Power System Dynamics

Prof. M. L. Kothari
Department of Electrical Engineering
Indian Institute of Technology, Delhi
Lecture - 38
Voltage Stability (Contd)
(Refer Slide Time: 00:53)

Friends, we continue with the study of voltage stability.

(Refer Slide Time: 01:06)

Today, we shall studythe determination of shortest distance to instability, the continuation power
flow analysis and at the end we will study the techniques which can be used to prevent the
voltage collapse or voltage instability. Now let us try to understand briefly what do we mean by
the shortest distance to instability.
(Refer Slide Time: 01:39)

The purpose of this study is to determine the smallest stability margin that is whenever you are
operating at a certain loading condition then we would like to know that how much increase in
load can be made made so that the system becomes unstable that means how far we are from the
from the instability but our interest is to find out the shortest distance.

In fact actually suppose you are operating at a certain loading condition then then the load can
vary in a variety of manners right. Then for each particular combination of loading if you in
stretch the load in a particular direction then you will reach even particular point where the
system becomes unstable. We want to know what is the direction in which when we stretch the
loading so that the instability occurs with the minimum distance.
Now to understand this basic point, we consider here a simple radial system radial system. In this
radial system you have one source, one transmission line and say let us say the load here, we will
call it P, I am considering there simplest system but any multi machine system and large system
the there are several loads connected at various buses and and therefore whenever you want you
can say increase the loading, the loading can be increased in variety of manners right. But we
know actually that when you increase the load at a one particular loading condition condition the
system becomes voltage instability occurs. So system becomes voltage instable and at that
loading condition if you find out the Jacobian of the matrix then that Jacobian becomes singular
right.
(Refer Slide Time: 04:20)

Now here for this simple radial system we plot here actually in the PQ plane. This is the load
reactive this is the load in per unit that is the active power P on this side is the reactive power
that is you put P on this side P here and the reactive power Q on this axis. Now we can find out
one one surface if you any point on that surface surface will lead to if you operate at that point
then it will lead to voltage instability. In case it is a large system with number of buses right that
surface comes out to be a hyper surface right and in this particular case the the simple radial
system right the we get actually a curve right.
Now this is the curve, now suppose you are operating initially at this point called Po Qo that is
initial loading condition is denoted as Po Qo and suppose you increase the load P and Q in at
random. Let us say you increase in this direction, so that you come and reach the this this surface

as or actually the the curve as this you call as surface S or curve S right. Now at this point the
system becomes unstable.
Now suppose now the question is actually that what is the shortest distance to instability to find
out the shortest distance, obviously in this particular case the shortest distance one can find out
first you find out the normal at this point one to the surface, let us call this is the normal at this
point call it say eta 1 then the again go back to the initial loading condition and stretch the load in
parallel or in the direction of this normal that is second time when you are stretching you are
stretching in this direction this is parallel to this you reach this .2.
Then once you reach the point two again you find out the normal at this point eta 2 and then
again go back to the initial condition and stretch the loading in the direction parallel to the
normal. Then you will lend to a point where the distance between the operating initial operating
condition and the new operating condition will be minimum that is one can find out, suppose you
you represent actually the initial operating condition by as a vector rho, a parameter vector rho.
Now this parameter vector rho is the initial operating condition and let us say rho psi is the final
operating condition then our interest is to find out this distance that is the rho psi minus rho norm
norm of this quantity. This will be minimum right and the for a simple two machine system not
two machine systems for a single radial system I have illustrated that you start from initial
condition stretch the loading in any direction. Here, P is increasing while Q is decreasing like
that and you reach to a new point then at this point one the see this point one lies on this surface
this is the which represent the unstable operating condition then the then the normal which you
find out at this point right. Now you stretch the in the direction of the normal and therefore you
keep keep on doing this till you get the minimum distance therefore in the multi machine system.
We denote actually the the loading condition loading condition in terms of initial P and Q
through a parameter and we find out the final as rho star and in case the rho star is such a loading
condition.
(Refer Slide Time: 10:25)

So that the moment you are operating this rho star lies on the hyper surface which is which
represent the unstable operating condition and and that our objective is to find out the the norm
of this quantity that rho naught minus, rho star minus rho naught norm of this line and this rho
minimum and this process is a documented in various papers, how to find out for a multi
machine or a large system this node, the purpose of this obtaining the shortest distance is to to
note that at what stability margin we are operating because whenever you are operating system
you would like to maintain certain stability margin all the time.The next point we will study is
the continuation power flow analysis. The continuation power flow analysis is very important
and is a very important tool which has been developed for for obtaining the critical operating
conditionin. In fact as we know that if you operate if you operate near the critical point or at the
critical point then the Jacobian becomes singular that is the Jacobian matrix, the Jacobian matrix
becomes singular at the voltage stability limit.
Consequently the conventional power flow algorithms are prone to convergence problems that is
the the moment the Jacobian becomes singular right the convergence problems arises and
therefore if you try to plot actually the um we call PV curve right then we will be in a position to
get certain points on the PV curve by conventional load flow analysis but the moment you reach
closer to the instability poin, you will find the Jacobian becomes singular.
(Refer Slide Time: 11:15)

Therefore to solve this problem the continuous power flow algorithm has been developed that is
the continuous power flow analysis overcome this problem by reformulating the power flow
equations. So that they remain well conditioned at all possible loading conditions this allows the
solution of power flow problem for a stable as well as unstable equilibrium points that is when
you look at the at the PV curve right then the upper portion of this PV curve represent this stable
operating points or equilibrium points but the lower portion right, they are the unstable. Now this
these points when you cannot compute or we cannot get by conventional power flow equations
or conventional power flow algorithm.

(Refer Slide Time: 12:11)

Now this continuation power flow approach has been well documented and the most important
research paper where this continuation power flow has been discussed is written by V. Ajjarapu
and C. Christy. The continuous power flow, the continuation power flow a tool for steady state
voltage stability analysis. IEEE PICA conference proceedings page numbers 304 to 311, it
appeared in may 1991 these very standard reference paper for understanding the continuation
power flow algorithm. We will briefly briefly study the salient features of this continuation
power flow algorithm basic principle.
(Refer Slide Time: 12:54)

The continuation power flow analysis uses uses iterative process involving predictor and
corrector steps as we will discuss just now that is the if the basic principle in this continuation
power flow is that the two steps. First is suppose we are operating at a initial point, first we find
out through the predictor step right the and then from that predictor step we go to the into the
character step that two steps involved and these steps are followed attentively to get the solution.
(Refer Slide Time: 13:47)

To understand basic concept let us look at this graph, this graph shows actually the the load on
this axis and the bus voltage on this axis now this is a PV curve which is plotted in plotted part of
it can be plotted by repeated application of load flow analysis right. Now suppose we are
operating at this initial operating condition at A, the first step will be we we find out at this
operating condition A a tangent vector that is there is a tangent vector which we find out, for
example this is the tangent vector at this operating condition. Then the next step is persue you
find out the tangent vector we want we want to find out what is the step length therefore the step
length for example in this case shown is A to B therefore the step length is also a important
decision to be taken.
Now once you come to this point B, next step is at this from this point we come to the actual
solution C that is called character step from B to C that is at this if you see here actually that this
graph which is the firm graph that shows the actual solution that of this is the exact solution, this
graph shows the exact solution I will just draw it with the different color to make it more clear
that is this blue graph is I have shown here is the exact solution that is we want to come from A
to C but how do we come from A to C the step is at A you find out a tangent vector then you
select a judiciously the step length then from this point B is not on the solution exact solution. At
point B you apply character step and come to point C right.
Now this this approach is to be applied to find out the solution for different points on this graph
here it is possible to get solution so that we can get the critical point. For example this is the
critical point and then you can get points which are below the critical point also that is the

complete part of the complete you can say PV curve can be obtained for a particular bus in the
multi machine system.
(Refer Slide Time: 16:42)

Now let us study actually the algorithm the mathematical formulation the basic equations are
similar to standard power flow analysis except that the increase is in load is added as a
parameter. Generally, in a conventional power flow what we really do is that loads are known to
us and we solve the problem. Now here what we do is that increase in load is added as a
parameter that is increase in load is added as a parameter this is one difference here the
reformulated power flow equations with provision of increasing generations as the load is
increased may be expressed as.
Now the point here is that is any system when I increase in the load right then I may have to
increase the generations also right. So that the load generation match is achieved right therefore
whenever you increase the load in a particular fashion then you have to increase the generations
also that is the what it writes here is the you reformulate the power flow equations with provision
of increasing generations as the load is increased. The the load flow equations can be formulated
in this fashion F theta V equal to lambda times K where, F is a non-linear function of theta and V
it means F theta V is represents actually F theta V equal to lambda K, it represents the set of nonlinear algebraic equations okay. Here here F is a function in fact general F is a function and this
equation is a is actually a vector equation a large number of equations are there in vector
equation.
Here lambda is called the load parameter, theta is the vector of bus voltage angles, V is the vector
of bus voltage magnitudes and K is the vector representing percent load change at each bus that
is K is the vector representing percent load change at each bus. In fact here here when you look
at the equations what you find here is that is lambda into K. We can fix actually some percent
load changes and multiply by a parameter lambda. The magnitude of lambda varies from 0 to

some critical value right. It means this the amount of load change which we put here can is
adjustable.
(Refer Slide Time: 17:56)

(Refer Slide Time: 18:44)

The above set of non-linear equations is solved by specifying a value for lambda such that
lambda is between 0 and lambda critical where, lambda 0 stands for base load condition, when
lambda equal to 0 it means we are not giving any increment in the loading condition and lambda
equal to lambda critical deposit at the critical load that is they may be value of lambda is equal to
lambda critical then we have reached the critical loading condition.

(Refer Slide Time: 19:32)

(Refer Slide Time: 20:14)

The equations which we have reforming for put here that is the equations which we are put as F
of theta V equal to lambda K right. This equation can be reformulated or re arranged in the form
F F theta V lambda equal to 0, K is a constant lambda is a variable parameter right these are the
set of non linear algebraic equations. Now here to apply the continuation load flow algorithm as
I have discussed they are two steps, one is called predictor step, another is called corrector step.
First, let us examine the predictor step once a base solution has been found lambda equal to 0.

(Refer Slide Time: 20:38)

(Refer Slide Time: 22:03)

A prediction, a prediction of the next solution can be made by taking an appropriately sized step
in the direction tangent to the solution path that is our interest is to find out find out actually the
predictor step it is, let us find out next solution, next solution find out next solution a prediction
of the next solution can be made it is a prediction by taking an appropriate sized step in the
direction tangent to the solution path that is we start one initial condition, find out the tangent
that is the direction that is the first task in predictor process is to calculate the tangent vector. It is
the what we have discussed here the tangent vector is very important in and therefore deep in the
predictor step the step is how to calculate the tangent vector the approach is very straight

forward. We we have obtained the differential of this equation that is d of f theta v lambda, this
function can be written as f naught d theta plus fv dv plus f lambda d lambda, this is equal to 0.
Now here this f theta, fv and f lambda these are the the matrices of partial derivatives and this
equation can be arranged in this form f theta, fv, f lambda that is this matrices of partial
derivatives are arranged and into this vector d theta, dv, d lambda equal to 0. Since actually we
have theta the dimensional of theta is equal to number of buses in the system right similarly or
you can say actually d theta and dv right these are n vectors and lambda is of course one scalar
quantity.
(Refer Slide Time: 23:12)

(Refer Slide Time: 23:56)

Therefore, this vector d theta, dv and d lambda this vector is given the name tangent vector that
is tangent vector is defined as d theta, dv, d lambda. Our interest is to find out this tangent vector
to find out the tangent vector we have just now seen what we really do here is this is the case but
now the question is how to solve this problem. Now if you look here here so far the partial
derivatives are concerned right this there are the number of unknowns I have now increased by
one lambda is the additional parameter which we have added and therefore there is a necessity to
add one more equation here.
So that you can solve this for this tangent vector that is one of the components of tangent vector
is set equal to plus 1 or minus 1 that is we have first our step is how to solve this problem how to
get the tangent vector right therefore the approach is that first we we add a rho vector ek ek to the
set of differential equations or do this Jacobian matrix ek. This vector ek accept the k th element
all other elements are 0 this is a rho vector and and our interest is that we want to make one of
the component of the tangent vector equal to plus 1 or minus 1.
(Refer Slide Time: 26:05)

So that when this rho vector accept one quantity others are all 0 certain when you multiply this
you will find actually that the delta lambda will come out to be equal to plus 1 that is here we are
making actually this ek ek in such a fashion so that the you get d lambda. One of the elements of
one of the elements of the tangent vector equal to one, for example if you want to make one of
the elements of voltage component right that is say let us say the voltage of bus 1 dv1 or dv2 any
one or similarly phase phasing allot any of the bus voltages that is in this you can make one of
the elements equal to 1, it may plus 1 or minus 1, plus 1 is corresponding when you are operating
on the upper part of the PV curve and minus 1, when you are operating on the lower part right.
So in this reformulated equation we have now, we have now a situation where where we can
compute this tangent vector okay.
Now the this imposes a non-zero norm on the tangent vector is that by by this approach by
adding this rho vector ek and making one of the elements as plus minus 1 right what was have

achieved is that two things which you have achieved first thing is that this rho vector right. It it
becomes a non-zero norm tangent vector that if a find a find in norm of this tangent vector then it
will come out to be non-zero, it will not become zero right. Second is guarantees the augmented
Jacobian will be non-singular that is the all Jacobian which you have augmented. Now this
Jacobian becomes non-singular and you can find out the tangent vector that is one tangent vector
is found once not one once once tangent vector is found.
(Refer Slide Time: 27:05)

(Refer Slide Time: 27:53)

The prediction of the next solution is as follows that is what we really do is that we first compute
the tangent vector and the moment you compute the tangent vector the new tangent vector is

obtained as theta not not tangent vector this is the tangent vector d theta, dv and d lambda, this is
the tangent vector. The new operating condition that is theta v and lambda obtained as the initial
values of this vector plus sigma times the tangent vector this sigma is the step length sigma is the
step length step size okay.
By step size sigma is chosen so that the power flow solution exist with the specified continuation
parameterthe idea here is that the step size sigma should be such that such that now you can
perform the normal power flow solution and obtain the obtain the complete solution that is you
can find out the all the voltages and their phase angles. I will just see here, generally you will
find out actually that in case suppose the step size is large then from that predicted solution you
will not be in a position to get the corrected that is actually the low power flow solution when
you try to perform right the solution will not give actually this the the exact solution or the
required solution.
(Refer Slide Time: 29:43)

In that case we we reduce the value of sigma again repeat till we find out actually that in a
character step. We get the solution if for a given step size a solution cannot be found in the
character step the step size is reduced and the and the character step is repeated until a successful
solution is obtained. This is actually a very important at what should become we do not know
what should be characterized the what should be the step size. Suppose you take a very small
step size then you will require large number of repetitions due to a large step size, it will not
converse and therefore one has to take very judiciously these a step size next step step is the
character step the character step is idea of the character step is to really perform actually the load
flow and get the solution.
Now again the, if you see here actually this function f theta, v lambda right. The number of
unknowns are theta v and lambda right but the number of equations will be one equation less
because the the when you have formulated the number of equations you have added a term
lambda into k but number of equations were still the same. Now to get the solution what is to be

done is we add one more equation this equation is written as Xk minus eta equal to 0 that this Xk
this is very important point here the Xk is the state variable selected as continuation parameter
what are the state variables all the all the phase angles, all the bus voltages right and lambda they
are the state variables here right and therefore what we do is that Xk is one of the state variables
and this is chosen as a continuation parameter and and eta stands for value of Xk value of Xk that
is the predicted value of Xk because Xk is one of the one of the state variables right and therefore
if you look here which is our process then we start from the initial operating condition there we
find out the tangent vector and suppose you start from point A and go to B, B is the predicted
solution therefore at this B we know all the values of we know the value of the complete state
vector right and therefore Xk, Xk is is the continuation parameter which is chosen and it is one of
the state variables and value of Xk is chosen equal to equal to lambda which is the which is the
predicted value of Xk predictor value of continuation parameter.
(Refer Slide Time: 32:36)

Therefore, the number of equations which now we have will be one more additional equations
you added and therefore this set of equations can be solved by a normal normal load flow and
you will get the solution therefore this is what is called character step. Now the question
basically is that how to solve this problem, how to choose actually the continuation continuation
parameter or continuation variable the Xk that is because Xk is one of the state variable to be
chosen as the continuation parameter the tangent component of lambda d lambda is positive for
the upper portion of the VP curve 0 for the critical point and negative for the lower point, so to
be already mentioned.
The question is how to select the continuation parameters right obviously one can choose some
some any one of the any one of the state variables as continuation parameters but the but the for
optimum solution the approach is a good practice is to choose the continuation parameter as the
state variable that has the greatest rate of change. In fact for to find out what we do is that we
find out the the tangent vector and in this tangent vector the element which has highest value is

chosen corresponding to that the chosen as the continuation parameter or that state variable
which is highest or greatest rate of change is chosen as the continuation parameter.
(Refer Slide Time: 33:11)

Let us look at the a flow chart of this continuation power algorithm. The flow chart is as usual
you start your problem. First step is run the conventional power flow on base case, run the
conventional power flow and the on the base case and find out actually the initial solution then
specify continuation parameter. Now here at this stage how to specify the continuation parameter
we have not calculated the tangent vector and therefore the suggestion is you can choose lambda
itself which is the which is the load parameter as a continuation parameter right.
(Refer Slide Time: 34:17)

The next step is calculate tangent vector for which the equation has already been specified that is
you calculate the tangent vector, next is if critical point has been reached that is you have to
check whether you have reached the critical point or not if we at if you have reached the critical
point you stop there. Otherwise, otherwise choose continuation parameter for next step.
The first step the continuation parameter was chosen arbitrarily and I told you that we can choose
the log parameter as the continuation parameter. But here, now we once you have this tangent
vector we can choose the continuation parameterthen after choosing this continuation parameter
do the complete the predict the solution out of this prediction you go for the correction that is
perform the correction part and then return back to this point again and this process continues till
you reach the critical point and you can go below the critical point also and got get the other
points operation. This is a very important algorithm which we have discusses.
(Refer Slide Time: 36:26)

Now the problem here is that should we use the continuation load flow algorithm right from
beginning or should we use it actually when we reach the near the critical point thus the answer
is obviously, you first solve this continuation solve this problem by normal conventional load
flow that is you are operating at initial condition, you give increment in load again perform the
load flow analysis find out the new solution and till you come very close to the critical point, you
can keep on using the conventional load flow but the moment you reach the critical point or near
the critical point the Jacobian becomes so at critical point become singular and therefore both or
or closure to the critical point you can now resort to the continuation load flow algorithm and
obtain the points operating points which are the critical operating points.
The the idea here is that the continuation load flow algorithm it takes more time to get the
solution because it has two important steps the predictor and corrector steps and so far the the
conventional load flow is concerned you can you can increase the load in a particular direction
and find out the solution.

(Refer Slide Time: 38:06)

Next point, we will discuss is what can be done and how the system can be designed and
operated. So that we avoid the voltage collapse situation that is we want to operate the system so
that the we can prevent the voltage collapse. Now here we will divide this our discussion into
two different headings one is the system design measures that is when you design the system you
you take care so that it has a inherent stability margin right and then next is operating measure
that is when your system is already there how to operate the system, so that the voltage collapse
is avoided.
System design measures what are the design measures which can be adopted for for having a
system which will have a large so voltage stability margin and voltage collapse would not take
place there. Obviously, when we have discussed this voltage stability problem, the voltage
stability problem is basically the problem of inadequate reactive power supply. It is a situation
where the system has has less reactive power supply capability, it cannot supply the required
amount of reactive power and the voltage collapse takes place therefore obviously the first
solution or first design the approach should be design measure should be have apply apply
reactive power compensating devices or adequate reactive power compensating devices, apply
we should have various sources of reactive power and that these reactive power sources should
be applied very judiciously.

(Refer Slide Time: 39:01)

We will discuss this application part in the next step second will be control the network voltage
and generator reactive power output that is that is when a system is under the design stage design
measure itself right you provide certain certain controls which can be used for for controlling the
network voltage and the generator reactive power output that is you should have the controls so
that you can increase or decrease the reactive power output from the generating devices then
there may be certain certain protections and controls we should have proper coordination,
sometimes the protection there was use when they are controlling a load let us say right and
when the arrangement is there whenever the voltage is decreasing you can do load shedding and
voltage will recover.
Therefore, load shedding is one of the controls and therefore whatsoever protection and control
devices you incorporate in the system, load control devices or voltage control devices all should
be properly have proper coordination with the protection systems then also have proper control
of the transformer tap changers where they are the voltage control devices you have to provide
certain arrangements so that you can control actually the control the tap changer positions. Then
next is under voltage load shedding if there is a last resort in case you find their voltage is
sinking voltage is going low you you do that load shedding.
For example, under frequency load shedding all of you know right when the system frequency is
going down we do load shedding so that the frequency is recovered right. Similarly, when the
voltage is low one can resort to what side call under voltage load shedding but this this should be
done very judiciously and this should be neither than last resort for for for saving the system
from voltage collapse right therefore the point is that these measures which I have put here as
design measures and therefore you should have a provision in the system so that you have a
provision of under voltage load shedding.
As a as a built of strategy to to avoid voltage collapse phenomenon are voltage instability
phenomenon. In case suppose it is provision is not exist it will not work right and generally you

will find that the that the human intervention may sometime success be successful there will not
be successful but here when I talk about this this is the automatic under voltage load shedding
scheme.
(Refer Slide Time: 43:20)

Now let us discuss this things in slightly more detail, application of reactive power compensating
devices. We know that we have the various reactive power sources our interest here is that you
should design your system so that you have adequate stability margin that is that is when you
plan for the reactive power sources, you plan in such a fashion so that adequate voltage stability
margin by proper selection of compensating devices.
(Refer Slide Time: 43:55)

In fact here the selection of sizes what should we size of the compensating devices what should
the ratings, what should be the locations all these things should be done by by a detailed system
study covering the most onerous system condition for which the system is required to operate
satisfactorily, idea here is idea is that when you are doing this design you have to you can say
determine what should be the location of the reactive power sources what should be their sizes
and what should be the type in the sense that is if control or is it fixed or whether is way which
should be continuously control or else we discrete control that the idea here is that when you
right at the design stage you have to perform a detailed system study or detailed system
optimized study you have to be done. So that you find out actually the sizes locations type of
devices and that should all include the most onerous or most most actually the most heavily
loaded condition right.
(Refer Slide Time: 45:22)

We wanted at that condition system should be stable, third is design criteria on maxim allowable
voltage drop following a contingency are not often satisfactory from voltage stability point of
view. Sometimes whenever, we design the application of reactive power sources the one
approach will be that okay suppose the certain contingency occurs right what is the maxim
permissible voltage drop and based upon that you design the reactive power sources but the
suggestion is that instead of going for this type of situation one should design from the point of
view of stability margin that is the stability margins should be based on mega watt and MVAr
distances to instability that is how much real power, inductive power increment can be put on
that system right till instability occurs that is what is that point actually I have already discussed
the minimum distance to instability therefore that criteria should be we must we must design our
system. So that there is a minimum inbuilt voltage instability.

(Refer Slide Time: 46:30)

(Refer Slide Time: 46:39)

Next the control of network voltage and generator reactive power output again the design step.
Now here, so far actually the reactive power sources are concerned the generator is one of the
most important reactive power source and the generators have automatic voltage regulators, one
way is that you you a regulate the voltage at the terminal at the generator, another way is that
using load compensators you you regulate the voltage at a point away from the generator
terminal that is the point which you choose for regulation may be not the terminal voltage of the
generator suppose this is generator, this is the step of transformer that is you can regulate
actually the field current of the generator through AVR. So that you maintain the voltage on the
high voltage side of the transformer constant this is normally done with the help of load

compensation devices the load compensators are provided to take care of this, this the AVR
regulate the voltage on the high tension side of or part away through the step of transformer.
You can always regulates through that some voltage may not be at this point may not be at this
point but in between that what you manage to decide that is the load compensation of the
generator AVR regulate the voltage on the high tension side or part away through the step of
transformer. This is beneficial effect on voltage stability by moving by moving the point of
constant voltage electrically closure to the loads, in the sense that what is happening that this
constant voltage point is now coming closure to the loads right. This is one approach that this
instead of regulating the terminal voltage you regulate the voltage at some other point using the
AVR load compensation devices.
(Refer Slide Time: 48:31)

Then many utilities are developing secondary control or secondary voltage control schemes for
centrally controlling voltages and generator reactive power output. In the sense that instead of
actually having the this they dis-analyzed voltage controlled you an take this system as a whole
right and monitor the system and control the voltages of the network from a central point of
view, control all the generators all actual the reactive power sources centrally, so that you
maintain actually a good voltage profile and maintain a voltage stability margin. This is this is a
new modern approach where we go for system wide control.
The next is the coordination of protection and controls because we have provided certain
protections so that when is suppose system is overloaded the protections will will trip the
equipment right. Therefore, tripping of equipment to prevent an overload condition should be the
last resort not in the necessary that suppose system is operating and there is a transmission line is
the overloaded right the protection system look at the overloading and may trip the line but this it
should be considered as a last resort that is your protection particularly the tripping or protection
system wherever possible adequate control measures, automatic or manual controls may be

automatic or manual. So the provided for relieving the overload condition before isolating the
equipment from the system this point is very important here idea is that here is a system which is
operating.
(Refer Slide Time: 49:30)

(Refer Slide Time: 51:04)

Let us say overloading takes place the protection system will try to look at the overloading and
trip the line. Our interest is that we should try to relieve the overload by say by say tripping some
loads before before tripping the generator or transmission line or so on that is the equipment
before isolating the equipment here the equipment means basically is the generator transformer
and transmission lines. This is what is the meaning of coordination of protection and controls.

Next about the control of tap changers but this is also playing very important role tap changers
can be controlled either locally or centrally so is to reduce the risk of voltage collapse in fact
what happens is that under certain situation the operation of tap changer is helpful under others
operating condition of situation right the tap changer will not be in a position to increase the
voltage but but that is going to reduce the voltage on the contrary that when you tried to you can
see increase the voltage the reactive power flow increases voltage drops right therefore idea here
is that where the tap changing is detrimental.
(Refer Slide Time: 52:04)

So detrimental a simple method is to block the tap changing when the source side voltage sags
and unlock when the voltage recovers right that is again actually very centralized control we
have to, there is also potential for the application of microprocessor based ULTC control
strategies such a strategies need be develop based on the knowledge of the load and distribution
system characteristic that is here microprocessor base means basically it is going to be intelligent
type of control systems right. The next step is discussed was the under voltage load shedding.
Now to cater to unplanned or extreme situations it may be necessary to use under voltage load
voltage load shedding schemes. The load shedding provides a low cost means of preventing
widespread system collapse in the sense the before before the system collapse is right it is better
to can say do some load shedding and rely the system from the overloading. The main cause of
you can say the collapse is again the overloading more reactive power demand than what can be
supplied and therefore if you reduce some of the loads or if you disconnect some of the noncritical loads right then one can save the system this approach is also used actually even for our
a for improving the angle stability of the system under load, under load shedding.

(Refer Slide Time: 52:36)

(Refer Slide Time: 53:37)

Then we talk about the system operating measures, what measures can be adopted so that when
we operate the system, operate the system right the system will not go into into voltage collapse
phenomena. The approach is very simple you operate the system so that it is a sufficient stability
margin it means right now at the operating stage you design that yes loading should not go below
a above a particular limit so that you have sufficients voltage stability margin. This point is also
very important is called the spinning reserve, the spinning reserve the concept is the generators
generators are the reactive power sources right and this reactive power can be obtained quickly
by regulating the excitation right and therefore what is said is that you should you should operate
initially the system.

So that other reactive power sources are used and the reactive power capability of the generator
is kept reserve because you have various reactive power sources like shunt capacitors,
synchronous condensers, may be SVC, may be state comment so on right, use then first and the
load the generator. So that generator is operating at nearly the very use the power factor
condition is supplies the real power so it has a reactive power capability and use this reactive
power capability to save the system from voltage collapse that is actually the right at the design
steps. Next is operators action, idea here is that these are the two which you can plan at the at
the operating stage when you operate your system, next is the operators reaction, operators
intervention, how the operator can can actually monitor the system, look at the complete system
as a whole and take necessary action.
(Refer Slide Time: 55:47)

I will talk about the operator reactions slight in more detail, the operators must be able to
recognize voltage stability related symptoms and take appropriate remedial action such as
voltage and power transfer controls and possibly a last resort load curtailment. This is the most
onerous task which is put on the operator that is the operator should be in a position to to
recognize the voltage stability related symptoms the, right. So that this operator will take
remedial action before the voltage instability occurs, it means the operator has to be well trained
and he can find out that yes there is a possibility of voltage instability which may take place and
therefore he takes certain measures and it should have certain certain authority to take those
measures. Of course the last resort is the load curtailment if you feels that yes without load
curtailment the system cannot be saved he should have the authority to do the load curtailment
and he should have that type of experience and training.
So that he can make out actually that yes yes at this parse at this operating condition system is
vulnerable is prompt to voltage instability and you should know the load remedial measures to be
taken to save the system. It is very difficult task and that is why actually we require a highly
trained personal to operate the system, operating strategy that prevent voltage collapse need be

established in the sense here here the meaning of this is the operating strategies that prevent
voltage collapse need be established.
(Refer Slide Time: 57:22)

Right at the beginning when you are operating your system you have to establish that what
should be the what should be the strategy so that we if this happens this measures should be
taken that should be available to the operator an online monitoring and analysis to identify
potential voltage stability problems and possible remedial measures should be invaluable in this
regard is always online monitoring. With this I have I have completed the discussion on voltage
stability what we have discussed in the voltage stability the how to analyze the dynamic stability
problem this is done by complete time domain simulation then one can apply the certain tools
static tools to to analyze the voltage instability problem.
We have seen the PQ sensitivity analysis, we have also seen the QV model model QV analysis i
have also discussed the continuation load flow for so and so forth. At the end we have discussed
the various measures that can be taken to prevent the voltage collapse in the system. Thank you
very much!