 discussing another important element in a power system. Our lectures so far have been concentrated on modeling a synchronous machine which itself was a fairly long and tedious process. In the last class, we described some simplified models of a synchronous machine. Of course, the there is practically no end to the amount of detail one can go in our discussion of synchronous machine modeling. There are in fact, a few topics which we have not covered one of them being the saturation performance of a synchronous machine. How would you change the modeling in case saturation exists? We will not discuss this much in detail in this course. In fact, we will just carry on. I can refer you to the books which which I had mentioned right at the beginning of the course. You can refer to them and there are some interesting references relating to saturation modeling. Now, remember what is the main issue there? When you try to model a synchronous machine with saturation consider remember it is no longer what is known as a linear machine. In that sense, you cannot you know get a flux current relationship which is linear and as a result of which it becomes difficult to apply the full machinery of DQ transformation. Remember that when we did the modeling of a machine, when we derived the inductance matrices which relate the fluxes in the A winding and the currents in the A, B, C, D winding and so A, A, B, C, F, G, H, K windings. You will notice that what we did was of course, you know try to do some kind of superposition of fluxes M M F's etcetera. You know we effectively used superposition in order to determine the nature of the inductance matrices. You can no longer do so in case saturation exists and that really queers the pitch and as a result of which there there is not a nice or a neat or a mathematically rigorous way to approach you know saturation in a synchronous machine. Of course, one may argue that again you know whenever you are modeling there is the physical laws are known and one should be able to model even saturation by actually computing the electromagnetic fields and you know the flux configuration which exists during saturation of a synchronous machine. But that would be really very tough and it is not justified when doing the stability kind of studies when we are studying slow electromechanical transients. But under certain circumstances it can actually affect the result. For example, the even the steady state behavior of a machine if one does not consider saturation one can end up with you know a fair degree of error and that is the reason why people are worried about it the and although a very rigorous way of tackling saturation is not really been discussed in the literature. But some ad hoc techniques have been discussed and I refer you to the books by Padyaar, Kundur and good discussion exists also in Sauer and Pi which discusses some of the theoretical implications of various saturation models. So, I the basic model which we have derived in the DQ reference frame we tweak it a bit we tweak it we do not really go ahead and try to start from scratch and try to derive a saturation model which is absolutely rigorous. But we just simply tweak the DQ model to account for saturation and it is quite ad hoc and you can say a pragmatic approach is usually followed. We do not discuss this any further I refer you to the books which I have just mentioned. We move on to today's lecture which is on excitation systems. Now, to look at the role of excitation systems let us just look look back what at what we have been doing we have studied a synchronous machine connected to a voltage source or an infinite bus sooner or later we will have to consider synchronous machines connected to other synchronous machines to loads to a network and try to infer you know infer how a power system behaves an integrated power system behaves. But even before we interconnect a synchronous machine to a network and try to study that kind of system we can look at the two important inputs which are there in a synchronous machine that is one of them is of course, the mechanical power or the mechanical torque and the second thing is the field voltage where we have been using the symbols t m and e f d in our synchronous machine model. In fact, all the simulations so far we took e f d to be some kind of constant in fact, we did simulate step changes in the field voltage or e f d. But we did not really have any kind of continuous control over either the mechanical power or the field voltage. But these two are essentially the inputs to our synchronous machine. Now, if you look at where we are right now we have done the synchronous generator modeling in which we have the rotor mechanical equations and you also have the machine flux equations a differential equations in the fluxes of the machine and the rotor mechanical equations are generally formulated in terms of delta and omega and given the mechanical the rotor angle the mechanical speed and the fluxes one interacts with the network you can connect the generator to a network which may consist of a voltage source it may be just a load or it may be other elements. So, you have typically a generator connected to a network and connected to other elements which could be other synchronous generators it could be other loads and so on. Now, the generator itself has two inputs you have got your mechanical power or the mechanical torque and you have got the field voltage these two things are in fact things we need to be controlled. Now, if you look at another figure the power apparatus which controls the mechanical power is essentially the turbine and a boiler boiler of course, in case of a steam turbine driven machine. So, you have got a boiler in a turbine in a steam turbine driven machine which surely gets the mechanical power at the shaft of at the shaft of a generator. The power apparatus which generates the field voltage for a synchronous machine is called as an exciter and it is usually consisting of at least one controlled power electronic equipment. So, in fact you will find that the exciter is a controlled element by which you can control the field voltage and it the control is via power electronic converters. Now, the valve or the gate control of a synchronous machine really controls the mechanical power input to the machine. So, you can control both the mechanical power and the excitation to a synchronous machine now there are various ways you can generate this field voltage we will consider two of the most common ways one can generate field voltage for a synchronous machine. So, we have to actually when we talk about excitation system one of the things we have to discuss is the power apparatus that is the excitation system and of course, the control of the field voltage itself. We kind of hinted when we considered the simulations in the past two lectures that if we we need to change the field voltage we need to change the field voltage as the generator is loaded otherwise we may not be able to operate the generator acceptable in the case which we simulated we saw that trying to load a synchronous machine without simultaneous control of the field voltage resulted in a loss of synchronism when the machine was loaded up to its rated value. So, we do require some kind of a control over the field voltage that is a very important idea. Now, the various ways of course, one can obtain the power apparatus or the the configuration of the power apparatus in order to excite a synchronous machine. Now, the major controllable element in any of these excitation systems is as I mentioned some time of power electronic converter. In fact, it is usually a thyristor based control rectifier. So, most of the generators you will find have got a controllable element in the excitation system which is the controlled thyristor bridge. So, that is what is essentially there in a synchronous machine. Now, one of the important things you should remember at this point is that a synchronous machine has got an extremely large synchronous reactance. What do you mean by large? In relative terms if one wants to understand this if you have a synchronous machine. Suppose you have got a synchronous machine which is unloaded it is operating at no load. So, the field voltage which you would require certain field voltage in order to get rated the rated voltage at the generator terminal. So, you will have to actually give a field voltage which is represented temporarily as a battery. The field excitation you would have to give. So, that you got the rated voltage. Now, the important point here is if I start loading a synchronous machine. If I start loading a synchronous machine you will find that. So, I load the synchronous machine you load it and you will find that the voltage keeps on dropping and this drop can be very significant. In the sense that if you take a typical synchronous machine you will find that you will not even be able to load it to its full value full rated value unless you increase the field voltage. For example, a synchronous machine say with an x d of 2 per unit and let say it is a x d and x q are equal. Then the per unit power per unit power will be equal to if your e f you have got e f d into the voltage at the load divided by x d into sin delta. So, if I connect the synchronous machine to a voltage source whose line to line r m s is v. Then the per unit power is this. Now, if I keep my e f d at the 1 per unit v is also 1 per unit. Then the amount of power you can actually push is half maximum power you can push is half per unit. So, if I have got a synchronous machine a synchronous machine connected to another voltage source. Then in that case the amount of power you can transfer is limited unless you change e f d. So, this is what is done when you load a synchronous machine from no load to full load you would need to change this e f d and very very significantly. In fact, you may have to even double the amount of field voltage in order to load whenever you load a machine from no load to full load conditions. In fact, if you look at a typical generator which is used in the Indian systems is a 247 MVA generator. This is a typical unit sizing which is found in most in Indian power systems. You will find that the no load voltage field voltage this is the voltage applied at the field at no load is 102 volts roughly and the current under open circuit conditions is this the field current. So, this is under open circuit conditions this gives you 1 per unit at terminals. However, if you load this machine to its full rating you will have to apply which is value which is more than double a field voltage. So, that you will get 1 per unit at the terminals again. So, you see that you need to really change the field very substantially the reason of course, is that the x d of a synchronous machine is very very large or in other words the armature reaction is very large. If you just connect a synchronous machine you connect a synchronous machine to a resistive load. These are just a schematic representation of that and you go on increasing the load by decreasing the resistance. You will find that the amount of power you can actually deliver has a maximum and that maximum is a very low value. In fact, the equivalent of a synchronous machine electrical equivalent of synchronous machine in steady state if it does not have any saliency is simply a voltage source of magnitude e f d x d and the resistance r and you know that if x d is large the maximum power transfer is going to be limited. You are not going to rather I should say the power transfer in this situation is limited unless I change e f d. So, I hope I made a good case that you really need to have a system in which typically for large generators you need to have an excitation system which is very well controlled and has got a very large range as well. So, from no load to full load you really need to change the field substantially. So, one example of exciter the power apparatus if you look at is the static excitation system and what you really have here is the voltage which appears at the terminal of the main generator that is our generator which we which we are studying in fact is rectified after stepping it down by a controlled thyristor base rectifier and then the d c value is fed to the field of the generator. Remember of course, this is a controlled rectifier. So, I can control the d c value the d c value of it is fed back into the generator and this is one way you can excite a generator in fact it may somewhat you know worry you initially because the voltage which is required to be rectified in order to feed a d c voltage to the field winding is in fact being obtained from the terminals of the main generator itself. And of course, if the main generator is under open circuit conditions one may argue that there is no voltage at the terminals of a synchronous machine if no field voltage is provided. So, as a result you will get no a c voltage at the terminals of a controlled rectifier and the d c voltage is also not going to will not really have any value it will be 0. So, this whole system may not work, but actually if you look at it it is of some kind of positive feedback system if there is some residual magnetism available in the generator it can generate a small a c voltage if that a c voltage is enough to forward bias the devices used in the controlled rectifier usually thyristors then that would cause a small d c voltage the d c voltage would cause some field current which will enhance the existing if it enhances the existing residual voltage residual flux which is there in the machine will find it the voltage increases and some kind of a you know positive feedback mechanism will ensure that the machine self excites. So, this actually can happen in a practical situation of course, because you know you require adequate residual fluxes to generate initially an a c voltage will forward bias the thyristors we do not actually connect the synchronous machine from scratch in this fashion what we usually do is start it up with a battery. So, your field voltage field is initially fed via a battery and then after that this particular configuration the system switches over to this configuration in which the voltage generated at the terminals of a generator itself is used to power the field in this fashion. Now, this in fact can be actually shown in a laboratory using simple diode rectifier. So, if you actually replace the control rectifier by a diode rectifier and just you know feed the output of a generator back onto its field winding through a diode rectifier you find at the voltage builds up on its own you know. So, it is a it is kind of spontaneous increase. In fact, it is an interesting exercise for you to show that in fact, this if you write down the differential equations or the dynamical equations corresponding to this scenario you should be able to show that in fact, this is a unstable system and therefore, itself excites. So, if you give any non-zero initial condition it builds up the voltage builds up on its own. One small caution again in a real system the residual voltages may not be residual fluxes in the synchronous machine may not be adequate to generate just that initial kick to start this self excited system. And as a result of which you may actually have you may actually have to use the batteries in a power station to initially excite the machine and then switch over to this configuration. So, what I will do now is just show you a small video clip of how one can simply excite a synchronous machine by simply connecting its output back onto the field via a diode rectifier. A diode rectifier in fact, is not a controlled rectifier. So, we will not be able to achieve much control over the voltage which we are getting. I will just show you that the voltage suddenly kicks and the machine still self excites. So, what I will do is connect the diode rectifier or the input of the diode rectifier to the output the terminals of a synchronous machine in the laboratory. Then the DC terminals of the rectifier I will feed it back to the field of a synchronous machine. Then I will start rotating the machine slowly and at a particular point you will find it this whole system excites on its own. So, let us see that video clip. So, this is our setup setup in the laboratory. What I have done is I have connected initially the static control rectifier is connected to the field winding, but I also have a diode rectifier which right now is open. So, that is what was shown to you. The input of the diode rectifier is of course, the terminals of the ABC terminals of the generator itself. What I will do is I will disconnect the existing controlled rectifier and instead of that I will connect the output the DC terminals of the diode rectifier to the synchronous machine field. So, that is what you are seeing here. So, the diode bridge is connected to the generator terminals on the AC side and the DC terminals are connected to the synchronous machine field winding. So, this is what I have done. Of course, if I do not rotate the machine there will be no voltage induced and nothing will happen actually by doing this, but what I will do now is slowly start rotating the machine. Remember that I am not separately exciting it the output of the output voltage at the terminals of the DC machine itself of the synchronous machine itself is being used to excite the machine. What I am doing now is starting the prime over which is the DC machine what you are seeing here is I have applied the field voltage to the DC machine. Now, I am applying the armature voltage to the DC to the DC machine is the prime over to the AC machine. As soon as I start the started this way you will find that the machine starts rotating you will shortly see the machine rotating. What really we wish to show you is that after a certain speed the voltage kicks and the machine the synchronous machine self excites. So, what you see is that there is some voltage at the terminals of the machine also you see there is a field synchronous machine field current and a synchronous machine field voltage. So, the machine of course, is rotating at a low speed. In fact, at a very low speed itself you find that there is enough voltage to trigger self excitation. So, just by connecting the output of a machine to a diode bridge rectifier and feeding it back to the synchronous machine field we are able to in fact, demonstrate that self excitation can occur. So, let me just repeat what I said just draw a schematic of what I showed you. So, what I had is a synchronous machine its output was simply rectified using a diode rectifier and it was fed to the field winding and you saw that after a certain speed is acquired by a synchronous machine of course, the synchronous machine is driven by a DC machine. You find that there is adequate voltage to trigger a kind of positive feedback or you know the self excitation phenomena. Right now remember that in order for this to work well the voltage here the residual flux in the machine should be enough to forward bias the diodes in this bridge at least at some speed. So, there at some speed the voltage magnitude here should be adequate to trigger self excitation. Otherwise of course, one will have to use the station batteries for what is known as field flashing initially and after that one can switch over to this configuration. So, what you have here is of course, a static excitation system. A static excitation system requires a brushes and a slip ring to in fact, two slip rings and brushes to convey the field voltage to the field winding which is usually rotating in a typical synchronous machine. So, if you look at some interesting pictures which I have got here which is courtesy the western regional power committee Mumbai. You will find that this is a snapshot of a synchronous machine what you see here right at the end are in fact, the slip ring brush arrangement you see this is actually luckily it is exposed for us here. So, you can see that the brushes and the slip rings. So, this is a snapshot of that you get a close up also. So, you see those brushes rubbing against the slip ring. So, this is the end region of a end it is on one side of the synchronous machine. In fact, if you look at this another snapshot what you see here is on one side is the place where the slip rings are on one side you have got the slip rings through which the field voltage is conveyed. In fact, the exciter itself is in another room and the voltage is conveyed to these slip rings via the brushes. On one at one end you see these green structures here the blue structure here is of course, the synchronous generator itself the green structures here are in fact, the turbine which really control the mechanical power input to the synchronous machine. Another kind of excitation system is what is known as the brushless excitation system this likely looks a bit more complicated than our static excitation system in which the exciter itself is static it does not move and the voltage which the exciter gives is conveyed via slip rings and brushless arrangement. Now, a brushless excitation system on the other hand has got a slightly different structure. What you have essentially I will just try to you know describe it here a rotating permanent magnet a rotating permanent magnet is there in a permanent magnet generator. So, a rotating permanent magnet causes voltage to be induced in the stator the stationary part of a permanent magnet generator. The voltage output of the permanent magnet generator itself is fed this is a this is fed to a controlled rectifier this is again a thyristor based rectification system. This is a controlled rectifier in the sense that the DC voltage is a function of the AC voltage as well as the control signals which is essentially the firing angle delays which is obtained from a control system. We shall discuss this control system it is also called a voltage regulation system. So, this is a controlled rectifier by which we can actually control the output which eventually goes to the main generator. But of course, there are unlike a static excitation system there are several steps before this is actually done. What you have here is of course, the control rectifier which controls the output of this is now DC the output of the control rectifier is DC. The permanent magnet stator the control rectifier are both stationary whereas, the magnet of the permanent magnet generator of course, is rotating. The DC output of the control rectifier is fed to the to the field winding often of an AC generator. Now, this is not the main generator which we are talking of this is a generator of the excitation system. Now, the field winding of this particular AC generator remember is stationary. So, on the rotor of a synchronous of this particular synchronous generator the rotor has got the armature winding the stator has got the field winding. So, the three phase armature windings are in fact, on the rotor of this machine this is called an excitation system generator. Now, output of this synchronous generator is three phase AC. So, I have got rotating armature windings. So, you are getting rotating winding which are in which three phase AC is induced AC voltages are induced. Now, these three phase AC voltages are fed to a rotating this is also rotating uncontrolled rectifier which is nothing but a diode bridge a three phase diode bridge which is also rotating. So, this R on top here indicates rotating structure. So, you have got rotating structure a diode bridge which is rotating the output of this diode is fed to the field winding which is also rotating. So, the final field voltage is conveyed to the field winding of the main generator the generator which we are really interested in directly you do not have to have a slipping brush arrangement because the rotating the diode bridge also is rotating along with the field winding. So, it is a direct connection you do not really have to have a slipping brush arrangement. So, I will just repeat this again you have got a permanent magnet generator in which you get get three phase voltage is induced on the stator the three phase voltage output of the permanent magnet generator itself is rectified using a controlled rectifier. The output of the controlled rectifier is fed to the stationary field winding of a excitation alternator or excitation synchronous generator. The three phase voltages of this generator are excited on the rotor of the machine they are on the rotor of the machine the output of that is fed to diode bridge which is rectified and fed to the main field and does not require slip rings. So, some large generators in fact have this kind of arrangement. Now, of course, I have been talking of a controlled rectifier and so on. What exactly is a controlled rectifier? It is in fact an arrangement of a thyristors typically it is the kind of rectifiers which I use in most excitation systems are using thyristors. So, controlled rectifiers are made out of thyristors if you look at a thyristor three phase thyristor bridge it is made out of six thyristors the input of course, is the three phase AC by AC input and the output is DC and that is what I have been representing as this box here. So, this is equivalent to a box with three phase inputs and the DC input in this fashion DC output in this fashion. One important point which you should note at this point I do not know whether it is visible on the screen. So, I will just redraw it here. So, if you take a thyristor bridge which is schematically denoted as I showed you sometime back remember that a thyristor bridge has if you denote the voltages and currents in this fashion the V d c can be positive or negative, but I d c is always positive. So, that is one important thing which you should remember that this particular rectifier does not allow current to flow in the negative direction. Now, we have a small video clip which shows you controlled rectifier operation. In fact, you can by manual you can manually in the in the video clip we are showing we are showing the voltages which are developed in a synchronous machine due to application of this excitation voltage. The excitation voltage itself is the output of a controlled rectifier and the controlled rectifier is controlled by controlling the delay angle of the thyristor bridge. So, you can actually by doing that you can control the DC component of the voltage which appears across the thyristor bridge. Now, remember one small point which you should remember this thyristor bridge if it uses 6 what you call a thyristor bridge consisting of 6 thyristors as I shown you sometime back you can look at it again. In that case the d c voltage is V d c will have the 6th harmonic it is a d c voltage with 6th harmonic and a d c component itself. So, you have got a d c 6th harmonic 12th harmonic and so on. No lower order harmonics are present other than of course, the d c component itself. So, you have got the d c component 6th 12th and so on. So, this is known as often called a 6 pulse thyristor bridge. So, what we will do is now see a simple situation here a simple video clip which will demonstrate to you how thyristor bridge voltage the output d c voltage can be changed by controlling the delay angle. So, that will be done manually in the video clip which will be shown to you. We do not start the machine for this purpose we just switch on the excitation system and apply a d c voltage to the field winding. The aim of course, is to show you 6 pulse operation this is the static excitation box in which we have got a 6 pulse bridge. You will have to pay attention to the ammeter and voltmeter on your right. What we will do now is to reduce the firing angle from greater than 90 to less than 90 after a point at an average d c voltage which is greater than 0 appears and a continuous current is established and what you see here is the output of a 6 pulse bridge near about 70 or 80 degrees. Now, we are increasing the d c voltage by decreasing the delay angle and you see of course, that the ripple comes down and it average value seems to be going up. You can see the ammeter voltmeter as well as the CRO on your left. Now, what we will do is we have of course, decreased the voltage and made firing angle here about 30 or 40 degrees. We will do now by increasing the firing angle again we can decrease the d c voltage and now you see again the voltage coming down the d c voltage and the ripple of course, increases. You would have noticed of course, if the ripple is a of course, it is not very clear on the CRO it is a 6 harmonic ripple. Now, before I go ahead and you know you know discuss something more about the excitation system itself. I mentioned to you that there is a need to have some kind of continuous control over the excitation system because excitation voltage which is given to the synchronous machine because the synchronous machine has got a very poor regulation because of having a large value of x d. So, this is something which I discussed just some time back. So, what I will do now is show you a small a second a third video clip of the drop a very precipitous drop in voltage once you start loading a synchronous machine by a resistive load. So, what I will do is start the synchronous machine set the field voltage at a certain field voltage. So, that you get roughly the rated voltage at the generator terminals then what I will do is load the synchronous machine by a resistive load. I simply a passive resistive load as I try to decrease the resistance from I mean if it is open of course, the resistance is infinity, but as I start loading it that is I reduce the resistance from a certain value I go on decreasing the resistance and I load the synchronous machine you will find what happens is that this terminal voltage of a synchronous machine drops and as a result of that you will find that in fact the synchronous machine is not able to take on much power because the voltage drops so much that it goes beyond the maximum power point of you know of this particular situation of this particular source. So, as I go on decreasing the resistance I try to load the machine, but unfortunately the terminal voltage goes on dropping so eventually the machine does not get loaded at all. So, this is what you will see in the next video clip. So, the machine has been started via the prime mover now what I will do is adjust the field winding right now there is no voltage which is there across the field I will change the delay angle of this thyristor bridge and gradually try to develop some voltage across the field and therefore the terminal voltage will appear yeah. So, I kind of try to change the delay angle so that I get the rated voltage at the terminals of the synchronous machine. Now what I will do is load the machine by connecting a resistive load to it so this is being done gradually so you can keep an eye on the power meter yeah. So, now the you can see that load is slightly increasing as I introduce a resistance, but what is very striking is the voltage initially which was at 230 volts decreases as I go on loading the machine in fact if I go on loading the machine the voltage in fact drops almost to half of what the rated value was. So, if I don't touch the field winding voltage what I am showing you now is I am readjusting the field voltage so as to I am readjusting the field voltage so as to get back to the rated value yeah. So, unless I do that the voltage will drop to a very low value and we will not be able to load the machine adequately. So, what I will just repeat what I did I loaded the machine and you saw that if I kept the field voltage constant you would find that the terminal voltage of the machine drops and in fact you are not able to take on the complete power the actual power which is delivered to the load is not we cannot increase it beyond the point because of the large source impedance in the form of x d, but if I increase E f d that is the field voltage I can get back the voltage back to the rated value. So, that is what you really need to do if you look at what needs to be done in a typical excitation system is to have some kind of continuous control we did not have it in our the demonstrations which I showed to you so far. In fact you can see that the there is no continuous control I had to manually adjust the field voltage of the excitation system this is not desirable because load could change suddenly and then you may have a sudden dip in the voltage. So, you always need to have the excitation system in continuous control mode. So, what you need to do for example the most simplest thing would you need to do is monitor the terminal voltage of a synchronous machine in case it drops you keep adjusting the field voltage. So, that the you know the voltage is maintained. So, you adjust the field voltage in such a way now this really brings us to a new dimension. So, to speak in our course we will be we have so far been talking about modeling of power apparatus we can of course talk in terms of now how you really introduce control systems which themselves may be dynamical systems mind you. So, how do you have control continuous feedback systems introduced into our models so that we can accurately describe their effects. So, for example, right now one of the ways one of the things you would probably do is measure the terminal voltage of a generator. So, you measure the terminal voltages of a generator. So, what you do is of course have a p t and feed it to a regulator the regulator in fact gives the appropriate signals to the controlled rectifier of your excitation system it could be a brushless excitation system or a static excitation system and that feeds voltage to the generator field. So, this excitation system could be a brushless excitation or a static excitation system, but in both cases you do have a controlled rectifier the signals to the controlled rectifier to enhance the voltage or reduce it are in fact obtained from the voltage regulator. Now, what is what is a voltage regulator? The voltage regulator itself is some kind of control system it is a dynamical system, but it is not a power apparatus it is basically consisting of some hardware which tries to implement certain mathematical functions. Remember that the control signal to a thyristor bridge is not what is known as a high power signal it is just a it is has enough strength to convey to a thyristor or to the gate of the thyristors to delay their firing. So, the power levels which which are here which are used by control system are much much lower than the actual power rating of the apparatus it is trying to control. So, in that sense although we will be modeling these regulators etcetera they are also going to be differential equations and dynamical systems in most cases, but they are not power apparatus they are in fact low power apparatus they essentially signals. So, for example, you could give some set point to rather set point is the value like the terminal voltage of your synchronous generator to be is the value at which it should run. You measure the actual voltage which is generated step it down and get it to measurable or signal levels a low power signal you can say you have a comparator this is some hardware it is it is some kind of built in hardware comparator or that is using analog electronics you make a comparator or using even digital systems you can implement this using some software. So, we will of course, discuss these things a bit later in the maybe in the next class. So, by comparing this you will know the error and then by some control law the control law could be just a simple gain or an amplifier you could determine the control signal which is to be given to the control rectifier which is a power apparatus. So, the this is the power apparatus. So, the output of this is a control system is a signal which is given to this power apparatus. Now, this power apparatus interprets this signal appropriately and appropriately changes the output of the voltage of this rectifier. Now, there is some mapping of course, between the value which is obtained here and how much change it causes here. So, I one way of doing that is if I the output of this change is by delta alpha how much is the voltage change here. So, that is something you should know beforehand before you design this control system. So, what this is one way of controlling the voltage if there is a larger the error the larger is this correction which you make here. So, of course, if the voltage is low if V is less than V ref this error will be present and you should of course, control design your control system. So, that it drives the power apparatus to rectify this situation correct this situation. So, it changes the signal given to the control rectifier. So, that the voltage increases. So, this is what it will do under the circumstance where voltages are low. So, it is a continuously acting of course, this is very important it is a continuously acting control system. So, this is one thing which you should remember you need to do this in addition to just having the power apparatus you have a continuously controlled control system. Now, remember that once one of the things which I hinted to you I talked to you about is you need to know how much you need to change the output of a control system and map it to what the power apparatus of what the power the excitation system the way it behaves. So, for example, in a brushless excitation system which I shown you sometime back you should have in your hand a mapping of how this control signal change in this control signal changes the DC output of this. How the change in DC output of this changes the AC voltage output of the synchronous generator and correspondingly how this change reflects here in the final change in the field voltage. And of course, once you change the field voltage we know how it affects this main generator by just the synchronous machine equation which you have been discussing all this while in the previous lectures. So, you know how a synchronous machine behaves, but you need to model all these components here that is the rectifier itself then the AC generator it is also a generator. So, you may wish to model this in detail I mean the amount of detail is something which is based on our engineering judgment you also need to model a behavior of a diode bridge rectifier. So, you need to model not only you know these are not just algebraic relationships between the input and output you may actually have to model some of these components at least as dynamical systems as differential equations. So, what you have is this power apparatus which is the synchronous machine itself now you have got another power apparatus which is the excitation system which you need to model in some detail. Now, the amount of detail depends on the kind of studies you are doing. So, as I mentioned some time back in a brushless excitation system you have a generator the excitation system itself has a small generator there it is not as large of course as the main generator that itself may have to be modeled in some detail, but there of course on the other hand there are some studies which really do not require you to model these things in great amount of detail you will get more or less the same results even if you use a simplified model. So, these and some other issues will be discussed in our next lecture.