PV Part A PDF

(Refer Slide Time: 04:16) To understand the photovoltaic cell, let us start with another PN Junction the well-known diode. Let us connect this diode in a circuit, a typical circuit for this would be something like this, where the diode is part of a much more complex external circuit as shown here....

(Refer Slide Time: 04:16) To understand the photovoltaic cell, let us start with another PN Junction the well-known diode. Let us connect this diode in a circuit, a typical circuit for this would be something like this, where the diode is part of a much more complex external circuit as shown here. Let us put in some terminals so this portion of the circuit the diode along with these terminals is of interest and let us study its characteristics before we try to understand the photovoltaic and cells characteristic. Let us call this terminal as A for anode and let us call this terminal K for cathode and we know that the current always flows from the anode to the cathode in this case the diode we call this as the current I. Another parameter terminal parameter of interest is the voltage across the terminals A and K we call that Vak. So it is of our interest to study the diode PN Junction in terms of the current through the diode and the voltage across its anode cathode terminal Vak. So with this polarity of voltage V ak being taken as positive that is the non arrow end as a common point for probing and the arrow end as the positive terminal for probing to the voltage and the direction of the current as shown here as positive, then we say that the power flows into the device. The device is acting as a sync and the power flow is into these one port terminals. The object of interest now is the diode part. So, we will bring the focus to the diode and this diode in its present representation as it is drawn in this circuit with the current flowing into the terminals anode terminal and with the voltage indicated as this and the power flowing into the diode terminals the diode acts as a sync which means it receives power and only dissipates it cannot generate. So this particular portion of the diode circuit is now a sync circuit and not a generator circuit. We will gradually see how we make it into a generator circuit and what extra components we need to add in order to bring about the model of the photovoltaic cell. Let us now make some space for drawing the characteristic. We will reduce this portion and keep it there. Let us have the x-axis and we shall mark it as Vak this is the voltage axis and then we have the y-axis we shall mark it as i and draw the I-V curve. The I-V curve of this particular diode is very familiar to all of us we will stick to drawing mainly the forward portion of the characteristics which of course things like this. So this is a familiar static curve of the diode and we know how this has come about. Now from this how do we develop the photovoltaic cell model. We see that the first quadrant is involved in dissipation and is the dissipation mode of components basically sinks where in the current flow is into the terminals are shown. The fourth quadrant is a generation quadrant. Here the voltage is still in the same direction and only the current has become negative or current as reverse direction here in which case the power flow also reverses direction which means the power is flowing out of the terminals and therefore acting as a generator. So this portion of the I-V characteristic is of interest to us because we would like to see how this diode can become a PV cell and also a generate. Let me drag this here, a copy of it here and increase the size so as to make it more legible. So in this quadrant we see that the current is negative with respect to what we have represented here if this was supposed to be the positive direction of the current flowing into the terminal, negative would be direction of the current flowing out of the terminal. And the object here, the diode in this case plus something else will act as a source and the power is actually now flowing out of the terminal. Because the product of these two will result in a negative value which means negative power. So in this quadrant fourth quadrant this component or object is behaving as a source but how does the current here flow in this direction because we all know that the diode can handle current flow only in the direction from anode to cathode. How can one make the current flow in this direction out of the terminal. Across the diode we add a current source 'ip' in such a direction the current is flowing in this fashion as shown. Only under this condition, you will see that this current splits at this node into the diode id as shown here and into the terminal i as indicated here. Therefore, you see that, through the diode the current is still flowing from the anode to the cathode but at the terminal the current is flowing out of the terminal. So if you look at this whole block as a whole the current flows out of the terminal voltage is still retaining the same polarity the power 'is' flowing out of the terminal and therefore this whole block acts as a source this is actually the principle of the photovoltaic cell. This current source 'ip' is actually the photocurrent which is dependent upon the solar radiation intensity. More the solar radiation intensity higher is the value of the 'ip', larger will be this current and larger will be the current flowing out of the terminal and power. There are a few other components and non- idealities also that will come into the model but this basically will indicate how the photovoltaic cell is behaving as an electrical source from an electrical engineers point of view. Let us study it just a little bit further before we develop the equations for that. 'ip' is the photocurrent which is directly proportional to the solar intensity, the solar power that is incident on the surface of the panel. If 'ip' is zero that is under dark condition, the characteristic is like this with the bias at the x-axis line. As the light intensity increases the photocurrent 'ip' increases and this whole characteristic starts coming down by amount equivalent to the photo current. So increasing 'ip' would mean the shifting of the characteristic like this. Higher the incident power incident solar power the more the characteristic will shift towards the fourth quadrant. So any operating point on this part of the curve would mean that the photovoltaic cell is operating in the generating mode. So normally the photovoltaic cell is considered to be a generator and one would like to see that it is in the first quadrant. Therefore, we now redefine the current, the voltage remaining the same but the current the direction of the current we will take it as positive for this axis when the current goes out of the terminal as shown here and not like what it was defined before for the case of the simple diode. So we would not like to have this but would like to use this as a reference now and this we would like to bring it to the first quadrant which would mean we have to flip the current axis. And that is done by just simple flipping of the y-axis because the current has just flipped the direction. So this here forms the characteristic the I-V characteristic of a photovoltaic cell. Consider the I-V characteristic of a typical photovoltaic cell observe that for some portion of the I-V characteristic the photovoltaic cell behaves as a constant current more or less constant current for this portion of the characteristic the photovoltaic cell would behave like more or less a constant voltage source so the photovoltaic cell has the unique feature of being both a combination of a constant voltage source and the constant current source. Let us draw a line is the constant current line let us draw another line with a constant voltage line, the constant current line if you take, it gives an idea of the slope of the constant current portion and therefore, it implies existence of a shunt resistance a high value of shunt resistance across a constant current source. So we can include a non ideality or shunt, a higher value of shunt resistance across the constant current source as shown here. Likewise the voltage line, the slope of it to the voltage portion of the characteristic would imply a series impedance in series with the terminals so it would appear as though we have a series impedance at the terminals like this. So let us include this non-ideality also to the existing model. Minor redrawing and relocation of the components, this forms the equivalent circuit model of a photovoltaic cell. This has a symbol which looks like this, this envelope like symbol is the symbol of a photovoltaic cell it represents either a photovoltaic cell or a photovoltaic model. There are two terminals, the anode terminal and the cathode terminal. This is the terminal voltage and the terminal current generally flowing out of the anode terminal. So here, we have the entire photovoltaic cell with a characteristic, the equivalent circuit model and the symbol.  Indian Institute of Science Design of Photovoltaic Systems Prof. L.Umanand Department of Electronic Systems Engineering Indian Institute of Science, Bangalore NPTEL Online Certification Course (Refer Slide Time: 00:19) We have here a photovoltaic cell, the symbol of a photovoltaic cell, the terminal voltage v and the terminal current i that is supposed to flow out of the terminal 'a' here is indicated and we also know we have seen before, the equivalent circuit model of this photovoltaic cell and that is like this, where you have this constant current source representing the photo current the photo current ip is basically directly proportional to the incident solar power. This is primarily resource, rest all other parameters are sinks, dissipaters and we shall now try to study this equivalent circuit model a bit further and try to arrive at the equation for the terminal current with respect to the various parameters of the photovoltaic cell. So using this model, we shall further get some more insight into the photovoltaic cell which will be useful for selection choice of the photovoltaic cell. (Refer Slide Time: 01:57) Let us clear some place and position the equivalent circuit here. The, looking at the equivalent circuit the current ip is equal to id the diode current plus the current through the resistance R shunt plus the terminal current i. If you consider this as the reference node, the voltage at this node again can be seen that it is equivalent to v plus this drop and this drop is having a potential which is positive here and negative here. And therefore, you have at this point v plus iR s. Therefore, i flowing current flowing through R shunt is v plus iRs divided by R shunt. Rearranging we get the current terminal current which is ip minus the diode current id minus the current flowing through R shunt which I can write as v plus iRs by R shunt. (Refer Slide Time: 03:45) Now the diode current, we know from the PN Junction theory, i d can be written as I0 which is the reverse saturation current e to the power of voltage across the diode which is nothing but v plus iRs by an ideality factor n into VT minus one. So this is the current equation for the diode it comes from the PN Junction theory which you will find it in any electronics PN junction chapter. Typical reference would be the integrated circuits electronics by Millman and Halkias. Now what is VT, n and I0t. I0 is the reverse saturation current, VT is the volt equivalent of temperature, VT is the volt equivalent of temperature and given by Boltzmann constant into the temperature divided by q. q is electronic charge in coulombs, K is the Boltzmann constant, T is the temperature in degree Kelvin. And if you substitute the Boltzmann constant electronic charge, you will get this to be a value T by 11600. n is a parameter which is dependent upon the material and it has a value equal to 2 for silicon and it has values which are different for other semiconductor materials. Now I 0 itself called the reverse saturation current, reverse saturation current, is also dependent on the material and the doping of the P and the N junctions. Not only that I0 is dependent on temperature. (Refer Slide Time: 06:25) So this is given by the following relation, K, T to the power of m, e to the power of minus V GO by nVT, the same n VT coming into the picture here. Where K is a constant which depends upon the dimensions of the PN Junction and also the material properties and V GO is numerically the equivalent band gap energy in electron volts. So V GO is basically the forbidden band gap energy which is EGO in electron volts. So this, this is again a numerical value which will come in there. V T of course is known which is same as, as written about T by 11600. n again is 2 for silicon. T is the temperature in degree Kelvin. Some typical values are like this, you have M which is equal to 1.5 for silicon and V GO varying from 1.16 to 1.21 again depends upon the grade of purification whether it is electronic rate solar grade, the solar grade for PV cells will be more closer to 1.16 volts. (Refer Slide Time: 09:22) So these are the typical values using which you can get the reverse saturation current for a particular PN Junction device. The entire model of the photovoltaic terminal current can now be written as ip is the photocurrent the directly proportional to the incident solar radiation minus I not, e to the power of V terminal voltage plus iR s by n VT minus the current flowing through the shunt resistance which is given like this. So this would form the terminal current model of the PV cell and this can be obtained easily from the equivalent circuit as shown above. So this equation of the current, a word of cohesion at this point, you see that the terminal current i is a function of itself. I appearing here in the equation so this means that this is an acausal equation which means that the present state of i is dependent on the present state of i itself. And therefore it is an algebraic equation and you can land up in problems when you do simulation. However, in practice you should understand that the diode is not an ideal diode it has junction capacitances and the junction capacitance across the diode will take care of the causality problems which means the voltage here will be a state and it will have history and memory and therefore the current here will not cause a problem, if you simulate this particular circuit in spice. Because, spice takes the real model of the diode along with the junction and diffusion capacitances. Whereas if you try to simulate this equation in Simulink in MATLAB, as an equation it will give you algebraic loop problems. So for that what would can be done is to use a memory block history block, pass this current through history block and use that to calculate the terminal voltages here. This would give some memory effect and can make the simulation work without problems. However, for our analysis and selection of devices and to understand the PV cell this model is more than sufficient and we will use this model to understand the PV cell further and characterize it.  Indian Institute of Science Design of Photovoltaic Systems Prof. L. Umanand Department of Electronic Systems Engineering Indian Institute of Science, Bangalore NPTEL Online Certification Course (Refer Slide Time: 00:17) In this clip, let us discuss the parameters of the photovoltaic cell. For this, let us have the model of the PV cell. This is the equivalent circuit model of the PV cell. We have the i p the photo current, the diode part, the shunt non-ideality and the series non-idealities coming here and these are the terminal voltages and the currents of the PV cell. Let us have in place the IV characteristic of the PV cell too. We will need this for our discussion now. Let me put down for you, the terminal current model of the PV cell that we discussed and developed in the last clip. So, we now have the terminal current model of the PV cell also written down here. Now looking at the IV characteristic, there are three significant points on the IV characteristic. We will discuss all these three significant points, one by one. The first point is at the intersection here. So let me mark that. So this is one point that we need to discuss. And I will call this as the short circuit point, shortly you will know why it is so. I will call this one as Isc, I short circuit. Now, this is origin 0, you will see that, this point is a intercept on the y axis when the voltage V is equal to 0, which means the terminal voltage is short circuited. It apparently would mean that the terminal voltage has been shorted like this. So, under such conditions you will get this Isc point, which would mean that for this particular significant point V is equal to 0, I is equal to Isc, we are setting it to this Isc and if we apply these constraints to this equation we will see that the short-circuit current point Isc is given by i p minus I0 e power zero plus Isc Rs by nVT minus 1 minus... So this is the equation after having substituted V = 0 and I = I sc the terminal currents. Now we have to further constrain that Rs is very very small compared to the shunt and I sc Rs is tending towards 0, it is a very small value of R s being very negligible, so which would mean that as a first step as an approximation so that we understand the relationship between the parameters, this is negligible, we can remove it from the equation. This portion, Isc Rs by nVT will tend to 0 so e 0 is 1 and therefore this entire diode current portion let us remove from the equation and you will see that I sc will equal Ip, the photocurrent which is proportional to the solar power which is incident. This we would call insolation, later on I will explain on this term insolation, but for now understand that insulation is the incident solar power. So the main take away from this critical point that we have been discussing is that that is the short circuit point occurring when the terminal voltage is short circuited. And the short circuit point is called Isc and this Isc is proportional to the incident solar power. (Refer Slide Time: 05:41) Next we shall discuss the second important, significant point in the IV characteristic, which is around this point and we will call that as V oc or the open circuit point. So this is the next important operating point that one has to consider. This we will call it as Voc. Now note that at this point, the current is 0 and the voltage thus obtained here is the open circuit voltage which means that here nothing is connected in the external circuit there is no current flowing through that, that current is 0, implying an open circuit character of PV cell. Now for this the constraints are, V will be set, the voltage terminal voltage will be set to V oc and the current terminal current is 0. So likewise, let us apply these currents to this equation and see what we obtained for the Voc terminal character, so you see that terminal current is 0, Ip – I0 into.... all this expression Voc by nVT minus 1, Voc by R shunt, I being 0. So this is the expression. Now here again we could say that R shunt is much greater numerically compared to Voc. And therefore we could remove this from the equation without loss of generality so that we get a much better picture of what is happening. And now repositioning these variables you Voc is equal to nVT logarithm of ip plus I0 by I0. So, this would be the equation that you would obtain. So, observe that there is a logarithm coming into the picture, V oc is related to ip the insolation but in a logarithmic way. So that, you have to keep in mind that if the insolation changes, if the incident solar power changes the variation of Voc here will be in a logarithmic manner. So if ip increases due to increase in the solar radiation Voc will increase logarithmically whereas Isc will increase linearly with the incident solar power, so this is the difference between this significant point and this significant point here. (Refer Slide Time: 09:54) I have now zoomed into the PV cell IV characteristic to show the effect of solar radiation change on the IV curve so this is IV curve and we see that this is the short circuit I sc point, this is the open circuit voltage Voc point. Now suppose that the solar power is changing what happens to the characteristic. If you take the readings of the IV curve at a different solar incident power you will see something like that and at a still higher solar power you will see something like that and you see that the short circuit points are increasing linearly whereas the V oc points are increasing in a logarithmic way as we just saw from the equation that we just developed. (Refer Slide Time: 10:57) There is another important and significant point related to IV characteristic of PV cell and this third significant point relates to the maximum power that can be transferred from the PV cell. Consider this IV curve and let us retain the same x-axis that is let it be the voltage axis, the y- axis we can include even the variable, power variable P which is the product of v and i. Consider for example this point the origin where i equal to 0 and v equal to 0, so there will be a power point which is P equal to v i i.e. zero and at this point P is V oc into i which is 0 and therefore power is 0 again here. So somewhere in between current will be nonzero, voltage will be nonzero and you will get a hill type of curve. So if you look at the power curve, it will be something like this having plotted this power curve using P equal to v i, now this power curve is having a maximum at this point and let us denote it by Pm the max power that the photo light cell can generate. Now if you look at the projection of the max power point on to the IV characteristic, you will see that somewhere at this point, it will intersect the IV characteristic and we shall call that voltage corresponding to that maximum power point as Vm and the current corresponding to the IV point as Im. And this point we shall call as the peak power operating point, so this is the point that is very important and the choice and selection of the PV cells too and we would like also to operate the PV cell at this operating point which means even the electronics, the electronic load to the PV cell should behave in such a manner that the PV cell is most of the time operating in this region where it is capable of delivering the max power from the PV cell and thereby utilizing it to the so least.  Indian Institute of Science Design of Photovoltaic Systems Prof. L.Umanand Department of Electronic Systems Engineering Indian Institute of Science, Bangalore NPTEL Online Certification Course (Refer Slide Time: 00:17) Having looked at the I-V characteristics and the significant points on the I-V characteristics, it is probably now a goodtime to look into the data sheets. Studying the datasheet and trying to map the datasheet parameters to the I-V characteristic significant points will give great insight into the character of the I-V characteristics and also to select the PV panels. We shall have a look at the datasheet and try to consolidate our understanding of the I-V characteristic of the PV panel. (Refer Slide Time: 00:55) This page shows the datasheet of photovoltaic modules. This is a poly crystalline 210 watts to 240 watt module. You see many columns here, each column represents a particular package panel and these are the parameters of interest to us and then let us see how they map to the IV characteristics. We will look at one typical panel of a particular wattage which is 240 watt peak and try to study each of the parameter. (Refer Slide Time: 02:00) And see how the map to the I-V characteristics that we study. For that let us place the I-V characteristics of there here so that you will be able to understand it better along with the datasheet. We now have here, the I-V characteristic of the PV panel. Consider these parameters and let us take this column, means we are taking a 240 watt PV panel. Now let me consider isc, this is 8.99 amps and let us mark it here 8.99 amps. V oc as given in the data sheet is 36.72. So we can write that down here 36.7 volts and we also have further parameters Imp and Vmp, Imp is the current at peak power point, Vmp is the voltage at peak power point they correspond to. This is V mp which we have used the term V m and this is Imp. So if you look at these two and map it on to the PV panel, this is equal to 7.96 amps. And this is 30.18 volts. Now, this is a 240 watt panel, what it basically means is that we have 240 watts as the peak power the panel is capable of supplying and that is, this point as indicated here. You could also get it by multiplying 7.96*30.18 volts. You will notice that the term p is used here, p represents peak, so generally in photovoltaic module datasheet terminology what is used is watt peak implying that it is the peak power point. So normally we would write this as P now one question arises, we have 240 Watts peak and this is the currents and the voltages as we see on the I-V curve. At what incident solar power do all these values apply. So normally there is a standard incident solar power and that is one kilowatt per meter square and at a temperature 25 degree centigrade. Now this is standard insolation we call it a standard insolation and 250 centigrade as the standard temperature. So if it is not specified all these values are given for this standard incident solar power per meter square and at a temperature of 250 centigrade ambient temperature.