Solar Energy
# PV: Engineering and Advanced Concepts

One simple way to explore the effect of concentration on PV performance is to revisit the simple circuit model for a PV cell. In the simple circuit model, a photo-generated current source \(I_{PG}\) is in series with a diode, and an electrical load can be put in parallel with that diode.

In this chapter, we added some resistances to the simple circuit model to more accurately reflect the operation of real PV cells.

Which parameter in the simple circuit model would be directly influenced by concentrating the sunlight incident on the cell?

In reality, when we concentrate the sunlight incident on a PV cell and increase \(I_{PG}\) (but keep other external parameters like cell temperature constant), this shifts the IV curve up, slightly improving \(V_{OC}\) and fill factor.

Thus, there is an efficiency improvement with concentration. The plot below shows the Shockley Queisser limit for unconcentrated sunlight compared with sunlight concentrated 1000 times. As you can see, using concentration has the potential to improve efficiency by a few percentage points, depending on the bandgap energy used.

While there is the potential to improve efficiency of PV systems with concentration, there are also some potential pitfalls. One way that concentration can reduce performance is that lenses (and mirrors) aren’t 100% efficient, so not all of the sunlight incident on the concentrating optics will be successfully directed to the PV cell.

Besides optical efficiency being below 100%, what is the other main performance drawback to using concentration?

Suppose we have a PV module which absorbs 60% of the sunlight incident on it as thermal energy, which it needs to dissipate to its surroundings at \(\SI{20}{\celsius}\) via convection, and the PV module has a convection coefficient of \(\SI[per-mode=symbol]{10}{\watt\per\meter\squared\per\kelvin}\). As a reminder, temperature rise \(\Delta T\) can be calculated as heat dissipated divided by convection coefficient times convection area: \[\Delta T = \frac{A_{module}\alpha Q_{solar}}{A_{conv}h}\] This means that under unconcentrated sunlight (\(\SI[per-mode=symbol]{1000}{\watt\per\meter\squared}\)), the temperature rise of the PV module would be \(\SI{30}{\kelvin}\) and the operating temperature of the PV module would be \(\SI{50}{\celsius}\). (Note that the convection area is double the module area, since the module can dissipate heat from the front and back of the module)

What would the operating temperature of the PV module (in celsius) be if we concentrated the incident sunlight 500 times, and added a passive heat sink to the back of the module which increases the area for convection by 50 times? Only consider convection for heat dissipation, do not consider radiation.

Suppose we have a PV module under concentration which generates \(\SI{400}{\watt}\) of electricity when exposed to \(\SI{1000}{\watt}\) of sunlight (corresponding to 40% efficiency).

What is the overall system efficiency (in percent) if \(\SI{30}{\watt}\) are required to pump cooling water behind the cell to maintain a low operating temperature that achieves a high PV efficiency?

Optical losses from imperfect concentrating optics, increased operating temperatures, and energy costs of active cooling all reduce PV performance. The plot below shows the SQ limit for unconcentrated sunlight, compared to the SQ limit for concentrated sunlight with an elevated cell temperature and 90% efficient concentrating optics. For some bandgap energies, the cell using concentration performs worse!

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Thus, in practical terms, concentration often leads to lower performance. This begs the question: when is CPV actually used? In practice, CPV is typically implemented with certain types of efficient but expensive PV cells, as using concentration with these expensive cells can reduce overall cost.

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