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Jun 23, 2011

Solar Panel Output Versus Temperature

The SAS Solar Farm data (available in the JMP File Exchange) has proven to be a rich topic for discussion and exploration. Besides the cool factor from green technology, the factors (such as sunlight, wind, temperature) can be understood by anyone, and yet the interactions are complex and not all linear. One issue that came up in the comments to my original post was the effect of ambient temperature on the power output. Rather than try to create an accurate model to account for sun position and solar panel angle, I tried some basic visual exploration to get a feel for the relationship of temperature and power.

A fair starting point is a basic plot of power versus temperature for the whole data set.

Here, I've set the graph transparency to 0.3 to give a point cloud effect. The visual is not too helpful except to get us to think about the other factors that are conditioning the relationship between power and temperature. Factors we have in our data set include time of day, day of year and solar irradiance. Other factors we might derive or get externally include solar angle, panel temperature and weather conditions.

Eschewing complex models, I tried conditioning the data on irradiance (sunlight) and time from solar noon (as a proxy for panel angle and sun position). The idea is that, say, two hours before noon and two hours after noon would have the same panel angle and sun position but likely different temperatures and power output levels. Solar noon, also called local apparent noon (LAN), is where the irradiance peaks on sunny days. We only have data in 15-minute intervals, and solar noon seems to be between 12:15 and 12:30 for the Cary, NC, area, and I chose 12:30 for my calculations. From that I calculated Minutes from LAN. Here's the power versus temperature conditioned on both Irradiance and Minutes from LAN.

Most of the panels show a slight negative relationship, as expected for solar cells. Eyeballing the trends suggests about 3kW per degree Celsius, or about 1% per degree. That seems a little high from what I've read, and I think it's because the panels still contain a bit of mixing of different conditions.

To go a step further, I decided to look at individual pairs of times equidistant from solar noon. With plenty of pairs to look at, I filtered it down to pairs with strong power output, a significant temperature difference (more than 4°C), a similar irradiance value and on a single array.

Each line connects a matched pair of temperature/power readings for a given day and panel angle (assuming the angle is proportional to minutes from local area noon). Now we can see that most pairs exhibit a small negative relationship, though there are a few outlier slopes in both directions. What accounts for those? Using Distribution or Tabulate, we find the median slope to be about -1.2 kW/°C, which is about 0.3% per degree based on an average 350kW base.

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solar panels supplier wrote:

These graph show clear picture of the solar power panel output and temperature. Thanks for the all the graphs and information.

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buy solar panles wrote:

This is valuble info for solar consumers in Australia, thanks alot for the graph

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Peter solar power wrote:

Nice graph. thanks for sharing the information.

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jules marcogliese wrote:

I live in Kern county (high desert) of which SDG &E will installing up to 5400 acres of comercial solar panels by the end of 2012. I am situated in the middle of the project about 50 feet away. I am conserned about the heat disburstment as I am sure these hundreds of panels will heat up and increase my land temperture by 10 to 20 degrees. Is this posible? and is there electromagnic radiation danger....and are there any studies to refer to.

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Roel Solar Panels wrote:

Hi Xan, I really enjoyed the article. I work with Solar Panels myself and I understand that there are lots of complexities. Those graphs are really interesting. Good work!


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Eric the Solar Panel Guy wrote:

hey greg. Looks like some interesting research. I just came by to say that it'd be helpful post units on your graphs. Thanks and good work!

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Douglas M Okamoto (Data to Information to Knowledge) wrote:

1. Calculate daily energy supply in kilowatt-hours from January 1, 2009 to August 31, 2009, using the trapezoidal rule for numerical integration of solar power in kilowatts over 96 = (24)(4) fifteen-minute intervals per day. Daily energy supply averaged 4,750 kwh during the first eight months of 2009.

2. Specify a single exponential smoothing or ARIMA (0,1,1) model for daily energy supply and estimate parameters using the JMP time series analysis platform.

3. Forecast energy supply and 95 percent confidence intervals during September and October (see Attachment).

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Top 10 JMP Blog posts of 2011 - JMP Blog wrote:

[...] Solar Panel Output Versus Temperature (2009) [...]

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