 Welcome to this second lecture on power system dynamics and control. In the previous class, we had focused and discussed one important phenomena that is the loss of synchronism. We will continue the theme of describing certain stability phenomena in a power system in this particular lecture. So, in this particular lecture, we will cover some other phenomena like voltage and frequency stability. It is a brief overview. The next 40 lectures will actually focus on all the nitty gritties of this particular phenomena. Just to recap what we did last time, we discussed the structure of power systems that is we saw that most of the typical large power systems which are there today are synchronous gritties that is they consist of a large number of large synchronous generators interconnected to each other by AC lines. So, once we have interconnection by AC lines, we discuss this that in steady state we ought to have frequency same throughout it should be the same throughout the grid. One of the problems of course, which we are likely to face is that although the frequency should be same throughout the grid under some large disturbances or large power transfers you may have loss of synchronism. So, normally synchronous machines which are connected by AC lines tend to remain in synchronism because of the nature of physical loss which of course, we shall discuss later in this course. Loss of synchronism is an important phenomena. Today, we will learn two other phenomena that is frequency and voltage instability and to do that we will illustrate a few simple examples. First of all let us answer the questions which were asked in the previous lecture. How many synchronous grids are there in India or may be in your country if you are not of India? How many HVDC links are there? How many of these HVDC links are synchronous links embedded in the synchronous grid and how many of them are synchronous links? So, the answer to this question is as follows. India is at present that is in 2009 divided into two synchronous grids. The southern part of the peninsula forms one synchronous grid that is the synchronous generators in this part of the system are interconnected to each other by AC lines. The second grid synchronous grid in India is the rest of the system the rest of the country is actually another synchronous grid. So, if you start off with one generator here say at Trombay and you follow the AC line parts you can go to another generator in the same system synchronous grid through only AC line parts. So, all the generators in this northern part of the grid are actually in synchronism in steady state. So, they run at the same electrical speed in steady state of course, there are asynchronous links between the southern grid and the other grid. So, for example, there is an HVDC long distance HVDC link from one state to the other here it is between Talcher and Kolar then there is another just here it is a very short it is called a back to back DC link it is an asynchronous link there is another here these are all asynchronous links. So, these are asynchronous links connecting to synchronous grid. So, these two grids actually can be at different frequencies of course, there are HVDC links which are embedded in the AC system. For example, there is a HVDC link within this grid embedded within the AC system it is a long distance HVDC link. So, there is in fact, one here there is another here there is a short distance link here. So, this is a Chandrapur Padga link this is the Rihand Dadri link and this is a short link which was actually not useful long distance transmission. These links although they are present in the synchronous grid they do not really cause you to have an asynchronous grid. However, these are asynchronous grids with controlled power flow the power flow on these links DC links does not depend on the phase angle here and here that is an important thing about the interconnects between these two regions. In this region you have got a lot of AC lines in which power flow of course, is a function of the phase angular differences of the voltages at the two ends of the line. Now, just to illustrate the fact that we have the same frequency prevailing all throughout the grid at a given amount of time all throughout asynchronous grid. I shall just show you the snap a snapshot of the frequencies reported on the websites of the load dispatch centers at various locations within the country. In fact, I will show it to you at three locations all these locations are more than 1000 kilometers apart. So, you see this is a screenshot of the frequencies reported at various points in the grid at more or less the same time. So, the time is approximately 1135 it is not actually measured at the same time everywhere. So, what you see in the west and the east that is at Mumbai and Kolkata the frequencies are almost the same actually my statement earlier was that in a synchronous grid the electrical speeds of all machines and the frequencies are should be the same, but of course it is not strictly speaking true there are two reasons for that at any given moment of time a power system is subjected to a lot of disturbances. So, actually they could be small disturbances really like I shot off the switch of a bulb here that is a disturbance on the system. So, the system is not strictly speaking in steady state at any point of time they are always small or large disturbances in the system. So, electrical speeds are not exactly the same if you measure them, but another issue which is probably more important at this point of time is that the frequencies are not measured at exactly the same time point of time also. So, you may find some differences in the frequencies as measured in two places. So, although the western part of the system and the eastern part of the system are a part of the synchronous grid of India a synchronous grid of India you will find that the frequency is slightly different from each other. In fact, if you look at the frequency in the southern part of India you can look at the slide you will find that it is different quite different from what prevails in the western east which is not a surprise because the southern part of India is a different synchronous grid. The normal frequency of both the the southern grid and the rest of the India grid is actually 50 hertz, but you see that the frequency is not exactly 50 hertz it is around 49.5. So, it obviously means we are not strictly regulating the frequency in India we allow it to actually change within a band. In a few moments from now I will also tell you how this frequency is actually determined and what determines that your frequency is 50 hertz obviously it has something to do with the speeds of the generators. So, let us move on to the topic of today that is frequency stability in the grid. So, in this particular lecture I will be covering the voltage and frequency instability phenomena the control hierarchy in a power system because there is a need for you to know what are the typical feedback control systems what are the manual control actions and so on a bit about the stability criteria and the impact of stability issues on the power system. So, let us move on to frequency stability you may have guessed that the frequency of a grid or at least at a particular bus in a simple system like a synchronous generator connected to a load would be dependent on the speed of the generator. In fact, the frequency of voltage is induced on the stator of a synchronous machine depends on the speed of the machine the electrical speed of the machine. Of course, this particular definition of frequency needs to be modified when one comes to a multi machine system because then we will have to talk about local frequency. But let us just first talk about the frequency of a simple isolated system for example, a synchronous generator connected to a load the frequency of this bus in steady state will be the same as the frequency electrical speed of rotation of this synchronous generator. So, if it is a 4 pole 1500 rpm machine it is effectively going to create EMFs of 50 hertz at this bus at its terminal. The load is connected at this bus and let us say we will denote this load power as P L. Now, what determines the speed of the electrical machine well it is determined by Newton's law it says that the rate of change or the speed of the machine is equal to this is a mechanical speed is equal to the difference of torques the mechanical torque which is provided by the prime mover and the electrical torque electromagnetic torque which is created by a currents term of the machine. Remember that torque is given by power divided by the angular velocity the attentive among you would have noticed that there is a minor error here the torque is given by power divided by the mechanical speed. So, in this expression we should have P m minus P e divided by omega m. So, of course, we have corrected it a few minutes later, but it would be good for you to note this down once again we should have P m minus P e divided by omega m. So, these are the two torques which determine the speed of the machine as per this relationship. Of course, this is the dynamical equation of the machine if we are in steady state we will have P m minus P e by omega equals to 0. So, this is only under steady state. So, if actually I have a synchronous machine say which is running on no load that is P l is equal to 0 in that case we will have P e also equal to 0 because in sinusoidal steady state if you neglect all losses P l is equal to P e. So, what you will have is that if open circuit machine which has P l is equal to 0 is suddenly loaded. So, this P e is non-zero before when you load it suddenly becomes sorry it is 0 initially and when you load it it becomes non-zero what is likely to happen is there will be a sudden imbalance in this mechanical input and a load. If that happens the speed will change for example, if P e is less than P m you will find it the machine P e is less than P m the machine will accelerate or if P m is greater than P e the machine will accelerate and vice versa if P e is greater than P m. So, the speed of the machine is really determined by this equation. Now, the point is if P m minus P e is a constant non-zero number the machine will never reach a steady state because this quantity here will always be non-zero therefore, machine will either accelerate or decelerate constantly. So, what we really need to do is understand how the system reaches an equilibrium. If you want the system to reach an equilibrium if it starts off with P m not equal to P e for example, initially let us say P m is equal to P e and suddenly I change the load. So, P e becomes something different how does this system reach an equilibrium the two ways the system could reach an equilibrium to reach an equilibrium P m minus P e should be equal to 0. Now, remember that P m and P e can be function of speed for example, if P e or the load which you put is the that of a fan or a pump it is a function of frequency. So, actually this is a function of frequency the mechanical power input to the synchronous machine the prime over input also could be made a function of frequency. For example, if I have got a system which changes the mechanical power input to a machine whenever the load changes or the frequency changes. So, both these things could be functions of frequency. So, the final frequency to which a system like this settles down to will be determined by the solution of this equation. So, if we have for example, a diesel generator set at our home and we connected to our loads that is incandescent bulbs or fluorescent tubes or fans or pumps in that case what we will see is that the diesel generator will have a control system which changes the power when the speed changes it is called a governor a speed governor. So, this is one of the mechanisms by which you can attain equilibrium. So, this is as far as a single machine and a load is concerned what happens when say you have got two machines say a system like this two machines synchronous machines supplying a load which is present at this point. So, what determines the frequency or what ensures the frequency equilibrium under this situation? Now, if you have got two machines you have got two equations for the first machine let us say they are the same number of poles. So, things will become a bit easier actually you can use the subscript m 1 I think I missed it out in the previous equation this m denotes mechanical speed. Now, what you notice here is if I add these two equations I can write them like this a little bit of algebra which I am skipping pay close attention to this this is the cumulative inertia of the machines machines this quantity can you recognize this quantity this quantity may be familiar to most students who have done a physics course this is called the center of inertia of the system. So, the rate of change of center of inertia of the system depends on the cumulative torques on the system. So, if I want this particular system to be in equilibrium I should have. So, what you have here is this now if I am talking of a system which is basically two synchronous machines connected by ac lines and a load here we must have in steady state why is this. So, assuming that the machines have the same number of poles what it means here is that the mechanical speeds have to be equal in steady state that is basically the synchronism condition we have seen this in the previous lecture that if the speeds are not equal or the frequencies of the two generators are not equal you may have a loss of synchronism phenomena. So, what we should have is this which also really means that p m 1 plus p m 2 is equal to p 1 plus p 2 p 1 and p 2 are the electrical power outputs of the two machines. Now, in sinusoidal steady state and neglecting losses it is easy to see that the total electrical power output of the machines should be equal to the load power. In the previous lecture I discussed loss of synchronism remember loss of synchronism is when the relative speeds of the machines or the relative frequencies at different buses are not equal. So, you may lose synchronism loss of synchronism is an is basically something to do with the relative speed of the machines it is not something to do with the common motion or the center of inertia motion. So, that is in our mind have some kind of clarity regarding this relative motion stability pertains to in asynchronous grid all machine should be in synchronism. So, that is what it should really you know pertain to whereas, common motion the stability of the common motion determined is determined by the load generation balance. So, whatever I meant common motion or whenever you are I have talked about a center of inertia motion I am really referring to the common motion. So, we have to ensure that machine should stay in synchronism in a synchronous grid and the common motion also should be stable. So, we should ensure load generation balance otherwise what will happen is you can have a situation where relative motion is stable, but this whole system the center of inertia of the system is constantly moving. So, what we should ensure is that the center of inertia speeds in a synchronous grid should be near about 50 hertz it should be steady at 50 hertz or 60 hertz in some systems. So, what we should have when we have suddenly for example, load trip if the load trips in a system there will be a transient imbalance between the cumulative generation and the cumulative load. So, if there is an existing load and it gets tripped then you will find that there is a imbalance between the total generation and the total load and as a result the center of inertia of the system accelerates. So, if you look at the first figure that is the figure on your left you will find that as soon as such a disturbance occurs there is some relative motion and the system frequency tends to rise and settle to another frequency, but of course eventually all the machines remain in synchronism. So, all the generator speeds tend to become equal after sometime there may be some interplay between them exchange of power between them, but eventually the system reaches a steady state in which all frequencies are equal all the generator speeds are equal and the center of inertia speed equals to the generator speed in steady state. Now, what ensures that it reaches steady state that something we have discussed before governor action as well as the load frequency dependence the fact that loads themselves of functions of frequencies ensure that eventually you reach an equilibrium that is if you find a sudden load generation imbalance the frequency tends to change as soon as there is a change in frequency inherently loads like fans etcetera change their power output. So, if frequency falls in fact fans will move just that little bit slower and draw little bit less power similarly you have control systems like governors which are present on most prime mover systems which if which effectively increase the power the prime mover powers in case the frequency goes down and decrease power in case the frequency goes up. So, this kind of control systems exist on most generators the of course the important point is that if you have got controllers which are aiming to keep frequency constant or near constant they should be coordinated properly. So, that is one of the interesting issues we will discuss sometime later in this course. So, when you have got governors present on many machines all of them are trying to maintain the frequency at some particular on here keep it almost constant in that case you will find that you need to coordinate the governor. So, that they share that excess power appropriately. So, that is something which we learn later look at the case in which there is a sudden generation trip if there is a sudden generation trip the total generation in the system becomes less than the load at that frequency, but as you will find that the frequency the machines decelerate the center of inertia of the machines which would be somewhere here would decelerate and then reach an equilibrium based on the governor as the load frequency characteristics. It is important to differentiate this center of inertia motion from loss of synchronism if there is a large disturbance this is what the generator speeds may look like here you have got one machine whose speed becomes altogether different from the frequency of another machine. So, if you have got a synchronous machines in which synchronous machines are connected by ac lines and there is a large disturbance you may lose synchronism. So, please differentiate between the center of inertia motion as is evident from these figures the movement of the center of inertia motion and the unstable relative motion which is seen in this particular figure. So, this is the loss of synchronism phenomena another phenomena which is often seen in the grid because of which could be because of improper feedback controls or the inadvertent effect of some feedback controls is poorly damped oscillations. So, even for small disturbances sometimes you will find that the system does not settle down quickly to an equilibrium I mean you will find that it just goes on oscillating and sometimes even these oscillations grow with time in case in case of certain feedback controllers. So, these are the things which we will learn in this course, but the important point is differentiate between relative motion and common motion. So, common or center of inertia motion is dependent on low generation balance and center of rather the relative motion is rather loss of synchronism is a phenomena in which relative motion is really important. Now, let us just consider a system like this you have got a generator it has got a local load, but another generator it has also got a local load say this is supplying 1000 megawatts let us assume there are no losses for simplicity this is 500 megawatts. So, this generators actually through over this line exporting this is an AC line exporting 500 megawatts this is say 700 megawatts and this is 200 megawatts the total load is equal to the total generation. So, the center of inertia is not going to the speed is not going to change let us assume that this is a situation which exists at a particular time and the system is in synchronism and in steady state. Now, because of some disturbance or say a loss of synchronism suppose the relays trip the circuit breakers at two ends of this line suddenly. So, you have got this line is tripped out in that case you have got two systems. Now, you have two separate systems if the frequency in this system is to remain constant in that case the generation load would need to be balanced, but look at the generation at this point of time it is 1500. So, the frequency will suddenly shoot up the mechanical power and electrical power are this are not the same. So, the frequency will suddenly shoot up unless we do something it will exceed may be 1 or 2 hertz above 50 hertz which was say the nominal frequency at the beginning of this disturbance prior to this disturbance. So, it will suddenly shoot up by more than a hertz if that happens in this will suddenly the generator will trip out due to over speeding. So, this whole island will collapse. So, it is important that as soon as an island is formed immediately some emergency control measures have to be taken to make this generator to reduce this generation. So, you need to have governors should try to reduce this generation quickly. Similarly, in this under generated island you suddenly have a large amount of load and less generation. So, what you need to do here is trip out the load quickly and increase the generation if you can again through governors. So, once you island suddenly you are left with glaring differences between the generation and the load moving on to another interesting phenomena which has been observed that is voltage stability. So far we have been talking about the frequency and relative angle or relative frequency motion of synchronous machines. We will move on to the stability of the voltage magnitude at a particular point in the grid. Now, when does this problem really arise that is the question we will ask ourselves just having low voltage in steady state does not necessarily mean that you have got voltage instability. Normally if you have got a system say a synchronous generator which is supplying some load let us just talk of a single synchronous generator. So, that we do not have to worry about relative loss of synchronous phenomena in this particular system. So, just to highlight the problem of voltage stability just take a single machine connected to a load. Now, if you have got a single machine connected to a load if we increase the load at this point typically it is an inductive load most fans and pumps and major loads are inductive in nature they draw basically some reactive power. So, you will find that there is some voltage drop along the line which carries this power to this point. So, one would expect as you increase the load here the voltage here will keep dropping. Now, this is this is not necessarily mean any kind of instability for example, just take this even more simplified system. So, let us take a generator connected via transmission line to a simple resistive load something like this this is E. Now, normally what is the power at what is the power drawn by this load you will find that it is E which is the magnitude remember the phase is not play any role as far as power in this load is concerned. So, we will only talk about the magnitude of the voltage source E divided by the impedance this is the current. So, square the current multiplied by R that is equal to the power in the load. Now, you will notice that the power is actually a non-linear function of the resistance. So, in fact P L is equal to I will just simplify this E square upon x square plus R square into R. So, this is the power. So, if I change R power will change another thing is the voltage here voltage magnitude here will be nothing but E into R upon this is the magnitude of the voltage at this point. You can verify that this is nothing but V square by R. So, you will get again the same answer if you do V square by R if I want to increase the power dissipated by the load. So, if you got I will just draw it again if I want to increase the power dissipated by this load what should I do increase R or decrease R well normally one would expect that if I decrease the resistance one would increase get a larger power output. What will have is power is going to be 0 at R is equal to 0 do you agree with that if I increase the resistance and make it close to make it very large then also you would expect that the power is again 0. So, what you have is some point there is a maximum to this power. So, what is this point? So, P is equal to E square R upon x square plus R square it is easy to show that this occurs when R is equal to x. So, the thing is that in case my resistance value is this and I want to increase the power what should I do I should decrease the resistance, but if I am here that strategy will not work because if I try to decrease the resistance my power actually reduces. So, in fact this is the basic origin of a problem called voltage instability. So, if you look at say a load which is not constant, but controlled suppose I use the rule I am a very selfish load I say whatever be the resist voltage here I will draw the same amount of power. So, what my rule is rule is going to be is that I want to get the same amount of power irrespective of what voltage appears here. So, what rule I will follow is decrease R if P L is what I is is lesser than what I desire. So, if I use this rule I may land up into problems if I am at this point in the curve. So, if I reduce R in fact my power will reduce if my power reduces I again apply the rule I again reduce the resistance my power further reduces and you will find that you will be driven down the voltage the power will be actually driven down and the resistance value will go on decreasing and it is not difficult to show this this is the magnitude of the voltage and the power for this particular system. So, if I actually decrease R power increases voltage also decreases, but actually B square by R still increases at this point is the maximum power point R is equal to x. If I decrease R the voltage drop will be much faster in some sense I would not say use the word faster you can say that the voltage drops. So, much that the decrease in R does not cause an increase in power. So, what may happen is that if you apply this rule if you have got a control system which applies this rule you will find that if you go beyond this point your voltage will be driven downwards typically of course, if voltage goes below a certain point there are sometimes in many loads under voltage relays which will trip out the load or the control action will sees at a certain point, but the point is that you have not achieved much by decreasing resistance if you are in this part of the curve you are actually going to worsen the situation. So, this if you have got a load which draws power and it changes its resistance or impedance as per this rule you are likely to have instability if you are somewhere beyond this point. So, this is the basic you know problem of voltage instability you may ask of course, that normally we would design R x to be very small why would we normally have an x which is a large value. The answer is yes normally your x is not very large and in fact, the possibility of R becoming equal to x is very remote in a normal system, but in case you have for example, the loss of a large amount of transmission line distribution lines in that case you may have a system impedance becoming fairly large. Even more prominent is a situation like this see this voltage source which I have shown you here is actually a synchronous generator and I have shown this as x and this is R actually in a real system this is how it looks a synchronous generator is not actually a perfect voltage source it is a voltage source behind a synchronous reactance. So, actually you may ask the question is this figure is not the same as this obviously unless of course, I maintain this to be e how will I maintain this see this figure and this figure convey the same thing if this point here is maintained at a voltage e, but the point is that this e is maintained constant how by the synchronous generator itself the field voltage of a synchronous machine can be controlled so that the terminal voltage of the machine equals e or nearly you know almost maintained regulated at e. So, in a normal system this x is not normally very large it is never anywhere close to the load resistance, but there is one problem here this e is not a constant strictly speaking it is regulated roughly regulated by synchronous machine which has certain limits for example, what happens when this synchronous machine hits the field heating limit that is I cannot increase the field voltage and thereby the field current more than a certain limit. Then this control is lost and I am no longer able to regulate this to e in that case it is meaningless to talk of this e as a constant. In fact, this becomes at the limits this is a synchronous reactance at the limit this is how your system is going to look like. So, this is a constant this is a large impedance synchronous reactance of a machine is large this is the transmission line reactance. Now, this system can be prone to voltage stability because this impedance is suddenly very large and this is a constant contrast this with this situation wherein the synchronous machine is able to maintain this e by changing the magnitude of the terminal voltage of the machine that is by changing I will repeat this sentence contrast this with the situation where e is maintained constant by the synchronous machine by changing the field voltage applied to it. So, this is a good situation. In which we are able to maintain this e at a constant value, but once the field voltage hits its limit you cannot increase the field current beyond a certain limit otherwise it will heat up the field winding. So, there is a limit to this if this limit is hit suddenly the picture changes here you got a very large system impedance behind a voltage source which is internal voltage source of the synchronous machine is practically a constant. So, this can cause a potential voltage stability problem because the system impedance suddenly becomes very large. Now, you may ask the question I have I was talking of a load whose resistance is changing in a controlled way that is it is decreasing the resistance whenever the voltage falls down or the power is less than the desired power this kind of control rule under certain circumstances may lead you to sudden drop in voltage. Now, when does this actually occur for example, do we have a control resistance well you can have a control resistance, but a more typical phenomena which mirrors the same thing is this one you have got a load resistance which actually does not change, but it is supplied from a tap changing transformer the tap of the transformer keeps changing. So, the voltage here drops down the tap a is increased the tap a is increased the effective resistance which the system sees in fact is variable. So, although I talked about a variable resistance basically a more typical situation is likely to be like this of course, the same issues are here to in fact the same arguments are valid here because this tap a is increased whenever the voltage here falls if the voltage say falls below 1 per unit here you will increase the tap. If you increase the tap the voltage here is like you think it will increase to 1 per unit near 1 per unit and therefore, the load power can be maintained a constant, but this of course will not be true if r by a square has exceeded x. So, that is what or other has decreased below x. So, if r by a square decreases below x any kind of change in a the tap will actually cause decrease in the power. We will next move on to the other issue, other issues relating to stability they are mainly caused by feedback control system within the power system in the power grid. Now, before we look at the control systems which exist in a power grid of course, that is something we will discuss in the course later on prime mover controllers excitation system controllers. You look at the problem in two ways there are two kinds of things which you normally do in a power system. One is manual actions manual control actions based on supervision. The second type are automatic feedback controllers these are the typical feedback controllers which are learnt in your control systems course. They are used typically regulators kind of they are typically voltage regulators and governors these are all automatic feedback controllers. The third thing which you will see is emergency controls. Emergency controls are control actions like tripping of load whenever there is a large imbalance of load in generation when in a for example, in an under generated island one can have a emergency control scheme wherein if the frequency falls you trip out the load. So, try to get the you know center of inertia frequency within an island within certain limits. So, this is called an emergency control. In fact, emergency control kind of overlaps with in some way with protection systems as well equipment protection systems. Now, if you look at the control hierarchy in a power system you will find that there is at the highest level manual supervision in which you know an energy control system center actually looks at the great monitors it suggests changes in power flows in certain lines for example, by adjusting the load in generation at the two ends of say a transmission line. So, that you are not having the danger of going to an unstable situation. So, this is what is you can say supervisory preventive control which a manual or a person in a load dispatch center does and this may be over a you know very long time this is also feedback control. Actually, if you look at the control hierarchy in our system in India you have got regional energy control centers which coordinate with other synchronous grids. For example, the western regional load dispatch center which is in Mumbai coordinates with the southern regional load dispatch center is another synchronous grid. The regional load dispatch center monitors the overall grid and also sometimes gives instructions to state load dispatch centers. The state load dispatch centers themselves directly communicate with power plant operators, load stations and so on which is in their jurisdiction. The regional load dispatch center may have a few assets which are under its control for example, interstate tie lines, centrally owned plants and centrally owned lines. So, this is basically the manual control hierarchy. However, eventually whatever an energy control center say say a state load dispatch center communicates with a power station to reduce its power output. In that case the power plant operator adjusts the prime mover system to reduce the steam input to the turbine and eventually the generator the output power reduces because mechanical power eventually reduces. If you reduce the electrical power output reduces in case you reduce the mechanical input to the turbine. Of course, the energy control center may actually give instructions at a slightly higher level. In the sense they may say reduce the reactive power output of your generator. So, what actually a power plant operator will do is reduce the field voltage not directly. He may have a what is known as a voltage regulator whose reference voltage he reduces which eventually reduces the field voltage of the generator and as a result of which the generator may reduce its reactive power output. An energy control center may also have control over components which are there in the network. For example, a high voltage DC system you can control the power output of a high voltage DC system or the reactive power output of certain reactive power compensators within the network. The energy control center may also sometimes do a bit of load shading in case there is a severe load there is a severe generation deficit. So, remember that eventually at the lowest level you normally have a control system which responds to the scheduling orders of an energy controller a system operator. You look at a typical control system the typical control system like voltage regulator of a synchronous generator. What it does is it compares the measure terminal voltage of a generator to the reference value this is set by the system operator himself. It is passed through a controller which may be a proportional controller or a P I controller and that determines the firing angle of the thyristor bridge which controls the field voltage which is fed to the field winding of a the alternator and therefore, the terminal voltage is changed. So, if V ref is not equal to the terminal voltage you may find that the controller adjusts or changes the final output voltage in this fashion. You may also have emergency or stabilizing controllers which modulate the voltage reference so as to improve stability. So, this is something we learn later in this course. To come to near important point in this somewhere at the close of this lecture how does stability eventually affect your system operation? Now, if you are near instability now of course, this statement itself requires some kind of definition then a system operator tries to take control actions so as to reduce or change certain parameters within a power system. For example, you may change the power flow in certain lines. So, stability criteria have to be defined much in advance. For example, a system one would normally like it to operate in a certain way. For example, you would like it to be reliable in the sense that if one power system component is stripped the whole system should not lose synchronism or it should not become unstable. So, when a system is operating a system operator kind of evaluates the stability of the system for certain potential disturbances. So, for example, he may evaluate that if there is a three phase fault at this bus at this point of time followed by the clearing of the lines incident of the bus will cause this particular disturbance can cause a loss of synchronism he will try to take control actions like changing the power flows of the lines which are incident to that bus. This is one possible action of course, I am not saying this is the correct action to take, but he can take these kind of actions. So, whenever he sees that any potential disturbance can cause a loss of stability he will try to change the operating point. Changing the operating point in a power system is done by changing the generation of the load this has economic repercussions. So, basically stability has got economic repercussions. So, we cannot whenever you have a system with poorer stability it is more prone to a fault and if you want prone to instability then you have to pay more in order to get a certain kind of reliability because you will basically try to operate a system which is more which is meets your stability criteria and if you do that you may have to actually move to a kind of an economic schedule of power generation and loads. So, this something of course, we will try to understand later when we understand preventive control. Even while planning if you find that for typical load generation scenarios your system is unstable a system planner may have to put in some money and build more infrastructure like more transmission line. So, that for that particular projected scenario the system is stable. So, this even in planning which is which could be on a long horizon a system operator has to take into account stability issues. In fact, one if for example, your feedback controls in your system are not are causing instability in that case you may even not be able to operate. For example, there have been situations in the past wherein suddenly you know almost it appears spontaneous to a system operator that a system oscillation started building up. You had oscillations in frequency voltage power flows because of the feedback control systems which are there in your system. If this occurs actually in practice it is a very difficult situation because a system operator may not do know what to do if it observes spontaneous oscillations seemingly spontaneous oscillations in the grid. So, design of feedback controllers appropriate feedback controllers also involves some engineering cost. In fact, if a system is prone to these oscillations or they have been observed very often under certain operating conditions you may have to invest time and engineering effort to design or even you know manufacture proper controllers which will prevent this kind of situation from arising. So, to recap we have just discussed voltage and frequency instability phenomena by some simple examples. We have discussed hierarchical control and the impact of stability on power system operation. Of course, our last discussion has been a bit brief. We will return back to this topic when we come to emergency and preventive controls later in this course. In the next lecture, we will really start off with the nuts and bolts of this course the analysis of dynamical systems. Till now we have been looking at more of an intuitive picture of everything. Einstein had said that the most incomprehensible thing about nature is that it is comprehensible. So, although what we seem to be this course when we are entering into the nitty gritties of this course what we have set out ourselves is to understand the behavior of a large grid and I mentioned last time it is lots and lots of elements. The point is that by a systematic and scientific attack to the problem we will be actually able to understand these things rigorously or at least approximately if not of course, there is no meaning to perfect rigor in an engineering course, that we will be able to basically from the equations and the models of the system we are going to be able to understand all these phenomena quite well enough to design controls for them. Thank you and we will meet in the next lecture.