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The Terminal Characteristic of
a Shunt DC Motor
The output characteristic of a shunt dc motor can be derived as
follow:
Straight line with a
negative slope
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The Terminal Characteristic of
a Shunt DC Motor
For a constant VT.
Armature reaction (AR) : flux weakening effect causes
the speed is increased according to equation (9-7).
Use of compensating winding, flux is constant.
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Example Problem
Example 9-1 on page 541
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Nonlinear Analysis of a Shunt
DC Motor
Referring to magnetization curve in Figure 9-4, the flux φ and EA of a
dc machine is a nonlinear function of its magnetomotive force.
Since the change in EA cannot be calculated analytically, the
magnetization curve of the machine must be used to accurately
determine its EA for a given magnetomotive force.
The field current can be determined directly from its magnetization
curve for a given speed ω0.
If a machine has armature reaction, its flux will be reduced with each
increase in load. Thus, the net magnetomotive force in a shunt dc
motor is reduced due to armature reaction’s magnetomotive force
as
19
Nonlinear Analysis of a Shunt
DC Motor
The equivalent field current of a shunt dc motor is given by
The resulting voltage EA can then be determined by locating that
equivalent field current on the magnetization curve.
How can the effects of a given field current be determined if the
motor is turning at other than the rated speed specified in the
magnetization curve ?
According to the induced voltage equation,
For a given effective field current, the flux is fixed. Then,
See Example 9-2.
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Example Problem
Example 9-2 on page 545
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Speed Control of Shunt DC
Motors
There are two common methods
1. Adjusting the field resistance RF (and thus the field
flux).
2. Adjusting the terminal voltage applied to the
armature.
and one less common method in use for speed control
of shunt dc motors.
3. Inserting a resistor in series with the armature
circuit.
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1. Changing The Field
Resistance
To summarize the cause-and-effect behavior involved in this method
of speed control:
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1. Changing The Field
Resistance
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A Warning About Field
Resistance Speed Control
In Equation (9-7), the no-load speed is proportional to the reciprocal
of the flux in the motor, while the slope of the curve is proportional to
the reciprocal of the flux squared.
Therefore, the flux φ↓ causes the slope of the torque-speed curve to
become steeper. Then,
- Speed ω↑ is increased.
- Induced torque τind↓ is decreased for the rated armature current IA.
In case of τind < τload , then the speed will be decreased instead of
increased.
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2. Changing The Armature
Voltage
To summarize the cause-and-effect behavior in this method of speed
control:
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2. Changing The Armature
Voltage
Slopes of the torquespeed curves remain
constant.
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3. Inserting a Resistor in Series
With the Armature Circuit
According to the Equation (9-7), an external resistor can be inserted
in the armature circuit, so the slope of torque-speed curve is
increased. See Figure 9-15.
- Wasteful method due
to large copper losses
of the inserted
resistor.
- Poor speed regulation
- Rarely used.
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Armature Voltage Control & Field
Resistance Control
In armature voltage control
=> increasing voltage from 0 to rated voltage @ rated field current
=> flux is constant
=> speed increases from 0 to rated speed (base speed)
In field resistance control
=> decreasing field current from rated field current @ rated voltage
=> flux is reducing
=> speed increases from rated speed (base speed) to higher speed
As a result, the dc motor can be operated over a wide range of
speeds.
Shunt & separately excited dc motors have excellent speed control
characteristics.
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Armature Voltage Control & Field
Resistance Control
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Armature Voltage Control & Field
Resistance Control
In the armature voltage control, the flux is constant, so the maximum
torque in the motor is
This maximum torque is constant regardless of the speed.
The maximum power of the motor at any speed under armature
voltage control is
Thus, the maximum power out of the motor is directly proportional to
its operating speed under armature voltage control.
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Armature Voltage Control & Field
Resistance Control
In the field resistance control, the flux does reduce φ↓
In order for the armature current limit not to be exceeded, the
induced torque limit must decrease as the speed increases.
When φ↓
↓
As φ ∝ 1/ω or τmax ∝ 1/ω, then
Thus, the maximum power out of a dc motor under field current
control is constant, while the maximum torque varies as the
reciprocal of the motor’s speed.
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Example Problem
Example 9-3 on page 555
33
The Effect of an Open Field
Circuit
What would happen if the field circuit actually opened while the
motor was running ?
⇒ Flux φ would drop drastically down to residual flux
⇒ EA = Kφω would drop with it
⇒ IA = (VA – EA)/RA enormously increases
⇒ τind is higher than τload
⇒ ω keeps going up until over-speed.
(This condition is known as runaway)
Field loss relay is normally included to disconnect the motor from the
line in the event of a loss of field current.
Stabilized shunt motor: a turn or two cummulative compounding
winding to the dc shunt motor’s pole, which counteracts the
demagnetizing magnetomotive force of armature reaction.
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9.5 The Permanent-Magnet DC
Motor
Permanent-Magnet DC Motor
Poles are made of permanent magnets instead of field coils.
Advantages:
- No copper losses of field circuit
- Smaller motor due to elimination of field winding
Common in smaller fractional and subfractional-horsepower sizes.
Disadvantages:
- Permanent-magnet cannot produce as high a flux density as an
externally supplied shunt field
- PMDC motor have a lower induced torque per ampere of
armature current with the same size and construction
- PM demagnetization due to large armature magnetomotive force
- PM demagnetization due to excessive heating (overload)
- Speed control method by field current control is not possible
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Permanent-Magnet DC Motor
Typical ferromagnetic material for stator and rotor cores.
For applications of rotors
and stators, a
ferromagnetic material
should be selected as
small as Bres and HC as
possible (narrow
hysteresis loop).
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Permanent-Magnet DC Motor
Typical ferromagnetic material for permanent-magnet.
For poles of PMDC motor,
a ferromagnetic material
should be selected as
large as Bres and HC as
possible .
Large Bres => large flux
Large HC => large
withstanding of
demagnetization due to
armature reaction
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Permanent-Magnet DC Motor
Permanent-magnet : ceramic (ferrite) & rare-earth materials
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9.6 The Series DC Motor
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Induced Torque in a Series DC
Motor
Equivalent circuit of series dc motor
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Induced Torque in a Series DC
Motor
Flux in the machine can be given by
The c is a constant of proportionality. The induced torque is given by
Since the torque is proportional to squared armature current, a series
dc motor gives more torque per ampere than any other dc motor.
Applications requiring very high torques such as starter motors in
cars, elevator motors, and traction motors in locomotives.
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The Terminal Characteristic of
a Series DC Motor
Assuming that the magnetization curve is linear.
The flux in the motor is given by
This equation will be used to derive the torque-speed characteristic
curve for the series motor.
The derivation of a series motor’s torque-speed characteristic starts
with Kirchhoff’s voltage law:
From Equation (9-20), the armature current can be expressed as
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The Terminal Characteristic of
a Series DC Motor
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The Terminal Characteristic of
a Series DC Motor
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The Terminal Characteristic of
a Series DC Motor
If no load is connected to the
motor, it can turn fast enough to
seriously damage itself.
Never completely unload a series dc
motor, and never connect it to a
load by a belt or mechanism that
could break.
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Example Problem
Example 9-5 on page 565
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Speed Control of Series DC
Motors
Only one efficient way of armature voltage control to change the
speed of a series dc motor.
If the terminal voltage is increased, the first term in Equation (9-23)
is increased, resulting in a higher speed for any given torque.
Today, the introduction of solid-state control of variable terminal
voltage makes the speed control of series dc motor more efficient.
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9.7 The Compounded DC Motor
The Compounded DC Motor
A compounded dc motor is a dc motor with both a shunt and a
series field.
Long-shunt connection
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The Compounded DC Motor
A compounded dc motor is a dc motor with both a shunt and a
series field.
Short-shunt connection
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The Compounded DC Motor
Dots of two field coils are the same convention as dots in
transformer. Current flowing into a dot produces a positive
magnetomotive force.
If the current flows into the dots on both field coils, the resulting
magnetomotive forces add to produce a larger total
magnetomotive force. => cumulative compounding
If the current flows into the dot on one field coil and out of the dot
on the other field coil, the resulting magnetomotive forces subtract
to produce a smaller total magnetomotive force. => differential
compounding
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The Compounded DC Motor
Long-shunt connection:
Long-shunt connection:
Plus sign => cumulatively compounded dc motor
Minus sign => differentially compounded dc motor
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The Torque-Speed Characteristic of a
Cumulatively Compounded DC Motor
Two kinds of fluxes added in the motor:
- Constant flux (like shunt dc motor)
- Variable flux proportional to its armature current (like series dc
motor)
As a result, the cumulatively compounded dc motor has extra torque for
starting (like series dc motor) but it does not overspeed at no load (like
shunt dc motor).
At light loads, the series field has a very small effect, so the motor
behaves approximately as a shunt dc motor.
At very large loads, the series field becomes dominant, so the torquespeed curve begins to look like a series motor.
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The Torque-Speed Characteristic of a
Cumulatively Compounded DC Motor
Full-load condition
No-load condition
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The Torque-Speed Characteristic of a
Differentially Compounded DC Motor
The shunt magnetomotive force and series magnetomotive force
subtract from each other.
As IA increases, the flux decreases => speed increases
As speed increases, another increase in load (variable load torque
characteristics) => IA increases
. . . keeps continue . . .
So, the result is that a differentially compounded motor is unstable and
tends to run away.
This instability is much worse than that of a shunt motor with
armature reaction.
Starting procedure must be taken care due to large armature current.
So, it is almost never intentionally used for applications.
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The Torque-Speed Characteristic of a
Differentially Compounded DC Motor
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The Nonlinear Analysis of
Compounded DC Motor
Example 9-6 on page 571
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Speed Control in the Cumulatively
Compounded DC Motor
Speed control in cumulatively compounded
dc motor are the same as those available for
a shunt dc motor:
1. Change the field resistance RF
2. Change the armature voltage VA
3. Change the armature resistance RA
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9.8 DC Motor Starters
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DC Motor Protections
The purposes of protection equipment are
1. To protect the motor against damage due to
short circuits in the equipment
2. To protect the motor against damage from longterm overloads
3. To protect the motor against damage from
excessive starting currents
4. To protect a convenient manner in which to
control the operating speed of the motor
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DC Motor Problems on
Starting
At starting conditions, the motor is not turning, and so EA = 0.
Since the internal resistance of a normal dc motor is very low
compared to its size, a very high starting current flows.
This high starting current is probably over 20 times the motor’s rated
full-load current.
Solution is to insert a starting resistor in series with the armature to
limit the current flow until EA can build up to do the limiting.
This starting resistor must be removed as speed builds up.
See Figure 9-29 for a manual dc motor starter.
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DC Motor Problems on
Starting
Design R to limit the
current. Within the
desired bounds.
A person move its
handle to gradually cut
out the circuit.
For automatic starter
circuit, design the
control circuit that
shut the resistor
bypass contacts at the
proper time.
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DC Motor Starting Circuits
Figure 9-30 shows some devices commonly used in motor control
circuits.
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DC Motor Starting Circuits
Figure 9-31 shows one
common motor-starting
circuit using these
components.
The field loss (FL) relay is
used in the circuit to protect
the runaway condition.
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DC Motor Starting Circuits
Figure 9-32 shows the better motor-starting circuit.
Relays 1AR, 2AR, 3AR (with different working
voltages) sense the value of EA (or ωm).
Since if the motor is loaded heavily and starts more
slowly than normal, its armature resistance is still
cut out when its current falls to the proper value.
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9.10 DC Motor Efficiency
Calculations
Losses in DC Motors
To calculate the efficient of a dc motor, the following losses must be
determined:
1.
2.
3.
4.
5.
Copper losses
Brush drop losses (may lump together with copper losses)
Mechanical losses (may lump together with core losses)
Core losses
Stray losses
Issues for copper losses:
1. RA varies with temperature.
2. AC component voltage occurs in the rotor conductors during
normal operation, the RA increases due to skin effect.
IEEE Standard 113 (Reference 5) deals with test procedures for dc
machines.
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Example Problem
Example 9-8 on page 593
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9.11 Introduction to DC
Generators
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Introduction
There is no difference between generator and
motor except for the direction of power flow.
Five major types of dc generators:
1. Separately excited dc generator
2. Shunt dc generator
3. Series dc generator
4. Cumulatively compounded dc generator
5. Differentially compounded dc generator
These various types of dc generators differ in
their terminal (voltage-current) characteristics.
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Introduction
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Introduction
DC generator are compared by their voltages, power ratings,
efficiencies, and voltage regulations.
Voltage regulation (VR) is defined by the equation
where Vnl is no-load terminal voltage
Vfl is full-load terminal voltage
All generators are driven by a source of mechanical power, which
is usually called the prime mover of the generator.
Prime mover may be steam turbine, diesel engine, even electric
motor. These prime mover may vary widely in speed
characteristics.
73
Introduction
It is customary to compare the VR and output characteristics of
different generators, assuming constant speed prime movers.
DC generators are quite rare in modern power systems.
Even dc power system such as those in automobiles now use ac
generators plus rectifiers to produce dc power.
See Figure 9-42 for equivalent circuit of dc generator.
See Figure 9-43 for simplified version of equivalent circuit of dc
generator.
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Introduction
75
Introduction
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9.12 The Separately Excited DC
Generator
The Terminal Characteristic of a
Separately Excited DC Generator
Equivalent circuit of separately excited dc generator is shown in
Figure 9-44.
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The Terminal Characteristic of a
Separately Excited DC Generator
Terminal characteristic of a separately excited dc generator is the
plot of VT versus IL for a constant speed ω
What happens in a generator when the load is increased ?
79
The Terminal Characteristic of a
Separately Excited DC Generator
In dc generators without compensating windings, an increase in IA
causes an increase in armature reaction (field weakening effect).
This flux weakening causes a decrease in EA↓ = Kφ↓ω, further
reducing the terminal voltage of the generator.
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Control of Terminal Voltage
Terminal voltage can be controlled by changing the internal generated voltage
Ea of the machine.
See Figure 9-46(a) for a separately excited dc generator driving a resistive
load.
See Figure 9-46(b) for effect of a decrease in field resistance on the terminal
voltage of generator when it is operating under a load.
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Control of Terminal Voltage
decrease in field resistance
(flux increased, EA increased)
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Nonlinear Analysis of a
Separately Excited DC Generator
The relationship between EA and magnetomotive force is a nonlinear
function. The magnetization curve of the generator must be used to
accurately calculate its output voltage for a given input voltage.
In addition, armature reaction (AR) – field weakening is another
nonlinear effect, causing the EA reduced as load increased.
The total magnetomotive force and equivalent field current are then
The difference between the speed of the magnetization curve and
the real speed of the generator must be taken care by
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Example Problem
Example 9-9 on page 600
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9.13 The Shunt DC Generator
Voltage Buildup in a Shunt DC
Generator
The equivalent circuit of shunt dc generator is shown in Figure 9-49.
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Voltage Buildup in a Shunt DC
Generator
Assuming that generator is initially no load.
How does an initial voltage appear at the terminals of the machine ?
Voltage buildup in a dc generator depends on the presence of a
residual flux in the poles of the generator.
When a generator first starts to turn, an internal voltage will be
generated which is given by
Then, VT↑ => IF↑ = VT↑/RF
IF↑ => mmf ↑
=> φ↑
φ↑
=> EA↑ = Kφ↑ω
=> VT↑
. . . keep continue . . .
until the at the point VT,nl & IF,nl before the saturation point in the
magnetization curve.
87
Voltage Buildup in a Shunt DC
Generator
In real generator, the voltage
does not build up in discrete
steps.
Instead, both EA & IF increase
simultaneously until steadystate conditions are reached.
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Voltage Buildup in a Shunt DC
Generator
There are several possible causes for voltage to fail to build up during
starting.
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Voltage Buildup in a Shunt DC
Generator
There are several possible causes for voltage to fail to build up during
starting.
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Voltage Buildup in a Shunt DC
Generator
Since the magnetization
curve specified at a certain
speed, the critical resistance
also is lower with lower
speed.
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The Terminal Characteristic of
a Shunt DC Generator
As the load increases, so IA↑ = IF + IL↑
Then, VT↓= EA – IA↑ RA
Then, VT↓ => IF↓
Then, IF↓ => EA↓
Then, further decrease VT↓= EA↓ – IARA
As a result, the voltage drop-off is steeper than just the IARA drop in
a separately excited dc generator.
The voltage regulation is worse than the voltage regulation of the
same piece of equipment connected separately excited.
See Figure 9-52.
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The Terminal Characteristic of
a Shunt DC Generator
93
Voltage Control for a Shunt
DC Generator
There are two ways to control the voltage of
a shunt dc generator:
1. Change the shaft speed ωm of the
generator.
2. Change the field resistor of the generator,
thus changing the field current.
Change VT => Change EA= Kφωm
where φ ∝ IF
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The Analysis of Shunt DC
Generators
Firstly, the armature reaction (AR) is ignored. See Figure 9-53.
Field resistance line => VT line
Magnetization curve => EA line
IARA = difference between EA line and VT line
Next, Figure 9-54 shows the VT and IL curve.
95
The Analysis of Shunt DC
Generators
Firstly, the armature reaction (AR) is ignored.
Different two curves because of
hysteresis in the stator poles.
Load is increasing.
Load is reducing.
IL = IA - IF
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The Analysis of Shunt DC
Generators
Now the armature reaction (AR) is considered.
The armature reaction
produces a demagnetizing
magnetomotive force (field
weakening).
IF* = IF - ℑAR/NF
See Figure 9-55 for final
terminal voltage due to
armature reaction.
Triangle exactly fits between
the possible VT line and EA line
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9.14 The Series DC Generator
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The Terminal Characteristic of
a Series DC Generator
The series field has only few turns of wires, but much thicker than
wire in a shunt field.
The equivalent circuit of series dc generator is shown in Figure 9-56.
99
The Terminal Characteristic of
a Series DC Generator
The magnetization curve of a series dc generator looks very much like
the magnetization curve of any other generator.
At no-load, IF = 0
=>
small VT (with residual flux only)
As load increases, IA↑ = IF↑ =>
=>
=>
=>
=>
=>
=>
EA↑ rapidly
IA(RA+RS) ↑ but slower than EA↑
VT↑
machine approach saturation
EA becomes almost constant
IA(RA+RS) is predominant effect
VT starts to decrease
See Figure 9-57.
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The Terminal Characteristic of
a Series DC Generator
machine approach saturation
This characteristic of
series dc generator is
bad constant-voltage
source.
Its voltage regulation
is a large negative
number.
Series generators are
used only in a few
specialized
applications such as
arc welding.
101
The Terminal Characteristic of
a Series DC Generator
Series generators used in arc
welding are deliberately
designed to have a large
armature reaction, which give
the terminal characteristics as
shown in Figure 9-58.
102
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9.15 The Cumulatively
Compounded DC Generator
The Terminal Characteristic of a
Cumulatively Compounded DC
Generator
The cumulatively compounded dc generator is a dc generator with
both series and shunt fields connected such that the magnetomotive
forces from two fields are additive.
The equivalent circuit of
cumulatively
compounded dc
generator is shown in
Figure 9-59 for longshunt connection.
Figure 9-60 for shortshunt connection.
104
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The Terminal Characteristic of a
Cumulatively Compounded DC
Generator
The cumulatively compounded dc generator is a dc generator with
both series and shunt fields connected such that the magnetomotive
forces from two fields are additive.
The equivalent circuit of
cumulatively
compounded dc
generator is shown in
Figure 9-59 for longshunt connection.
Figure 9-60 for shortshunt connection.
105
The Terminal Characteristic of a
Cumulatively Compounded DC
Generator
Total magnetomotive force including armature reaction on this
machine is given by
The equivalent effective shunt field current for this machine is
(Long-shunt connection)
(Long-shunt connection)
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The Terminal Characteristic of a
Cumulatively Compounded DC
Generator
As the load increases, so IA↑ = IF + IL↑
At this point two effects occur in the generator:
These two effects oppose each other about VT.
Which effect predominates in a given machine ?
107
The Terminal Characteristic of a
Cumulatively Compounded DC
Generator
The question can be answered by taking several individual cases:
108
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The Terminal Characteristic of a
Cumulatively Compounded DC
Generator
The question can be answered by taking several individual cases:
All these possibilities are illustrated in Figure 9-61.
109
The Terminal Characteristic of a
Cumulatively Compounded DC
Generator
110
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The Terminal Characteristic of a
Cumulatively Compounded DC
Generator
It is possible to realize all these voltage characteristics in a single
generator if a diverter resistor Rdiv is used.
large Rdiv (>>RS) => overcompounded
small Rdiv (<<RS) => undercompounded
111
Voltage Control of Cumulatively
Compounded DC Generators
Similar to shunt dc generator, the techniques of voltage control for
cumulatively compounded dc generators are exactly the same.
112
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Analysis of Cumulatively
Compounded DC Generators
Equations (9-53) and (9-54) are the key to describing the terminal
characteristics of a cumulatively compounded dc generator.
Equivalent shunt field current due to the effects of the series field
and armature reaction is given by
Thus, total effective shunt field current is
113
Analysis of Cumulatively
Compounded DC Generators
See Figure 9-63 for final
terminal voltage when
generator is loaded.
Upper tip of triangle touches
the magnetization curve (EA
line)
Leftmost edge of triangle
touches the shunt field
current line (VT line)
114
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Analysis of Cumulatively
Compounded DC Generators
Figure 9-64 shows this process repeated several times to construct
complete terminal characteristic for the generator.
IL = IA - IF
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9.16 The Differentially
Compounded DC Generator
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The Terminal Characteristic of a
Differentially Compounded DC
Generator
The differentially compounded dc generator is a dc generator with
both series and shunt fields connected such that the magnetomotive
forces from two fields are subtractive.
Figure 9-65 for longshunt connection.
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The Terminal Characteristic of a
Differentially Compounded DC
Generator
Total magnetomotive force including armature reaction on this
machine is given by
The equivalent effective shunt field current for this machine is
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The Terminal Characteristic of a
Differentially Compounded DC
Generator
Referring to cumulatively compounded dc generator, two same effects
occur in this differentially compounded dc generator acting in the
same direction.
Both of these effects tend to decrease VT drastically as load increases.
Figure 9-66 shows its typical terminal characteristic.
119
The Terminal Characteristic of a
Differentially Compounded DC
Generator
120
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Voltage Control of Differentially
Compounded DC Generators
Similar to shunt dc generator, the techniques
of voltage control for differentially
compounded dc generators are exactly the
same.
1. Change the speed of rotation ωm
2. Change the field current IF
121
Graphical Analysis of a Differentially
Compounded DC Generator
To find the terminal characteristic of the differentially compounded dc
generator, refer to Figure 9-67.
Both series field and
armature reaction are
subtractive from the shunt
field.
To find the terminal voltage
for a given load,
Triangle exactly fits between
the field current line (VT line)
and the magnetization curve
(EA line)
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Graphical Analysis of a Differentially
Compounded DC Generator
Figure 9-68 shows this process repeated several times to construct
complete terminal characteristic for the generator.
IL = IA - IF
123
EEE 118: Energy Conversion
Dr. Mongkol Konghirun
Department of Electrical Engineering
King Mongkut’s University of Technology Thonburi
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