辅导EEET 3032讲解Matlab程序

日期：2021-05-04 02:35

16/04/2020
1
DC Machines
Dr. Mohammed H. Haque
School of Engineering

EEET 3032 – Electrical Machines 1
Topics
• Ideal electrical machines
• Induced voltage and torque equations
• Commutation and armature reaction
• Construction and operating principle
• Classification
• Equivalent circuit, power flow diagram, losses and efficiency
• Characteristics of various dc machines
• Speed control of dc motors
• Motor and load torque matching
• Dynamics of dc machines
EEET 3032/M. H. Haque/2019 2
1
2
16/04/2020
2
Electric Machines
An electric machine converts electrical energy into mechanical energy or mechanical
energy into electrical energy
Generator: Converts mechanical energy into electrical energy
Motor: Converts electrical energy into mechanical energy
Electromechanical energy conversion
EEET 3032/M. H. Haque/2019 3
In Electrical System:
Primary quantities are voltage (V or E) and current (I)
In Mechanical System:
Primary quantities are torque (T) and speed (?m or n)
AC Machines: Electrical system is AC
DC Machines: Electrical system is DC
EEET 3032/M. H. Haque/2019 4
3
4
16/04/2020
3
Coupling Magnetic Field
The coupling medium between the electrical and mechanical systems is magnetic
field and is essential in all electromechanical energy conversion processes
Coupling
Magnetic
Field
Mechanical
System
Electrical
System
E and I T and ?m
Coupling magnetic field between electrical mechanical systems
EEET 3032/M. H. Haque/2019 5
For an ideal (or lossless) machine
Electrical energy = Mechanical energy
? Electrical power = Mechanical power
Electrical power: Pe = E?I (W) in DC circuit
Mechanical power: Pm = T??m (W)
? For an ideal machine
Pe = Pm ? EI = T?m
Machine speed is usually measured (or given) in revolution per minute (rpm). However, in power
calculation, machine angular velocity (in radian/sec) is used. The relationship between speed n (in rpm)
and angular velocity ?m (in rad/sec) is
nm ?
?
?
?
?
?
=
60
2?
?
That is ?m and n are linearly related and the proportionality constant is 2?/60
EEET 3032/M. H. Haque/2019 6
5
6
16/04/2020
4
Electromagnetic Energy Conversion
Two basic electromagnetic phenomena are:
• A moving conductor in a magnetic field induces voltage. This is called
generator action.
• A current carrying conductor in a magnetic field produces force. This
is called motor action.
In all electric machines, both actions/effects are taken place simultaneously
EEET 3032/M. H. Haque/2019 7
Induced Voltage
The induced voltage or emf (e) in a moving conductor in the presence of a magnetic
field is given by
e = BLv (V) when B, L and v are mutually perpendicular
B = magnetic flux density, T or Wb/m2
L =conductor length in magnetic field, m
v = relative velocity between field and conductor, m/s
The polarity or direction of induced voltage (e)
can be determined by the Right Hand Rule (RHR)
as shown in the figure
Electric machines are designed in such a way that
B, L and v are mutually perpendicular
EEET 3032/M. H. Haque/2019 8
7
8
16/04/2020
5
A Simple Generator
Consider a coil rotates in a magnetic field produced by two poles (N and S) as shown in
the figure. Coil ends are connected to two rotating slip rings. Stationary brushes are
placed on the rotating slip rings to extract the internal induced voltage. External load is
connected between the stationary brushes.
The resultant voltage appears
between the slip rings A and
B is alternating (but not DC).
EEET 3032/M. H. Haque/2019 9
Generation of Unidirectional Voltage
• Commutators are used to convert the internal AC induced voltage into unidirectional
output voltage.
• Commutators can be considered as mechanical rectifier.
EEET 3032/M. H. Haque/2019 10
Commutator
9
10
16/04/2020
6
• Coil sides and commutators change position simultaneously because they are on the
same structure
• Connection between brushes and commutators changes whenever the polarity of the
induced voltage is revered
• Thus, the polarity of output (or load) voltage remains unchanged. The output voltage
is unidirectional but pulsating as shown in the figure. It has high ripples.
EEET 3032/M. H. Haque/2019 11
How to Reduce Ripples?
Ripples can be reduced by using a large number of armature coils connected in series
• First consider that only two coils A-B and C-D are placed at right angle and
connected in series
• The phase shift between EAB and ECD is 90
0 and the resultant voltage ER is EAB + ECD
as shown in the following figure
EEET 3032/M. H. Haque/2019 12
11
12
16/04/2020
7
Comparison of Output Voltage
(a) 1-coil;
(b) 2-coil;
(c) 8-coil
EEET 3032/M. H. Haque/2019 13
Construction of DC Machines
Stator: Provides the physical support and magnetic poles
Rotor: The main winding (where the voltage is induced) is placed in the rotor. The rotor
of a DC machine is also called armature
Three essential elements in DC machines are
• Production of magnetic field or flux. Usually electromagnets are used
• Rotating coils/conductors where the voltage is induced
• Brush-commutator arrangement (to convert AC voltage to DC voltage)
Field coil on a pole piece A complete armature
EEET 3032/M. H. Haque/2019 14
13
14
16/04/2020
8
Field Windings and Representation
There are two sets of field windings
• Shunt field winding: Consists of a large number of turns with fine wire and
carries less current (usually a few % of rated current). It has high resistance
• Series field winding: Consists of less number of turns with heavy wire and carries
large current (usually the load current). It has low resistance
To produce magnetic field, it is not necessary to use both field windings simultaneously.
Representation of Field Windings
A field winding is represented by a coil as shown in schematic diagram. It consists of
resistance (R) and inductance (L). For steady state analysis, L is ignored and thus only R
is considered.
Schematic diagram Electrical equivalent circuit
R
EEET 3032/M. H. Haque/2019 15
Representation of Armature
Armature consists of a large number of conductors where voltage is induced. For
steady state analysis, the armature inductance (L) is ignored and thus its equivalent
circuit consists of induced voltage E and the resistance Ra. Note that E is not
constant.
E
R
a
Brush
Schematic
diagram
Electrical
equivalent circuit
EEET 3032/M. H. Haque/2019 16
15
16
16/04/2020
9
Classification of DC Machines
The characteristic of a DC machine depends on the field winding(s) used (series or
shunt) to produce flux. Classification of DC machines is based on mutual connection
between the armature and field windings.
(a) Separately excited
The shunt field winding is connected to a separate
DC source Vf. The series field winding is not used. V
t
E
Shunt field
V
f
(b) Self-excited
The armature induced voltage/current is used to excite the field circuit(s). A separate
DC source is not required. Self-excited machines can further be classified into three
categories (i) Shunt, (ii) Series and (iii) Compound
EEET 3032/M. H. Haque/2019 17
(i) Shunt: The shunt field winding is connected in parallel
with the armature. The armature terminal voltage is the
same as the shunt field voltage. Series field winding is
not used in a shunt machine.
VtE
S
h
u
n
t
fi
e
ld
(ii) Series: The series field winding is connected in
series with the armature. Thus, the armature current is
the same as the series field current. Shunt field winding
is not used in a series machine
V
t
E
Series field
(iii) Compound: In compound machines, both series and shunt field windings are
used. There are two possible connections of compound machines (1) short-shunt and
(2) long-shunt.
Vt
E
Series field
S
h
u
n
t
fi
e
ld Vt
E
Series field
S
h
u
n
t
fi
e
ld
(1) Short-shunt (2) long-shunt
EEET 3032/M. H. Haque/2019 18
17
18
16/04/2020
10
DC Generators
EMF or Induced Voltage Equation
The emf or induced voltage in the armature of a DC machine is directly proportional
to the flux ? produced by the poles and the angular velocity ?m of the rotor or
armature. The induced voltage (E) can be expressed as
E = kφωm Volt
Here k is a constant and it depends on the rotor or armature of the machine.
Induced voltage (E) depends on the following three factors:
• Flux ? produced by the poles
• Angular velocity ?m of the rotor or armature
• Constant k representing the size of the machine
EEET 3032/M. H. Haque/2019 19
This is called voltage equation or EMF equation
Magnetization Curve
The flux is usually produced by passing current through the field winding(s). The flux
induces voltage in the armature when it rotates. The variation of induced voltage
against the field winding current (at constant speed) is called magnetization curve.
The procedure of generating the magnetization curve is as follows
• Run the machine at a constant speed (rated speed)
as a separately excited generator without any load
(or open circuit condition)
• Measure the terminal voltage Vt for different values
of fields current If. Note that at no load, the
armature current is zero and thus the internal
voltage E is the same as the terminal voltage Vt
VtE
If
Rf
Rrh
Vf
EEET 3032/M. H. Haque/2019 20
• Plot the induced voltage E against the field current If and is called the magnetization
curve of the machine
• The magnetization curve is also known as Open Circuit Characteristic (OCC) or no-
load (NL) characteristic
19
20
16/04/2020
11
Magnetization Curve
Magnetization curve has three
distinct regions:
• Linear region (E is directly
proportional to If, i.e. E = k1If)
• Transition region (relationship
between E If is nonlinear)
• Saturation region (E ? constant,
independent of If)
Magnetization curve or OCC or no-load characteristic
Residual Voltage
The induced voltage E for If = 0 is
called residual voltage. The residual
voltage is the induced due to residual
flux in the poles and is usually very
small (about 5% of rated value)
EEET 3032/M. H. Haque/2019 21
Effects of Speed and Flux on Voltage
Voltage equation: E = k??m
The ratio of the voltage (for two different conditions, say ‘1’ and ‘2’) is given by