 See, I will start DC to AC inversion inverters. There are two purposes. One is, yesterday we found that even in DC to DC converter, even in DC to DC converter, there is a inversion stage. Are you with me? Especially, if there is a significant difference between input and output voltage, if there is a significant difference between input and output voltage, you may have to use a transformer or you have to use a transformer. And if you use a transformer, depending upon the power level, you may have to use a bi-directional excitation entire the BH curve. And therefore, that is nothing but, nothing but converting DC to AC. And another application, another application is, again I have a high voltage DC that I have to convert it into, that I have to convert that to a 50 hertz AC, 50 hertz AC. So, inverters you may have to use or two types of inverters in a solar system or solar PV photovoltaic system. One is, one is a high frequency inverter, high frequency inverter and second one is, second one is a 50 hertz inverter, 50 hertz inverter. Principle of operation is the same, but then, but then, let us see which circuit topology is suitable for low frequency application as well as for high frequency, high power application. A power rating will change as power rating changes, what sort of a configuration is suitable, we will discuss. Simple basics. Yeah, I am saying DC to AC. I mean, what I mean when I am saying AC, it implies that average value of the output voltage is 0. It does not mean that output voltage waveform is AC, sorry, output voltage waveform is a sinusoidal. It need not be, I am saying that when I am saying AC, average value of the output voltage is 0, average is 0, that is all. It could be a square wave as well. In the sense, I can have input is 12 volt DC, output could be, see there are basically where do we use inverters, so happens that I do not know any other source other than fuel cell may be, when the solar cell output is DC, almost all the sources, if the conductor is rotating a magnetic field, voltage induced in the conductor is AC, AC. And then, why do I require DC to AC converter? Except in this application, so happens that this is a solar course and output of the solar cell is DC, but bulk of the remaining power generation source, so that we have output voltages, output voltages AC, AC. So, when I am saying the inverters, first thing that comes to my mind is looks like this inverter is used for, gentlemen, what is the, this one joke like, I do not know, you have anything to share? Yeah, no, no, the person sitting, yeah, I think that is good. First thing that comes to my mind is maybe looks like it is for a motor drive application, motor drive application. Other than, it comes to my mind maybe it could be for residential or for an UPS, bulk of the inverters are for motor drive application, where the principle of operation is the same, but then only difference is frequency of the output voltage or the voltage of, output voltage of the inverter changes with, with frequency, changes with frequency. Whereas, if I want to have, if I am using it as an inverter, using as an UPS, output voltage is fixed, 230 volts, 50 hertz AC. Now, we will concentrate only on this aspect, I do not want to concentrate on, concentrate on the inverter drives. I will start with simple things. Yeah, what are the basic type of inverters? There are two types of inverters. Input voltage could be a, a, a steep, steep voltage source or I can have a, I can have a, a current source, I can have a current source. What are the features of a, what are the features of a voltage source inverter and what are the features of a current source inverter? The features are, I have a voltage source, voltage source, either a battery or, or, or a charge capacitor, tries to maintain a constant voltage. What are the features of a capacitor? Voltage can, voltage cannot change, but then current can change instantaneously. So, in voltage source inverter, this link, link current can change, can change instantaneously. Are you with me? Current can change in an instant, instantaneously in a capacitor. So, basically, I think it looks like if this current can change, I need to have bi-directional switches. Current can change. So, I do not, I do not know a switch which can carry current instantaneously in both the directions. But then, but then voltage across the capacitor cannot change and then it says, so this voltage, polarity of this voltage will not change. So, I need to have a device which can carry the current in both directions, but it need not block the voltage in both the directions. It has to block only positive voltage. It need not block negative voltage, but then it should be able to carry current in both directions. So, we need to construct such a switch. Whereas, whereas the current source, current source voltage across an inductor can change instantaneously. So, therefore, voltage at this point can change instantaneously, but then this current cannot change instantaneously. So, it is a unidirectional current. So, here I need to have a device which can block voltages in both the directions and can carry, should be able to carry current only in one direction. Is that ok? So, bulk of the inverters today are voltage source inverters, voltage source inverters. But then it so happened yesterday I showed that people are talking about mean, mean time between, mean time between failures, MBT. It should be of the order of some 20 years or so. So, weakest link happens to be capacitor. So, the people are asking, can we have an inverter without a battery? Sorry, without a, without a capacitor, without a capacitor. So, I do not, whether we will be able to, whether we will be able to successfully attempt, people are thinking of using a current source and trying to modify the pass actor configuration. Thought process is now to use or to propose a pass circuit which does not use a huge capacitor here. Size of the capacitor is very big here. Of course, you can use a small capacitor that is allowed. So, basically if that is the case, the trend is to go in towards the current source. What are the issues there? If time permits, we will discuss. Bitly I will draw, all of us know, bitly I will draw for some purpose I am discussing that, do not get, basic configuration. S 1 is closed, S 1 is closed, voltage applied to the load is, load is V dc by 2. After some time, after some time, I will open S 1, I will open S 1. Since it happens to be a voltage source, I need not, need not worry about providing a path. Current can change, I will open S 1, closes to voltage across the load is, load is minus V dc by 2. I am assuming the load to be R L, inductive load, inductive load. I am applying a dc voltage to this load, dc is being, dc means V dc by 2, a constant dc is applied for t by 2 seconds, t by 2. S 1 is closed for t by 2, S 2 is closed for t by 2. Voltage applied here is V dc by 2, voltage applied here is minus V dc by 2. So, average is, average is 0, average is 0. A dc is applied to R L load. So, therefore, how does the current wave form look like? Gentlemen, how does the current wave form look like? What is the point? Exponential, fine, in the sense, I should not, exponential, when it is exponential? No, no, no. Yes, it is exponential, when is it exponential? Initial period is linear. In an R L circuit, excited by a dc, yes, exponential after tau may be, isn't it? Initial portion, how does it look like? How does the current wave form look like? Initially, it is, it is linear. If I allow the current to, exponential means it is almost getting saturated may be, saturation. We are inching towards a steady state, inching towards a steady state. Initial, remember this another point, very important point, I will, we require this. Initial portion is linear. So, the current wave form look like, the voltage wave forms are like this. At steady state, fine, this is at t is equal to 0, current starts from 0, increases and decreases. So, if you see at steady state, it looks something like this. Voltage is positive, voltage is positive, current is, current is, current p, in this way, current is negative. So, which part of the device is carrying the current? Positive voltage, voltage applied to the load is positive. So, it can happen only when, only this point is connected to this point, voltage applied is positive. Current is negative, positive direction of current is from a to b. So, current is flowing from, flowing from b to, yes, so therefore, that current, that current has to flow through d1. So, positive voltage, positive current is carried by S1, positive voltage, negative current will be carried by d1. So, one observation that you need to make is, just though I am closing S1 is a controllable switch, it does not mean that, that device is carrying the current. Current may not or current will not flow through it for some time. Is that okay? Though I have closed the switch S1, where did I close the switch? I had, in this period entire zone, S1 is closed, but then it starts carrying current from, from, from q, q, q to r. Only in this period, current flows through it. In this p to q, current carried by, carried by the diode, by the diode, by the diode, by the diode. So, S1 d1. So, if I replace that load by an inductor, if I, if I replace that load by an ideal inductor, how does the current waveform look like? Sir, gentleman, yeah, if I replace the load by an ideal inductor, how does the current waveform look like? No, no, it cannot be, it has a unique, the answer is what it can be, what it should be rather than what it cannot be. The moment you are saying what it cannot be, there is a host of other possibilities, a key possibility here. How does it look like? I am replacing that RL load by an inductor. How does the current waveform look like? Linear, linear, linear, L dA by dt is equal to V. L dA by dt is equal to V. V is constant. So, dA by dt is constant. L dA by dt is equal to V. V dC is constant. So, dA by dt is equal to V by L, again constant. So, I increases linearly till the inductor saturates. Assuming the inductor is in the linear region, sorry, if assuming that inductor does not saturate, current increases linearly and decreases linearly. It is basically a triangular wave at steady state. So, this is a voltage waveform, applied voltage waveform to the inverter, this is the current waveform. So, this is T by 2, this is T by 2. So, if I want to have 50 hertz supply, I have to keep S 1 should be on for 10 millisecond and S 2 should be on for 10 millisecond, 10 millisecond, S 1 on, S 2 on, it should not be off. So, what happens? Applied voltage is positive, current is negative. So, power is negative. In other words, source is receiving power. Applied voltage is positive, current positive, source is supplying power. Applied voltage is positive, negative, current positive, power negative. Therefore, source is receiving and source is supplying. Average is 0, average is 0 at steady state. I am neglecting the losses in the inverter and I am neglecting the i square r losses in the inductor, i square r loss plus the hysteresis and whatever losses are 0. So, therefore, a very important result, very important result, average power consumed by the load is 0. If under ideal condition, power, average power, average power supplied by the sources, sources, come on answer, just now you have to copy, is 0. So, I can replace that battery by capacitor, charge the capacitor once and forget about it, it will go on forever under ideal condition, high enough. Under non-ideal condition, what do I need to do? No, keep on charging does not mean anything. So, at under non-ideal condition, the losses that are taking place are device losses, inverter losses, that are inverter losses and i square r losses in the inductor. They are, basically they should be as small as possible, as small as possible, are you with me? So, what is your conclusion? What is our, what inference can we draw? What inference can we draw? What inference can we draw? No, in the sense, the power that is required by the inverter to supply a large cube is very small. In other words, delta P is required to supply, supply, supply the losses, which is a small amount of power that is required, a small amount of power that is required to supply, for the inverter to supply or to feed this inductor. So, what is the power, what is, see this source is feeding an inductor. So, basically it is a DC to AC converter or I have a AC source, which is feeding an ideal inductor. In other words, the power factor of the load is, power factor of the load is 0 or in other words, power supplied, power consumed by the load is 0, it is entirely reactive power, entirely reactive power. So, on that, so therefore, the cube, reactive power is cube, cube drawn by this source is equivalent, is equal to the rating of that inverter. Are you with me? That rating could be much higher, but then to supply that cube, inverter requires a very small amount of P, a very important result, very important, may be very obvious. Most of the things in this are obvious things that tend to become very obvious for us, someone, so that is the problem. So, active power input is only the inverter losses, active power input inverter is only the losses. First of all, so if I neglect the losses, it is taking of the portable generator, it is supplying an inverter, suppose I have a portable generator, if it is supplying an inductor, what is the fuel input? What is the fuel input? Suppose, I have a portable generator, supplying an ideal inductor, what is the fuel input? Fuel input is 0, it is a perpetual motion, it can go on forever, it can go on forever. Otherwise, a very small amount of fuel that is required to supply that cube. So, why am I discussing this? Why am I discussing this? Because I had asked you a question, why am I discussing this? A inverter feeding an inductive load, why am I asking this question? Reactive power concern. I said that in the sense, we have installed a high power inverter to feed the power to the grid. During the fulls, may be in the afternoon when the peak time, the inverter is supplying the full power to the grid. In the evening, there is no sun insulation now and at that time grid is a distribution network is loaded by, loaded by inductive loads, it requires reactive power, are you with me? Now, you told me that if I connect capacitors there, what will happen? Reactive power supplied by the capacitor depends on the supply voltage, Reactive power supplied by the capacitor depends on the voltage of the network there. V divided by x c is i c, v comes down as v comes down, i c comes down. When v comes down, when the system is loaded by inductive loads, v comes down, isn't it? So, when the system is loaded by inductive load, v comes down, at that time system requires high Q, but capacitor is not able to supply that Q. So, we want a solution, we want a solution that Q supplied or the capability of the source to supply Q should be independent of, independent of the grid voltage, should be independent of the grid voltage. So, that is the requirement we will see. So, when the evening, when there is no sun insulation, this inverter can supply Q, but then in the night there is no sun energy. So, what do we do? What do we do? In the sense, in the evening or in the night there is no sun intensity at all, there is no active power at all. What do we do? How this inverter can supply Q? How this inverter can supply Q? No, we can draw power from the grid. You draw a small amount of power from the grid, grid in return you give, in return you give or reactive power. The closed loop control we will decide, we will discuss. Another question, control question that I want to ask is, see you are trying to draw the maximum power from the solar cell using an MPPT. Are you with me? Now, that power has to be fed to, fed to the grid. Now, how do I know how much power to feed it to the grid? How do I ensure? How do I ensure that whatever power that comes from the solar cell has to go to the, should be or to be, we should feed it to the grid. How do I ensure? How do I ensure? See, I do not know many of you have got that question. Solar panel, DC to DC converter, irrespective of the topology, I have a low voltage, may be here I have a reasonably high voltage, maximum I have used a MPPT. Now, this power has to go to the grid, through an investor I will feed it. How much power to feed here? Who will tell me? How do I know? How do I know how much power to feed to the grid? Are you reactive? I am talking about power. Who will tell me how much power to feed it to the grid? MPPT extracts the maximum power from the solar cell, it dumps in this capacitor. Now, that power has to go to the, now here is an inverter, here is an inverter. How do I feed that power? Exact power, whatever the power that comes from the inverter, how to feed it to the grid? How do I ensure? You may not have an answer right now, think about it, we will see. Are you with me? You got the question or no? How to feed the power to the grid, what exactly? That is all fine, that is all fine, in that sense leading, how much it should lead? Who will tell you? Fine, in the sense this voltage should lead, I know it is v1, v2 divided by x into sin delta is the power transfer, a grid. Now, I have two variable, delta is also it could be varied, I can vary, I can vary this voltage as well. Now, this power transfer is v1, v2 divided by x into sin delta that should be equal to the solar output of the solar cell plus the losses, plus the losses. How do I and I do not think it has to be continuous process, it should be some sort of a closed loop control is required there. What do I try to regulate? Now, how do I try to regulate? Fine, think it over during lunch break, maybe in the night tomorrow morning we will discuss, when it comes to grid connection. Another thing simple question that I have, I have a single phase converter, single phase inverter, single phase inverter. I am satisfying almost all the conditions in the sense, power that is fed or current that is flowing into the grid is sinusoidal, assume that current that is flowing here is, here is, here is sinusoidal, do not ask me how would I achieve it, achieve it. How does this voltage look like? Can I have a constant DC or does it pulse it? It is a voltage source inverter, it is a voltage source inverter. This capacitor is being charged, is this capacitor is being charged from the solar energy and this and I am dumping the power to the grid here. I have a single phase inverter, I am using whatever some techniques I will use and ensure that current that is flowing here is, is sinusoidal. I have a single phase inverter, afterwards I will have a three phase inverter, what will you observe or if I observe the voltage across the capacitor, how does it look like? No, it is not ideal, this is in reality. You got the question sir, I have a single phase and I have a three phase, same thing, single phase and I have a three phase, current somehow I have made this current to be a sinusoidal, how we will see later, what will happen to this voltage? Third? He is saying here it is 100 hertz triple and here, no, no, no DC, they are saying non-harmonic charge and discharge constant. Ma'am, why should there be 100 hertz? Why there should be 100 hertz? See, it is a 100 hertz, there will be 100 hertz pulsation, whether the energy is coming from solar cell does not matter here. If I am connecting this inverter to the grid, see all these principles are required. In the sense, tomorrow you will say why the DC link voltage is, that is one of the parameters criteria to choose this capacitor. How will you choose the capacitor here? You need to know, this in single phase case, there will be second order pulsation, there is a 100 hertz pulsation will be there, why? We will see and here under ideal conditions, under ideal conditions, under ideal conditions, no pulsation, no fifth and seventh. Under ideal condition, there are, there are no pulsations, why? Now, what is power power? Consider V is equal to Vm sin omega t and I is equal to Im sin omega t minus phi, minus phi plus or phi is 0, it does not matter. What is instantaneous power? V i. So, instantaneous, see I am assuming the current to be sinusoidal, voltage also is sinusoidal. So, therefore, under this condition, what is, what is the expression for P, instantaneous power P, there is V i cos phi, then, then that is all, come on. Sine of t omega t. Sine of t omega t is something, what is it? Sine of t omega t. Yeah, power in single phase pulsates as twice the supply frequency, a very important result which we teach our students in the first semester or second semester, very important result. Power in single phase pulsates as twice the supply frequency, this is average power. In addition, there is, there is a second harmonic pulsating component. Now, in three phase, in three phase, P in instantaneous power in three phase, instantaneous power in three phase, what is the expression? Sir, what is the instantaneous power in three phase? It is constant, there is no pulsating component there, instantaneous power in three phase is 3 V i cos phi, whereas here it is, here it is into cos 2 omega t term is there, pulsating component is there, twice the pulsating component, twice the pulsating component, pulsating component. Here it is, here it is constant, constant, constant. So, now, consider this circuit now. See, all these concepts are required to you, for you to design a closed loop as well, closed loop as well. Please, these concepts are very important. So, in the single phase case, now you may say that inverter is supplying, power is, it is equivalent to source is supplying a minus P, is not it? When I can say that source is drawing P, I can say that source is supplying. So, if the power supplied by this is pulsating at twice the supply frequency, if power supplied is pulsating at twice the supply frequency, definitely capacitor voltage also will pulsate at that frequency. Now, if power supplied is pulsates at twice the supply frequency, even voltage also will pulsate at twice the supply frequency. Whereas, in this three phase case, power supplied is constant, therefore, therefore, therefore, there will not be any pulsations. Under ideal condition, there will not be any pulsation. Under, what are the non-ideal conditions? What are the non-ideal conditions? What are the non-ideal conditions? No, unbalance one has to strike on you. What if, what if, if there is an unbalance? In a three phase case, if there is an unbalance, what happens? Come on. See your. . No, no, no. That goes so, why easily unbalance? Now, what is there? The moment there is an unbalance, how do I resolve it? Positive sequence and negative sequence. So, positive sequence three balance components constant, negative sequence, what will happen? Negative sequence, what is the characteristics? Why are they negative? They rotate in the opposite direction. What will happen to the power? Negative sequence, what will happen? Positive sequence, three balance quantities, same magnitude. Negative sequence, negative sequence, the direction of rotation is opposite. So, what will happen? . . . . . . . . . . If there is an unbalance, we resolved into positive and negative that is what we did. What we thought of a power system, in Spaß system of course, what next? How does it effect? I think please go through it. Think it over. When we discuss this, we will see. Please, see these are required because you will be, your inverter while supplying, there may be unbalance in the great. How does it affect the inverter? What will happen to the DC link? What sort of a of a pulsation will come. What sort of a pulsation will come if it is unbalanced? I was talking about see in the three phase case under ideal condition this voltage will not pulsate under non-ideal condition. What are the non-ideal condition? What I mean is I said I have assumed current to be a pure sinusoidal. Are you with me? Current is a pure sinusoidal. Can I have a pure sinusoidal current from an inverter? No. There is always there will be a high high frequency switching. I will just show you as a result. I will come back. This is the current waveform of an inverter. This is the current waveform of an inverter. It has it has it has it is not a perfect looks like a sine wave looks like a sine wave it is that 15 hertz current 15 hertz current. How would I achieve it? How did we get this sort of a current waveform will see approximately looks like sine wave. This is looks almost like a sine wave. So, if I write the Fourier series of this differently there is a sine omega t and and a high frequency component. So, so therefore, see the moment if if the current waveform has I am sine omega t and may be I am I am n into sine n omega t. Are you with me? Now product of sine omega t and sine n omega t what will happen? What is that product? A simple trigonometry and that is used here. It is not very difficult. Sine omega t and sine omega t there is an average high or not? Same frequency component there is an average component. Now, sine omega t and sine n omega t what is the average? Sine omega t into say sine omega t into sine 3 omega t what is the average? What do I get omega? Don't get nervous I say sine omega t into sine 3 omega t cos of cos of 2 omega t and cos of what is the average? The average of that is 0 is not it? So, sine vm sine omega t and is I am sine n omega t this average will be average will be average will be 0. Average is 0. So, therefore, but then it has a positive as well as a negative. So, capacitor voltage will pulsate at that frequency capacitor voltage will pulsate at that frequency high frequency. So, in a 3 phase if the current is pure sinusoidal DC link voltage is very stiff. If it is not or that voltage would not be very stiff if the current is current is non sinusoidal non sinusoidal. If the if the frequency of the current that is present in the output waveform is very high. So, DC link voltage will there be on the constant value there will be a high frequency switch in a single phase case it is not single phase case even if the current is sinusoidal even if the current is sinusoidal perfect sinusoidal there will be there will be 100 hertz pulsation there will be 100 hertz pulsation. So, things change when we go from single phase to 3 phase. So, inverter design capacitor selection is not the same for a single phase and a 3 phase they are different they are different. If this concepts are required because you have to sense the capacitor voltage you have to compare with the reference see consider a closed loop there is a reference there is an actual I cannot reference is always will be a constant value I cannot compare it with an pulsating value. So, I need to design a design a filter see I have come to that see this are basics that are required this basics we will use you will use while designing a control loop come back to 3 phase inverter I will quickly draw there are 3 legs 3 legs s 1 and s 4 are complementary. So, at any given time at any given time how many devices are on? At any given time 3 devices are on each leg 1 device is on each leg s 1 and s 4 are complementary s 3 and s 6 are complementary s 5 and s 2 are complementary at any given time 3 devices are on each leg in a voltage source current source is different current source is different. So, at any given time 3 devices are on one. So, I need to know the conducting state of conducting state of I need to know the conducting state of these 3 devices the moment I know the conductive state of this devices I know the conducting state of conductive state of this devices and therefore, I can estimate what is the output voltage here are you with me? If I know the conducting state of these 3 switches I can estimate I can estimate the output voltage of the inverter how do I estimate? How do I estimate? How do I estimate? Yeah excellent yeah you have to apply KVS see if I said conducting voltage if I know the conducting state this voltage is either on or off. So, if it is on I know see the problem here I know the voltage of this point of potential of this point with respect to with respect to centre point or with respect to negative DC bus in a 3 phase you do not require in fact centre point may not be available in 3 phase case this centre point is required for half bridge are you with me? To connect the load between these 2 in a 3 phase case this point is not required fine you can analyze it without this point no problem. If this point is available S1 potential of A potential of A either it is VDC by 2 or minus VDC by 2 or potential of A is either VDC or 0. If I take the negative as the reference VDC as potential of A is VDC or 0, but then for the load for the load for the star connected load I need to know the voltage of line A with respect to it is neutral I need to know VIN, VBN and VCN are you with me? How do I calculate this? There is no connection between the neutral point and the inverter reference inverter may be I can take as a negative DC bus or at the centre point, but then to determine the load current waveform I need to know the phase voltages I need to know the phase voltages for a star connected load VIN, VBN and VCN what is the relationship between what is the relationship between these voltages these are known as the pole voltages these are pole voltages and the phase voltages what is the relationship between line voltages and pole voltages? How do I determine the phase voltage? How does the phase voltage waveform how does it look like? How do we draw those steps? How do you draw the steps and what is the locus of the phase voltage? How does it look like? How does it look like? A hexagon has 6 sides fine good excellent do not recall subtraction of 2 pole voltages what it will give? What is the subtraction of pole voltages? What they will give? Pole voltages, pole voltages VA0, VA0 minus VB0 what it will give? That will be 9 volt, VA0 minus VB0 is VAB, but I want VIN, why did you subtract pole voltages? Why cannot you write? We want VIN is not it? Can we write, can we use KVL and write an expression for VIN, what is VIN, what is VIN, what is VIN? Sir, what is VIN? Is KVL you have to use and what is VIN in terms of pole voltages? VIN is VA0 plus VIN neutral is come on tell me I know this voltage VA0 I know plus V0 VIN excellent why there is an hesitation? It has to be complete is not it? VIN plus VNO is equal to V, V that is all, VBN plus VB, VBN NO is equal to OB similarly VCN NO is equal to, now you may say that you do not know what is NO, you can get isn't it? What is the problem? Not load, you gave me the equation VA0 is equal to VIN plus VNO, VB0 is equal to VVN plus VNO and VC0 is equal to add them, what do you get? What do you get sir? VIN plus VBN plus VCN is 0, 3NO, 3NO is equal to VA0, VB0 plus VC0 therefore, VNO is equal to one third VA0, VB0, VC0. Now what you do? See I know VA0, I know VB0, I know VC0, I need to find out VIN, VBN and VCN, I need to find out VIN, VBN, VCN, I know VA0, VB0, VC0. See now I found out VNO in terms of VA0, VB0, VC0, substitute here, substitute here, so you can get, what do you, what do you with me? VNO is one third VA0, VB0, VC0, substitute in this, I can get VIN in terms of VA0, VB0, VC0, VC0.