Tutorial Class
Section 2
Section 3
Section 4
ProblemClass-1
2.1 An R-L-C series circuit is connected to a 230V
50Hz power supply. Assume that R=1, L=0.1H and
C=1000F. Calculate the current, real power, power
factor and complex power, with the help of a ph
4. An R-L-C series circuit is connected to a 230V
50Hz power supply. Assume that R=1, L=0.1H and
C=1000F. Calculate the current, real power, power
factor and complex power, with the help of a phasor
diagram.
Z R jL
1
jC
1 j100 0.1
230
V
Z 1 28.24 j
230
ELEC209: ELECTRICAL CIRCUITS AND
POWER SYSTEMS
ELEC209: ELECTRICAL CIRCUITS AND
POWER SYSTEMS
Revision
Dr Ali Al-Ataby
aliataby@liv.ac.uk
Part I: Electrical Circuits
Various Flux Definitions-Cond
Various Flux Definitions
1
11 is the flux produced in coil
29/11/2012
ELEC209 ELECTRICAL CIRCUITS AND
POWER SYSTEMS
Lecture 7- Synchronous
Generators
Dr Ali Al-Ataby
aliataby@liv.ac.uk
1
29/11/2012
CONTENTS
Construction
Operation principles
Equivalent circuits
Over/under excitation and power flow
Review Question
Two-Port Networks
Models of two-port networks
Many complex passive and linear circuits can be modelled by a two-port network
model as shown below. A two-port network is represented by four external variables:
voltage V1 and current I1 at the input port, a
2.1 An R-L-C series circuit is connected to a 230V
50Hz power supply. Assume that R=1, L=0.1H and
C=1000F. Calculate the current, real power, power
factor and complex power, with the help of a phasor
diagram.
Z R jL
1
jC
1 j100 0.1
V
230
Z 1 28.24 j
23
Tutorial Class
Section 2
Section 3
Section 4
ProblemClass-1
2.1 An R-L-C series circuit is connected to a 230V
50Hz power supply. Assume that R=1, L=0.1H and
C=1000F. Calculate the current, real power, power
factor and complex power, with the help of a ph
Three Phase Systems.
So far circuit analysis has been performed on single-phase ac circuits, i.e. there has been one circuit with a
number of different voltage and current sources which were not synchronised in any purposeful way.
In a three-phase system
ELEC209 Electrical Circuits and Power Systems
3. Components of a power system
3-phase AC circuits
Components of a power system
Generators
Transformers
Transmission lines
17.6 MW
16.0 MW
28.8 MVR
-16.0 MVR
59.7 kV
17.6 MW
28.8 MVR
40.0 kV
16.0 MW
16.0 MV
ELEC209 Electrical Circuits and Power Systems
5. Energy sources
In the UK,
The primary source of electrical energy is fossil fuels
coal
oil
gas.
This is followed by nuclear.
Then hydro and wind power.
5-1
ELEC209 Electrical Circuits and Power Systems
F
ELEC209 Electrical Circuits and Power Systems
2. Power, power balance and power systems
Power, VARs, apparent power and complex
power
Power balance
Organisation of power system
Failures of power system
2-1
ELEC209 Electrical Circuits and Power Systems
ELEC209 Electrical Circuits and Power Systems
7. Synchronous Generators
Construction
Operation principles
Equivalent circuits
Over/under excitation and power flow
7-1
ELEC209 Electrical Circuits and Power Systems
Although induction generators are used
ELEC209 Electrical Circuits and Power Systems
4. The per unit system
If you follow electrical power from a generator through
transmission and distribution systems to customers, you
find a path similar to the following one:
1
22kV
2
400kV
3
132kV
5
4
66kV
Three Phase Power Systems
1. The circuit below is a balanced three-phase star-star connected system. The
generator supplies rated nns voltages of 240V at 50H: in the positive phase
sequence. All generator and line impedances are negligible and each phase
Magnetically Coupled Circuits
Problems sheet-1
1. When one coil of a magnetically coupled pair has a current of 5.0A, the resulting
fluxes ell1 and 21 are 0.2mWb and 0.4mWb, respectively.
If the turns are N1 = 500 and N2 = 1500, find L1, L2, M and the coe
Supple mentary Questions
First-Order Circuits
Q1. The capacitor of the below figure is initially charged to 40 V. Find the
mathematical expression for v C after the closing of the switch.
Solution:
The network is redrawn as fo llo ws:
1
Ali Al-Ataby
Q2. F
Supplementary Questions
Three-Phase Systems
Q1. For the - system shown in the figure below:
a. Find the phase angles 2 and 3 for the specified phase sequence.
b. Find the current in each phase of the load.
c. Find the magnitude of the line currents.
[120o
Supplementary Questions
Magnetically Coupled Devices
Q1. For the transformer in the figure below:
a. Find the mutual inductance M.
b. Find the induced voltage v1 if the flux 21changes at the rate of 450 mWb/s.
c. Find the induced voltage v2 for the same r
FIRST-ORDER TRANSIENT CIRCUITS
ELEC209: Lecture 4 03
Ali Al-Ataby
aliataby@liv.ac.uk
CONTENTS
Inductive circuit switched to AC
Capacitive circuit switched to AC
2
Inductive circuit switched to AC
Consider the following circuit:
Let the voltage source be
09-10-12
Quiz
A magnetically coupled circuit is shown in the figure below. The
direction of current in each loop is as shown in the figure.
a) Calculate the two currents, I1 and I2.
b) If voltage source 2 was replaced with a variable voltage source
and ad
Problem Sheet 3
First-Order Circuits
Q1. The capacitor of the below figure is initially charged to 40 V. Find the
mathematical expression for vC after the closing of the switch.
Solution:
The network is redrawn as follows:
1
Dr Ali Al-Ataby
Q2. For the ne