*It may be possible to drive up solar PV plant output with better panel heat dissipation, but a better thermal model is necessary first.*

A great way to reduce the cost of solar power is to increase the output of the solar plant. Solar photovoltaic (PV) panels lose efficiency when they operate at higher temperatures, and unfortunately, they generate heat and operate well above ambient temperature. So, a potential opportunity to boost power plant output is to dissipate heat better to drive up efficiency. After recently seeing a not-uncommon 7% thermal loss in a PVsyst simulation, my intention was to write about the value proposition for better panel heat transfer. However, it seems that panel thermal behavior in an operating plant is not very well understood. What seems to be needed first is further scientific study to understand what governs panel temperature in real solar plants. Then, a clear assessment could be made for the potential to boost output from better heat dissipation. Before the design engineers get to work, perhaps the boffins should have another go at it.

**Reduced Efficiency with Increased Temperature**

What is well known is how solar panel power decreases with increased temperature. Solar cells use a p-n junction in a semiconductor to form a band gap across which electrons jump on their way to generating electric current. As the temperature of the cell increases, the band gap decreases, and the open-circuit voltage decreases with it. Although the current slightly increases, the net effect is a drop in power. Either a detailed model of the solar cell can be used to find the power output for a given cell temperature, or the power at a reference temperature of 25°C can be adjusted by a temperature coefficient. Using this second method for a nameplate 400W Trina panel, the panel power output at 800W/m^{2} falls more than 6% from 320W at 25°C to 302W at 41°C, which is the stated panel nominal module operation temperature (NMOC). 6% matters. Getting 6% efficiency back would be like getting a 60% off coupon for a project’s solar tracker, and the industry fights hard for far less. But, the NMOC is not a very relevant number so it is not clear that there is a 6% boost to be had.

**Panel Temperature and Heat Dissipation**

During operation, the panel temperature rises to an equilibrium temperature such that the heat generated by the panel is equal to the heat transferred to the environment. Of the light incident on the panel, some light, say 10%, is reflected. The remainder is absorbed by the panel, which converts around 20% of the incident light to electricity. The rest of the incident light is converted to heat.

Heat dissipation takes the form of convection and radiation. With convection, picture the wind cooling the panel (forced convection) or the air adjacent to the panel warmed by it and then rising away from the panel (natural convection). Convective heat transfer depends first on the temperature difference between the panel and the air temperature, . It also depends on other factors, including the size of the area transferring heat, the wind speed, the air density and viscosity, and geometric aspects of the hot surface. Radiation heat transfer, which does not use air flow, depends on , where the ambient temperature is the temperature of whatever is in view of the panel, such as the sky, the ground, and any nearby structural elements. A surface property called emissivity matters too.

Ambient temperature, panel heat generation, wind speed, wind direction, and panel tilt (for a tracker) all vary throughout the day and the year. It would be fair to expect a model for panel heat transfer to be not so simple but still feasible for a computer simulation.

**Forced Convection (Wind-Driven) Heat Transfer**

We could go way into details on heat transfer. Let’s just touch on one fundamental part of forced-convection heat transfer, i.e. how the wind cools the panels. Forced convection depends strongly on how turbulent the flow is at the surface. A non-dimensional number called the Reynolds Number can account for whether a flow is laminar or turbulent and for how turbulent the flow is, and accurate forced-convection heat transfer correlations all rely on the Reynolds Number for the flow. Applied to a flow along a flat plate, it looks as in Equation 1.

Eq. 1:

*ρ* is the air density, which varies with air temperature and site altitude. *v* is the flow speed near the surface. *L* is length, i.e. distance from the leading edge of the surface. *μ* is the viscosity, which also varies with temperature.

When the flow is laminar, i.e. very smooth with no turbulent eddies, the Reynolds Number is small. A larger Reynolds Number reflects a transition to turbulent flow, and a large Reynolds Number predicts turbulent flow. Along a flat surface, the flow starts as laminar and transitions to turbulent as show in the diagram below.

If convective heat transfer depends on the Reynolds Number, a model for panel temperature should include the following variables:

- Wind speed at the panel surface. This is different from wind speed at 10m above ground, and it may be different for a perimeter row of a solar field versus an interior row since the perimeter row may block the wind for interior rows.
- Wind direction relative to the row of panels
- Site altitude, since this will affect air density
- Ambient temperature, since this affects air density and viscosity
- Distance across the row of panels, for example 2m if the row is 1 panel wide

Other factors besides the Reynolds Number matter too. Panel tilt may also matter by changing the flow of wind around the panels. Tilt will also affect how air warmed by the panel rises away from it during natural convection. Characteristics of structural members around the panel may matter too. They may obstruct air flow or alternatively disturb the flow to generate turbulence at a lower wind speed than if the flow were undisturbed.

**Solar Plant Models in Use**

I reviewed three solar plant software tools for this, PVsyst, PlantPredict, and HelioScope, and none of them capture key factors that would affect heat dissipation from the panel to the ambient air. Start with PVsyst. It uses a simple thermal model, as in Equation 2, that says that the the temperature difference between the cell and ambient air is equal to the panel heat generation times a heat transfer resistance (This is analogous to Ohm’s Law where electrical potential difference equals current times resistance; E = I*R.). The form of the equation is good, but the calculation for heat transfer resistance does not capture the factors that affect heat transfer. The PVsyst help file sums up the issue saying, “the determination of the parameters *U _{c} *and

*U*is indeed a big question.” Right. You need a new set of empirical constants for every new situation, which means the model’s usefulness is limited. PVsyst is clear in the help file that the model has substantial room for improvement.

_{v}Eq. 2:

PlantPredict uses a model done by a Sandia National Lab. team in 2004, written in Equation 3. This team made measurements on two rows of panels on fixed tilt racking at one site. With one panel type, one racking type, and one site, their model matched panel backside temperature with an error of +/-5°C, using empirical constants that were chosen to make the model fit the data. If the difference in temperature is, say, 20°C, then an error of 5°C means 25% error, which shows room for improvement. Since the heat transfer resistance term is not based on the characteristics of the system, the model cannot really be used to predict how a new racking system with a different arrangement of panels on a very different site would behave. The heat generation term is also high by ~30% since it assumes all of the incident light is converted to heat, neglecting that some is reflected and some becomes electricity.

Eq. 3:

HelioScope allows the user to pick one of the two models above.

**Assessing Theoretical Limits for Panel Temperature**

When thinking in terms of improving a design, it can be helpful to have a theoretical upper limit for performance to show how much room there is for improvement. Panel temperature cannot be any lower than the temperature of the heat sink to which it is dissipating heat, i.e. the ambient air. (Setting aside expensive schemes like water cooling the panels.) Perhaps a Temperature Efficiency could be defined to show how much power the panel makes compared with how much it would theoretically make if the panel were set to the ambient air temperature, in other words if heat dissipation were perfect, as in Equation 4.

Eq. 4:

This would show for a specific site weather profile what the loss from elevated panel temperature is. A more detailed temperature efficiency might incorporate heat generated by the panel and the wind speed. Clever engineers could use such an efficiency to keep score for how well the power plant design maximizes power output by minimizing panel temperature.

By contrast, when PVsyst indicates a “thermal loss” in its energy loss diagram, it really shows the relative power output compared with the power output at the reference temperature of 25°C. An example PVsyst simulation for a hypothetical 1-axis tracker project in Bakersfield, California using a 400W Trina panel states a -7.1% “thermal loss.” This does not say there is 7.1% energy that could be saved; it just says the panels make 7.1% less power than if they were at 25°C. A second simulation for a much colder site in Sitka, Alaska yields a thermal loss of +0.4%. Efficiencies are never above 100%! This is only saying that the panels operate below 25°C on average. 25°C is not really a meaningful temperature for any site, really. Reframing loss from solar panel temperature in terms of an efficiency could be more helpful to designers.

**Getting to a Value Proposition for Improving Heat Transfer**

A better solar panel heat transfer model and a framework of efficiency would help engineers approach the problem of making solar panels operate cooler to generate more power. While I was hoping to write about the value proposition for better heat transfer, further clarity on panel thermal behavior in the operating environment should come first. Research scientists and engineers might take on the problem to enable better engineering of solar power plants.