B THE SOLAR ARRAY. Theory

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1 10. THE SOLAR ARRAY You will study a number of the electrical properties of the silicon solar array, its power output and optimum load resistance for maximum power. The silicon solar array is being used increasingly as an alternative source of power for reasons of portability, economy, and environmental friendliness. Solar arrays or panels, consisting of a number of solar cells, can be found in fixed installations in factories and homes, in mobile installations like Theory Why Study the Solar Array? experimental cars, satellites and spacecraft. 1 The electrical characteristics of the array can be investigated quite adequately with direct current (DC) meters. This experiment is an ideal application of the theory and practice acquired in the introductory experiment DC Circuits. Most solar arrays have a flat geometry, consistent with the need to capture the maximum amount of sunlight (Figure 1). Some are fabricated on a glass substrate, like the one used here, and are fragile while others have a flexible metallic backing which A First Look at the Solar Array enables them to be bent into convenient shapes and to be used in applications requiring some ruggedness, like pleasure boats and spacecraft. Connecting a solar array is very simple two wires connect the array to the external circuit. Figure 1. The solar array used in this experiment. A wooden frame and plastic cover protect it from accidental damage. B10-1

2 10 The Solar Array Photovoltaic Conversion The physics of the silicon solar array involves a good deal of the theory of electricity, electronics and quantum mechanics, subjects which are only surveyed in a first course in physics. The emphasis here, therefore, will be on the practical uses of the array as an alternative source of power, its power output for various light and load conditions. The cell (Figure 2) is the basic building block of any array. Each cell has the capability of converting solar energy directly into electrical energy by a process called photovoltaic conversion. The cell is essentially a large-area PN junction diode (or rectifier) made from two pieces of silicon fused together. 2 One piece is doped (or implanted with an impurity element) so as to yield an excess of free electrons (N type) while the other is doped with a different type of element so as to yield a deficiency of free electrons or an excess of holes (P type). One layer of the cell is made thin enough to enable photons of light to penetrate to the junction and there to interact with free electrons. A free electron which absorbs a photon in such an interaction is raised from the valence band to the conduction band. The result is an increase in the density of minority carriers in each semiconductor type hole density is increased in the P-type material and free electron density is increased in the N-type material. These carriers, if they reach the junction before recombining (meeting carriers of the opposite type and therefore annihilating one other), are swept across the junction by the electric field which exists across the junction. Once across the junction the carriers are free to move through an external circuit and deliver power to a load. Single cells are typically able to deliver about 0.5 volt to an open circuit. Numbers of cells are typically connected together in series to form arrays with voltage outputs of 6, 9, 12 volts, and so forth, and in parallel to provide whatever output current is desired. to next grid P-type N-type grid + foil Figure 2. The silicon solar cell (often in the form of a circular disk). Silicon solar arrays, because of their relatively low power output, are not often used as stand alone power sources. An array is most often used as a trickle charger for a higher-power source like a lead-acid battery or gell-cell. Under normal usage conditions the battery is connected to the main load (house wiring, etc) and is not connected to the array. For recharging (during periods of nonusage), the battery is disconnected from the main load and is connected to the array. In the marketplace, therefore, solar arrays are B10-2 Characteristics of Arrays commonly described as to the maximum power, P MAX, they can deliver to a common load type (like a lead-acid battery), the open circuit voltage, V OC, they can deliver (with no load connected) and the short circuit current, I SC, they can supply (when the output terminals of the array are short circuited). These parameters are quoted for the array for one full sun, which is the illumination received in an outdoor position on the equator at high noon on a summer day. For the array you will be using in this experiment, P MAX is about 1 W, V OC about 13

3 The Solar Array 10 V and I SC about 100 ma. Your measurements will yield different values from these as you will be using your array in a light box under an artificial light source which produces an irradiance of much less than one full sun. Solar arrays are intended to be used outside in full sunlight. To calculate the efficiency of an array one must know the solar irradiance, that is, the amount of power per cm 2 falling on it from the sun. The solar irradiance above the earth s atmosphere is known from measurements aboard satellites to be about 140 mw.cm 2. But at the earth s surface the irradiance is reduced due to absorption by clouds and scattering of various kinds. On a bright clear day at high noon (with the sun directly overhead) the irradiance on the surface at the equator is about Full Sun Conditions 95.6 mw.cm 2. (But see also endnote 3.) You will use this information to calculate the efficiency of your array. The efficiency of a device is written % efficiency = power out power in x 100 [1] The efficiency of an ideal cell is theoretically about 22%. On account of certain losses within real cells typical efficiencies are about 11%. Obviously a great deal of research is ongoing to improve the efficiencies of solar cells. The equivalent circuit of the cell is a somewhat advanced topic, mostly of interest to students who have taken a course in electronics. It might, however, help you to explain some of your experimental results so a survey of the subject is given here. The cell is best described electrically in terms of its equivalent circuit, one example of which is drawn in Figure 3. The double circle symbol on the extreme left represents a source of constant current, I PH, which is the current produced by light (photons) falling on the cell. The next symbol to the right is that of the PN junction diode. Some of the current produced by the light flows back across the junction forming a diode current or I D. The cell is not without internal electrical losses which can be modelled as an effective series (or internal) resistance R S and an effective shunt resistance R SH. In the ideal case R S would be small enough and R SH large enough so the effects of both could be neglected. In fact, however, R S is not constant but depends on the illumination and to a lesser extent on the cell s temperature. Not surprisingly the cell s temperature depends on the illumination. Expressions can be derived by applying basic electricity theory to Figure 3. Applying Kirchoff s The Equivalent Circuit of the Array junction rule to node P (assuming R SH is infinitely large) gives I = I PH I D. [2] An expression for the diode current I D is well known from the theory of the PN junction diode (see the experiment The Semiconductor Diode ): I D = I 0 exp ev kt 1, [3] where I 0 is the reverse saturation current, e is the electronic charge, V is the output voltage, k is Boltzmann s constant and T is the absolute temperature. The IV photovoltaic characteristic for the cell then becomes I = I PH I 0 exp ev kt 1. [4] Experimentally, the functional relationship given by eq[4] is more-or-less observed as shown by the shape of a typical IV curve reproduced in Figure 4 for some arbitrary irradiance. Included on Figure 4 is a typical power output curve. The effect of a B10-3

4 10 The Solar Array higher irradiance is to shift the IV characteristic upwards and to increase P MAX. A higher irradiance also increases V OC very slightly. It is the object of this experiment to show that the curves of Figure 4 really do describe the solar array issued you. P I I PH R I S D R SH R L V Figure 3. The equivalent circuit of a silicon solar cell connected to a load. (The load is to the right of the dashed line.) Output Current (ma) Maximum Power Short Circuit Current Isc Open Circuit Voltage Voc Output Power (mw) Output Voltage (V) Figure 4. A typical IV curve for a solar cell (or array) subject to some level of irradiance. This graph was exported from Excel and modified to emphasize special features. Notice the power goes through a maximum in the knee reagion of the current. B10-4

5 The Experiment The Solar Array 10 Exercise 0. Preparation Orientation Identify the main parts of the equipment: one silicon solar array inside a cardboard light box, one high-efficiency fluorescent light source, two digital multimeters Model DT-890D, and one variable resistance box. Note the switch on the aluminum box that supports the light source. Please treat the solar array gently. It is formed on a glass substrate and breaks easily. The Array With the power to the light source OFF, remove the cover of the light box and peer inside. Notice the inside of the light box has been lined with aluminum foil to maximize the amount of light falling on the array. Notice the array is mounted in a wooden frame for protection. Gently remove the array from the box and measure the array s area with a meter stick. When finished, replace the array in the box and the cover on the light box. First Observations Turn the light source ON with the switch in the high position. With one of the digital multimeters measure the array s open circuit voltage V OC and short circuit current I SC. What happens to V OC and I SC when you switch the light to the low position and then OFF? Exercise 1. IV Characteristic and Power Output In this exercise you will attempt to obtain your own IV characteristic and power output curve. Assemble the circuit of Figure 5, turn the light source ON and select the high light position. For various values of R L (starting from, say, 90 kω ) and working downwards measure I and V. Be sure to take enough data to enable you to observe a definite P MAX. A good procedure is to start at V OC and take measurements at 0.5 volt intervals, 18, 17.5, 17, etc. To plot the IV curve and to calculate the power enter your data into an Excel spreadsheet. Plot a graph like is shown in Figure 4. What is P MAX in mw? For what value of load resistance R L does it occur? Repeat the above for the other light setting. How does the different light levels affect I SC, V OC and P MAX? Does P MAX occur for the same R L? It can be shown that at P MAX, R L = R s. Do you conclude therefore that R S is a constant or depends in some way on the irradiance? A I Array R L V Figure 5. Circuit for studying the IV characteristic of a solar array. For R L = 0, V = 0, I = I SC ; for R L =, V = V OC, I = 0. B10-5

6 10 The Solar Array Exercise 2. Practical Matters In this exercise you will study the array under full light conditions (if it is a sunny day!) Take the array itself with one meter and connecting wires outside to the work area on the sixth floor patio (your TA will point the way). While outside quickly measure I SC (full sun) and V OC (full sun). Return to the lab. From this knowledge of I SC (full sun) and V OC (full sun) you should be able to estimate P MAX (full sun). Assuming an outdoor solar irradiance of 95.6 mw.cm 2, calculate the total solar power incident on your array. From your estimate of P MAX (full sun) calculate the efficiency of your array. Examine the poster in the lab entitled Map of Solar Energy in the United States and Canada. This map shows the availability of seasonal and yearly solar radiation that can be used for heating houses and water supplies in the United States and southern Canada. Generalized contours show the daily solar radiation averaged over the year. The unit used on the poster is BTU/ft 2 /day. (BTU stands for British Thermal Unit.) From this poster find the solar radiation value for Toronto and convert it to Joules per meter squared. A useful conversion factor is 1 BTU ft 2 = x 10 6 Jm 2. Now calculate a revised value of the efficiency based on this new value of solar radiation. Exercise 3. Optional Advanced Topic Make some attempt to apply eq[4] to describe the shape of your experimental IV curve. (Note that I SC = I PH for V = 0.) In fact, this model is simplistic. To fully account for the shape of the IV characteristic an additional curve factor must be added (for full details consult the sources in endnote 1). B10-6

7 The Solar Array 10 Videos and Physics Demonstrations on LaserDisc The story of an American entrepreneur who developed the first practical flexible solar panel is chronicled in Japan s American Genius, Tape #107. from Chapter 66 Quantum Physics Demo Solar Cells Activities Using Maple E10The Solar Array This worksheet expands on some of the mathematical aspects of arrays. It enables you to enter the data you collected in the experiment, The Solar Array, to fit and plot it. Stuart Quick 94 EndNotes for The Solar Array 1 The teaching literature contains a number of papers on the silicon solar cell used in an undergraduate physics experiment like this one. The contents of this guidesheet are largely based on the paper by D. W. Kammer and M. A. Ludington, Laboratory Experiments With Silicon Solar Cells, American Journal of Physics, 45, (1977). But see also P. Mialhe and J. Charette, Experimental Analysis of IV Characteristics of Solar Cells, American Journal of Physics, 51, (1983) and A. Khoury, J-P. Charles, J. Charette, M. Fieux and P. Mialhe, Solar Cells: A Laboratory Experiment on the Temperature Dependence of the Open-Circuit Voltage, American Journal of Physics, 52, (1984). 2 The physics of the PN junction diode is discussed at some length in the experiment The Semiconductor Diode. 3 There is a poster in the lab that displays in map form average values of solar irradiance across North America. B10-7