We have seen solar photons at work, creating minority carriers that speed towards the solar cell’s output terminals under the magical influence of the p–n junction. But how is all this internal activity reflected in the cell’s power generation, and what voltages and currents are produced at its terminals? Figure 2.9 (a) helps answer the question with an equivalent circuit summarising the cell’s behaviour as a circuit component. It consists of a diode representing the action of the p–n junction together with a current generator representing the light - generated current I L.
In dark conditions IL is zero and the cell is quiescent. If an external voltage source is connected the cell behaves just like a semiconductor diode with the characteristic shown in part (b) of the figure . We choose to define the current I as flowing into the circuit and in the dark, it must be the same as the diode current ID. Note also that since a diode is a passive device that dissipates power, the cell’s dark characteristic lies entirely in the first and third quadrants (I and V both positive, or both negative). But if sufficient sunlight falls on the cell to turn it into an active device delivering power to the outside world, the current I must reverse and the characteristic will shift into the fourth quadrant (Inegative, V positive) shown shaded in the figure.
This equation confirms that the diode I – V characteristic is shifted down into the fourth quadrant by an amount equal to the light - generated current IL. This is shown in Figure 2.10 (a).
Most people are unfamiliar with curves in the fourth quadrant, so for convenience the I – V characteristics of a solar cell are normally ‘flipped over’ to the fi rst quadrant. This is equivalent to plotting V against − I. Part (b) of the figure illustrates a family of such curves for a typical crystalline silicon cell rated by the manufacturer at 2 Wp. Each curve represents a different strength of sunlight, and hence a different value of IL. You will recall that PV cells and modules are normally rated in peak watts (Wp), indicating the maximum power they can deliver under standard conditions (insolation 1000 W/m2, cell temperature 25°C, AM 1.5 solar spectrum). Therefore we should first consider how the rated power of 2 W prelates to the 1000 W/m2 I – V curve.
In general the cell’s power output equals the product of its voltage and current. No power is produced on open circuit (maximum voltage, zero current) or short circuit (maximum current, zero voltage). The full rated power is obtained by operating the cell slightly below maximum voltage and current at its maximum power point (MPP), shown as P1 against the 1000 W/m2 curve, and corresponding to about 4 A at 0.5 V, or 2 W. We can only obtain the promised output power by operating the cell at its MPP. Three other curves are shown for lower insolation values of 750, 500 and 250 W/m2; each has its own MPP (P2, P3, P4) indicating the maximum power available from the cell at that particular strength of sunlight.
Note that the maximum voltage produced by a silicon solar cell is about 0.6 V, considerably less than the 1.5 V of a dry battery cell. This means that it is essentially a low - voltage, high - current, device and many cells must be connected in series to provide the higher voltages required for most applications. For example the PV module previously illustrated in Figure 2.1 has 72 individual cells connected in series, giving a DC voltage of about 35 V at the MPP. Higher voltages may be obtained by connecting a number of modules in series.
The I – V characteristics suggest another important aspect of the solar cell – it is helpful to think of it as a current sourcerather than a voltage source like a battery. A battery has a more or less fixed voltage and provides variable amounts of current; but at a given insolation level the solar cell provides a more or less fi xed current over a wide range of voltage. The maximum voltage of the cell, its open - circuit voltage Voc, is given by the intercept on the voltage axis and lies in the range 0.5 V – 0.6 V. It does not depend greatly on the insolation. The close relationship between the diode characteristic of the p – njunction and the I – Vcharacteristics in sunlight, illustrated in Figure 2.10(a), means that the open - circuit voltage is similar to the forward voltage of about 0.6 V at which a silicon diode starts to conduct heavily.
The maximum current from the cell, its short - circuit current Isc, is given by the intercept on the current axis and is proportional to the strength of the sunlight. Other things being equal it is also proportional to the cell’s surface area. It represents the full fl ow of minority carriers generated by the sunlight and successfully ‘ collected ’ after crossing the p – n junction. The above parameters are further illustrated by Figure 2.11 . The blue curve shows a typical I – Vcharacteristic at 1000 W/m2 insolation, labelled with the short - circuit current, open - circuit voltage, and maximum power point. The red curve shows how power output varies with voltage; the maximum value is Pmp = Imp × Vmp. Since the current holds up well over most of the voltage range, it follows that the cell ’ s output power is roughly proportional to voltage up to the MPP. This emphasises once again the importance of operating the cell close to the MPP if its power output potential is to be realised. A widely used measure of performance that refl ects the overall quality of the cell is its fi ll factor (FF ) given by:
An ‘ideal’ cell in which the current held right up to the short - circuit value, then reduced suddenly to zero at the MPP, would have a fi ll factor of unity. Needless to say, practical cells do not achieve this; the I – V characteristic in the fi gure has a fi ll factor of about 70%. Equation (2.4) shows that graphically it is equal to the ratio between the areas of the small and large shaded rectangles in the figure.
So far we have not considered the effects of temperature on cell performance, but actually they are quite important, especially in the case of crystalline silicon. Many people imagine that solar cells are more efficient if operated at elevated temperatures, perhaps thinking of the type of solar - thermal panel used for water heating. But solar photovoltaic cells like to be kept cool – they do very well in strong winter sunshine in the Swiss Alps! In hot climates cell temperatures can reach 70 ° C or more and system designers often go to considerable lengths to ensure adequate ventilation of PV modules to assist cooling.
The main effect of temperature on a cell’s I – V characteristic is a reduction in open - circuit voltage, illustrated by Figure 2.12 . We have repeated the 1000 W/m2 curve for the 2 Wp cell already shown in Figure 2.10 (b) for the standard temperature of 25 ° C, and added two further curves for 0 and 50°C. The open - circuit voltage changes by about 0.1 V between these extremes, corresponding to 0.33% per°C. Note that the temperature coeffi cientis negative; in other words the voltage decreases as the temperature rises. There is a much smaller effect on the short - circuit current.
Generally the cell loses power at elevated temperatures, a more serious effect with crystalline silicon than most other types of solar cell. You have probably noticed one major omission from this discussion – an explanation of effi ciency. At the start of this chapter we noted that commercial crystalline silicon modules have typical effi ciencies in the range 11 – 16%, but we have not so far explained the reasons for this apparently rather disappointing performance. Returning for a moment to Figure 2.10 (b) it is not clear from our discussion why this cell, which probably receives up to about 14 Wp of incident solar energy, only manages to convert 2 W p into electrical output. Where does the rest go, and why can ’ t the efficiency be dramatically improved by better design? This raises some fundamental issues which we tackle in the next section.
0 comments:
Post a Comment