 In this last lecture of this course, we will study the stability improvement of a power system. In particular, we will focus on the possible instability which occurs in case of large disturbances that is the relative angular instability which occurs due to large disturbances which causes loss of synchronism between synchronous machines. So, when I say improving stability, we shall look at measures in operation planning or design which can actually allow us to operate the system more securely that is for credible disturbances one can you know the system is stable for credible large disturbances. So, today's lecture is on stability improvement for large disturbance stability. Now, as you know just to keep matters in perspective, angular instability is essentially consists of two phenomena loss of synchronism which is basically a large disturbance phenomena it is also called transient instability. We also saw in the last lecture that angular instability can also manifest in terms of small disturbances and that is due to undamped oscillations or power swings and power swings could be you know the damping of power swings could be improved by making changes in controller controllers or augmenting or having auxiliary control controllers for controllable elements in a power in the power system like the excitation system in a generator or HPDC power flow control we can actually ensure that these swings are actually stable. We also saw the phenomena of voltage stability in which we could have a voltage collapse at certain buses due to lack of reactive power reserve because of for example, generators hitting their field current limits a weak network and loads which try to draw the same amount of power in spite of prevalent low voltage conditions. So, combination of these circumstances could in certain conditions cause a voltage collapse. In fact, if the loads maintain a constant power or you know kind of maintain constant power by the use of tap changing transformers one way to avoid voltage instabilities to recognize such a situation is developing and disable transformer traps. So, that your load is not aggressive load will fall if the voltage falls. So, this is one way you can improve voltage stability. We also saw right in the beginning of the last three lectures that we can have better frequency stability that is better load generation balance by using governors or emergency control in the form of under frequency relays or df by dt that is rate of change of frequency relays. Remember often when we are talking of stability problems or any stability problems in a power system we also will encounter the phenomena of line overloads transmission line overloads that is thermal heating overload. This is not really a stability problem it is a quasi static problem in the sense that heating could occur even if there is no stability problem you can have loading of transmission line above the thermal limits. In that case you are actually having a steady state problem of heating. So, it is not exactly a stability problem, but the main stability problems which we do face of course, are angular instability voltage instability and frequency instability. Of course, if you design some of the feedback control systems in your you know in your controllers incorrectly you can actually cause some pattern or more to go unstable. So, this is something which also which also can occur. Now, there is one important thing when we are talking about angular or frequency instability we have shown I have shown you this kind of a crude analogy of a multi machine system. You have two important things to worry about in a multi machine system. One is frequency instability or in other words the center of inertia motion of the system which depends upon the sum of rather the load generation cumulative load generation balance in the system. In addition you have got relative motion which you have to worry about that is the problem of power swings and relative motion can also be large disturbance unstable and that is what we have called as transient instability. So, these are the mainly the phenomena associated with the electromechanical system. Of course, we have seen that power swings can you know be unstable small signal unstable or small disturbance unstable due to the effect of feedback controllers like high gain automatic voltage regulators in the system. Again let us just try to understand it using these plots which I shown you in previous lectures as well. Today's lecture actually is worried about large disturbance angular instability. So, we are really talking about the lower left hand system in which after a large disturbance the speeds of the generator deviate from one another and you may have a situation where there may be large fluctuations in voltage and power in the system. So, this of course phenomena occurs in synchronous grids only where that is in grids in which synchronous machines are interconnected by AC lines. If machines lose synchronism that is they run at different speeds you will have unacceptable variations in power voltage and so on. This can be of course understood easily using the simple example which is shown on the slide where you have got two it is a kind of idealized scenario. You have got two sources which are running at different frequencies and if you plot the three phase power the total three phase power you will find that if you have got two sources with different frequencies the power flow through the transmission line will kind of oscillate at the difference frequency. And the power flow actually undergoes variations which may be I mean the power flow you can go even negative I mean you can have both negative and positive variations. So, the variation is very very significant. So, in case you have got a loss of synchronism scenario where you have got two you know synchronous machines running at different frequencies while still being connected by an AC line this is unacceptable. And typically it leads to voltage at some part of the grid you know under it makes the voltage undergo very large variations. In fact, if you look at the this lower graph here it shows the instantaneous voltage in the midpoint of the system and you see that in case the two systems lose synchronism that is they operate at two different frequencies then your voltage at the midpoint the envelope of the AC voltages even touches 0 at certain points. So, this is of course, unacceptable and usually if you have got distance relays they mistake this variation in voltage in fact the voltage at some point becomes 0. So, they think it is a fault and if that happens they trip the line. So, the system actually separates out in fact you effectively have an uncontrolled system separation in case distance relays trip after the loss of synchronism. In fact, if two machines are going out of synchronism due to a large disturbance this is a large disturbance phenomena in that case you have to separate out the two systems. In fact, for the western grid of our country it was seen that typically whenever you had a loss of synchronism you would have the western part and the eastern part of the system splitting. So, this is a typical cut set which is seen you have got the eastern part and the western part of the system splitting and thereafter of course, you have got two islands which are formed in the system or two separate synchronous grids which are formed in the system. So, this kind of uncontrolled system separation can occur following loss of synchronism. This is not although it the whole course has been kind of theoretical in the sense of telling you the theory modeling and there after drawing inferences about the dynamic behavior. I am not really shown you a loss of synchronism after following a large disturbance. We did see right in the first lecture a situation where if you went on increasing the path output of a synchronous machine which is connected to a voltage source you come to a point where it loses synchronism, but loss of synchronism can also occur after a large disturbance and what you see here of course, is one such practical situation which did occur in our western grid several years ago and if you look at these graphs the first graph is the voltage in the a phase then the current in the a phase then the voltage in the b phase the current in the b phase voltage in the c phase and the current in the b c phase. So, what you notice very clearly is the signature of loss of synchronism this is a voltage which is measured at some at a location in the grid after the loss of synchronism. You see this typical signature where the voltage dips down to 0 and again rises this is a scenario this is a typical signature which is seen this is in fact over a 400 k v line in the system. So, this is a real life example of a loss of synchronism in fact this idealized scenario which we saw using a two machine example is something what is happened in a bigger scale in the in a real grid where the groups of machines in the east part of the system have lost synchronism with the machines in the west part of the system. And this particular in fact measurement was taken for a real life event real life response after a large disturbance and what was really being measured was the voltage on this particular line and this is what was really seen at one bus in this system. So, this is a typical signature of a loss of synchronism it really occurs it really does happen in a real grid after a large disturbance of course the loss of synchronism events occurring in grids happened very rarely in fact I had to really dig out you know various disturbance records and you know consult my colleagues in the industry to get this particular situation where system actually did not lose synchronism. It does not normally lose synchronism because you operate it or design it or plan it in such a way. So, normally you loss of synchronism events are not seen now we will just discuss what really I mean by this, but before that let us just summarize what we have learnt or what are the main aspects of angular instability. One of the aspects of angular instability is the stability after small disturbances which can be actually analyzed by linearized you know Eigen analysis of the system. This is what we did in fact in you know in the previous lecture we just discussed what happens for small disturbances how we can improve the small disturbance stability by improving the control systems or augmenting them with auxiliary controllers. Now, remember that small disturbances relates to the relative angular oscillatory behavior and it is a property of the equilibrium in the sense that any disturbance small or large can excite these oscillations and under certain situations these may be unstable, but having power swings is not actually a problem as long as the oscillations die out. In fact, any disturbance will lead to you know these typical you know oscillations which you will see in the responses of the generator speed, but these are not problem they are not a problem if the oscillations die out. We really are facing a small disturbance problem only these oscillations do not die out I mean the you have got sustained oscillations or growing oscillations. This is something which may be of which may be a real worry. Large disturbance instability on the other hand which is also called transient instability is disturbance dependent it depends on the magnitude of the disturbance and one important point which is which has to be appreciated that in any synchronous grid that is a grid in which I have got large number of synchronous machines connected by transmission lines transient instability will always be an issue in the sense that you never get rid of this problem in the true sense. You will always find in a synchronous grid a large enough disturbance which leads to instability. Now the key problem is for a credible disturbance credible I mean a disturbance which seems realistic does the system remains stable or not. So, when I say large disturbance stable it is of course disturbance dependent on the magnitude of the disturbance. For typical or credible magnitude of disturbances is the system stable or not would be a more engineering like question, but remember that the large disturbance stability phenomena as such will always be there in a system power system. Remember when I say large disturbance instability it also means that this arises due to the non-linear nature of a power system otherwise small disturbance stability and large disturbance stability would be equivalent in a linear system there is no such distinction, but in a non-linear system large disturbance behavior may be significantly different from small disturbance behavior. So, for small disturbances the system may be stable oscillations may be dying out, but for large disturbances you can always cook up a large enough disturbance in a synchronous grid which will make your system unstable. So, this is what I mean by the large disturbance instability being disturbance dependent, but it always being an issue in a synchronous grid. So, just to look at just to reemphasize what I am trying to say transient stability if you look at this particular figure suppose you have got a multi machine system transient instability in a two machine system was in fact simulated if you look at the lecture number 38 or 39 you will find that we have actually simulated a two machine system in which you can have transient instability following a fault. So, let us just see a typical situation another typical situation where you could have transient instability. So, you have got a system in which there are four generators each of them say generating 1000 megawatt and you know you have got two loads or two low buses in which loads are actually you know accumulated that is 1000 megawatt and 3000 megawatt they are here at this bus and at this bus and since there is of course load generation balance is generating 4000 megawatt there is a load of 4000 megawatt. So, center of inertia frequency will be stable, but here of course we are assuming no losses are there the total load generation is balance, but you need to transfer 1000 megawatt from this system to that system because there is more load here than the generation here. Now, suppose these are typical situation you know there is a fault on one of these transmission lines. Now, if there is a fault on one of these transmission lines typically if your protection system is well designed and is operating well it will be detected quite soon enough and there will be circuit breakers will be opened at both ends of this transmission line and this fault gets cleared or de-energized. Now, once you trip open this lines this particular line on which is faulted you have to the load generation scenario of course is not changed in the meantime. So, what you will have effectively is that the power which is flowing through two lines will have to now flow through one line and what would be a steady state scenario would be this that 1000 megawatt flows through the remaining line, but the key issue here is this is the steady state scenario because the system is undergone a fault and a line tripping thereafter some transients will be you know created and the basic point is that the system moves from one equilibrium to another or rather there is a fault and the system deviates substantially from the original equilibrium the equilibrium itself changes or the question is whether the system will settle down to this new equilibrium. So, this is the equilibrium condition after a large disturbance, but the point is that you may either be stable and the power flow may go from the remaining in the remaining line from 500 megawatts to 1000 megawatts. So, the transient in this particular line earlier the power was 500 megawatts now it is 1000 megawatts under steady state the question is that you will of course have a transient initially 500 megawatts was flowing through the line then there was a fault. So, the power dips because the voltage would dip in the system the power flow dips in the line then the fault is cleared by tripping the line and the system tries to go to this new equilibrium and this is the response if the system is stable. So, you would say that the system is large disturbance stable for this particular disturbance and if you look at the generator speeds you will find that the generator speeds also the relative motion stabilizes after some time that is the speeds of all generators remains in synchronism what would happen if the system was not stable this is what would happen you would find that the generators speeds would deviate from each other one set would accelerate one set would decelerate and if you look at the power transients in the transmission line you will find these very large variations what we had discussed sometime back the power will start pulsating at a very with a very large magnitude and this is an unstable situation this is a large disturbance unstable situation. So, of course if you are unstable there is nothing you can do you have to disconnect the two systems remember the system are still connected. So, you need to disconnect the two systems otherwise the transient variations can be large enough to damage equipment. So, once you have tripped out or separated out the two systems you have formed two islands and you have the island one has more generation, but less load, but island two has less generation and more load. So, there will be a dual problem which you need to solve that is whether the system after you know this system islanding has taken place whether the individual two individual islands whether the center of center of inertia frequency within those islands is going to stabilize or not. So, we get a frequency stability problem after islanding has occurred of course the frequency can stabilize provided you have got mechanisms to ensure this load generation balance that is you have governing systems or under frequency load shedding schemes which ensure that there is generation load balance. For example, in island two you need to do quick load shedding in order to ensure that the island is stable otherwise you will in no time the frequency will drop down to such an extent in island two that you will have to trip out the steam turbine turbines and therefore, you will have a complete blackout in that region. So, you need to take quick actions after this if the system is unstable. So, how do we improve transient stability or large disturbance stability? Unlike you know the problem which we discussed in the previous class this is a large disturbance instability problem. In fact, by tweaking controls a little bit you know or having auxiliary controllers which modulate you know some voltage reference say of an automatic voltage regulator etcetera you may not be able to get you know improve upon this transient stability. Of course, you can make large changes in controllers you can have controllers you know kind of you can make controllers act in such a way that they actually improve transient stability as well. What do you mean by improving transient stability? For a given credible disturbance if the system is unstable you make changes in the system so that the system becomes stable. So, of course, when I say how do you improve transient stability it can mean three things. How do you improve transient stability in a system during planning? So, what do you do when you plan a system so that your system is transient stable see a planner knows the transient stability is always going to be an issue in a synchronous grid. So, when the system is being planned say for you know you know if you are doing short term or long term let us say talk about long term planning you are sure that you know some new generation is going to come up some new load loads are going to come up and you know you are going to have different kind of power flow scenarios in the system. A system planner what he does is he kind of predicts or forecast the kind of load and generation scenario and he carries out what is known as transient stability studies. What are transient stability studies? They are essentially simulation studies on how the system behaves following credible disturbances. So, there are set of disturbances or contingencies with which a planner will consider like loss of a major generating plant or a fault you know a three phase fault at a particular bus which is cleared by primary protection or a single line to ground fault at certain important buses which is cleared not by the primary protection, but by the backup protection or the loss of an HVDC pole. So, these kind of scenarios of worst you know kind of worst case but credible scenarios you know they should not be incredible scenarios. What do mean by incredible scenarios? You should not consider scenarios of disturbance scenarios which are very very unlikely to occur, but the loss of a transmission line following a fault is a very common occurrence you know in a given day you may find that you know at least three or four such events may take place in a large synchronous grid like in India. So, if you look at the disturbance reports which are you know put out by many of these utilities you will find that they have given you will find very not not infrequently there will be faults you know single line to ground faults and so on which is result in transmission line tripping and so on. These are large disturbances because when you have a fault for some duration the voltages everywhere come voltages go down there may be sudden changes. So, you can consider a fault is a very large disturbance. So, these things continually occur. So, for a credible disturbance is something which we which we think has got some reasonable probability that will occur. So, a planner system planner will try out many probable such probable contingencies and ensure that the system is stable even under stress conditions that is unusual load and generation patterns again credible patterns in which certain lines are loaded more or less. So, this kind of exercise is done in planning though sometimes you may a planner may find that for credible disturbances which he may simulate using a trans instability program that the system is not stable in such a situation he will think of augmenting the transmission system. So, he may think of for example, you know building a new transmission line he may in fact think of that that is a way of going forward. Now, how does you know of course, I have told you that you know whenever a system is not transiently stable I mean it is not stable for credible large disturbances one of the ways of improving stability is to strengthen the transmission system what is the basis of saying that. Now, if you look at to understand that we will consider a simple machine connected to an infinite bus through a say a reactance x this is a representation of a transmission line. You know that the power flow for an idealized or very simple model of a generator as a voltage source behind a reactance the power flow versus delta that is the phase angular difference between this generator this you know which is representative in some ways of the rotor position and this infinite bus is given by this power angle characteristic that is e e b sin delta by x plus x dash this is of course, the simplest model assuming that the generator is represented by classical model a transmission line by simple x network transients stator transients everything is neglected in that case you come to this power angle characteristic. And if you recall what you have done in your undergraduate years if you have got a system which has got say two transmission lines x and x in that case the power angle characteristically e b e b sin delta divided by x by 2 plus x dash because the two transmission lines in parallel. Now, if there is a fault here this is a typical kind of study which we did when we were undergraduates and studying power systems you give a fault on one of the transmission lines at one end the fault is detected and then cleared out. So, this is a typical fault or large disturbance scenario which we considered while trying to study trans instability. So, under normal operating conditions will be having this equilibrium condition here if there is a fault the electric this is of course, the mechanical power the intersection of the electrical power and the mechanical power defines the operating delta. Now, if there is a fault electrical power suddenly becomes equal to 0. So, the machine accelerates then the fault is cleared and you are have you are now left with only one transmission line because this trans faulted transmission line is tripped out. So, a post fault power angle characteristic will be like this it will be somewhere lower like this and one of the things we studied in our undergraduate years when we when we were attacking this problem was for such a scenario and for such simple single machine infinite bus system with a very simplified generator model one could show that if at the point of fault clearing your rotor angle had deviated due to the disturbance to this point delta then the system is stable if this area is more than this area. So, the system is stable if this area is more than this area this was called equal area criterion. So, although in this particular course in some sense we never use this criterion the emphasis of this course was you know trying to model a synchronous machine in more realistic kind of detail. So, we did not use such simple models to show loss of synchrony in fact, we did a two machine system simulation in which we gave a fault and then we showed that for a large enough fault the system is unstable we did not actually use equal area criterion to show that the system is unstable we did a simulation for large very large system to get quantitatively accurate results simulation may be the only way which you can assess stability quantitatively accurately that is what I mean, but from a conceptual or a roughly you know if you want to get a rough or approximate answer then one may use equal area criteria like analytical tools for simplified system models and get approximate you can approximately assess transient instability as done in this example. So, if you got a single machine infinite bus for this fault and a very simplified model the equal area criterion which is derived not in this course, but in the first course of power systems tells that this area if it is greater than this area then the system is stable and this can be said without simulating the system because this is a very simple system. Now, this equal area criterion although we have not used for getting quantitatively accurate results it can easily tell you what needs to be done in case you want to improve stability. So, we will use equal area criterion not to get exact quantitative results, but to suggest what can be done to improve stability. So, let us just talk of the planning option a planning option says is strengthen the transmission system what do I mean by that suppose my system had three lines instead of two in that case the power angle curve is enhanced because now you have got p is equal to electrical power is given by e e b sin delta x by 3 plus x dash this is really got enhanced this is the electrical power versus delta. So, for the same power flow if I give the same disturbance it is more likely that if there is of course, one line trip after a fault an equal area criterion would say after one line trip this becomes p e is equal to e e b sin delta by x by 2 plus x dash. So, now what you have got is a much more enhanced area because this is slightly enhanced compared to the earlier case in the earlier case the post fault of post fault power angle curve was e e b sin delta x plus x dash which is much lower. So, if I may say so the decelerating area in this case is much larger than the earlier case. So, it appears that if you strengthen the transmission line say by decreasing the reactance effective reactance of interconnection then it appears that you can improve transient stability. So, this is what I meant when I said you strengthen the transmission system you make another transmission line or alternatively you can do another thing you can take the same transmission system as before and compensate it by using series capacitors this will reduce x. So, using series capacitors is another way in which you can enhance transient stability. In fact of course, one interesting point is that if having series capacitors can under certain circumstances destabilize torsional oscillations in a synchronous turbine generator system this was what we called sub synchronous resonance not always sometimes it could happen, but anyway here we are talking of a distinct application where we are using series capacitors rather the series the use of the series capacitors is essentially to improve the transient stability of the system because the x is reduced. So, we are actually enhancing the power angle electrical power versus delta and therefore, having a larger decelerating area and as per equal area criterion which can give the stability behavior of a simple system by increasing this decelerating area where effectively ensuring that this area is greater than this area and therefore, for this disturbance the system will be stable. Let us look at the other you know way you can improve stability that is more obvious you reduce the you know extent of the disturbance itself. So, if your disturbance is cleared very fast then you will find that instead of being cleared here you are clearing it out here. So, this area reduces. So, you are clearing it earlier clearing I mean the fault is detected and the faulted element is removed before the variables deviate too much from the original equilibrium. So, if I am able to clear this fault a bit earlier I ensure that this area is smaller and this area is larger. So, the system becomes more stable. So, improving the protection system that is you know detecting the fault fast enough and tripping out the opening the circuit breaker at two ends of the faulted element would really if you do it fast enough one can improve stability. But of course, there are limitations to how fast you can do detection of a fault. Actually the problem is not so much about how fast you can detect a fault, but how fast you can detect it reliably. So, usually a relay will take about half a cycle to one cycle to reliably you know it reliably you know detect that there is actually a fault taken you know you for example, a relay should not trigger on noise or noisy input. So, typically a relay would a good relay would take a little bit of time and ensure that it does not trip out something on a false alarm. So, typically you know you can say the state of the art would be that at fault you know a fault on say an extra high voltage system would be detected in roughly you know between it will take approximately a cycle to detect reliably you can you can be sure that there is a fault. So, relay detects that there is a fault and not it is not a false alarm in about you know slightly less than one cycle to one cycle and then it gives a tripping command to a circuit breaker. The circuit breaker opening time also you know may be a cycle or two. So, the state of this is the you know the kind of best case situation. So, in three or four cycles you can expect that the fault will be cleared under the best case scenario. So, there are limitations to how fast you can do equipment protection it is already if you look at the state of the art in EHE systems you can clear out faults in three or four cycles. So, that is possible. So, there is a limitation on how much faster you can go than this. In fact, if you try to make it faster you may compromise in the sense that the you may have tripping due to false alarms you know due to noisy input or you know that kind of things can occur. So, you need to have a dependable kind of relaying system which does not trip on a false alarm it does not give a false alarm and trip out elements. So, there is a limitation to how much you can design fast protection schemes. So, this is essentially a design issue means you know you cannot make protection faster than a certain you know a certain time scale. The other way you can actually improve stability which is of course, not apparent directly apparent using equilibrium criterion is try to make proper use of your equipment. In the sense see for example, every synchronous machine has got an excitation system. The excitation system can you know is usually designed to have fairly large transient limits I mean you can actually have very high ceiling voltages or limiting voltages in a static excitation system. You can actually just for a few you know just for a short time you can actually inject you know fairly large field voltage. You can have a large voltage at the field applied at the field. Although typically under steady state conditions under say full load conditions in a say a round rotor machine you may have field voltage typically operating at around 2.5 to 3 per unit, but during transients you can actually boost up the field voltage to around 6 or 7 per unit plus or minus 6 or 7 per unit. This kind of range is given so that you can actually ensure a quick response time of the excitation system. Remember the field winding is a relatively slow subsystem. So, if you want to get fast response you have to really push it hard. That is why you have got rather large ceiling voltages for short duration. You cannot of course, apply very large field voltages like 6 or 7 per unit for a long time, but for short while you can boost up the field voltage and boosting up the field voltages to some extent like boosting the internal voltage of a synchronous machine and that is seen to improve the transient stability of the system. So, a very prudent use of the transient you know transient limits or the transient rating of the power system equipment seems to be a good idea. Another example of this is when you have got a synchronous grid which also has got an HVDC link embedded in it. So, if you got an HVDC link embedded in a synchronous grid it is a still a synchronous grid because you have got a parallel AC line connecting the generators and the two at the two sides of the system. The point is that in case for example, you have got a disturbance say these are two AC lines you have got a fault on this line and this line gets cleared. Now, there may be an issue of loss of synchronism. So, what normally is one of the good ways of ensuring transient stability is to temporarily boost up the power in the DC link. So, you boost up the power in the DC link and that can decelerate the two you know the angular deviation or the angular speed deviation between the two machines. So, this machine is accelerating and this machine is decelerating to transiently boost up the power in the HVDC link. Typically, an HVDC link also allows you a transient over heating for a very short while say half a second or 1 second you can boost up the power to a fairly large value. I mean for example, in 1000 megawatt HVDC link you may be able to go for just a second or so to 1500 or so megawatts that really could help in this transient. So, you could transiently boost up the power and ensure that the deviation between the machines is not too large. So, most HVDC links would have this feature of boosting power transiently during disturbances. So, these are two examples in which you can prudently use the transient capabilities of equipment controllable equipment to improve transient stability. The third way you can improve transient stability is through preventive control and emergency control. Preventive what do you mean by preventive control? Look at this. So, if you have got a system, we will again use equal area criterion. This is a pre-fault system. This is a power angle curve for the post-fault system. This is pre-fault. This is post-fault. I am sorry. So, typical equal area analysis suppose yields you these areas and you find that this area is less than this area you may be unstable. So, this is an approximate equal area kind of analysis. Now, so this is the system reactance x p is the p m is equal. So, electrical power output is equal to mechanical power output in steady state. So, p m is the steady state electrical power output of the generator. Now, if p m is large, you see for the given fault and clearing time, this area you is more than this area. Suppose this is the typical or a particular scenario which is there. Now, if p m is not so large, but operate the generator at not at this p m, but at p m dash which is less than p m. I can actually come to a situation where this area is more than this area. So, if I am during actual system operation, if the operator senses or you know by doing simulation studies realizes that is current operating condition is such or the mechanical power output of the generators, the load patterns etcetera as such. The system is transiently unstable for credible disturbances. Then, one of the ways he can actually improve it in this particular situation, single machine infinite bus situation, he can reduce p m. So, instead of operating at this operating point initially, you operate at this operating point. If you operate at this operating point, it is likely that the decelerating area will be more than the accelerating area and therefore, you can have for the same disturbance better stability. In fact, you may not lose stability or you may not lose synchronism for large disturbances. If your initial operating power is lesser. Now, in a multi machine system, you know suppose there is a initial power flow of 500 megawatt on both lines, this is 1000, this is 3000, this is the generation here is 4000 megawatts sorry 2000 megawatts here and 2000 megawatts here. Suppose, there is a fault, there is a line clearing for this clearing time, suppose you see that the system is unstable. Then, one way of improving stability is to decrease the initial power flow through this system. What it would mean of course, is to do some generation scheduling rescheduling. What you can do is instead of this being 2000, this being 2000, you can have this as 1500. So, you reduce this power output of this generator, increase the power output of this generator. Now, you have 250 megawatts flowing here and 250 megawatts flowing here and for this power flow scenario, it is possible that you may be transiently stable for this particular disturbance. For a single machine infinite bus, this can be easily understood from this you know these accelerating and decelerating areas. For a multi machine system, it would mean that the power flow through an interface can be reduced if it is seen that this system tends to separate across this interface. So, one of the ways of reducing transient instability is of course, trying to reduce power flow through interfaces. Of course, remember that whenever a system in a multi machine system or system loses transient instability, it can lose it in many ways in the sense that you can have different combinations of machines from in groups and separating out against other groups of machines. And which group separates against which other group or which machines constitute a group depends on the disturbance. So, that is one interesting and complicated challenge in the assessing transient instability. But, suppose I know that the system separates in such a way that this machine separates out from this machine in a two machine system there is no other way you can separate out. In that case, I know the interface you know between the you know the cut set you can say and you try to reduce the initial flow through the cut set you may improve stability. So, this is called preventive control wherein a system operator realizes that the system may not be stable for this particular disturbance and therefore, he reduces the interface flow at interfaces which characterize the accelerating and decelerating machines for that particular disturbance. So, this is called preventive control, but remember like the augmentation of a transmission system or adding a series capacitor in a transmission system. This will have an economic you know it will have an economic penalty in some sense in the sense that you are you can reduce or improve the transient stability in this case by rescheduling generation. Now, it may so occur that this may be a cheap generator and this may be a costly generator. So, by doing this you are incurring an economic penalty. So, improving transient stability is really going to require some amount of you know you know it will require us to spend a bit of money. So, if you want to be more secure you know you have to pay a bit of money that is a whole problem with transient stability in case you are unstable. The other way you know so you know actually when I say an operator does this he actually does it in the sense that he while a system is operating he actually gets the data from various remote measurements and he tries to evaluate the system state or the system operating condition every 10 seconds to 1 minute. Once he knows what the system you know operating condition of the system is after all he is sitting at a control center he is getting remote measurements from that he is inferring what is the operating condition what are the flows what are the phase angular differences for a particular operating condition. Now, once he gets this information what he does is runs transient stability simulation programs or variations of equal area kind of analysis to find out whether the system will be stable or not for credible disturbances. And if he finds that the system is stable for credible disturbances according to the simulated response he will flag the system state as being normal, but in case the system could go unstable if a credible disturbance were to occur then he will flag the state as alert in the sense that the system is operating an alert state and the system may lose instability if a credible disturbance were to occur at that operating condition. In such a case he will flag the system as an alert system condition and thereafter he will try to reschedule the power flows so as to reduce the interface power flows along certain interfaces which really characterize the separation of machines. For example, in a two machine system the interface the tie lines which connect the two machines really define the interface. So, he will try to reduce the power flow through the interface, but he will try to do it in such a way so that there is a minimum economic penalty in the sense that you lose lesser money by rescheduling or reducing cheaper power in increasing you know generation from costlier sources. Remember that the interface across which machines accelerate or decelerate depends on the disturbance itself. So, you know it would not be correct to say that he reduces a system operating operator he or she would reduce the power flow through the interface. There are many possible interfaces and depending on the disturbance for which the system goes unstable a particular interface power flow may be more critical and a system may a system operator may tweak around the load or even the mainly the generation schedule. So, that the system interface power through those interfaces reduces and thereby transition stability improves for that particular disturbance possible disturbance. This is called preventive control he may do it in an optimal way in the sense there may be many machines in one group many other machines in the other group and he may tweak around the power flows or the power schedule in such a way that is minimum economic penalty. So, that is called security constrain optimal power flow and he may be doing it every half an hour or so and this is the way a system is operated securely and as a result of which it is quite rare in a synchronous grade that you have got this transient a large disturbance instability problem. Although disturbances are continually occurring in a day they may be one or two major faults in a transmission system as in our country in a big power system as in our country, but you rarely the lights are always on that means that the system is operating stably. So, one of the beauties or one of the important things about the system operation power system operation is that it needs continuous monitoring and evaluation and assessment of stability and system operating changes will have to be made online in case the system operator senses that the system may go unstable for some credible disturbances. He senses it of course, not by actual sensing, but by simulating the system. So, there in we have he uses some numerical integration program which integrates numerically integrates the power system dynamical equations. Another way of course, this is of course, we can try to do improve stability is through emergency control that is you the emergency control also is called heroic action. You have you kind of predict or sense that an actual disturbances occurred and the system is going out of step in spite of preventive control. See of course, because of preventive control one does not expect that the system will go transiently unstable for a credible disturbance, but sometimes if there is a mistake or error in our assessment, because you have not a disturbance much more you know much larger in magnitude than has been anticipated in our simulations occurs. In that case preventive control may not be adequate the system operator would have sense that the system could be go unstable for a certain disturbance and he does some preventive control, but that preventive control is not adequate it is not adequately implemented say or the system as I said the system disturbance magnitude may be much more than what was considered in our simulation. In that case a system may actually go unstable in spite of all these precautions which were taken. In such a situation as the system is going unstable can we trigger certain control actions and get back the system and ensure that it does not go unstable this kind of thing is conceivable, but not easy. So, there are two possibilities that because of inadequate preventive control or inability to anticipate a very large disturbance which actually occurs eventually you may actually go out of step in that case you are going out of step as a system is evolving you have to predict that you are going out of synchronism and if you are going out of synchronism you trigger control actions like generation load tripping or use specialized devices like dynamic breaks I will not describe to you today what a dynamic break is you can do a search a literature survey on this and see what a dynamic break is it is a device to improve stability. So, you see that the system is going out of synchronism. So, you quickly take some actions and prevent the system going out of synchronism or allow graceful system separation you know allow islanding, but the thing is you allow you do not allow uncontrolled system separation what you do is you try to form islands you know which are controlled island formation you trip out certain lines and form islands. So, that there is good load generation balance in that area the island. So, that there is a greater possibility that the island survives. So, both these possibilities exist in this in the latter possibility you are allowing loss of synchronism, but you are separating out the areas and you are forming the areas based on some previous study which you have done that there is better load generation balance in this area. So, let us form an island consisting of these generators and these loads with the knowledge that the system is going out of synchronism, but of course you would be nice if the system did not go out of synchronism at all because that would involve no generation or load trippings, but the problem is how do you predict out of step operation in real time and how do you determine the quantum of control actions. In case you are going for separation of the system then how do you do the have a good adaptive choice of separation points. So, these are the kind of problems which may come up in emergency control remember that the time window in which you have in order to act is quite small just a few seconds you know 1 or 2 seconds you have to act and do this thing before otherwise you may not be left with you may be having unviable islands in which frequency collapses or rises beyond 51 or 52 hertz and that causes a complete black out. So, we have do not have much of time to really do this, but one can conceive and one can try to do the best under the circumstances and people have in fact if you look at this particular example just to show you that just by looking at the rotor angles for a short while you may not be able to tell what happens after some time. So, prediction is a very difficult problem this particularly this particular example shows a system simulation in which the system breaks into 3 groups of machines this can occur also. So, it really shows you are predicting instability is quite a tough problem just from available measurements to predict whether this how the system is going to behave in real time is really going to be tough in fact faster than real time you have to make a prediction and then take some control action. So, this kind of problem is a very very tough problem and robustness of emergency controls will always be a very big issue, but nonetheless such kind of emergency control schemes have been conceived in fact you have got several in the world in such kind of heroic actions in which you determine some kind of signatures of transient instability and then take some control actions to prevent instability that kind of thing is conceivable, but robustness will always be an issue under such circumstances. So, with this we kind of close our course and we have really discussed in this particular lecture ways of improving stability. If you just recap what we have done in this course we started off with the analysis general analysis techniques and then we spent quite a bit of time in modeling of synchronous machines and some other elements there after we did using simple systems small signal analysis numerical simulation and try to I try to show you some of the phenomena stability phenomena which can be analyzed. In fact one of the course of Einstein which which I did mention in the first lecture was that the most incomprehensible thing about this universe is that it is comprehensible. In some ways you can even apply this to a power system of course a power system is a part of the universe. So, obviously this code applies to it also, but what I mean to say is that by systematic analysis and use of analytical tools all these phenomena can actually be predicted all using synchronous machine model all the systematic modeling techniques and analysis techniques can allow you to analyze these kind of phenomena. And of course if you can analyze the phenomena you can often find out or predict or design ways of improving stability. So, in fact I did show you some real life disturbance plots etcetera in this course and all the stability most of the stability phenomena which you know which we discussed in this course. In fact all of them have actually been observed in practice and analyzed also and replicated using these analysis tools. So, this is what I would like you to take back with you after doing this course there are lot of things which we could not cover like you know we could not cover in detail how to make large scale power system analysis programs or large scale Eigen analysis programs small signal stability programs. But with the tools which you have learnt in this particular course and the model which you have learnt and the case studies which you have done in this course I hope it will be a good starting point to actually take on these studies although we could not cover it in this particular course. So, with that we end this course and I hope you