Power System Dynamics, Control and Monitoring

Prof. Debapriya Das

Department of Electrical Engineering
Indian Institute of Technology, Kharagpur

Lecture – 01
Power System stability

Welcome to this another course that your Power System Dynamics Control and
Monitoring. So, before starting this course, of course say that your little bit I would like
to tell that whenever you are teaching this course you just I would like to tell that you
have; at least you have studied electrical machines as well as power system analysis for
you know for under graduate student. Those who have already read machines particular
synchronize machines and your what you call this power system analysis you will find
things are very very comfortable, right. And, for post graduate student analysis call as
they can or if they want they can opt it, right. And, apart from that in various colleges
that many faculties are there if they if they (Refer Time: 01:12) this thing they can also
go through this lecture, right.

So, basically this is power system dynamics and control it is slightly different then other
courses. Although you will see that what you call that half of the portion or even more it
will be mainly your modelling and other thing for synchronous machines. So, apart from
that for this course you will study transient stability analysis for multi machine system
and your automatic generation control and deregulator environment. And at the same
time we will see the state estimations. If time permits I will see little bit some little bit
more thing if you can add.

So, only thing is that this course those who are aware of this syllabus and other thing in
various colleges, right so, I will see that you know this your what you call assignments or
questions whatsoever that it can be solved in a classroom; that way I have planned, right.
And, and just see how is it; and mostly whatever I will show you it is basically I have
scanned my class note and based on that we will study that and you will find that things
are little different. But, only for undergraduate students first I would like to tell that you
have covered if you have competed electrical machines as well as power system analysis
then you are welcome and you will find things are very very comfortable for you, right
an fizzy and resource caller also can and teachers also I will all faculties of various
colleges also I will encourage it. Just go through this, right.

(Refer Slide Time: 03:00)

So first thing is that dynamics and control, right; so first thing is that whenever we study
that power system dynamics and control the first what we will see that power system
what you call that power system stability, right. So, in that case the definition of the
stability, right: so it is something like this. The property of a power system that enables it
to remain in a state of operating equilibrium under normal operating conditions, right and
to regain an acceptable state of equilibrium after being subjected to a disturbance, right.

This is will be find as a power system stability. That means, if it is subjected to some
disturbances, right then naturally, but it will remain, it will come back to it is original
equilibrium point or may be in the vicinity of the equilibrium point then system should
be your what you call power system will be remains stable, right.

So, that is that property of a power system that enables it to remain in a state of operating
equilibrium under normal operating conditions and to regain an acceptable state of
equilibrium after being subjected to a disturbance. That means, acceptable equilibrium
acceptable state of equilibrium means that it will be very close to it is previous
equilibrium point right, and it will remain stable. So, that is what to you call we define as
power system stability, ok. So, just let me clear this.
Now, next is your power system instability, right.

(Refer Slide Time: 04:33)

So, another one is power system instability initially first two – three hours lecture this
will scan from a your what you call from photocopy. So, that is I will slightly frame after
that things will be alright, right. So, now question is that next is power system instability,
right. So, instability in a power system may be manifested in many different ways it
depending on the system configuration and operating mode, right. So, basically in power
system you will find a power generating plan basically they are synchronize machine or
synchronize generator, right. So, let me clear it let me move it up mathematics will come
little later, right.
(Refer Slide Time: 05:16)

So, in power system since power system rely on synchronous machine for generation of
electrical power; that is synchronous generator, right, a necessary condition a necessary
condition for satisfactory system operation, right. This is satisfactory system operation is
that all synchronous machine remain in synchronism, right. So, they should not be fall
they should not be fall out of step, right. So, all will be your remain in synchronism this
aspect of stability is influenced by the dynamics of generator rotor angles and power
angle relationship, right.

So, your derivation other things later we will see.

(Refer Slide Time: 06:07)

So, instability may also be encountered without loss of synchronism. If it is what you call
if machine synchronous machine is fall out of step, then what you call there will be loss
of your synchronism, loss of your stability, right. So, because all the machines they
swing a new machine; that means, they are what you call that is your they are in coherent
group; that means, they are increase or decrease of the speed same, right.

But if one of the machine fall out of step; I will loss synchronism that instability may
happen. For example, a system consisting of synchronous generator feeding an induction
motor load through a transmission line becomes unstable, because of the collapse of the
load voltage, right. So, that is previously saw that loss of your what you call that your
synchronism.

The second thing is that is system consist of suppose synchronize generator facing an
just one minute here an is written twice, right just hold on an is written twice, feeding an
induction motor load through a transmission line become your unstable, because of the
collapse of the load voltage. So, this is also another kind of unstable system can occur,
right. So, maintenance of synchronism is not an issue in this instant, right. If you want of
maintain the power system stable that all the machine should stay unison they should be
in synchronism right, but in this case synchronism is not an issue, right. So, instead the
concern is the stability and control of voltage, right. This is another example of
instability.
(Refer Slide Time: 07:51)

So, this form of instability can also occur in loads covering an what you call extensive
area supplied by a large system, right. So, that means, one thing is that your power
system rely on synchronous generator or generation of electric power, a necessary
condition for satisfactory system operation is that synchronous machine remain in
synchronism, right. This aspect of stability is influenced by the dynamics of generator
rotor angles and power angles relationship. If any machine for it is out of state then it
will be unstable.

An another example is given that is synchronous machine feeding and induction motor
load, right and if there is a collapse of load voltage then what you call unstable condition
may arise, right.
(Refer Slide Time: 08:41)

So, another thing is in the evolution of stability the concern is the behaviour of the power
system when subjected to a transient disturbance. The disturbance may be small or may
be large, right. So, this disturbance it may be small disturbance or a very large
disturbance small disturbance is in the form of your load changes take place continuously
right and the system your what you call adjust itself to the changing conditions, right. If
actually in the power system you will find small disturbance are always there because
loads are switched on-off, on-off. This kind of disturbance is there, it is not ideally stable,
right.

So, question is that that you have to what you call some disturbance is there, but system
is stable, right. So, here before moving further I will put a question, right and you answer
when you will go through this your video lecture at the time you put the answer in the
forum the question is suppose, suppose you are staying in the hostel right and you are
sleeping, but you are stable right or in a what you call in your TV hall, right. They are
perhaps you are watching TV some cricket match or soccer match at that time you are
also watching everything, but you are stable, right. When you are walking on the street
and gossiping with your friends you are also stable, right, when you are coming to your
institute and attending the classes you are also stable, when you are going to the library
and reading books you are also stable, right.
So, you are sleeping you are stable, you are watching TV you are stable, right, you are
you are reading books in the library was stable, you are attending the classes you are
stable and you are walking with your friends, right, and gossiping on the street,
whatsoever which one you like most, right. This is a question to you. I want a good
answer among all these things, right. So anyway, that is what you call that continuously
some disturbance is happening, but power system remains stable, right.

(Refer Slide Time: 10:44)

So, because load loads are switched on and off, right. So, system must be able to operate
satisfactory under these conditions and successfully supply the maximum amount of
load, right. It must also capable of what you call that it must also it must also be capable
of your surviving numerous disturbances of a severe nature such as a short-circuit on a
transmission line, right. So, loss of a large generator or load or a loss of a tie between
substation; just hold on, let me clear it let move it, then I will tell you.
(Refer Slide Time: 11:26)

So, I mean if it happens that what you call if large disturbance happen of a severe nature
such as short circuit on a transmission line or loss of large generator or a load or loss of
the tie between two substation. That means, actually what happened this one your this
one that your loss of a tie, just hold on, that loss of a tie between two substation that
mean I mean two substations and loss of a timing that is 3-phase transmission line it is a
tie line, right if all of a sudden that power goes off, right. So, all these things so, in that
case that your what you call that I mean this kind of problem will give you your what
you call unstable system operation, right.

So, the system response to a disturbance involve much of what you call the equipment,
because whenever any fault or any such things happen you have your what you call. So,
many your what you components in a power system and all will be effected because of
this I mean this kind of the large disturbances, right.
(Refer Slide Time: 12:38)

For example, for example, a short circuit on a critical element followed by it is your
isolation by protective relays will cause variations in power transfer what you call
machine rotor speed and bus voltages. That means, what you call it will there will be
variation in power transfer, then it will change also machine rotor speed, and also the bus
voltages, right.

So, the voltage variations will actuate both generator and transmission system voltage
regulators, right because if volt happen many components are there. So, although relay is
there to isolate the system, but all these things will be effected, right. And, speed
variations will actuate your prime over governors. Prime over means for say for example,
for thermal power plant it is turbine, sorry because turbine and generators they are
coupled together, right.
(Refer Slide Time: 13:38)

So therefore, this speed variation will actuate prime over governors and the change in tie
line loadings may actuate your generation control, because whenever you will study that
your automatic generation control in deregulated environment we will see that two
power system was interconnected by tie lines. Tie lines means it is 3-phase transmission
line, right.

So, all these things will be your what you call actually be affected, right.

(Refer Slide Time: 14:11)

So, in therefore, the changes in voltage and frequency will affect loads on the system in
varying degrees depending on their individual characteristics, right. So, the idea is that
your here we are making it that the changes in voltage and frequency will affect loads or
the system in varying degrees depending on their individual characteristic, because load
you will if you were aware of it the loads will find may be sensitive to the may different
type of loads are there.

So, many load are sensitive if the voltage magnitude as well as the system frequency. So,
based on that that will also affected, right in your; just hold on, let me go up.

(Refer Slide Time: 14:54)

In addition devices used to protect individual equipment may respond to variation in

system variables and thus affect the system performance. That means, if some kind of
short circuit happens many things actually will be affected, right. In any given situation
however, the responses of only a limited amount of equipment may be significant
because all these things generally will not be consider, but a limited your what you call
amount of equipment may be significant not all, right.
(Refer Slide Time: 15: 28)

So therefore, many assumption assumptions are usually what you call made to simplify
the problem, and to focus on what you call factors influencing the specific type of your
stability problem, right. So, as a whole we need not consider as a whole all the things,
but only those things will be affected more, right.

(Refer Slide Time: 15:53)

So, next we will come to that rotor angle stability. So, this is a your this is actually it is
the ability of interconnected synchronous machines of a power system to remain in
synchronism; that is rotor angle stability. The stability problem involve the study of the
electromechanical oscillations inherent in power system, right.

So, this is actually later that we will see many things first we will see slowly, and slowly
it will take time means how to develop the synchronous machine model, right. And then
we will your see that your participation factor also because different modes are there,
right. So, those things those things also we will identify right some Eigen values, Eigen
properties all will be required. And, at the end of this course if time permits then I will
come to the excitation system of synchronous machine various excitation system, if
times permits, right

Because those excitation of excite us it will take time, right. This I have decided if
everything goes fine if I get two – three hours more at the end then only I will come to
that, but otherwise I have to skip it, right.

(Refer Slide Time: 17:13)

So, the fundamental factors actually in this problem is the manner in which the power
outputs of synchronous machines vary as their rotors your what you call oscillates, right.
(Refer Slide Time: 17:21)

Now, synchronous machine characteristics; basic characteristic associated with

synchronous operation the essential elements the field and the armature; I told you that
because we have already studied electrical machines that we have to see that your field
and the armature. Normally the your what you call the field actually is on the rotor the
field is on the your rotor and the armature is on the stator for synchronous machine, right
and field winding is excited by direct current.

So, how is this field excited is excited by direct current, what is this mechanism? If I find
time then at the at the your what you call at the end of this course if I find couple of
hours time then I will definitely try to tell you, right. Actually we read many things in the
book also revised excited another thing. But whatever little bit I have learn from those
who are in really in the power station what they have told about this your what you call
that excitation of synchronous machine if time permits I will tell you what you call at the
end of this course couple of hours if I get extra, right.
(Refer Slide Time: 18:33)

So, when the rotor is driven by a prime mover prime mover means it is a turbine, right;
when the rotor is driven by a prime mover that is turbine, turbine and synchronous
generator they are coupled together, right. the rotating magnetic field of the field winding
inducers alternating voltages in the three-phase armature windings of the stator, right,
because armature is on the stator and field is on the rotor for synchronous machine, right.

The frequency of the induced alternating voltages and the resulting currents that flow in
the stator windings when a load is connected depends on the speed of the rotor, right.
Therefore, the frequency of the stator electrical quantities is the synchronized with the
rotor mechanical speed hence the name is synchronous machine, right.

So, question is that that when the that is why underline once again that when the rotor is
driven by a prime mover prime mover means the turbine and generator coupled together.
But let me tell you there will be no gear mechanism in between this turbine there is no
geared direct directly it is coupled, right. If rotating magnetic field of the field winding
induces alternating voltages in the three-phase armature windings of the stator.

The frequency of the induced alternating voltages and of the resulting currents that flow
in the stator windings when a load is connected depends on the speed of the rotor. The
frequency of the stator electrical quantities is synchronize if the rotor mechanical speed,
right. So, just hold on, right.
(Refer Slide Time: 20:22)

So, hence the designation is synchronous machine, right. So, or otherwise it is constant
speed machine, right. So, that is why it is called your synchronous machine.

(Refer Slide Time: 20:33)

When two or more synchronous machines are interconnected right when two or just hold
on when two or more synchronous machines are interconnected. The stator voltages and
currents of all the machines must have the same frequency and the rotor mechanical
speed of each is synchronized to this frequency, right. Therefore, the rotors of all
interconnected synchronous machines must be in synchronism, right. They are I mean in
general they are will be in coherent group, right they are increase or decrease speed will
remain speed, right. So, all will be in synchronism. But, all the time due to some small
disturbance the speed is slightly varying it is changing very little this way that way, plus
minus, this way it is varying, right, but they will never lose the synchronism or they will
never fall out of step, right.

(Refer Slide Time: 21:33)

So, the physical arrangement that is your just hold on the physical arrangement that is the
spatial distribution of the stator armature winding is such that the time varying
alternating currents flowing in the three-phase windings, right what you call produce a
rotating magnetic field that under steady state operation rotates at the same speed as the
rotor, right. Therefore, the physical arrangement that is spatial distribution of the stator
armature winding is such that the time varying alternating currents flowing in the three-
phase winding, right is produce a rotating magnetic field that under steady state
operation rotates at the same speed as the rotor. Just hold on.
(Refer Slide Time: 22:20)

The stator and rotor fields with each just hold on the stator and rotor field react with each
other, and an electromagnetic torque results from the tendency of the two fields to align
themselves, right.

Now, in a generator that is in a generator this electromagnetic torque opposes rotation of

the rotor, right. So that the mechanical torque must be applied by the prime mover to
sustain rotation prime mover means the turbine, right. Therefore, in a generator of the
electromagnetic torque opposes rotation of the rotor, so that the mechanical torque must
be applied by the prime mover to sustain rotation. For example, that your single machine
infinite bus system right some you have studied that your transient stability analysis, just
see those diagram and how thing mechanical and electrical torque some rotation and
some direction is given clockwise anticlockwise right t a minus t e, right.

So, this is the idea.

(Refer Slide Time: 23:30)

So, some the electrical torque I have writing in bracket in power. Later we will see that in
power unit values; we will see that torque and power is same when you will neglect the
your; what you call that losses we will find that torque per unit values torque and power
same. In this course we will also study power unit system for synchronous machines that
will be slightly per unit same for whether power system and this, but here slightly
different you will find, right. Later we will see that then that and cover that one also we
will take some time.

So, the electrical torque that is why I am writing in power you assume what you call per
unit output of the generator is changed only by changing the mechanical torque input by
the prime mover. This is single machine infinite bus, something some something we have
studied also, right. So, the effect of increasing the mechanical torque input is to advance
the rotor to a new position relative to the revolving magnetic field of the stator, right.
(Refer Slide Time: 24:44)

So, now conversely, a reduction of mechanical torque, conversely a reduction of

mechanical torque or power input will be will retard the rotor position I mean
deceleration, right. So, under steady state operating condition the rotor field and the
revolving field of the stator have the same speed, right. So, where when it is steady state
operating condition rotor field and the revolving your and the revolving field of the stator
they have the same speed. However, there is an angular separation between them
depending on the electrical torque output of the generator, right.

(Refer Slide Time: 25:33)

The terms torque and power have been used interchangeably, right. So, just hold on. So,
the terms torque and power have been used interchangeably, right. Now, the average
rotational velocity of the machines is constant even though there may be small
momentary excursions above or below synchronous speed, right. It is above or below
right synchronous speed per unit value of torque and power are in fact, very nearly equal;
that means, because machine lose is negligible, right. Later we will see if lose we ignore
then you will find in per unit values power and torque will be remain same, that will
prove, that will prove later because this course actually have full of mathematics only,
right. I mean you will later you will see that full of mathematics that is why I told that we
will set the assignment questions such a fashion such that you can answer in the class
room, but it is a full of mathematics, right.

(Refer Slide Time: 26:41)

Now, for example, these diagram; this is actually later after one or two hours lecture later
we will find things are ok; this is actually scanned from a photocopy, right. So, this is my
generate suppose this is one generator this is machine 1, right this is my generator I am
just redrawing it for you once again. This is one this is my this is transmission line
impedance, this is line and this is your a motor is there, this is machine to a motor is
there, this is a single line diagram, right. Suppose, now if you take the generator for
above resistance only reactants generator reactance is a x g, line reactance is x l, right
make it a these thing right like reactance is x l and motor reactance is x m, right and
terminal just let me let me move little bit up.
(Refer Slide Time: 27:30)

Just make it further right this one. So, in this case what you call and this motor reactants
x m and here the voltage is E T 1 and here the voltage is E T 2, right. And this is your
idealized model, because resistance we have consider and this is your generator voltage
E g and this is E m motor side.

(Refer Slide Time: 28:00)

Now, if you draw your the phasor diagram, right so, what we have taken we have taken
say E T 2, E T 2 as a reference suppose this is your reference E T 2 as a reference, right.
This is my E T 2, right, this is my E T 2. Now, we assuming that your current it showing
I this is the current I it is lagging current say current is lagging right this current is I,
right. Now, if you say what you call E T 2, E T 2 will be what? E T 2 will be E m plus j x
m. So, E T 2 is equal to this is my this is my E m this is my this is my E m, E T 2 is equal
to E m plus your j I x m. So, this angle actually 90 degree, right. So, E T 2 is equal to and
this is the current right, this is I x m.

Now, next is your E T 1 it will come, just let me clear it. If you come to this diagram
again the E T 1 will be j x l plus E T 2 because this is my E T 1. So, if current is showing
in this direction E T 1 will be E T 2 plus j x l. So, look at that that E T 1 will be E T 2
plus j your I your what you call I into j x l, sorry I into j x l, right; so here also I into x m
and here also I into your j x l, right.

And, one thing is there, one just one correction is there it is actually I is I is actually
lagging. So, what you call this angle your what you call it may not be your what you call
90 degree because I also have some angle I previously I wrote 90 degree it cannot be 90
degree because I also has some angle. If I angle 0, then it is 90 degree otherwise if I is
equal to your magnitude of I angle theta and this is j x m, so, basically it will be
magnitude of I say into x m, then angle your what you call 90 degree plus theta as
current is lagging so, theta will be your negative. So, in that case it will be your less than
90 degree. So, only 90 degree is possible if I what you call your angle 0 degree, but it is
not right, it is lagging from this one. So, it cannot be 90 degree right I over looked at one.

So, question is your what you call this one now E T 1 will be I into j x m E T 2 that is
why E T 1 is equal to E T 2 into I into your j x l, right and similarly your next one is your
then E g will be I into j x g plus E T 1. Therefore, E g is equal to your E T 1 plus I into j
your x g, right. So, this way you have to draw, but if I is known, angle is known, x g
value is known and then we can find out the exact angle and this is the phasor diagram,
right. So, for this system and you step by step if you make it then things are very simple,
right.

So now, delta will be the total angle delta between your E g and your E m, right. It will
be delta m plus your delta l plus delta g; so delta g plus delta l plus delta. This is the
angle between E g and E m this is the phasor diagram, right.
(Refer Slide Time: 31:07)

And, power angle characteristic you know from your power system analysis studies or
missing these things. So, this is my your what you call P versus delta curve, right; P-
angle characteristic.

(Refer Slide Time: 31:20)

And, therefore, the power transfer from the generator to the motor is given by P is equal
to E g E m upon x T sin delta, right. This we know, we have studied already in these
thing and x T will be sum of all the reactants. And this is equation 1.

Thank you very much. We will be back again.