Hello, I hope you've been learning from the lectures so far. In the previous lectures, you were presented the current voltage characteristic for a solar cell. Let us now consider this topic in more detail by working through an example question. The question is stated as follows. A solar cell has the following characteristics when tested under AM 1.5 conditions: a JSC of 35 milliamps per centimeter squared, a fill factor of 0.8, a Voc of 0.65 and output power of 18.2 milli watts per centimeter squared and an efficiency of 18.2%. Additionally, you may assume that nkT equals 25 mV, meaning that the cell temperature is about 25 degrees C and that the cell will not heat up at all during this question. The cell is now exposed to a light source under a concentration of 100x. What are the new cell photovoltaic parameters If we assume fill factor, nkT, and Jo do not change? If you wish at this point, you may stop the video and try to solve the problem on your own. If not, let's continue. To address the question, It is useful to consider the equivalent circuit for a solar cell as shown here. In its simplest form the equivalent circuit is made up of a diode in parallel with an ideal current source. The current versus voltage behavior of the diode, J diode is shown here. With Jo being the diode saturation current. Note: that if we were to short out the contacts, that is establish short circuit conditions that all the current must flow through the short circuit. Hence, the value of the current source is JSC. We can derive an expression for the open circuit voltage by observing that open circuit, all current from the source flows through the diode. Setting these two currents to be equal and solving for the voltage, we get the following approximate expression for the open circuit voltage. This is one of the most important equations to remember in photovoltaics. So take a moment to think about what it means. We can now consider how the equivalent circuit for a solar cell would change under concentration. Most obviously, exposing the cell to a photon flux 100 times greater will increase the value of the current source and therefore JSC by a factor of 100 as shown here. As it has been stated that the temperature of the diode does not change, the diode characteristic will remain the same. We can therefore write the expressions for the Voc in both cases as follows. To make the math a little simpler, we can rewrite the expressions in the natural logarithm form as follows. Now, what interests us is the change in Voc under concentration. So we can simply subtract these two expressions, which gives us the following one; the Voc will increase by nkT times the natural log of 100, an increase of 150 mV. Notice that this is true independent of the initial value of Voc. If we now increase the concentration by another factor of 100 to achieve a concentration of 10,000 times, the Voc would again increase by 115 mV. Let's now fill in the table for the cell. Under one sun and under 100 times concentration. Firstly, we can put in the values that we got from the stated problem. The only value not given was the irradiance which we know is 100 mW per centimeter squared as this is under Am 1.5. Under 100 times concentration this irradiance will be increased by a factor of 100, giving 10,000 milliwatts per centimeter squared. As we stated, this also means that the JSC will increase by the same factor. Two other elements remain unchanged, the fill factor and nkT. This leaves us with Voc, which we calculated would increase by 115 millivolts. We can use the three photovoltaic parameters to obtain the aerial output power and dividing by the instant irradiance we obtain the new efficiency of the cell. It's important to note here why the efficiency of the cell increased. The concentration of light increased the JSC by a factor of 100. But since the concentrating element of lens or mirror, would now occupy the full size of the old cell. We're not increasing the JSC, we normalized the size of the panel. However, this increase JSC causes an increase in Voc. And this is where the efficiency gain comes from, provided we can keep the diode cool and precisely focus all the light onto the device. Through this work problem, I hope you've gained some insight into the effect of changes in illumination on solar cell behavior. I also hope you have gained some insight into how concentration can help make cells more efficient. Thank you for your attention.
