we have studied the construction and working of solar cells in the previous lecture now we have to discuss about the equivalent circuit and the characteristics of ap injection solar cell okay so first of all let us see the equivalent circuit of an ideal solar cell so what do you mean by an ideal solar cell ideal solar cell means a solar cell that is having no losses that does not have any losses a solar cell with no losses so if there are no losses that means there will not be resistances in the equivalent circuit so ideal solar cell will not have any resistances so this is the equivalent circuit of an ideal solar cell it can be represented as a current source in parallel with a diode and this current source is denoted as i p h which represents the photon generated current the current is generated as a result of receiving solar radiation or photo and it is denoted as iph and this current will be directly proportional to the irradiance that is power in the solar cell so the photon current iph is directly proportional to solar radiation the intensity of solar radiation or the irradiance that is power in the solar cell okay and the junction diode can be represented by a diode itself so this is the diode and in the ideal diode this photon generated current flows like this and a part of the current will flow through the diode and remaining obtained at the output so this i represents the output current or load current provided by a solar cell so we can write the equation for i as i is equal to iph minus id so this will be equal to iph minus id what is id we can use the general equation for the diode current that is i 0 into e raised to q v divided by alpha kt minus 1 so here i zero is the reverse saturation current of the diode i zero is the reverse saturation current and it can also be called as dark current so why it is called so so when there is no solar radiation that is under dark condition what will happen this diode will be iph will be zero in that case now photon current will be there when there is no solar radiation so under that condition this diode will be reverse biased so the current flowing through the diode will be the reverse saturation current i zero that is why i zero is also known as dark current now q is the charge of an electron that is 1.602 into 10 raised to minus 19 coulomb v is the voltage coming across the diode so here v is the voltage across this diode divided by alpha kt alpha is the diode ideality factor a constant known as diode ideality factor k is the boltzmann's constant and t is the temperature of the system in kelvin okay so this is the equation of current obtained from a solar cell from an ideal solar cell now we know that all solar cells are not ideal there will be losses so in order to account for these losses we have to add include resistances in the equivalent circuit so now let us consider the equivalent circuit of a practical solar cell so a practical solar cell comprises of parasitic resistances so definitely there will be resistances in the equivalent circuit of a practical solar cell so let us see how these resistances arises from where these resistances comes into the equivalent circuit okay so in the equivalent circuit we have series resistances as well as shunt resistance so so we have seen the construction of a pn junction solar cell phasor cell so we know that there are metallic contacts on the p layer and in layer there were metal grids and also the p layer as well as the n layer have some resistances to the flow of current so all these resistances are combined together and is represented as a series resistance r s in the equivalent circuit so a solar cell metal conducts and metal grids and then resistance of direction in addition to that appeal air semiconductor and layer semiconductor node resistance very physical resistance so all these resistance are combined together and this included as a series resistance in the equivalent circuit represented as rs okay now there will be a leakage current across the p-n junction across the junction or across the depletion layer there will be a leakage current and in order to represent this leakage current a shunt resistor is added because this current is flowing across the junction so we have to use a shunt resistor to represent this leakage current so that is represented as rsh so we have to minimize the leakage current so this shunt resistor will have a higher value of resistance and the series resistance affects the drop of voltage so it has to be minimized it will have a minimum value so in the equivalent circuit the series resistor will have a minimum value will have a small value and this shunt resistor will have a high value okay so this is the equivalent circuit of a practical solar cell and now let us write the equation for the output current so in this case output current i will be equal to iph minus id minus current passing through this rsh that is iph minus id minus i rsh so the equation becomes i p h minus i d equation 4 coming through the diode which is i 0 into e raised to q into voltage across the diode so here due to the presence of rs voltage across the diode becomes v plus i into rs so instead of v in the previous case we have used v here so that is the voltage across the diode so in a practical solar cell voltage across the diode becomes v plus irs so the remaining part of the equation is the same minus i r sh current flowing through this r sh so it will be equal to voltage across this resistor divided by its resistance so voltage across rsh will be v plus irs so v plus irs divided by its resistance rsh so this is the equation for output current of a practical solar cell now we have to draw the characteristics of the solar cell so a solar cell will be having two characteristics the current versus voltage characteristics and the power versus voltage characteristics so iv and pv characteristics we have to draw so both kera are drawn against voltage current is drawn against voltage we have to plot power also against voltage voltage has to be varied from a minimum value to the maximum value from 0 to its maximum value we have to vary the voltage now when will we get zero voltage across a pn junction diode so in order to get zero voltage we have to short circuit the output terminals so voltage across a short circuit will always be zero so zero voltage conditioning solar cylinder output in a short circuit so voltage across this short circuit will be zero and through a short circuit maximum current will flow we know resistance of the short circuit will be zero so current flowing through it will be maximum so when voltage is zero or under short circuit condition current flowing from the solar cell will be the maximum and this current can be represented as isc the short circuit current so this can be marked in the graph like this so we know when voltage is zero corresponding to zero voltage the value of current is isc which can be marked here okay when voltage is zero we will get the maximum current that is isc we have marked that current here so we go to this particular point in the graph so now what is the maximum value of voltage so we will get the maximum value of voltage when we open circuit the terminals of this solar cell so corresponding to open circuit the voltage will be maximum which can be denoted as voc the open circuit voltage and no current will flow through an open circuit so current will be zero under this condition so when voltage is maximum that is corresponding to voc voltage becomes maximum the current will be zero so we will get the second point this particular point so these are two extreme points of this iv characteristic current versus voltage characteristics of a solar cell and rest of the curve will be the voltage vi cara of a an ordinary pn junction diode when it is forward biased so we got these two points the point corresponding to zero voltage and current isc and point corresponding to zero current and voltage voc and the remaining part of the graph resembles the forward biased characteristics of an ordinary p n junction diode so we have got the v i carra the current versus voltage carrier of a solar cell now we have to draw the power versus voltage gear so as we have the vi carrier we can calculate the power corresponding to any voltage power is equal to voltage into current and we have the va carrier with us so we have the value of current corresponding to all the voltages so so from this graph calculate the power corresponding to different values of voltage at some random values of voltages calculate the value of power as the product of voltage and corresponding current so now plot that values of power in another graph against the corresponding voltages and then while plotting a graph the shape will be like this so we can see that at a particular point the power is maximum and this point is known as maximum power point and the voltage corresponding to that maximum power point is marked as vmp voltage corresponding to maximum power and the current corresponding to that maximum power is marked as imp the current corresponding to maximum power so this is the vi and pv characteristics of a solar cell first of all iv carri is plotted and from the scara we know the value of current at all voltages so we can calculate the power corresponding to different voltages and we will plot that values of power against voltage in another graph so joining all those points we will get the power versus voltage curve and the point at which the power is maximum is known as the maximum power point the corresponding voltage is marked as vmp and corresponding current is marked as inp so this is all about the characteristics of a solar cell and now we have certain parameters here which are important in the performance of a solar cell that is short circuit current is here open circuit voltage is here and some more parameters are there now let us see what are those parameters which are important in the performance of a solar cell so first one is the short circuit current isc we have seen isc before it is the maximum current that is obtainable from a solar cell when the output is short-circuited and this short-circuit current depends on the solar irradiance level area of the solar cell and characteristics of the material used for the cell so we know this isc short circuit current is directly proportional to iph this isc will be equal to iph minus id minus irs h so isc and iph are directly related and we know that this photon generated current is directly proportional to the solar radiance level the amount of solar radiation or the intensity of radiation that is received by the solar cell so isc depends on solar irradiance level and in addition to that it also depends on area of the solar cell and characteristics of the material used for the solar cell okay so isc is dependent on irradiance level and it varies linearly with irradiance level so it is directly proportional to irradiance level and this short circuit current is also dependent on the temperature of the solar cell but it varies slightly with temperature the short circuit current varies slightly with temperature and hence that variation can be neglected now the other parameter is the open circuit voltage voc so it is the maximum voltage across the solar cell terminals and it is obtained when the terminals are open circuited that is poc and it depends on quality of the material the material used for making this solar cell then it is a strong function of temperature and it varies slightly with irradiance we are considering short circuit current it is a strong function of irradiance and it varies slightly with temperature the case is different here the case reverses here voc is a strong function of temperature and it is a weak function of irradiance level and the equation for open circuit voltage in terms of short circuit current is voc is equal to vt into logarithm of isc divided by i0 plus 1 here vt is the voltage equivalent of temperature the temperature of that solar cell is converted to a voltage that is vt so voc is logarithmically related to isc that point is important so voc is logarithmically related to isc the short circuit current so next parameter the important parameter is the fill factor fill factor is defined as the ratio of the maximum power obtainable from a solar cell to the product of open circuit voltage and short circuit current so we know that vmp into imp is the power that a solar cell can produce maximum power that a solar cell can produce so maximum power output from a solar cell to the product of voc and isc that is the fill factor and the fill factor of a solar cell determines the quality of that particular cell so if the field factor is close to unity more power that means the array can give more power output okay and the typical values of fill factor is in the range 0.7 to 0.8 so field factor is a parameter that determines the quality of a solar cell its maximum value is 1. so next parameter is the conversion efficiency so it is the efficiency of a solar cell so we know efficiency is equal to output divided by input same expression can be used here so conversion efficiency of a solar cell will be the ratio of power output from a solar cell to the power incident on the solar cell so it is the ratio of electrical power output maximum electrical power output from a solar cell to the solar irradiance hitting the array to the power of the solar radiation input power is the power of the sun and output power is the electrical power so this output divided by input gives the conversion efficiency of a solar cell and usually solar cells are having very low efficiencies typical values are in the range 10 to 12 percentage so these are the various parameters performance parameters of a solar cell