﻿1 00:00:16,460 --> 00:00:24,840 Welcome to lecture number five of module two. In this module, the name is equipment and 2 00:00:24,840 --> 00:00:31,390 stability constraints in power system operation. So, this lecture is completely related to 3 00:00:31,390 --> 00:00:37,790 the stability definition concepts and its fundamental. And we will see that what are 4 00:00:37,790 --> 00:00:43,579 the various stability concerns and their definitions, why they are very important for the power 5 00:00:43,579 --> 00:00:46,039 system operation and control. 6 00:00:46,949 --> 00:00:53,379 To introduce with this definition, let us see why this stability is required at all, 7 00:00:53,379 --> 00:00:59,600 the stability analysis I mean power system stability has been recognized as an important 8 00:00:59,600 --> 00:01:07,800 problem, for such operation of system since 1920’s. In 1920’s the first case of the 9 00:01:07,800 --> 00:01:15,580 system instability, and after that it has gain momentum, and now are having a lot of 10 00:01:15,580 --> 00:01:21,009 instability and instability analysis of the system, to say that system is stable or not. 11 00:01:21,009 --> 00:01:26,290 Historically, the transient instability has been the dominant stability problem on most 12 00:01:26,290 --> 00:01:33,439 systems, and has been the focus of much of the industry’s attention concerning system 13 00:01:33,439 --> 00:01:38,719 stability. In the early days, people were only recognizing the instability phenomenon 14 00:01:38,719 --> 00:01:44,689 is as a transient stability. So, they were concerning in terms of that analysis, their 15 00:01:44,689 --> 00:01:50,090 mitigation, and their other related issues on only the transient stabilities. 16 00:01:50,090 --> 00:01:55,409 But due to the increase inter connections, the stress power system; that is keep on loading 17 00:01:55,409 --> 00:02:02,070 and keep inter connections, the voltage stability as well as the frequency stability, that even 18 00:02:02,070 --> 00:02:07,549 though along with the inter area oscillations, had become greater concern than in the past. 19 00:02:07,549 --> 00:02:12,950 And as I said it is more and more due to the interconnections highly loaded and the complex 20 00:02:12,950 --> 00:02:17,920 power system. The voltage stability frequency stability and the inter area oscillations 21 00:02:17,920 --> 00:02:22,700 are also very important, and that is that is why we have to go for various stability 22 00:02:22,700 --> 00:02:30,190 analysis. A clear understanding of different types of instability, and how they are interrelated 23 00:02:30,190 --> 00:02:34,949 is essential for the satisfactory design, and operation of power systems. 24 00:02:34,949 --> 00:02:41,910 So, we have to understand what are the various instability problems, and how they are interrelated; 25 00:02:41,910 --> 00:02:46,560 that is very important for the power system design and operation; means you have to design 26 00:02:46,560 --> 00:02:51,630 a power system that should be stable, and you should operate your power system in stable 27 00:02:51,630 --> 00:02:57,530 manner ,along with other criteria already we had seen, that the power system design 28 00:02:57,530 --> 00:03:05,269 and operation criteria include your power system quality, power system security, stability, 29 00:03:05,269 --> 00:03:10,930 reliability, and also that we should operate the power system in the least economic rate, 30 00:03:10,930 --> 00:03:16,180 means economical fashion. So, the cost of electricity is cheap and uninterruptable, 31 00:03:16,180 --> 00:03:25,560 and it should be better usable in terms of customers use. As well consistent use of terminologies 32 00:03:25,560 --> 00:03:31,709 is required, for developing system design and operating criteria, standard, analytical 33 00:03:31,709 --> 00:03:34,799 tools, and study procedures. 34 00:03:34,799 --> 00:03:40,769 So, the problem of defining and classifying, power system stability has been addressed, 35 00:03:40,769 --> 00:03:47,840 by several previous CIGRE and IEEE task force reports. Here, IEEE this institution of Electrical 36 00:03:47,840 --> 00:03:52,280 and Electronics Engineers task force. So, they have already defined, but again it is 37 00:03:52,280 --> 00:03:58,489 keep on reviewing this. And again those early days, means these earlier efforts; however 38 00:03:58,489 --> 00:04:06,549 do not completely reflect, the current industry needs up to now. So, we have to go for the 39 00:04:06,549 --> 00:04:15,169 clear definition again, based on the industry needs, experiences, and the understanding. 40 00:04:15,169 --> 00:04:20,780 In particular the definitions are not precise, because in the previous definitions were not 41 00:04:20,780 --> 00:04:28,840 precise. And the classification do no encompasses, all practical instability scenarios. As I 42 00:04:28,840 --> 00:04:34,500 said in the beginning, only we were concerned about the transient stability. Later on we 43 00:04:34,500 --> 00:04:39,740 introduce the transient stability, steady state instability, and also the voltage instability, 44 00:04:39,740 --> 00:04:45,409 but now a days again some more instability, and their basis may be a time frame depends 45 00:04:45,409 --> 00:04:51,050 upon the disturbance nature and so on so forth. So, we have to define and understand the various 46 00:04:51,050 --> 00:04:56,669 instability and stability phenomena’s in the power system. So, that is why this has 47 00:04:56,669 --> 00:05:02,349 created a need to review the definition, and classification of power system stability. 48 00:05:02,349 --> 00:05:09,639 So, we want the power system stable; in terms of designing, in terms of operation. So, whatever 49 00:05:09,639 --> 00:05:15,830 the kind of instability in the power system, is that must be reduced, that must be removed, 50 00:05:15,830 --> 00:05:22,430 so that we can have secure and stable operation of the power system. If you will see the power 51 00:05:22,430 --> 00:05:28,689 system stability old definition, as per the, it is the property of a dynamical system or 52 00:05:28,689 --> 00:05:35,139 its ability, to remain in state of operating equilibrium. This is very important operating 53 00:05:35,139 --> 00:05:41,990 equilibrium, under the normal operating condition, and to regain an acceptable state of equilibrium 54 00:05:41,990 --> 00:05:46,240 another equilibrium here, after being subjected to a disturbance. 55 00:05:46,240 --> 00:05:52,229 To understand this let us see here, let us suppose in a multi here directional plane, 56 00:05:52,229 --> 00:05:59,330 you are here your power system is operating at this point. So, this point is stable, initially 57 00:05:59,330 --> 00:06:05,759 in the normal condition. And if there is a disturbance in the system, and your system 58 00:06:05,759 --> 00:06:12,599 is moving to another system, here that is also stable. But there is a possibility that 59 00:06:12,599 --> 00:06:20,430 this trajectory, this state is stable this state is stable, but it may not always possible 60 00:06:20,430 --> 00:06:26,819 that the transition from this stable, stable A to this stable B is possible. So, it may 61 00:06:26,819 --> 00:06:31,669 be possible that, this may go for somewhere else, and then we can say our system is unstable. 62 00:06:31,669 --> 00:06:39,129 We know that this is you pre fault condition; initial normal condition where your system 63 00:06:39,129 --> 00:06:46,169 is operating, if there is any disturbance, then your system should go to another stable 64 00:06:46,169 --> 00:06:49,560 point B. B may be the different, again it depends upon 65 00:06:49,560 --> 00:06:54,219 the system scenario, change in the topology, change in the generation and the load scenario. 66 00:06:54,219 --> 00:06:58,749 It may be the same A point of course, but the disturbance one it is clear, then your 67 00:06:58,749 --> 00:07:04,749 system must go to your another stable point B, then we can say the system is stable, if 68 00:07:04,749 --> 00:07:11,659 it is coming to this point here through any region, but there is a possibility that this 69 00:07:11,659 --> 00:07:16,849 point no doubt the post disturbance is stable. Your initially stable, but your system can 70 00:07:16,849 --> 00:07:22,509 go somewhere else. It is not coming to your stable point, because it is time which is 71 00:07:22,509 --> 00:07:27,710 coming keep on going, and finally, it is unstable. So, here that is why it is a definition it 72 00:07:27,710 --> 00:07:33,479 is said, that your operating equilibrium under the normal operating conditions, means initial 73 00:07:33,479 --> 00:07:39,139 condition. Your system is in the equilibrium point, and it should regain or acceptable 74 00:07:39,139 --> 00:07:47,809 state of equilibrium after subjected to disturbance. So, it should come here stable then we can 75 00:07:47,809 --> 00:07:52,409 say our system is table, if this is not then it will be go away. 76 00:07:52,409 --> 00:07:58,509 Now, the new definition has been given recently, there was again another IEEE task force. It 77 00:07:58,509 --> 00:08:03,309 gives again concise definition of the power system stability. It includes all the stability 78 00:08:03,309 --> 00:08:09,289 concern, and the various stable analysis techniques are given in that paper, and this is again 79 00:08:09,289 --> 00:08:14,909 this committee was headed by the Prabhakundur, and even though we can see his book by stability 80 00:08:14,909 --> 00:08:21,069 is very. He defined all the stability in the very precise manner. So, as per new definition 81 00:08:21,069 --> 00:08:27,479 the power system stability, is the ability of an electric power system for a given initial 82 00:08:27,479 --> 00:08:31,860 operating. Here they have written the initial. Earlier it was the normal operator. Normal 83 00:08:31,860 --> 00:08:37,250 means the system at which your system is operating. So, it is better to say that the initial operating 84 00:08:37,250 --> 00:08:44,300 condition to regain a state of operating equilibrium, after being to a physical disturbance. Again 85 00:08:44,300 --> 00:08:51,650 the physical disturbance is of different types again there may be some fault, some loss of 86 00:08:51,650 --> 00:08:56,110 load, something happening you can say some loss of power, transmission line tripping, 87 00:08:56,110 --> 00:09:01,600 short circuit etcetera. So, if there is any disturbance, then it should regain another 88 00:09:01,600 --> 00:09:08,070 stable operating equilibrium, with the most system variable bounded, so that practically 89 00:09:08,070 --> 00:09:14,380 the entire system remains intact. So, your system should not lose the synchronous, 90 00:09:14,380 --> 00:09:23,440 and it should be in stable condition. The stability basically, depends. Now realize 91 00:09:23,440 --> 00:09:30,400 depends upon here initial operating condition, and the nature and the amount of disturbance, 92 00:09:30,400 --> 00:09:36,550 again the amount of which type. For example of a small change in the load is another type. 93 00:09:36,550 --> 00:09:40,940 There may be a severe load change. There may be small change in generation. There may be 94 00:09:40,940 --> 00:09:45,250 severe change in the generator; means suppose there is a one generator is out. another the 95 00:09:45,250 --> 00:09:50,470 nature, it may be the power outage, it may be load change, it may be the short circuit, 96 00:09:50,470 --> 00:09:54,020 it may be the tripping of the transmission line, it may be the tripping of any other 97 00:09:54,020 --> 00:09:59,830 equipment in the power system. So, the stability in total depends upon the initial state, where 98 00:09:59,830 --> 00:10:04,510 your system is operating right now, although it is no doubt it is stable, but at what label, 99 00:10:04,510 --> 00:10:10,200 means at which point how close to the instable position, and then the nature and the amount 100 00:10:10,200 --> 00:10:17,040 of the disturbance. We saw this power system security as well in our beginning lectures 101 00:10:17,040 --> 00:10:23,650 in module one; what is power system security. So, to recap it security is a system use to 102 00:10:23,650 --> 00:10:30,490 reflect a term power system stability, to meet its load demand, without unduly stressing 103 00:10:30,490 --> 00:10:37,500 its apparatus, or allowing network variable to stray from the prescribed range. 104 00:10:37,500 --> 00:10:48,030 Here this security is one step ahead. There is a possibility that your system here. For 105 00:10:48,030 --> 00:10:54,320 example, simple you are here, you are operating at here the voltage, well with your limit 106 00:10:54,320 --> 00:11:00,160 and your system is stable. Now, after the fault, after the disturbance you have to reached 107 00:11:00,160 --> 00:11:09,210 another point D, where this your V is not, means here this is you are not satisfying 108 00:11:09,210 --> 00:11:17,990 its limit; that is V limit upper, and here it is your V lower limit. So, system is stable, 109 00:11:17,990 --> 00:11:23,570 but it is violating the operating constraints. In this case I have taken the voltage, it 110 00:11:23,570 --> 00:11:27,880 may be your line flows, it may be the overloading of line flow as well, it may be violation 111 00:11:27,880 --> 00:11:33,990 of the reactive power limit and so on so forth. So, this pong is stable, this point is stable. 112 00:11:33,990 --> 00:11:40,420 In terms of stability we can say our system is stable, but in terms of security here this 113 00:11:40,420 --> 00:11:44,240 point is stable, this point is stable, but system is not secure. 114 00:11:44,240 --> 00:11:50,790 So, it is one step ahead, where we have to check the operating limits as well that it 115 00:11:50,790 --> 00:11:58,160 should be well within limit. So, that is your power system security. So, already we define 116 00:11:58,160 --> 00:12:02,540 the power system security, and we get the different kinds of security in terms of line, 117 00:12:02,540 --> 00:12:06,930 or megawatt security, or reactive power or voltage security, and then we have get the 118 00:12:06,930 --> 00:12:11,260 several states based on the security; that is normal state security state, alert state, 119 00:12:11,260 --> 00:12:19,030 emergency state restore it even so on so forth. So, you can see security is one step ahead 120 00:12:19,030 --> 00:12:27,450 than your stability. Now, this power system stability again can be classified in the different 121 00:12:27,450 --> 00:12:32,020 way different, again depends upon the quantity which were monitoring, and that can be one 122 00:12:32,020 --> 00:12:37,620 is your angle, another here that is called your angle. It may be your frequency it may 123 00:12:37,620 --> 00:12:39,200 be your voltage. 124 00:12:39,200 --> 00:12:45,860 So, if your monitoring quantity is your angle, then it is called your rotor angle stability. 125 00:12:45,860 --> 00:12:51,760 Means monitoring means what, I am just going to say means this parameter is more concern, 126 00:12:51,760 --> 00:12:57,910 than other these two parameters, then we can say this is rotor angle stability. And you 127 00:12:57,910 --> 00:13:03,180 know this rotor angle stability is directly angle, here this is related with directly 128 00:13:03,180 --> 00:13:09,060 your real power flow; however, this voltage is directly related your reactive power, you 129 00:13:09,060 --> 00:13:15,630 will see later. So, the rotor angle stability is a ability of interconnected synchronous 130 00:13:15,630 --> 00:13:24,280 machines of a power system, to remain in synchronism after being subjected to a disturbance. So, 131 00:13:24,280 --> 00:13:30,010 whenever there is a disturbance to your whole operating system, including your synchronous 132 00:13:30,010 --> 00:13:35,030 machines, your whole intact system must be in synchronous, then we can say it is rotor 133 00:13:35,030 --> 00:13:38,040 angle instability of the system. 134 00:13:38,040 --> 00:13:45,030 Now, what is the voltage. Here out monitoring quantity is the voltage rather than delta. 135 00:13:45,030 --> 00:13:52,430 So, the voltage stability is the ability of the system, to maintain voltage, so that when 136 00:13:52,430 --> 00:14:00,050 load admittance is increased load power will increase, and so that both voltage and power 137 00:14:00,050 --> 00:14:09,870 are controllable. What is voltage stability. To understand this is very. If you will see 138 00:14:09,870 --> 00:14:15,050 the two bus system, this is your real power, this is your voltage, and if you draw the 139 00:14:15,050 --> 00:14:20,440 Pv curve we will come to this voltage stability in detail, in later lectures of this module 140 00:14:20,440 --> 00:14:27,430 will come detail. So, better to understand here, let us see a voltage variation. We have 141 00:14:27,430 --> 00:14:33,350 our system let us suppose our generator, and here we have a transmission line, and this 142 00:14:33,350 --> 00:14:39,550 is your infinite bus, or you can say here we have a load here. So, we can draw the power 143 00:14:39,550 --> 00:14:43,910 which is flowing here, it will keep on increasing that will that is here load, then the voltage 144 00:14:43,910 --> 00:14:49,800 at this terminal this is your side bus this V as we can draw as per this characteristic, 145 00:14:49,800 --> 00:14:55,920 what does it mean. It shows that for one power. Let us suppose P naught here you have two 146 00:14:55,920 --> 00:15:00,900 voltages here as well as here; one voltage here, another voltage. Now which one is your 147 00:15:00,900 --> 00:15:07,530 operating voltage which zone is stable, which zone is unstable, you can see the top most. 148 00:15:07,530 --> 00:15:13,100 When the power is increasing your voltage is decreasing; that is obvious, but in this 149 00:15:13,100 --> 00:15:17,690 case you can see if your power is increasing the lower portion, this point is called nose 150 00:15:17,690 --> 00:15:23,790 point. So, the lower portion power is increasing voltage is increasing. So, this is a reverse 151 00:15:23,790 --> 00:15:31,290 one. And here what is happening, your admittance is increase when your load power is increase. 152 00:15:31,290 --> 00:15:38,730 So, this zone, the lower section here is called unstable, and it is you can say the voltage 153 00:15:38,730 --> 00:15:44,630 instability in this zone only operating voltage will be in this zone. So, this related with 154 00:15:44,630 --> 00:15:50,400 the voltage, when we monitor the quantity, where the quantity of concern is much voltage 155 00:15:50,400 --> 00:15:57,860 than your delta and the frequency, then it is called voltage stability. Another term 156 00:15:57,860 --> 00:16:02,310 is widely used; that is voltage collapse, people say the system is collapse or black 157 00:16:02,310 --> 00:16:08,050 out, whether due to the angle stability, or whether due to the voltage. So, the voltage 158 00:16:08,050 --> 00:16:15,180 collapse is the process by which voltage in stability leads to a black out, or very low 159 00:16:15,180 --> 00:16:22,420 voltage profile in a significant part of the system. Means when the system voltage go beyond 160 00:16:22,420 --> 00:16:29,150 its permissible limit, and it is persisting for a longer time, and then it is called the 161 00:16:29,150 --> 00:16:35,320 voltage collapse. It nearly to some times, the black out in that area. So, this is your 162 00:16:35,320 --> 00:16:40,680 voltage collapse definition. Now, in the frequency stability, as I said 163 00:16:40,680 --> 00:16:47,290 the three terms; delta, voltage, and frequency. So, the delta is related to your angle stability, 164 00:16:47,290 --> 00:16:52,630 voltage related to your voltage stability, and the frequency is related to your frequency 165 00:16:52,630 --> 00:16:59,190 stability. No doubt the delta and the frequency are directly related with the real power; 166 00:16:59,190 --> 00:17:03,990 however, there voltage is related to your reactive power. When we are just talking about 167 00:17:03,990 --> 00:17:08,750 the delta, we are observing the delta of the machines, it is basically angle of stability, 168 00:17:08,750 --> 00:17:13,770 when we are talking the frequency, where the delta everything is in normal state, but frequency 169 00:17:13,770 --> 00:17:19,689 is changing; that is severely, then it is your frequency stability. So, the frequency 170 00:17:19,689 --> 00:17:26,220 stability refers to the ability of a system, to maintain steady state frequency, following 171 00:17:26,220 --> 00:17:34,590 a severe system upset, resulting in a significant imbalance between generation and load. Basically, 172 00:17:34,590 --> 00:17:42,139 the frequency stability is concerned with this imbalance in the power. Means this instability 173 00:17:42,139 --> 00:17:49,580 occur, when there is a severe search, severe outage of your system generation and etcetera. 174 00:17:49,580 --> 00:17:54,899 So, what normally we do, we go for the islanding of the power system. So, there may be a possibility 175 00:17:54,899 --> 00:18:00,669 one island may not having the balance reserves, balance supply, and that may have the frequency 176 00:18:00,669 --> 00:18:07,289 instability. So, this is basically the severe faults whenever arise, then the frequency 177 00:18:07,289 --> 00:18:12,639 instability term comes into picture. 178 00:18:12,639 --> 00:18:18,370 let us see the, again the voltage stability voltage instability and the voltage definition 179 00:18:18,370 --> 00:18:29,440 as per the CIGRE. Voltage stability; a power system at given operating state, and subject 180 00:18:29,440 --> 00:18:36,580 to a given disturbance, disturbance includes your fault, may be variety of faults you know, 181 00:18:36,580 --> 00:18:44,110 is align to ground fault l l fault triple l fault. So, all the varieties of faults, 182 00:18:44,110 --> 00:18:49,950 tripping of the heavily loaded transmission line, outage of power generators. So, all 183 00:18:49,950 --> 00:18:58,370 these are the disturbances, is voltage stable, if voltage is near the load approach post 184 00:18:58,370 --> 00:19:05,330 disturbance equilibrium values. The disturbed state is within the region of attraction of 185 00:19:05,330 --> 00:19:11,279 stable, post disturbance equilibrium. Means here once the disturbance is there initially 186 00:19:11,279 --> 00:19:17,450 your system is operating in the instable mode, without violating the voltage, and after the 187 00:19:17,450 --> 00:19:24,809 disturbance. if the voltage is also well within limit, then it is called, and that equilibrium 188 00:19:24,809 --> 00:19:30,759 is must be stable, then we can say it is a voltage stable, and your system is, voltage 189 00:19:30,759 --> 00:19:34,809 stability is there. However, the instability the voltage of the 190 00:19:34,809 --> 00:19:39,499 instability. The voltage instability is the absence of voltage instability means there 191 00:19:39,499 --> 00:19:45,379 is no voltage instability and result in progressive voltage decrease or increase in both side. 192 00:19:45,379 --> 00:19:52,059 There may be voltage excessive increase. There may voltage decrease. Destabilizing controls 193 00:19:52,059 --> 00:19:57,490 reaching limit are other control actions line load connection load shedding; however may 194 00:19:57,490 --> 00:20:03,620 establish the global stability. Here in the voltage instability what happens. There is 195 00:20:03,620 --> 00:20:11,179 a possibility that the voltage of the fewer area, certain zone may increase, or decrease 196 00:20:11,179 --> 00:20:17,549 heavily, and that may destabilize the control actions. You know we have a lot of devices 197 00:20:17,549 --> 00:20:23,269 those are working on the voltage measurement. If the voltage is less, so under voltage really 198 00:20:23,269 --> 00:20:27,200 may operate picked up, and they may give you trip support command to the load shedding 199 00:20:27,200 --> 00:20:30,970 etcetera, because we under voltage or under frequency, the release are there, and they 200 00:20:30,970 --> 00:20:37,220 are normally go for load shedding etcetera. So, it may go for the load disconnection, 201 00:20:37,220 --> 00:20:40,990 then what will happen, then it is called the voltage instability. Means voltage has gone 202 00:20:40,990 --> 00:20:47,330 excessively down, or higher than its prescribed limit. So, the voltage collapse as per CIGRE 203 00:20:47,330 --> 00:20:52,860 definition, the following voltage instability, a power system undergoes voltage collapse, 204 00:20:52,860 --> 00:20:59,649 if the post disturbance equilibrium voltages near loads are below acceptable limits. Acceptable 205 00:20:59,649 --> 00:21:06,860 limits, here it is not only this operating limits. We can operate the system, smoothly 206 00:21:06,860 --> 00:21:13,779 even though outer than you voltage limit. As I said, the voltage limit here should be 207 00:21:13,779 --> 00:21:20,629 plus minus five percent, for ehb line, but in the voltage here is more than six seven 208 00:21:20,629 --> 00:21:25,570 eight percent it will not hamper your system stability your system can operate, but we 209 00:21:25,570 --> 00:21:30,690 do not want to operate, because that is a station that may lead to the instability phenomena 210 00:21:30,690 --> 00:21:36,379 later on. So, it is the acceptable limits normally it is again depends upon the system 211 00:21:36,379 --> 00:21:42,049 to system, how stress your system, at what loading your system is operating that is defined. 212 00:21:42,049 --> 00:21:48,360 So, the voltage collapse in a system may be either total; that is total black out or it 213 00:21:48,360 --> 00:21:55,539 is a partial. Partial again it is a confuses, and for whole let us suppose for our Indian 214 00:21:55,539 --> 00:22:02,529 case, we have the as I said in the previous lectures, that we have the five regions, we 215 00:22:02,529 --> 00:22:08,899 have the northern NREB northern regional electricity board, we have eastern regional electricity 216 00:22:08,899 --> 00:22:13,669 board, we have western, we have southern, we have north eastern as well as the eastern. 217 00:22:13,669 --> 00:22:19,440 We have five regions. So, in all the regions other states are connected, like in northern 218 00:22:19,440 --> 00:22:25,600 Uttar Pradesh people are connected in the northern region, it is your Rajasthan, Haryana, 219 00:22:25,600 --> 00:22:32,580 Punjab, Jammu and Kashmir, and Himachal Pradesh, of course Delhi is also inside that. So, they 220 00:22:32,580 --> 00:22:38,049 are connected. So, what happens, there may be possibility that few portion of whole this 221 00:22:38,049 --> 00:22:44,070 northern region is in out, means in dark black out. So, it is called the partial. If whole 222 00:22:44,070 --> 00:22:49,220 this region has gone, then it is a complete black out, even though some of the feeders, 223 00:22:49,220 --> 00:22:53,940 those are feeding to some village, some area, some municipality, something your urban area, 224 00:22:53,940 --> 00:22:58,440 and that feeder has gone due to the instability and the problem then it is called the partial. 225 00:22:58,440 --> 00:23:03,779 So, your this voltage collapse may be your partial or complete, again it is due to the 226 00:23:03,779 --> 00:23:08,730 voltage if it is beyond acceptable limits. 227 00:23:08,730 --> 00:23:15,600 So, the stability general definitions, let us see what is the stability phenomena. Basically 228 00:23:15,600 --> 00:23:23,990 the stability, is can be defined, can be understood by looking at the condition of equilibrium 229 00:23:23,990 --> 00:23:31,470 of two opposite forces. So, stability phenomena, basically can be realize by understanding 230 00:23:31,470 --> 00:23:38,629 the condition of equilibrium between two opposite forces, to understand this, here for any system 231 00:23:38,629 --> 00:23:38,899 here. 232 00:23:38,899 --> 00:23:43,909 Let us suppose you have a mass here, this let us suppose it is rotating. So, to hold 233 00:23:43,909 --> 00:23:49,409 it if one direction of torque is this, and another is opposite, then it will not rotate 234 00:23:49,409 --> 00:23:53,860 and their system will be intact, simple for one revolving. If you are having one force 235 00:23:53,860 --> 00:23:59,239 here, then it will keep on moving in unidirectional, but if you have another force, that you is 236 00:23:59,239 --> 00:24:04,629 trying to resist it and if both are equal. Here let us suppose your T 1 and your is the 237 00:24:04,629 --> 00:24:10,779 T two. If your T 1 is equal to the T two, then we say the system is stable, it is not 238 00:24:10,779 --> 00:24:16,340 moving. If one force is there, another force is opposite, but there is a possibility if 239 00:24:16,340 --> 00:24:23,100 anyone of this is increasing or this equation is not satisfied, it is not this, then it 240 00:24:23,100 --> 00:24:28,980 will be adding one motion in any direction. Here, again if T 1 is more than T 2 it will 241 00:24:28,980 --> 00:24:34,190 be rotating in this direction otherwise T two. So, it is basically the equilibrium condition 242 00:24:34,190 --> 00:24:40,019 of two opposing forces. During the steady state, the mechanical torque 243 00:24:40,019 --> 00:24:47,600 is equal to electrical torque. Now come to the machine part normally this T 1 is nothing, 244 00:24:47,600 --> 00:24:54,070 but your Tm and this is your Te. Tm is the, in any machine. Here let us suppose your synchronous 245 00:24:54,070 --> 00:25:01,769 machine here, what happen here we give here you are the mechanical power and we get out 246 00:25:01,769 --> 00:25:08,019 electrical power. Means the power once the system is rotating, is the rotating the mass 247 00:25:08,019 --> 00:25:14,139 and this power we can say we have the torque, that mechanical torque, and here we are getting 248 00:25:14,139 --> 00:25:20,730 the electrical torque. So, if both during the steady state, the Tm is equal to your 249 00:25:20,730 --> 00:25:26,919 Te, and then it is called the steady state. But during the disturbance, this relation 250 00:25:26,919 --> 00:25:34,029 may not satisfy. And again I have one system is stable we will get this condition satisfy. 251 00:25:34,029 --> 00:25:39,649 So, during the disturbance period, when this is not satisfying, what will be the system 252 00:25:39,649 --> 00:25:44,799 behavior, and that is basically we have to study the behavior of the system during that 253 00:25:44,799 --> 00:25:47,830 one. Means we have the three conditions; one is 254 00:25:47,830 --> 00:26:00,509 called your pre fault condition, another is during fault condition, and third one is your 255 00:26:00,509 --> 00:26:10,350 post fault. So, these conditions, here the pre fault conditions it is satisfying this 256 00:26:10,350 --> 00:26:17,379 Tm is equal to Te. Your post fault must also satisfy this, if it is not satisfying, means 257 00:26:17,379 --> 00:26:23,159 your post fault system is not in equilibrium condition. So, the pre fault and the post 258 00:26:23,159 --> 00:26:30,360 fault is in equilibrium condition, but during the fault, means as I said in the multi directional 259 00:26:30,360 --> 00:26:38,029 here, multi variable space, your point here is the pre fault condition is A, the post 260 00:26:38,029 --> 00:26:44,559 fault condition here is B now during fault, whether your system is coming here, with the 261 00:26:44,559 --> 00:26:49,720 following trajectory or it is going somewhere else are unstable condition. So, basically 262 00:26:49,720 --> 00:26:55,659 the stability phenomena, is related with what is the condition here, it is also very much 263 00:26:55,659 --> 00:27:00,409 depends upon what is the condition of your pre fault, what is your condition of your 264 00:27:00,409 --> 00:27:05,119 post fault, and during what is your condition, what is your system behavior. 265 00:27:05,119 --> 00:27:11,809 So, we try to analyze these trajectories, if you can get this trajectory in this time 266 00:27:11,809 --> 00:27:21,220 domain. Then we can say and we can just whether system is stable or unstable. So, the change 267 00:27:21,220 --> 00:27:27,929 in electrical torque of synchronous machine, following perturbation or disturbance, can 268 00:27:27,929 --> 00:27:32,690 be resolve into two components, that the two components that change in the electrical terms. 269 00:27:32,690 --> 00:27:38,350 Whenever there is a fault in the system as I said here, there is a some fault in the 270 00:27:38,350 --> 00:27:42,049 system, let us suppose this is generator, and it is connected with your power system, 271 00:27:42,049 --> 00:27:48,659 if there is any fault in the system, this Pe or you can say Te will be changed. 272 00:27:48,659 --> 00:27:59,840 So, the change in this change in this Te, will be related with this equation, means 273 00:27:59,840 --> 00:28:06,179 we have two component; one component is called the synchronizing component, this is your 274 00:28:06,179 --> 00:28:12,059 synchronizing component, or synchronizing torque, and another is your damping torque. 275 00:28:12,059 --> 00:28:19,039 The damping torque; that is Td here, it is in the phase with the change in the speed 276 00:28:19,039 --> 00:28:25,059 deviation. How about your synchronizing torque; that is in phase with your angle deviation 277 00:28:25,059 --> 00:28:31,649 difference in angle. So, the lack of sufficient synchronizing torque, results instability, 278 00:28:31,649 --> 00:28:41,200 through a periodic drift in the rotor angle. Means if there is a lack of your synchronizing 279 00:28:41,200 --> 00:28:48,659 torque Ts, then it will give you this change in delta which is moving. And it is aperiodic, 280 00:28:48,659 --> 00:28:53,330 means you system here like this, it may be form here it may go like this. It will be 281 00:28:53,330 --> 00:29:01,999 not, you can say not oscillating in nature. So, it is aperidoic drift in aperiodic change. 282 00:29:01,999 --> 00:29:10,269 Another component is your Td del omega is the damping torque, and this damping torque 283 00:29:10,269 --> 00:29:15,519 basically if there is a insufficient damping torque, then it will result in the oscillatory 284 00:29:15,519 --> 00:29:21,960 instability. Means your system here will be what will be going, it will be keep on increasing, 285 00:29:21,960 --> 00:29:26,950 and it will be oscillating, because it is a change in the speed here, and means change 286 00:29:26,950 --> 00:29:31,499 in the delta means, if speed is changing, so change in delta also there. So, the rotor 287 00:29:31,499 --> 00:29:39,869 angle instability can be categorized into the two, based on the large or smaller disturbance, 288 00:29:39,869 --> 00:29:46,429 and those are here I can say small signal or we will see the transient stability. 289 00:29:46,429 --> 00:29:52,769 There are two types of rotor angle instability; one is your small signal instability. Basically 290 00:29:52,769 --> 00:29:59,749 in this we analyze with the small disturbance. Small disturbance is nothing, but change in 291 00:29:59,749 --> 00:30:06,169 your load, and change in generation, this is small, but the certain amount is small, 292 00:30:06,169 --> 00:30:10,769 but the certain change, and it is always happen in the power system, because in the power 293 00:30:10,769 --> 00:30:15,779 system, you know this load it is keep on changing, and generation is following that. So, generation 294 00:30:15,779 --> 00:30:21,029 and load are keep on changing and that is always there in the system. So, we have to 295 00:30:21,029 --> 00:30:27,889 analyze the behavior of the system with these changes, and that is always there. So, the 296 00:30:27,889 --> 00:30:35,340 small signal also known as by small disturbance stability, is ability of power system to maintain 297 00:30:35,340 --> 00:30:40,899 synchronism under small, but sudden. So, that is why here I am saying it is a small, but 298 00:30:40,899 --> 00:30:47,739 sudden disturbances, and those are always present due to the change in load and generation. 299 00:30:47,739 --> 00:30:56,369 In this case the system equations are linearized due to small disturbance, means we have to 300 00:30:56,369 --> 00:31:00,480 linearize as you know the power system is non-linear equation, non-linear phenomena. 301 00:31:00,480 --> 00:31:09,210 So, those non-linearity can be linearized, and then stability can be studied. Instability 302 00:31:09,210 --> 00:31:16,720 that may result can be of two forms; means again it can be two forms; one is the steady 303 00:31:16,720 --> 00:31:22,549 increase in the rotor angle, due to lack of synchronizing torque. As I said the synchronizing 304 00:31:22,549 --> 00:31:30,139 torque that is your Ts here delta S, and another is your rotor oscillation of increase amplitude 305 00:31:30,139 --> 00:31:36,249 due to the lack of sufficient damping torque; that is Te delta omega. So, it can be due 306 00:31:36,249 --> 00:31:41,970 to this region or it can be with this region. So, this is no doubt it is oscillating, and 307 00:31:41,970 --> 00:31:48,119 you can here, it is keep on increasing with the oscillation and system become unstable. 308 00:31:48,119 --> 00:31:53,820 Here your angle basically keeps on drifting to change in delta continuously or it is over 309 00:31:53,820 --> 00:31:57,970 periodic change, and that is due to the lack of synchronizing torque. 310 00:31:57,970 --> 00:32:07,580 Normally the first one; means if you see without AVR, the constant field voltage the instability 311 00:32:07,580 --> 00:32:13,309 is due to lack of sufficient synchronizing torque; that is non-stability. So, the previous 312 00:32:13,309 --> 00:32:21,229 as I said the lack of synchronizing torque, will give your over periodic drift of the 313 00:32:21,229 --> 00:32:27,080 rotor angle, if there will be no AVR automatic voltage regulators, but now a day’s modern 314 00:32:27,080 --> 00:32:32,590 power system, they are having automatic voltage regulators. So, that type of concept here, 315 00:32:32,590 --> 00:32:39,279 this is normally is not happening. So, only the small signal stability, is of this concern, 316 00:32:39,279 --> 00:32:47,960 and we always go for the oscillatory type of instability appears. So with the AVR that 317 00:32:47,960 --> 00:32:51,570 is automatic voltage regulators means excitation system, automatic voltage regulators you have 318 00:32:51,570 --> 00:32:56,869 to control the voltage automatically, and that is basically due to the excitation system; 319 00:32:56,869 --> 00:33:01,259 that is allowable with the generators. So, all the modern generators they are equipped 320 00:33:01,259 --> 00:33:09,809 with the AVR’s. So, the instability with the AVR is normally through oscillations of 321 00:33:09,809 --> 00:33:15,489 increasing amplitude, means the second type of here, is small signal stability. Again 322 00:33:15,489 --> 00:33:22,999 this small signal stability, can be classified into the two forms, not two forms, it is four 323 00:33:22,999 --> 00:33:23,759 forms. 324 00:33:23,759 --> 00:33:30,489 That is first one is your local mode, or sometimes also called the machine system modes. Another 325 00:33:30,489 --> 00:33:37,820 is your inter area modes. Third one is your control modes, and forth one is your torsional 326 00:33:37,820 --> 00:33:45,979 modes of oscillation. Now, let us see what is your local mode. The local modes are associated 327 00:33:45,979 --> 00:33:54,779 with the swinging of units at generating stations, with respect to the rest of the power system. 328 00:33:54,779 --> 00:34:01,850 The local means localized at one or a small part of system, and this frequency of oscillation 329 00:34:01,850 --> 00:34:05,269 is normally 0.7 to 2 hertz. 330 00:34:05,269 --> 00:34:10,040 To understand this here, let us suppose here a power station system; let us suppose we 331 00:34:10,040 --> 00:34:20,720 have a OBRA power station; that is thermal power station we have. This is generator at 332 00:34:20,720 --> 00:34:26,230 OBRA, it is not one there are so many generators in OBRA, means we have here we have 4 into 333 00:34:26,230 --> 00:34:34,679 200, we have 5 into 200 we have, and then we have again 3 into 100, and also we have 334 00:34:34,679 --> 00:34:40,329 fifty also those are not working now a days, and it is connected with the rest of the UP 335 00:34:40,329 --> 00:34:46,869 and this NRB system. What happens we have other generators here, we have other generators 336 00:34:46,869 --> 00:34:51,599 here, in the system we have a more than 40 50 generators in a NRB region. So, if the 337 00:34:51,599 --> 00:34:58,119 any one of the units here at OBRA is oscillating, with respect to other system here. Means you 338 00:34:58,119 --> 00:35:03,950 can take this system as a standard, and then you can see the oscillation in this, any unit 339 00:35:03,950 --> 00:35:11,670 of OBRA then we can say it is a local mode oscillation. Another one is your inter area 340 00:35:11,670 --> 00:35:19,500 modes; means inter area modes of oscillations are associated with swinging of many machines, 341 00:35:19,500 --> 00:35:25,589 in one part of system against a machine in another part of systems, and two or more groups 342 00:35:25,589 --> 00:35:33,770 are connected with weak tie line, and this stability oscillation is normally 0.1 to 0.7 343 00:35:33,770 --> 00:35:37,890 hertz. To understand this here for example, let us 344 00:35:37,890 --> 00:35:45,569 suppose we have a one area here, and another area here. Means we have here UPPCL. Here 345 00:35:45,569 --> 00:35:50,230 we have a Rajasthan state electricity board, and we have the several lines those are connected 346 00:35:50,230 --> 00:35:57,900 with the different. There is a possibility, the generators in this area, and the generators 347 00:35:57,900 --> 00:36:03,640 are here, they are oscillating to each other. So, it is inter area, and this is due to the 348 00:36:03,640 --> 00:36:10,280 weak tie line between these two. So, it is called inter area modes of oscillation. So, 349 00:36:10,280 --> 00:36:15,510 the different between your local mode, local mode unit means one unit of any power plant 350 00:36:15,510 --> 00:36:24,299 is oscillating with the rest of the system, and that here it is 0.7 to 2 hertz. And here 351 00:36:24,299 --> 00:36:31,220 in the inter area modes of oscillation, the one area. Area may be your few generators 352 00:36:31,220 --> 00:36:37,990 may be a complete state, they are degenerators in that area or oscillating, with here the 353 00:36:37,990 --> 00:36:47,049 generators in another area. So, it is called inter area. 354 00:36:47,049 --> 00:36:53,740 Another term is called control modes of oscillation; the control modes of oscillation are associated 355 00:36:53,740 --> 00:37:03,039 with the generating units and other controls. The poorly tuned excitation system, governors, 356 00:37:03,039 --> 00:37:10,480 HVDC converters, SVC are usual cause of this type of instability. Basically this is related 357 00:37:10,480 --> 00:37:19,710 with the control functions, because if a generating units is here due to the control of that particular 358 00:37:19,710 --> 00:37:25,150 unit, and it is oscillation, then it is called control modes. Means due to the control, because 359 00:37:25,150 --> 00:37:29,549 various control in any generating units, it is your excitation control, it is your governor 360 00:37:29,549 --> 00:37:33,730 control. In the other, let us suppose you have some other extra devices like HVDC terminal 361 00:37:33,730 --> 00:37:36,680 is going on, and there we are having some SVC etcetera. 362 00:37:36,680 --> 00:37:41,990 So, all the controllers here they are oscillating to each other, and that is basically it is 363 00:37:41,990 --> 00:37:48,710 called control modes of oscillation. Another mode of oscillation is the torsional modes 364 00:37:48,710 --> 00:37:54,609 of oscillation, and those are associated with the turbine governor’s shaft system rotational 365 00:37:54,609 --> 00:38:00,569 components. Instability is caused by interaction with excitation control, speed governors HVDC 366 00:38:00,569 --> 00:38:05,559 control, and series compensated lines. So, this is torsional modes of oscillation. So, 367 00:38:05,559 --> 00:38:13,630 torsional mode of oscillation can be understood by knowing this generating station, is driven 368 00:38:13,630 --> 00:38:18,619 by the various types of turbines. It may be your high pressure turbine, or it may be your 369 00:38:18,619 --> 00:38:22,420 low pressure turbine, it may be your intermediate pressure turbine. Again depends upon the size 370 00:38:22,420 --> 00:38:27,730 of the generating power plant, it depends upon the whether we are going for the three 371 00:38:27,730 --> 00:38:33,140 stage, or two stage. Let us consider a big power plant, which is having units of 500 372 00:38:33,140 --> 00:38:34,640 or 200 megawatt. 373 00:38:34,640 --> 00:38:41,829 So, this is your synchronous alternator which is rotated by the turbines, and all the turbines 374 00:38:41,829 --> 00:38:48,359 here we can say this is your IP, this is your HP means high pressure turbine, that is coupled 375 00:38:48,359 --> 00:38:52,839 with another shaft, and we are having here your intermediate perfect turbine; that is 376 00:38:52,839 --> 00:39:00,880 your IP and then we are having your LP; that is low pressure turbines and then here it 377 00:39:00,880 --> 00:39:06,170 is connected with your shaft. So, this is your LP low pressure turbine, then we are 378 00:39:06,170 --> 00:39:13,309 getting three phase supply three phase power system that is connected. Here we know your 379 00:39:13,309 --> 00:39:19,369 steam is coming here to your IP, and once it is expanded here it is coming going out. 380 00:39:19,369 --> 00:39:23,299 Again your pressure is coming here, and then it is going out and finally, it is coming 381 00:39:23,299 --> 00:39:29,079 here. Normally again it is going to be a reheated, and then finally, it is coming here and this 382 00:39:29,079 --> 00:39:38,829 is your boiler. So, we have here shaft, and that is all this HP that is high pressure 383 00:39:38,829 --> 00:39:45,240 turbine, intermediate pressure turbine, low pressure turbine. All are on the same shaft, 384 00:39:45,240 --> 00:39:50,760 where your alternator that is your synchronous machine is connected. We had here the four 385 00:39:50,760 --> 00:39:57,410 rotating mass. So, all these four rotating mass, they are connected with the shaft, and 386 00:39:57,410 --> 00:40:01,599 that shaft is having some stiffness constant, it is not infinite. 387 00:40:01,599 --> 00:40:07,270 So, they are behaving just like it will take this example like here. So, this one mass 388 00:40:07,270 --> 00:40:13,520 it is connected between a spring and here is another mass. So, here it is rotating, 389 00:40:13,520 --> 00:40:19,829 and that another is opposing, and then finally, another mass here and then it is and so on 390 00:40:19,829 --> 00:40:25,789 so forth. What is happening if we analyze, then we have some critical frequency corresponding 391 00:40:25,789 --> 00:40:32,880 to all these masses. So, here we will get the one two and three; the frequency will 392 00:40:32,880 --> 00:40:38,970 be arising and that is called the torsional modes of frequencies, and that is some oscillation. 393 00:40:38,970 --> 00:40:44,339 So, this frequency if your system is here from zero hertz to, your operating system 394 00:40:44,339 --> 00:40:49,809 is 50 hertz. Normally we will find some frequency if you analyze complete system damn means 395 00:40:49,809 --> 00:40:54,539 including the turbines etcetera as well, then you will find some here you will find at the 396 00:40:54,539 --> 00:41:00,049 range of 2 hertz, and the remaining you will find intermediate less than 50 hertz per cycle. 397 00:41:00,049 --> 00:41:04,799 So, these basically frequency of oscillations are the torsional modes of oscillation. 398 00:41:04,799 --> 00:41:12,220 Normally one term is very popular from synchronous resonance, because if your system which is 399 00:41:12,220 --> 00:41:18,950 compensated transmission line, there is a possibility that due to this here some synchronous, 400 00:41:18,950 --> 00:41:23,150 some frequency that is the current which is entering into the system that may coincide 401 00:41:23,150 --> 00:41:27,289 with these frequency of oscillations, and then there will be huge resonance. What will 402 00:41:27,289 --> 00:41:32,200 happen if there is, that frequency is matching with the torsional modes of frequencies, then 403 00:41:32,200 --> 00:41:37,839 there may huge torque that is developed inside the shaft, and the shaft may be broken, and 404 00:41:37,839 --> 00:41:42,770 that is called your sub synchronous resonance, because at that frequency the resonance has 405 00:41:42,770 --> 00:41:47,740 occurred. So, this is basically your torsional mode, and here this is your; that is two hertz 406 00:41:47,740 --> 00:41:54,690 as I said is a local oscillation mode. So, this is your torsional mode of oscillation. 407 00:41:54,690 --> 00:42:02,940 Now, let us again go back to the various stability phenomena’s and that is defined as a transient 408 00:42:02,940 --> 00:42:09,299 stability, as I already discussed the small signal stability, means small disturbance 409 00:42:09,299 --> 00:42:16,240 stability concern. Here the transient stability is also known as the large disturbance stability, 410 00:42:16,240 --> 00:42:21,450 and it is the ability of the power system to maintain synchronism when subjected to 411 00:42:21,450 --> 00:42:27,660 a severe transient disturbance, severe. Again the severe I am just telling from beginning, 412 00:42:27,660 --> 00:42:34,240 that it may be your three phase fault; it may be severe power outage, and it may be 413 00:42:34,240 --> 00:42:38,609 other type of fault, it may be some trimming of some severely highly loaded some transmission 414 00:42:38,609 --> 00:42:44,529 line, then your transient stability phenomena will occur. In this case we cannot linearize 415 00:42:44,529 --> 00:42:51,430 the system, and we have to solve the system with taking the non-linearity of the system 416 00:42:51,430 --> 00:42:56,529 as well. So, instability here depends on the both initial operating point as well as the 417 00:42:56,529 --> 00:43:01,210 severity of the disturbance. So, we have to go for again the modeling of 418 00:43:01,210 --> 00:43:07,910 the load, modeling of the power system, including you generator system, including you excitation 419 00:43:07,910 --> 00:43:13,559 system, and that will be clubbed together and then we have to analyze. Normally these 420 00:43:13,559 --> 00:43:21,349 transient stability phenomena, we normally go up to 3 to 10 seconds; however this small 421 00:43:21,349 --> 00:43:28,339 signal stability phenomena analysis is require up to 10 to 20 seconds. Another is your dynamic 422 00:43:28,339 --> 00:43:36,839 stability concern; it is used for small signal stability with automatic voltage regulation. 423 00:43:36,839 --> 00:43:42,569 As I said the small signal stability again can be with the voltage regulators AVR’s 424 00:43:42,569 --> 00:43:49,690 or without AVR’s, but not this dynamic stability concern is not raised and IEEE as well as 425 00:43:49,690 --> 00:43:54,910 the CIGRE recommended that it cannot be used the dynamic stability, because most of the 426 00:43:54,910 --> 00:44:00,160 power generating stations they are equipped with the AVR, there is no question of talking 427 00:44:00,160 --> 00:44:06,240 about this with or without AVR. So, whatever we are going to make analysis with the AVR; 428 00:44:06,240 --> 00:44:10,680 that is your small signal stability if your disturbance is small, and if your disturbance 429 00:44:10,680 --> 00:44:16,579 is severe and transient in nature, then we have to go for the transient stability analysis. 430 00:44:16,579 --> 00:44:23,140 Again, the stability phenomena as I said it depends upon the severity of the difference 431 00:44:23,140 --> 00:44:29,650 we defined, and again this definition I am talking about the angular stability. So, from 432 00:44:29,650 --> 00:44:35,440 the looking at the point of view the severity of the system, severity of the fault we categorize 433 00:44:35,440 --> 00:44:40,619 into two; one is your small signal; that is small disturbance, and another is your large 434 00:44:40,619 --> 00:44:47,230 disturbance or your transient stability. But if you are going for the time frame, then 435 00:44:47,230 --> 00:44:50,510 it is called the long term stability, and it is your. Another is your short term stability, 436 00:44:50,510 --> 00:44:58,130 or it is your medium term stability. Long term stability and the midterm stability are 437 00:44:58,130 --> 00:45:03,630 now new in the power system stability, and that is basically due to the frequency stability. 438 00:45:03,630 --> 00:45:10,819 I will come to the total background of stability phenomena, and we will see no various again 439 00:45:10,819 --> 00:45:12,549 at concise way. 440 00:45:12,549 --> 00:45:20,230 So, long term stability focuses on slower and the longer duration phenomena, that accompany 441 00:45:20,230 --> 00:45:26,819 large scale upsets that invokes. The actions of slow processes controls and protections 442 00:45:26,819 --> 00:45:31,480 schemes. Basically in the power system, there is a various protection schemes, and if they 443 00:45:31,480 --> 00:45:37,770 are activated due to those, there may be different control action. This is slow and longer duration 444 00:45:37,770 --> 00:45:45,980 phenomena occur. So, it is called long term stability phenomena. This phenomena includes 445 00:45:45,980 --> 00:45:50,049 the boiler dynamics. You know all the boiler dynamics, all these mechanical devices. You 446 00:45:50,049 --> 00:45:56,880 must be very careful all mechanical devices, including governors, boilers, penstocks, consume 447 00:45:56,880 --> 00:46:02,609 dynamics. They are basically having the high time constant, large time constant compared 448 00:46:02,609 --> 00:46:07,260 to your electrical system. So, if you are going to include, and they are going to impact 449 00:46:07,260 --> 00:46:12,520 your instability of the system, then it is called your long term stability phenomena, 450 00:46:12,520 --> 00:46:18,880 and then you have to take into account the various dynamics; like value dynamics, governor 451 00:46:18,880 --> 00:46:25,369 dynamics etcetera along with your AGC, power plant, transmission system protection and 452 00:46:25,369 --> 00:46:31,150 controls transformer saturation off nominal frequency effects on loads and the networks 453 00:46:31,150 --> 00:46:35,569 all they are going to be included in the long term stability phenomena. 454 00:46:35,569 --> 00:46:40,410 In the midterm stability represents, basically the transition between the short term and 455 00:46:40,410 --> 00:46:48,029 long term responses, and focuses on synchronizing power oscillations, between machines including 456 00:46:48,029 --> 00:46:54,490 the effect of some slower phenomena, and possibility large voltage and frequency excursions. Here 457 00:46:54,490 --> 00:46:59,470 the large voltage and frequency excursions as I said, the frequency stability is due 458 00:46:59,470 --> 00:47:05,720 to the severe frequency deviation. So, if your frequency is suddenly changes, normally 459 00:47:05,720 --> 00:47:11,289 this situation occurs when there is a lot of balance in the power and supply. So, if 460 00:47:11,289 --> 00:47:16,609 there is a large voltage and frequency, then your this time long term and midterm stability 461 00:47:16,609 --> 00:47:21,609 is concerned, and normally they come into the now in the new definition they are coming 462 00:47:21,609 --> 00:47:25,960 in your frequency stability concept. 463 00:47:25,960 --> 00:47:34,380 So, typical time range you can see, for the short term or your transient, it is 0 to 10 464 00:47:34,380 --> 00:47:42,369 second. For midterm it is 10 to few minutes, and long term it is few minutes to ten’s 465 00:47:42,369 --> 00:47:49,049 of minutes, normally this times of range of interest. So, if you are analyzing the long 466 00:47:49,049 --> 00:47:53,849 term stability, then you have to go for the several minutes. If you are going for the 467 00:47:53,849 --> 00:48:00,630 short term, then it is few up to ten or to twenty seconds. Long term stability concern 468 00:48:00,630 --> 00:48:06,420 with the system response, with the major disturbances that involves contingencies beyond the normal 469 00:48:06,420 --> 00:48:14,859 system design criteria. Now, one thing we should always be concern, it is not possible 470 00:48:14,859 --> 00:48:23,119 to design a system, that can sustain all the possibility of the contingencies, all the 471 00:48:23,119 --> 00:48:28,490 possibilities of the faults. And again if it you are going to design a system that can 472 00:48:28,490 --> 00:48:33,480 sustain all the possibilities, all the faults, all types of trippings, all the consideration, 473 00:48:33,480 --> 00:48:38,140 then it is not possible and then it will very expensive if you are going to design that. 474 00:48:38,140 --> 00:48:43,299 So, what we normally go, we normally try to analyze the system with the most provoked, 475 00:48:43,299 --> 00:48:49,579 and the most credible contingency in the system, and based on that we analyze whole your stability 476 00:48:49,579 --> 00:48:56,049 phenomena. You can say it is your transient. Small frequency or voltage stability as well. 477 00:48:56,049 --> 00:49:04,099 So, the classification of stability analysis. The analysis of stability problem, identification 478 00:49:04,099 --> 00:49:11,410 of essential factors that contributes instability, and formation of methods to improve stability 479 00:49:11,410 --> 00:49:17,599 are greatly facilitated by classification of stability. So, classification are based 480 00:49:17,599 --> 00:49:24,640 on the following, that the physical nature of the resulting instability. The size of 481 00:49:24,640 --> 00:49:32,130 the disturbance considered, the devices processes and time span of your analysis, and most appropriate 482 00:49:32,130 --> 00:49:37,700 method of calculation and the prediction of stability. Here this calculation methods are 483 00:49:37,700 --> 00:49:44,829 also very important, sometimes your calculation methods, because all these methods we are 484 00:49:44,829 --> 00:49:49,140 normally suppose some stability for designing you are analyzing your system whether your 485 00:49:49,140 --> 00:49:53,920 system will be stable or not, then we have to solve certain sets of differential equation. 486 00:49:53,920 --> 00:49:58,289 So, for solving the differential equation that there are various methods, and again 487 00:49:58,289 --> 00:50:02,410 these methods are very much related with the initial guess. 488 00:50:02,410 --> 00:50:08,549 So, if your initial guess is very bad, then there is a possibility that you will not get 489 00:50:08,549 --> 00:50:15,150 the stable solution, but the system is effectively it will be stable. So, it does not mean you 490 00:50:15,150 --> 00:50:20,260 solution is not giving a stable solution, you can say your system unstable. So, appropriate 491 00:50:20,260 --> 00:50:24,619 calculation methods are also very important that which method you are applying, what is 492 00:50:24,619 --> 00:50:29,500 your initial guess etcetera that should very close to the post disturbance equilibrium, 493 00:50:29,500 --> 00:50:34,539 and again which type of stability you are predicting. So, what is the type of fault 494 00:50:34,539 --> 00:50:39,760 what is again, what is the size of disturbance consider what are the devices and processors 495 00:50:39,760 --> 00:50:46,710 that are going to be consider. So, these all are included in the classification of the 496 00:50:46,710 --> 00:50:54,549 stability problem. So, far we had seen the various type of stability classification, 497 00:50:54,549 --> 00:50:56,380 and again now I can summarize. 498 00:50:56,380 --> 00:51:02,619 So, you can see the power system stability here in this diagram. It is basically can 499 00:51:02,619 --> 00:51:08,359 be categorize in three groups; one is your angle stability, where we are concern about 500 00:51:08,359 --> 00:51:13,440 the delta. Another is your frequency stability, it is basically related with the frequency, 501 00:51:13,440 --> 00:51:19,569 and another is your voltage, there is voltage stability. So, again this angle stability 502 00:51:19,569 --> 00:51:25,190 can be classified into the two categories; one is your transient stability, and another 503 00:51:25,190 --> 00:51:31,039 is your small signal stability. Again to remind you the transient stability is also called 504 00:51:31,039 --> 00:51:37,049 your large disturbance stability phenomena, and the small signal is your small disturbance 505 00:51:37,049 --> 00:51:44,809 stability phenomena. All these two are basically related with the short term stability phenomena, 506 00:51:44,809 --> 00:51:49,940 and this basically related with your, this normally required 3 to 5 second, and here 507 00:51:49,940 --> 00:51:55,010 we go for the 10 to 20 second. So, whole this analysis is if you are going for the time 508 00:51:55,010 --> 00:52:00,799 frame, then this your angle stability is your short term phenomena, because it is less than 509 00:52:00,799 --> 00:52:06,400 one minute. Again, this small signal stability can be 510 00:52:06,400 --> 00:52:12,510 classified into the two group. As again I will claim one is your called the non-oscillatory 511 00:52:12,510 --> 00:52:19,539 instability, and another is your oscillatory instability. Here non oscillatory instability 512 00:52:19,539 --> 00:52:24,329 is due to the in sufficient synchronizing torque, if the automatic voltage regulators 513 00:52:24,329 --> 00:52:31,769 are not there, then this concern arise. But now a days most of the generators they are 514 00:52:31,769 --> 00:52:34,789 with the AVR’s; that is automatic voltage regulators. So, oscillatory instability is 515 00:52:34,789 --> 00:52:40,210 the major concern in the modern power system, and this is due to the insufficient damping 516 00:52:40,210 --> 00:52:45,400 in the system. And if there is insufficient damping term, so there will be some sustained 517 00:52:45,400 --> 00:52:51,049 oscillation in the power system, and if that oscillation is keep on increasing, then it 518 00:52:51,049 --> 00:52:57,789 is called oscillatory instability. But if this oscillation is keep on reducing r is 519 00:52:57,789 --> 00:53:02,859 stable then it not increasing, then we can say system is instable and it is oscillatory 520 00:53:02,859 --> 00:53:07,529 stable. Again here that oscillatory instability can 521 00:53:07,529 --> 00:53:14,319 be classified into the four categories; depend on different criteria; first one is your local 522 00:53:14,319 --> 00:53:21,329 or you can say plant modes. Again I said that it is due to the one plant one unit oscillate 523 00:53:21,329 --> 00:53:26,220 respect to the rest of the system. here inter area means two areas or oscillating to each 524 00:53:26,220 --> 00:53:31,589 other, again due to the weak tie lines, and the control modes if any power station there 525 00:53:31,589 --> 00:53:35,970 is various control various controllers are there they are oscillating and various control 526 00:53:35,970 --> 00:53:40,710 modes, and the torsional modes due to the rotating mass different turbines are there, 527 00:53:40,710 --> 00:53:45,420 and they have some critical frequency if they are some oscillations are critical frequency 528 00:53:45,420 --> 00:53:50,920 between that and that is called your torsional modes. To come to the frequency stability, 529 00:53:50,920 --> 00:53:56,430 here it is your midterm, or it is included in the short term, and then another is your 530 00:53:56,430 --> 00:54:00,900 long term. Long term here when we go for the long term 531 00:54:00,900 --> 00:54:07,769 stability, basically it is. Again here within here the midterm it is less than one minute, 532 00:54:07,769 --> 00:54:13,180 and long term it is more than one minute here it is note. Here what it is in the long term 533 00:54:13,180 --> 00:54:20,049 normally, we take the dynamics of your boiler, your governors all the dynamics and the slower 534 00:54:20,049 --> 00:54:25,099 dynamics processes if they are included, then it is called long term stability. Here in 535 00:54:25,099 --> 00:54:28,650 the frequency stability, basically it is due to the huge excursion, again of the frequency 536 00:54:28,650 --> 00:54:33,890 in the system. Normally if the systems become islanding, there in unbalance in real and 537 00:54:33,890 --> 00:54:38,450 reactive power huge power, then we can say this frequency stability phenomena is occurring, 538 00:54:38,450 --> 00:54:46,250 or you can say the system is frequency instable. Another third one is your voltage stability, 539 00:54:46,250 --> 00:54:51,130 and that voltage stability can be categorize into two part; one is your large disturbance 540 00:54:51,130 --> 00:54:56,430 voltage stability, another is you small disturbance voltage stability. Here again based on the 541 00:54:56,430 --> 00:55:03,210 disturbance. So, if your disturbance is severe, then if you are analyzing your stability, 542 00:55:03,210 --> 00:55:09,170 then it is voltage stability with the large disturbance, another is your small disturbance 543 00:55:09,170 --> 00:55:13,539 voltage stability. So, large disturbance voltage stability just 544 00:55:13,539 --> 00:55:17,339 like a large disturbance, that if there is a tripping of transmission line, tripping 545 00:55:17,339 --> 00:55:22,769 of your generators, or there is a some three phase fault, then it is if you are analyzing 546 00:55:22,769 --> 00:55:26,880 then it is voltage stability with large disturbance, and for the small disturbance; means if there 547 00:55:26,880 --> 00:55:32,809 is a change in the small loads, there is small gradual change in the voltage etcetera, then 548 00:55:32,809 --> 00:55:37,190 it is called the small disturbance stability. Again this voltage stability in terms for 549 00:55:37,190 --> 00:55:42,150 time frame. Here just I have taken combined together, means we have two type; it may be 550 00:55:42,150 --> 00:55:48,049 short term voltage stability problem or it is your long term voltage stability problem. 551 00:55:48,049 --> 00:55:52,740 The short term voltage stability involves the dynamics of fast acting voltage components; 552 00:55:52,740 --> 00:56:00,019 such as induction motors, electrically control loads, and HVDC conductors. The study period 553 00:56:00,019 --> 00:56:06,660 of interest is in the order of several seconds, and analysis required the solution of appropriate 554 00:56:06,660 --> 00:56:11,269 system differential equations. This is similar to the analysis of rotor angle stability, 555 00:56:11,269 --> 00:56:18,480 dynamic load of angle is often essential in this case, and in contrast to angle stability 556 00:56:18,480 --> 00:56:24,579 the short circuits near load are important, it is recommended that that the transient 557 00:56:24,579 --> 00:56:28,359 voltage stability not been used. Normally we should not say it is transient 558 00:56:28,359 --> 00:56:34,859 voltage stability. So, always we had to call it is a short term voltage stability. In the 559 00:56:34,859 --> 00:56:42,309 long term here the voltage stability involves the slower acting equipment; such as a type 560 00:56:42,309 --> 00:56:48,329 changing transformers, thermo statically control loads, generator current limits etcetera. 561 00:56:48,329 --> 00:56:54,910 The study period of interest may extend to several or many minutes, and long term simulations 562 00:56:54,910 --> 00:57:01,319 are required for analysis of the system performance. The stability is usually determined by resulting 563 00:57:01,319 --> 00:57:06,990 outage of equipment, rather than the severity of initial disturbance. Instability is due 564 00:57:06,990 --> 00:57:12,440 to the loss of long term equilibrium, when the load try to restore their power beyond 565 00:57:12,440 --> 00:57:18,200 this capability of the transmission network, and connect the generation. The post disturbance 566 00:57:18,200 --> 00:57:23,890 steady state operating points, being small disturbance unstable, or a lack of attraction 567 00:57:23,890 --> 00:57:33,349 to or they stable post disturbance equilibrium. So, this is complete your power system stability 568 00:57:33,349 --> 00:57:41,460 definition, and then broadly classification of the power system stability. 569 00:57:41,460 --> 00:57:46,839 Again to go for the next chapter and next lecture of this module, let us see the history 570 00:57:46,839 --> 00:57:56,109 of system stability problems. So, historical review of historical problems, or review of 571 00:57:56,109 --> 00:58:01,269 the history of the stability is useful for the better understanding of present day stability 572 00:58:01,269 --> 00:58:06,670 problem. So, our power system stability was first recognize, as an important problem in 573 00:58:06,670 --> 00:58:16,230 1920. The first laboratory test was reported on miniature circuit in 1924. In 1925, the 574 00:58:16,230 --> 00:58:23,960 first filed test on the practical system. Means first filed test on the practical system, 575 00:58:23,960 --> 00:58:27,470 they reported. Means first reported first reported test on the practical system. Early 576 00:58:27,470 --> 00:58:31,759 stability problem were associated with the remote hydro generating station connected 577 00:58:31,759 --> 00:58:37,279 with long distance transmission line, because earlier hydro generators were very prominent 578 00:58:37,279 --> 00:58:43,619 and then we had a long generating transmission lines, and then it was associated with long 579 00:58:43,619 --> 00:58:48,099 distance transmission slide. So, slide rules and the mechanical calculators were used at 580 00:58:48,099 --> 00:58:53,470 that time; hence formulations were simple. Generators were taken as simple voltage source 581 00:58:53,470 --> 00:59:00,519 behind the fixed reactances, and loads were taken as constant impedances. 582 00:59:00,519 --> 00:59:07,390 In early 1950s electronic analog computers were used. In 1950s also saw the digital computers. 583 00:59:07,390 --> 00:59:14,920 First digital computer program for power system stability analysis, was developed about 1956. 584 00:59:14,920 --> 00:59:22,470 In 1960s utility interest were on the transient stability. So, before 60s people were only 585 00:59:22,470 --> 00:59:26,539 concerned about the transient stability. Due to increased loading and interconnection, 586 00:59:26,539 --> 00:59:32,509 the power system exhibited the oscillatory instability proper modeling concern arisen. 587 00:59:32,509 --> 00:59:38,470 The significant R and D work has been undertaken in the last few years to gain better insight 588 00:59:38,470 --> 00:59:44,619 into physical aspects of these new stability problems. So, now a day we are going more 589 00:59:44,619 --> 00:59:50,500 and more detailed modeling calculations, and then we are analyzing the system, stability 590 00:59:50,500 --> 00:59:55,900 concern, and then we are designing the power system based on those criteria’s.Thank you.