Introduction To Z Transform

Introduction To Z Transform:

Z transform of a signal provides a valuable technique for analysis and design of the discrete time signal and discrete time LTI system.

Z transform of a discrete time signal has both imaginary and real part. The plot of imaginary part versus real part is called as the z plane. The poles and zeros of the discrete time signals are plotted in the complex z plane. Pole-zero plot is the main characteristics of the discrete time signals. Using pole zero plot we can check the stability of the system which we will see in the upcoming posts.

Advantages Of The Z Transform:

Following are some of the main advantages of the Z transform:

• We can simplify the solution of differential equation using z transform.
• By the use of z transform we can completely characterize given discrete time signals and LTI systems.
• The stability of the LTI system can be determined using z transform.
• Mathematical calculations can be reduced by using z transform. For example convolution operation is transformed into simple multiplication operation.
• Z Transforms:

There are two types of z transform:

1. Single sided Z transform.

1. Double sided Z transform.

The relation between x(n) and X(Z) is denoted as follows:

Where X(Z) is the Z transform of the signal x(n). The arrow is bidirectional which indicates that we can obtain x(n) from X(Z) also, which is called as inverse Z transform.

x(n) and X(Z) is called as Z transform pair.

Region Of Convergence (ROC):

“Region of convergence is defined as a set of all values of Z for which X(Z) has finite value. It is very important to denote ROC every time when we find Z transform.”

Significance Of ROC:

ROC will decide whether the given system is stable or unstable.
ROC is also useful for determining the type of sequence. i.e. whether the system is causal or non-causal, finite or infinite.

Long transmission lines molding

A power transmission line with its effective length of around 250 Kms or above is referred to as a long transmission line. Calculations related to circuit parameters (ABCD parameters) of such a power transmission is not that simple, as was the case for a short transmission line or medium transmission line.The reason being that, the effective circuit length in this case is much higher than what it was for the former models (long and medium line) and, thus ruling out the approximations considered there like.
long transmission line

1. Ignoring the shunt admittance of the network, like in a small transmission line model.
2. Considering the circuit impedance and admittance to be lumped and concentrated at a point as was the case for the medium line model.

Rather, for all practical reasons we should consider the circuit impedance and admittance to be distributed over the entire circuit length as shown in the figure below.
The calculations of circuit parameters for this reason is going to be slightly more rigorous as we will see here. For accurate modeling to determine circuit parameters let us consider the circuit of the long transmission line as shown in the diagram below.
long transmission line model
Here a line of length l > 250km is supplied with a sending end voltage and current of VS and IS respectively, where as the VR and IR are the values of voltage and current obtained from the receiving end. Lets us now consider an element of infinitely small length Δx at a distance x from the receiving end as shown in the figure where.


V = value of voltage just before entering the element Δx.
I = value of current just before entering the element Δx.
V+ΔV = voltage leaving the element Δx.
I+ΔI = current leaving the element Δx.
ΔV = voltage drop across element Δx.
zΔx = series impedence of element Δx
yΔx = shunt admittance of element Δx
Where, Z = z l and Y = y l are the values of total impedance and admittance of the long transmission line.
Therefore, the voltage drop across the infinitely small element Δx is given by

Now to determine the current ΔI, we apply KCL to node A.
ΔI = (V+ΔV)yΔx = V yΔx + ΔV yΔx
Since the term ΔV yΔx is the product of 2 infinitely small values, we can ignore it for the sake of easier calculation.
Therefore, we can write dI ⁄ dx = V y -----------------(2)
Now derivating both sides of eq (1) w.r.t x,
d2 V ⁄ d x2 = z dI ⁄ dx
Now substituting dI ⁄ dx = V y from equation (2)
d2 V ⁄ d x2 = zyV
or d2 V ⁄ d x2 − zyV = 0 ------------(3)
The solution of the above second order differential equation is given by.
V = A1 ex√yz + A2 e−x√yz --------------(4)
Derivating equation (4) w.r.to x.
dV/dx = √(yz) A1 ex√yz − √(yz)A2
e−x√yz ------------(5)
Now comparing equation (1) with equation (5)

Now to go further let us define the characteristic impedance Zc and propagation constant δ of a long transmission line as
Zc = √(z/y) Ω
δ = √(yz)
Then the voltage and current equation can be expressed in terms of characteristic impedance and propagation constant as
V = A1 eδx + A2 e−δx -----------(7)
I = A1/ Zc eδx + A2 / Zc e−δx ---------------(8)
Now at x=0, V= VR and I= Ir. Substituting these conditions to equation (7) and (8) respectively.
VR = A1 + A2 ---------------(9)
IR = A1/ Zc + A2 / Zc ---------------(10)
Solving equation (9) and (10),
We get values of A1 and A2 as,
A1 = (VR + ZCIR) ⁄ 2
And A1 = (VR − ZCIR) ⁄ 2
Now applying another extreme condition at x=l, we have V = VS and I = IS.
Now to determine VS and IS we substitute x by l and put the values of A1 and
A2 in equation (7) and (8) we get
VS = (VR + ZC IR)eδl ⁄ 2 + (VR −
ZC IR)e−δl/2 --------------(11)
IS = (VR ⁄  ZC + IR)eδl/2 − (VR / ZC − IR)e−δl/2--------------- (12)
By trigonometric and exponential operators we know
sinh δl = (eδl − e−δl) ⁄ 2
And cosh δl = (eδl + e−δl) ⁄ 2
Therefore, equation(11) and (12) can be re-written as
VS = VRcosh δl + ZC IR sinh δl
IS = (VR sinh δl)/ZC + IRcosh δl
Thus comparing with the general circuit parameters equation, we get the ABCD parameters of a long transmission line as,
A = cosh δl
B = ZC sinh δl
C = sinh δl ⁄ ZC
D = cosh δl


Book

• Power System Analysis by Grainger and W.D. Stevenson.
• Power System Analysis and Design by J. Duncan Glover,Mulukutla S. Sarma and Thomas J. Overbye.
• Power System Analysis by Hadi Sadat,
• Principles of Power Systems by Mehta.

   
Author        Bilal masood
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Long Transmission line Model

A major section of power system engineering deals in the transmission of electrical power from one particular place (eg. generating station) to another like substations or distribution units with maximum efficiency. So its of substantial importance for power system engineers to be thorough with its mathematical modeling. Thus the entire transmission system can be simplified to a two port network for the sake of easier calculations.The circuit of a 2 port network is shown in the diagram below. As the name suggests, a 2 port network consists of an input port PQ and an output port RS. In any 4 terminal network, (i.e. linear, passive, bilateral network) the input voltage and input current can be expressed in terms of output voltage and output current. Each port has 2 terminals to connect itself to the external circuit. Thus it is essentially a 2 port or a 4 terminal circuit, having two port network

Given to the input port P Q.

Given to the output port R S.
As shown in the diagram below.
Now the ABCD parameters or the transmission line parameters provide the link between the supply and receiving end voltages and currents, considering the circuit elements to be linear in nature.

Thus the relation between the sending and receiving end specifications are given using ABCD parameters by the equations below.

Now in order to determine the ABCD parameters of transmission line let us impose the required circuit conditions in different cases.

ABCD Parameters, When Receiving End is Open Circuited

two port network
The receiving end is open circuited meaning receiving end current IR  = 0.
Applying this condition to equation (1) we get,

Thus its implies that on applying open circuit condition to ABCD parameters, we get parameter A as the ratio of sending end voltage to the open circuit receiving end voltage. Since dimension wise A is a ratio of voltage to voltage, A is a dimension less parameter.
Applying the same open circuit condition i.e  IR  = 0 to equation (2)

Thus its implies that on applying open circuit condition to ABCD parameters of transmission line, we get parameter C as the ratio of sending end current to the open circuit receiving end voltage. Since dimension wise C is a ratio of current to voltage, its unit is mho.
Thus C is the open circuit conductance and is given by
 C = IS ⁄  VR  mho.
ABCD Parameters, When Receiving End is Short Circuited

two port network
Receiving end is short circuited meaning receiving end voltage VR  = 0
Applying this condition to equation (1) we get,

Thus its implies that on applying short circuit condition to ABCD parameters, we get parameter B as the ratio of sending end voltage to the short circuit receiving end current. Since dimension wise B is a ratio of voltage to current, its unit is Ω. Thus B is the short circuit resistance and is given by
 B = VS ⁄ IR  Ω.
Applying the same short circuit condition i.e  VR  = 0 to equation (2) we get


Thus its implies that on applying short circuit condition to ABCD parameters, we get parameter D as the ratio of sending end current to the short circuit receiving end current. Since dimension wise D is a ratio of current to current, it’s a dimension less parameter.
∴ The ABCD parameters of transmission line can be tabulated as:-
Parameter Specification Unit
A = VS / VR Voltage ratio Unit less
B = VS / IR Short circuit resistance Ω
C = IS / VR Open circuit conductance mho
D = IS / IR Current ratio Unit less

Book

• Power System Analysis by Grainger and W.D. Stevenson
• Power System Analysis and Design by J. Duncan Glover,Mulukutla S. Sarma and Thomas J. Overbye
• Power System Analysis by Hadi Sadat
• Principles of Power Systems by Mehta

     
Author        Bilal masood
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Short and Medium Transmission Line

The transmission line having its effective length more than 80 km but less than 250 km is generally referred to as a medium transmission line. Due to the line length being considerably high, admittance Y of the network does play a role in calculating the effective circuit parameters, unlike in the case of short transmission lines. For this reason the modeling of a  medium length transmission line is done using lumped shunt admittance along with the lumped impedance in series to the circuit.These lumped parameters of a medium length transmission line can be represented using three different models, namely-

1. Nominal Π representation.

1. Nominal  T representation.

1. End Condenser Method

Let’s now go into the detailed discussion of these above mentioned models.

Nominal Π Representation of a Medium Transmission Line

In case of a nominal Π representation, the lumped series impedance is placed at the middle of the circuit where as the shunt admittances are at the ends. As we can see from the diagram of the Π network below, the total lumped shunt admittance is divided into 2 equal halves, and each half with value Y ⁄ 2 is placed at both the sending and the receiving end while the entire circuit impedance is between the two. The shape of the circuit so formed resembles that of a symbol Π, and for this reason it is known as the nominal Π representation of a medium transmission line. It is mainly used for determining the general circuit parameters and performing load flow analysis.
medium transmission line

Nominal T Representation of a Medium Transmission Line

In the nominal T model of a medium transmission line the lumped shunt admittance is placed in the middle, while the net series impedance is divided into two equal halves and and placed on either side of the shunt admittance. The circuit so formed resembles the symbol of a capital T, and hence is known as the nominal T network of a medium length transmission line .

End Condenser Method

In this method, the capacitance of the line is limped or concentrated at the receiving or load end. This method of localizing the line capacitance at the load end overestimates the effects of capacitance.

Book

• Power System Analysis by Grainger and W.D. Stevenson

• Power System Analysis and Design by J. Duncan Glover,Mulukutla S. Sarma and Thomas J. Overbye

• Power System Analysis by Hadi Sadat

• Principles of Power Systems by Mehta

     
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Exact Equivalent Circuit of transformer

Exact Equivalent Circuit transformer

Resistances and reactances of transformer, which are described above, can be imagined separately from the windings (as shown in the figure below). Hence, the function of windings, thereafter, will only be the transforming the voltage.

The no load current I0 is divided into, pure inductance X0 (taking magnetizing components Iμ) and non induction resistance R0 (taking working component Iw) which are connected into parallel across the primary. The value of E1 can be obtained by subtracting I1Z1 from V1. The value of R0 and X0 can be calculated as, R0 = E1 / Iw and X0 = E1 / Iμ.

But, using this equivalent circuit does not simplifies the calculations. To make calculations simpler, it is preferable to transfer current, voltage and impedance either to primary side or to the secondary side. In that case, we would have to work with only one winding which is more convenient.

From the voltage transformation ratio, it is clear that,
E1 / E2 = N1 / N2 = K

Now, lets refer the parameters of secondary side to primary.
Z2 can be referred to primary as Z2'
where, Z2' = (N1/N2)2Z2 = K2Z2.   ............where K= N1/N2.
that is, R2'+jX2' = K2(R2+jX2)
equating real and imaginary parts,
R2' =  K2R2 and X2' = K2X2 .
And V2' = KV2

Now, as the values of winding resistance and leakage reactance are so small that, V1 and E1 can be assumed to be equal. Therefore, the exciting current drawn by the parallel combination of  R0 and X0 would not affect significantly, if we move it to the input terminals as shown in the figure below.


Now, let R1 + R2' = R'eq  and X1 + X2' = X'eq

Approximate Equivalent Circuit Of Transformer

If only voltage regulation is to be calculated, then even the whole excitation branch (parallel combination of R0 and X0) can be neglected.

Book

• Power System Analysis by Grainger and W.D. Stevenson

• Power System Analysis and Design by J. Duncan Glover,Mulukutla S. Sarma and Thomas J. Overbye.

• Power System Analysis by Hadi Sadat.

• Principles of Power Systems by Mehta.

     
Author        Bilal masood
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Synchronous Machines

Synchronous Machines

Like other electrical machines, synchronous machines can be operated as either generators or motors. We will concentrate on synchronous generators, then adapt the theory for synchronous machines.
The prinicples of operation of synchronous generators are relatively simple. They operate like the simple 3-phase generator discussed in the fundamentals section of the course.

Principles of operation

• Create a magnetic field on the rotor of an electric machine
• Apply an external driving force
• As the rotor rotates, a voltage is induced in windings on the stator
• The frequency of the induced voltage will be synchronised with the speed of rotation

ns=120fep

ns=120fep

Synchronous machine construction

A synchronous machine has two mechanical parts: a rotor and a stator. There are also two electrical parts to the machine: a field source and an armature winding. These basic fundamentals of an electric machine are like those for a DC machine, with one significant difference: The field source of a synchronous machine is on the rotor, the armature winding of a synchronous machine is on the stator. Like DC machines, the field source creates a magnetic field, the armature winding has a voltage induced in it by the field. Also like DC machines, the field can be produced using either a field winding or by using permanent magnets. PM (permanent magnet) machines are common in small sizes, whilst large machines are usually made with field windings. (There are some exceptions to this rule, e.g. multi-MW PM motors are built for ship propulsion and direct drive wind turbine generators)
In this part of the course, we will concentrate on wound-field synchronous machines.
Terminology

• The field winding is on the rotor
• The armature winding is on the stator
• There is sometimes a damper or armortisseur winding on the rotor
• The external driving force (e.g. steam or hydro turbine, diesel generator, jet engine) is called the prime mover

Book

• Power System Analysis by Grainger and W.D. Stevenson
• Power System Analysis and Design by J. Duncan Glover,Mulukutla S. Sarma and Thomas J. Overbye.
• Power System Analysis by Hadi Sadat.
• Principles of Power Systems by Mehta.
•         

Author        Bilal masood
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Generator and Transformer Models

In a generator, motion of a conductor in a magnetic field induces an EMF. In a transformer, it is the changing field that induces an EMF in a fixed conductor.

Schematic generator

Discussion: Generators

The structure of a simple generator is essentially the same as a motor. The difference is that now mechanical energy is converted into electrical energy. The electrical current to a load is via a commutator for an ac generator or slip rings if ac is required.

Basic ideas can be understood by thinking about a coil rotating in a uniform magnetic field.

Plane of coil at an angle to the magnetic field
Consider a coil of area A with N turns of wire rotating at a constant angular velocity w in a uniform magnetic flux density B. As the coil rotates, it cuts through the lines of flux. Another way to express this is to say that the flux linking the coil is changing.

At what point is the rate of flux-cutting greatest? (When it is horizontal in the diagram above; when it is vertical, the rate of flux cutting is instantaneously zero.)

Rate of flux cutting = induced EMF = BANwcos wt

with a maximum value, Eo = BANw when the coil is parallel to the field.

Demonstrations: A motor in reverse

Show that a motor can operate in reverse, as a generator. One starting point is simply to attach a weight to a small motor and to drop the weight. The motor works in reverse as a generator; the induced EMF can be monitored with a meter

 Practical transformers

Discuss reasons for energy losses in real transformers. These are readily identified as:

ohmic heating of the coils
eddy current heating of the core
hysteresis effects which heat the core
magnetic flux escaping
But even with these it is not unusual to find efficiencies of 95% and higher. Large transformers used in power transmission may be as much as 99.5% efficient.

Where electronics are being used, low voltage ac supplies are usually required so step-down transformers will be an essential part of the power supply. The output from a transformer is ac, so there will have to be some form of rectification (with diodes) and smoothing (with capacitors).

Transformer on the grid

A second widespread use is within the 'Grid' that supplies electricity to the consumer. The connection from a power station to the consumer involves a long length of wire and often, high currents. For a given section of the grid, the resistance, R is fixed and the rate of heating generated in the wire will be I2 R; this energy is wasted. To minimise this energy loss, the current should be as small as possible. To deliver a particular power (VI), a smaller current can be achieved by using as high a voltage as possible. The grid is designed so that transformers are used to step up the voltage at the power station before transmission. Step down transformers reduce the voltage in stages to the level required by industrial and domestic consumers.

Book

• Power System Analysis by Grainger and W.D. Stevenson

• Power System Analysis and Design by J. Duncan Glover,Mulukutla S. Sarma and Thomas J. Overbye.

• Power System Analysis by Hadi Sadat.

• Principles of Power Systems by Mehta.

     
Author        Bilal masood
lecture       04
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Balanced three phase circuits

There are two types of system available in electric circuit, single phase and three phase system. In single phase circuit, there will be only one phase, i.e the current will flow through only one wire and there will be one return path called neutral line to complete the circuit. So in single phase minimum amount of power can be transported. Here the generating station and load station will also be single phase. This is an old system using from previous time.In 1882, new invention has been done on polyphase system, that more than one phase can be used for generating, transmitting and for load system. Three phase circuit is the polyphase system where three phases are send together from the generator to the load. Each phase are having a phase difference of 120°, i.e 120° angle electrically. So from the total of 360°, three phases are equally divided into 120° each. The power in three phase system is continuous as all the three phases are involved in generating the total power. The sinusoidal waves for 3 phase system is shown below-

The three phases can be used as single phase each. So if the load is single phase, then one phase can be taken from the three phase circuit and the neutral can be used as ground to complete the circuit.
three phase power

Why Three Phase is preferred Over Single Phase?

There are various reasons for this question because there are numbers of advantages over single phase circuit. The three phase system can be used as three single phase line so it can act as three single phase system. The three phase generation and single phase generation is same in the generator except the arrangement of coil in the generator to get 120° phase difference. The conductor needed in three phase circuit is 75% that of conductor needed in single phase circuit. And also the instantaneous power in single phase system falls down to zero as in single phase we can see from the sinusoidal curve but in three phase system the net power from all the phases gives a continuous power to the load.


Till now we can say that there are three voltage source connected together to form a three phase circuit and actually it is inside the generator. The generator is having three voltage sources which are acting together in 120° phase difference. If we can arrange three single phase circuit with 120° phase difference, then it will become a three phase circuit. So 120° phase difference is must otherwise the circuit will not work, the three phase load will not be able to get active and it may also cause damage to the system.
The size or metal quantity of three phase devices is not having much difference. Now if we consider the transformer, it will be almost same size for both single phase and three phase because transformer will make only the linkage of flux. So the three phase system will have higher efficiency compared to single phase because for the same or little difference in mass of transformer, three phase line will be out whereas in single phase it will be only one. And losses will be minimum in three phase circuit. So overall in conclusion the three phase system will have better and higher efficiency compared to the single phase system.

In three phase circuit, connections can be given in two types:

1. Star connection
2. Delta connection

Star Connection

In star connection, there is four wire, three wires are phase wire and fourth is neutral which is taken from the star point. Star connection is preferred for long distance power transmission because it is having the neutral point. In this we need to come to the concept of balanced and unbalanced current in power system.

When equal current will flow through all the three phases, then it is called as balanced current. And when the current will not be equal in any of the phase, then it is unbalanced current. In this case, during balanced condition there will be no current flowing through the neutral line and hence there is no use of the neutral terminal. But when there will be unbalanced current flowing in the three phase circuit, neutral is having a vital role. It will take the unbalanced current through to the ground and protect the transformer. Unbalanced current affects transformer and it may also cause damage to the transformer and for this star connection is preferred for long distance transmission.
The star connection is shown below-
star connected source
In star connection, the line voltage is √3 times of phase voltage. Line voltage is the voltage between two phases in three phase circuit and phase voltage is the voltage between one phase to the neutral line. And the current is same for both line and phase.

Delta Connection

In delta connection, there is three wires alone and no neutral terminal is taken. Normally delta connection is preferred for short distance due to the problem of unbalanced current in the circuit. The figure is shown below for delta connection. In the load station, ground can be used as neutral path if required.
delta connected source
In delta connection, the line voltage is same with that of phase voltage. And the line current is √3 times of phase current. It is shown as expression below,

In three phase circuit, star and delta connection can be arranged in four different ways-

1. Star-Star connection
2. Star-Delta connection
3. Delta-Star connection
4. Delta-Delta connection

But the power is independent of the circuit arrangement of the three phase system. The net power in the circuit will be same in both star and delta connection. The power in three phase circuit can be calculated from the equation below,

Since, there is three phases, so the multiple of 3 is made in the normal power equation and the PF is power factor. Power factor is a very important factor in three phase system and some times due to certain error, it is corrected by using capacitors.

Book

• Power System Analysis by Grainger and W.D. Stevenson

• Power System Analysis and Design by J. Duncan Glover,Mulukutla S. Sarma and Thomas J. Overbye

• Power System Analysis by Hadi Sadat

• Principles of Power Systems by Mehta

     
Author        Bilal masood
lecture       03
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phasors

A phasor quantity can be expressed in one of two forms, polar or rectangular.  Polar notation refers to the phasor using its' magnitude (length) and angle (direction).  Rectangular notation refers to the phasor using its' real component and imaginary component.

In the polar form the phasor would be expressed as having a magnitude of 5 units at an angle of 53 degrees.  In the rectangular form the same phasor would be expressed as having 3 units in the positive real direction and 4 units in the positive imaginary (+j) direction.

Converting between polar and rectangular form is a technique that will be used very frequently when dealing with reactive circuit analysis and you must be equally comfortable converting from polar to rectangular and converting from rectangular to polar.

Polar To Rectangular Conversion

A couple of things to remember:
    1. When entering theta use the value as measured from the positive real axis (0 degrees).  The calculator will then give you the correct sign for the real and the imaginary components.
    2. Be sure that your calculator is set to the angle units you are planning on using.  If your problem is specified in degrees, make sure your calculator is set to degrees, not radians!
    3. Remember to account for metric prefixes such as m, k etc.

Rectangular To Polar Conversion

 When converting from rectangular to polar for the equations used are:
 R to P formula

The same reminders apply.  Additionally you must be sure that you specify the angle correctly.  Do not rely on the calculator to give you the correct angle.  The calculator will try and specify an angle between 0 and 90 degrees.
If:
Real is: and Imaginary is: Angle must be between:
Positive Positive 0 and 90
Negative Positive 90 and 180
Negative Negative 180 and 270 (-90 and -180)
Positive Negative 270 and 360 (0 and -90)
This means you may need to add 180 degrees to determine the angle correctly.

Book

• Power System Analysis by Grainger and W.D. Stevenson

• Power System Analysis and Design by J. Duncan Glover,Mulukutla S. Sarma and Thomas J. Overbye

• Power System Analysis by Hadi Sadat

• Principles of Power Systems by Mehta

     
Author        Bilal masood
lecture       02
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Unsymmetrical Faults

Unsymmetrical faults involve only one or two phases. In unsymmetrical faults the three phase lines become unbalanced. Such types of faults occur between line-to-ground or between lines. An unsymmetrical series fault is between phases or between phase-to-ground, whereas unsymmetrical shunt fault is an unbalanced in the line impedances. Shunt fault in the three phase system can be classified as;

1. Single line-to-ground fault (LG).
2. Line-to-line fault (LL).
3. Double Line-to-ground fault (LLG).
4. Three-phase short circuit fault (LLL).
5. Three-phase-to-ground fault (LLLG).

In single line-to-ground fault, one conductor comes in contact with the ground or the neutral conductor. A line-to-line fault occurs when two conductors are short circuited. A double line-to-ground fault occurs when two conductors fall on the ground or come in contact with the neutral conductor. LG, LL, and LLG are unsymmetrical fault while LLL and LLLG are the symmetrical faults. For this reason, balanced short-circuit calculation is performed to determine these large currents.

Effect of faults on transmission line

Faults can damage or disrupt power systems in several ways. Faults increase the voltages and currents at certain points on the system. A large voltage and current may damage the insulation and reduces the life of the equipment. Faults can cause the system to become unstable, and the three-phase system equipment operates improperly. Hence, it is necessary that, on the occurrence of the fault, the fault section should be disconnected. So, the normal operation of the rest of the system is not affected.

Book

• Power System Analysis by Grainger and W.D. Stevenson

• Power System Analysis and Design by J. Duncan Glover,Mulukutla S. Sarma and Thomas J. Overbye

• Power System Analysis by Hadi Sadat

• Principles of Power Systems by Mehta

Author        Bilal masood
lecture       12
Type         ppt
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Symmetrical Faults

Symmetrical & Unsymmetrical Faults

Normally, a power system operates under balanced conditions. When the system becomes unbalanced due to the failures of insulation at any point or due to the contact of live wires, a short–circuit or fault, is said to occur in the line. Faults may occur in the power system due to the number of reasons like natural disturbances (lightning, high-speed winds, earthquakes), insulation breakdown, falling of a tree, bird shorting, etc.

Faults that occurs in transmission lines are broadly classified as

1. Symmetrical faults
2. Unsymmetrical faults

Symmetrical faults

In such types of faults, all the phases are short-circuited to each other and often to earth. Such fault is balanced in the sense that the systems remain symmetrical, or we can say the lines displaced by an equal angle (i.e. 120° in three phase line). It is the most severe type of fault involving largest current, but it occurs rarely. For this reason balanced short- circuit calculation is performed to determine these large currents.

Book

• Power System Analysis by Grainger and W.D. Stevenson

• Power System Analysis and Design by J. Duncan Glover,Mulukutla S. Sarma and Thomas J. Overbye

• Power System Analysis by Hadi Sadat

• Principles of Power Systems by Mehta

Author        Bilal masood
lecture       10
Type         ppt
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Power System

Electric power systems are comprised of components that produce electrical energy and transmit this energy to consumers. A modern electric power system has mainly six main components:
 1) power plants which generate electric power,
2) transformers which raise or lower the voltages as needed,
 3) transmission lines to carry power,
 4) substations at which the voltage is stepped down for carrying power over the distribution lines,
5) distribution lines, and
 6) distribution transformers which lower the voltage to the level needed for the consumer equipment. The production and transmission of electricity is relatively efficient and inexpensive, although unlike other forms of energy, electricity is not easily stored, and thus, must be produced based on the demand.

Books

• Power System Analysis by Grainger and W.D. Stevenson

• Power System Analysis and Design by J. Duncan Glover,Mulukutla S. Sarma and Thomas J. Overbye

• Power System Analysis by Hadi Sadat

• Principles of Power Systems by Mehta

Author        Bilal masood
lecture       10
Type         ppt
Availability Available online
For read this book online or Download click the below link

Power System Analysis

Book

• Power System Analysis by Grainger and W.D. Stevenson
• Power System Analysis and Design by J. Duncan Glover,Mulukutla S. Sarma and Thomas J. Overbye
• Power System Analysis by Hadi Sadat
• Principles of Power Systems by Mehta

Author        Bilal masood
lecture       10.1
Type         ppt
Availability Available online
For read this book online or Download click the below link

Power System Analysis . Lecture #1

Based on William Stevenson's classic, Elements of Power System Analysis, this new senior/graduate text offers a completely modern update of this popular textbook. Covering such topics as power flow, power-system stability and transmission lines, the book teaches the fundamental topics of power system analysis accompanied by logical discussions and numerous examples.

Book

• Power System Analysis by Grainger and W.D. Stevenson

• Power System Analysis and Design by J. Duncan Glover,Mulukutla S. Sarma and Thomas J. Overbye

• Power System Analysis by Hadi Sadat

• Principles of Power Systems by Mehta

Author        Bilal masood
lecture        #1
Type           ppt
Availability Available online
For read this book online or Download click the below link

Solutions to Skill-Assessment Exercises Control Systems Engineering By Norman S. Nise 4th Edition pdf

Book          Solutions  Exercises Control Systems Engineering
Author       Norman S. Nise
Edition      4th
Type         Foxit Reader PDF Document (.pdf)
Availability Available online
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Project, Wireless Controlled Home Appliances (Using Bluetooth Module)

Project      Wireless Controlled Home Appliances  (Using Bluetooth Module)
Type         ppt
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Control System Engineering by Norman S. Nise 6th edition free download pdf

Book          Control System Engineering
Author        Norman S. Nise
Edition       6th
Type         Foxit Reader PDF Document (.pdf)
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A First Course in Numerical Analysis with C++ by prof.Dr. S A Bhatti 5th edition free download

Book          A First Course in Numerical Analysis with C++
Author        Prof.Dr. S A Bhatti
Edition       5th
Type         Foxit Reader PDF Document (.pdf)
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What is forecasting? Engineering Economics, Engineering Project Management,

Topic              What is forecasting?   Engineering Economics, Engineering Project Management,
Author           Adbullah Afzal
Superior universty lahore
Type               ppt
Availability Available online
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ADVANCED OPERATIONS RESEARCH, OPERATIONS RESEARCH TECHNIQUE: LINEAR PROGRAMMING ppt

Topic             ADVANCED  OPERATIONS  RESEARCH, OPERATIONS RESEARCH TECHNIQUE: LINEAR PROGRAMMING   
Author           Adbullah Afzal
Superior university lahore
Type               ppt
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Lecture Notes on Simple Interest, Compound Interest, and Future Values pdf

Topic            Lecture Notes on Simple Interest,  Compound Interest, and Future  Values pdf
Author           Adbullah Afzal
Superior universty lahore
Type               pdf
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Depreciation,Engineering Project Management Engineering Economics ppt

Topic             Depreciation,Engineering Project Management Engineering Economics ppt
Author           Adbullah Afzal
Superior university lahore
Type               ppt
Availability Available online
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Decision Trees.Engineering Economics, Engineering Project Management

Topic            Decision Trees.Engineering Economics, Engineering Project Management
Author           Adbullah Afzal
Superior universty lahore
Type               ppt
Availability Available online
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DECISION THEORY, Engineering Project Management, Engineering Economics

Topic            DECISION THEORY, Engineering Project Management, Engineering Economics
Author           Adbullah Afzal
Superior university Lahore
Type               ppt
Availability Available online
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Break Even Analysis , Engineering Economics ppt

Break even analysis is used to determine when your business will be able to cover all its expenses and begin to make a profit. It is important to identify your startup costs, which will help you determine your sales revenue needed to pay ongoing business expenses.

Topic             Break Even Analysis , Engineering Economics 

Author           Adbullah Afzal

Superior university Lahore

Type               ppt

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SOLUTIONS MANUAL Communication Systems Engineering by John G. Proakis Second Edition free download

Book            SOLUTIONS MANUAL  Communication Systems Engineering
Author            John G. Proakis
Edition           2nd
Type               pdf
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