DC MACHINES
The direct current (dc) machine can be used as a motor
or as a generator.
DC Machine is most often used for a motor.
The major advantages of dc machines are the easy
speed and torque regulation.
However, their application is limited to mills,
Magnetic Circuits
Lorentz Force
The force on a moving charge in a magnetic field is
proportional to the charge, velocity, and magnetic field
strength.
Faradays Law
Currents can be induced in wires by a changing
magnetic fields.
Lenzs Law
The induced cu
Resonance
Resonant circuits (series or parallel) are useful for
constructing filters, as their transfer functions can be highly
frequency selective.
They are used in many applications such as selecting the
desired stations in radio and TV receivers.
1
Se
FindEb
10 A
0.8
400
Eb
Ia
200V
Onecurrenttworeadings!
Alternating currents and voltages vary with
time and periodically change their direction
Sine Waves
Sine waves
by far the most important form of alternating
quantity
important properties are shown
Find the wattmeter reading. CC is the current coil. PC is the pressure coil.
The coil polarities are suitably selected to ensure a positive deflection.
a
3-PHASE
BALANCED
SUPPLY
400V
50Hz
100 + j0 O
100 + j0 O
cc
b
pc
c
Impedance
Resistor:
V=IR
The impedance is ZR = R
Inductor:
V = I jL
The impedance is ZL = jwL
Capacitor:
The impedance is ZC = 1/jC
CircuitAnalysisUsingPhasorsandImpedances
1.Replace the time descriptions of the
voltage and current sources with the
co
Complex Numbers
j = (- 1)
z
y
imaginary
axis
real
axis
x
Rectangular Coordinates
Z = x + jy
Polar Coordinates:
Z = z
Exponential Form:
Z = Z e j = ze j
x is the real part
y is the imaginary part
z is the magnitude
is the phase
y = z sin
x = z cos
2
No power losses are associated with capacitors and pure inductors in
an AC circuit
In a capacitor, during one-half of a cycle energy is stored and
during the other half the energy is returned to the circuit.
In an inductor, the source does work against th
Capacitance
Capacitance occurs when two conductors
(plates) are separated by a dielectric
(insulator)
Charge on the two conductors creates an
electric field that stores energy
+
Capacitance
The voltage difference between the two
conductors is proportio
ThreephaseCircuits
An AC generator designed to develop a single sinusoidal voltage for each rotation
of the shaft (rotor) is referred to as a single-phase AC generator.
If the number of coils on the rotor is increased in a specified manner, the result is
Three phase Connections
Both the three phase source and the three phase load can be
connected either Wye or DELTA.
We have 4 possible connection types.
Y-Y connection
Y- connection
- connection
-Y connection
Balanced Wye-wye Connection
Line current
1. Mesh analysis
Step 1: Name the meshes/loops in the circuit by assuming currents in the same
direction, preferably in the clockwise direction.
Step 2: Write the KVL equations for each mesh/loop.
o
o
If a branch is a resistive branch, use Ohms law to exp
Losses, efficiency and
characteristics of DC Machines
Open Circuit Characteristics
The O.C.C curve for self-excited generators whether shunt or series wound is
shown in above figure.Due to the residal magnetism in the poles, some e.m.f
(=OA) is gnerated e
N1 = No. of turns in primary
N2 = No. of turns in secondary
m = Maximum flux in core in webers = Bm x A
f = Frequency of a.c. input in Hz.
The flux increases from it's zero value to maximum value m in one
quarter of the cycle i.e. in 1/4 f second.
Therefo
Direct Current Motors
Principle of Operation
When a current carrying conductor is placed in a
magnetic field, it experiences a mechanical force
whose direction is given by Flemings left hand rule.
Constructionally, D.C. Generator and D.C. motor have no
ba
SteadyStateSinusoidalAnalysis
1.Identify the frequency, angular frequency, peak
value, rms value, and phase of a sinusoidal signal.
2.Solve steady-state ac circuits using phasors and
complex impedances.
3.Compute power for steady-state ac circuits.
4.Find
Magnetic Circuits
H
Amperes law: dl I
C
Lorentz force: F q B
v
Necessary to solve magnetic circuit
equations
Materials
Permeability m.
Vacuum has m0 = 4p x 10-7 H/m.
Materials:
Diamagnetic m < m0
Paramagnetic m > m0
Ferromagnetic m > m0
Superconduct
Phasor Diagram of a Transformer
Equivalent Circuit
Equivalent circuit referred to primary
Equivalent circuit phasor diagram
Approximate Equivalent Circuit
Equivalent Circuit referred to Secondary
Transformer Parameters Determination
Open circuit test
Shor
Regulation and Efficiency
Vno-load Vload
percent regulation
100%
Vload
Pload
Ploss
100%
power efficiency
100% 1
Pin
Pin
Normally the OC test is done in LV side.
Why?
SC test is done in HV side
The eqvt. circuit for no load test
The eqvt. circuit
Energy Storage Elements
Capacitors store energy in an electric field.
Inductors store energy in a magnetic field.
Capacitors and inductors are passive
elements:
Can store energy supplied by circuit
Can return stored energy to circuit
Cannot supply more en
Example-1
The switch in the circuit of figure 1 has been closed for a long time
and it is opened at t = 0. Calculate:
The initial value of iL and, the final value of . iL
The time constant for t 0.
An expression for iL(t) for t 0.
Initial Value i(0)
Time
Review of Last Lecture
Power at Receiving End
At Receiving End
Approximate formulae
Short line
Large X/R ratio
Power-angle characteristics
Circle diagram
At Sending End
Usage of the formulae while solving the examples
29/05/17 06:20
Power at Receiving End
Review of Last Lecture
Design parameters and materials of power system Components.
Mechanical design of transmission line
Parameters affecting
Various types of towers
Sag, Span, and Ground clearance
Calculation of conductor length, sag, and tension.
0
Voltage Distribution Along The Insulator String
Methods of Equalizing the Potential
Methods to improve string efficiency
Selection of m
Grading of units
Static shielding or guard rings
Semiconducting high resistance glaze layer on surface of
insulator
Sta
Review of Last Class
Compensation in Power System
Series compensation
Shunt compensation
Line Parameters
29/05/17 06:20
Line Parameters
Electrical Parameters
Resistance
Inductance
Capacitance
Conductance
Conductance is due to leakage over line insulat
Line Parameters
Review of Last Lecture
Resistance
Type of conductors (ACSR, AAC, AAAC, ACAR, Expanded
ACSR)
It depend on
Temperature
Dimensions
Frequency
Inductance
Internal inductance
External inductance
29/05/17 06:20
Inductance of the Lines
d
Ix
1m
Int
Review of Last Lecture
Inductance of three-phase line
Symmetrical spacing
Unsymmetrical spacing without transposition
Unsymmetrical spacing with transposition
Inductance of Composite Conductor
Inductance of Three-Phase Line
Symmetrical spacing
D
La Lb Lc
Review of Last Lecture
Lumped and Distributed Parameters
ABCD parameters of the transmission line
Transmission line models
Short transmission line
Medium transmission line
Long transmission line
29/05/17 06:20
Transmission Line Models
Short line : Length
Review of Last Lecture
Inductance of Composite Conductor
Bundled conductors
Inductance of double circuit line
Bundled Conductors
http:/en.wikipedia.org/
Bundled Conductors
Corona loss
Surface voltage gradient
Line reactance
Radio interference
Capacitance
Discrete Time Systems
Continuous feedback system
The continuous controller, enclosed in the dashed square, can be
replaced by a digital controller.
Discrete Control System
The digital system operates on discrete signals (or samples of the sensed signal)
r
If a function
f x
has derivatives of all orders at x0, then we can formally write
the corresponding Taylor series
f x f x0
f ' x0
1!
x
x0
f ' x0
2!
x
2
x0
f ' x0
3!
x
The power series created in this way is then called the Taylor series of the
funct
Semi log graph
s
G(s) 1
2
Draw approximate magnitude plot
20dB/Decade
20dB
0.1
1
2
10
20
100
5
G(s)
n 2
s 2 2 n s n 2
40dB / Decade
n
2
n
G (s) 2
2
s 2 n s n
u
n
1
G ( j )
1 u 2 j 2u
M
Gain in dB =20logM
1
u 1
M 1
u 1
1
M 2
u
(1 u 2 ) 2 4 2u 2
Upto =n
CONTROL ACTIONS
automatic controller
reference actuating error signal e(t) controller output u(t)
Input r(t)
Controller
feed back signal b(t)
Actuator
output c(t)
plant
Sensor
What is control action?
The manner in which the automatic controller produces
t
Unit step response of second order systems
C ( s) R( s) G ( s)
C (s)
n
2
D( s ) ( s n jd )( s n jd )
d n 1 2
s ( s 2 2 n s n 2 )
s 2 n
1
s s 2 2 n s n 2
s n
n
1
s ( s n ) 2 d 2 ( s n ) 2 d 2
c(t ) 1 e
n t
(cos d t
1
2
sin d t )
1 2
tan
sin 1 2
j