If a solar cell uses the same metering direction for both voltage and current like with standard diodes (load metering system), the characteristic curves shown in Figure 3.13 for illuminated and non-illuminated solar cells are obtained; this constitutes the idealized case using diodes with good reverse properties. The characteristic curve of an irradiated solar cell exhibits the same form as that of a non-irradiated cell and is simply shifted by Isc in the negative current direction by virtue of the fact that photocurrent and diode
of solar cell
l-v curve of
Figure 3.13 Idealized characteristic curve of a solar cell (illuminated and not illuminated) with an idealized good reverse blocking behaviour (low reverse current)
current flow in opposite directions (in comparing Figures 3.13 and 3.12, note that I — —I). The solar cell consumes power in quadrants 1 and 3, but it generates power when the cell is operated in quadrant 4.
No problems arise when solar cells are wired to solar modules, so long as measures are taken to ensure that: (a) the load on a shaded solar cell in the forward direction does not exceed more than about ISC (which the cell can tolerate without problems under open-circuit conditions); and (b) in the reverse direction it is not subjected to unduly high voltages, so as to avoid unduly high cell power loss. Unduly high stress can overheat solar cells and thus ruin an entire solar module.
For further details concerning solar cell characteristics under unusual operating conditions in power quadrants 1 and 3, see Chapter 4.
For solar cells, the characteristic curves of power quadrant 4 are of overriding importance as this is where they generate power. Hence in most cases only this characteristic curve is indicated, whereby the metering directions for Vand I shown in Figure 3.12 are used (generator metering system) so as to ensure that V and I are positive.
Figure 3.14 shows a characteristic curve I — f(V) for a solar cell. When used with low voltages, a solar cell is a virtually ideal source of current. But once voltages approaching open-circuit voltage VOC are reached, the current drops off fairly sharply (the diode in the equivalent circuit as in Figure 3.12 begins to conduct current).
In addition to current, power is also akey parameter since solar cells are used to produce electrical energy. Power is determined by multiplying current by voltage. Determining the power for each point along the characteristic curve I — f(V) results in the curve P — f(V), which is likewise shown in Figure 3.14.When a solar cell is in an open-circuit or short-circuit state, it produces no power. At a defined point known as the maximum power point (MPP), a solar cell reaches its maximum power and thus the value
Pmax = PMPP.
Using the simplified circuit of Figure 3.12, the following equation for determining VMPP can be obtained by rearranging the product P — V■ I from Equation 3.3 based on V:
In the interest of using solar cell power optimally, a connected consumer should be installed in such a way that it operates in as close proximity as possible to the MPP. However, this is easier said than done,
since the MPP site is determined by irradiance, temperature, manufacturing tolerance and ageing. A device that ensures that a consumer is always operating at the MPP is known as a maximum power point tracker (MPPT) or maximum power tracker (MPT).
The maximum power, Pmax — Pmpp — VMpp ■ Impp, that a solar cell can produce at the MPP is always lower than the value obtained by multiplying open-circuit voltage VOC by short-circuit voltage Isc. Inasmuch as a PV system needs to be able to withstand both open-circuit and short-circuit current, the ratio of Pmax to VOC ■ Isc is a key solar cell measurement value, along with efficiency. This ratio is known as the fill factor:
The fill factor for commercially available solar cells ranges from around 60 to 80%, while this factor for lab cells can go as high as about 85%.
For the simplified equivalent circuit of Figure 3.12, the fill factor can be determined quite accurately using the following equation [Gre95], [Wen95]:
As Equation 3.12 shows, a high Voc and low VT (low n close to 1, low temperature) promote a high fill factor.
The RS and Rp loss in the complete equivalent circuit diagram (see Figure 3.12) reduces the fill factor still further. According to [Gre95], approximately the following is obtained with characteristic resistance rch — voc/Isc:
As noted, a solar cell’s characteristic curve is determined by irradiance and solar cell temperature. Figure 3.15 shows the characteristic curves for the solar cell in Figure 3.14, with irradiance as parameter. Here, the short-circuit current is proportional to irradiance, whereas open-circuit voltage increases only slightly as irradiance rises.
This also means that solar cell voltage can be quite high even in the presence of very low irradiance – for example, at dusk. This fact should be taken into account when installing and servicing PV systems that exhibit relatively high voltages.
Inasmuch as the ratio between voltage at the MPP VMpp and open-circuit voltage VOC fluctuates only slightly, the MPP voltage is also somewhat lower for lower irradiance. In addition, under extremely low irradiance conditions, the voltage flowing through the parallel resistance Rp weighs more heavily on balance and results in an additional voltage reduction at the solar cell. On account of this reduced VMpp in the presence of low irradiance and the current flowing through Rp, solar cell efficiency is also lower in such situations. Figure 3.16 shows the efficiency of the solar cell in Figure 3.15, as a function of irradiance.
Figure 3.17 shows the characteristic curves for the solar cell in Figure 3.14, with cell temperature as parameter. In Si solar cells, open-circuit voltage decreases as temperature increases, by around 2 to 2.4mV/K (the temperature coefficient of VOC is -0.3% per K up to -0.4% per K); this decrease is attributable to the fact that diode threshold voltage in the equivalent circuit diagram decreases as for a standard Si diode. In this context, MPP voltage of course decreases as temperature rises. The fill factor FF likewise decreases as temperature rises (according to [Wen95], the FF temperature coefficient is
roughly —0.15% per K). Inasmuch as short-circuit current increases only slightly as temperature rises (the ISC temperature coefficient is only about +0.04 to +0.05% per K), power Pmax at the MPP also decreases as temperature increases.
For crystalline silicon solar cells, the temperature coefficient cT for Pmax ranges from about —0.4 to —0.5% per K. Inasmuch as PV system cell temperature can be 20 to 40 °C above the ambient temperature in the presence of high irradiance, this can provoke a considerable power drop and thus reduced efficiency at high temperatures; these parameters are often underestimated, however (see Figure 3.18).
Hence solar cells should be kept as cool as possible during operation, through the use of rear ventilation or the like.