Our World Statistics Day conversations have been a great reminder of how much statistics can inform our lives. Do you have an example of how statistics has made a difference in your life? Share your story with the Community!
Choose Language Hide Translation Bar
Solar Array Surprises

As you may have heard, SAS has a 1 megawatt solar farm in operation.

Naturally, I wanted to see what kind of data was available, and it turns out the power output is recorded every 15 minutes, even during the night (who knows -- maybe we'll get some power from the sunlight reflected by a full moon or from a passing comet). The output is measured separately for two halves of the farm called Array A and Array B. You can see the arrays, along with the sheep that maintain the grass at the solar farm, in the photo below.

Here's a graph of both arrays for the few sunny days in April we had here in Cary, North Carolina. I used the Data Filter to include only the sunny days and modified the axes to show only the daylight hours.

SAS Solar Farm data for sunny days in April 2009 in Graph Builder in JMP

The flatness of the power output curve is a testament to the sun-tracking rotation of the panels. They're on a horizontal axis that runs north-south, and so can turn toward east or west.

Two interesting features stand out:

  • There's a dip in the outputs around midday.
  • Array A lags Array B in the early morning.

  • I think I know why these things are happening. But what do you think the reasons are?

    In case you want to explore the solar farm data from April, it's available in the JMP File Exchange (scroll down to the bottom of the page to find the solar farm file).

    SAS Solar Farm photo is by Dave Horne.

    Article Labels

      There are no labels assigned to this post.

    Article Tags

    Sajal Aggarwal wrote:

    The Mid-day dips in the power curve of the arrays occur because of the inverter efficiency dips after the load increases above 80%.

    Try to plot the effieciency(ac output / dc input) and load. you will be surprised to see it


    Chris W wrote:

    It s not due to cell temp, the total incident radiation follows the same graph as the AC output power.


    William Burke wrote:

    Anli ,

    I am thinking That heat is Producing the Noon Dips.

    I have heard that solar cells do not particularly like a lot of heat, and colud be the reason that the output dips during mid day.


    Mark Aldon Weiss wrote:

    Very neato point. In my work -- with a thing called a vibrating sample magnetometer -- there is what I call "the pole gap temperature effect" or "pickup coil temperature effect". The changing resistance of the pickup coils with temperature manifest as a spuriously reported change in the magnetization (emu) of the sample. I developed an empirical correction for the effect along with a rigorously adhered to method (complete with stopwatch and thermometer with 0.1°C tics) of determining pole gap temperature in order to compensating for the systematic error. I guess the message is that scientist and statistician should always beware of systematic errors or changes or effects due to temperature. By the way, my empirically developed (primarily linear, but also a small quadratic term) agreed excellently with a MathCAD mathematical model published by IEEE folks on temperature and resistance. (Though that model is linear, I think my small 2nd order component is because I measure pole gap air temperature -- not wire temperature of the pickup coils.) Anyway, like I say, I guess everyone everywhere should beware temperature effects.


    Xan Gregg wrote:

    Nice work, commenters! Thanks. The main factors are the shade and rotation as Anli mentioned, but he guessed the wrong axis of rotation.

    Based on January data I've seen, the dip is much more pronounced in the winter, which is supported by the material Doug found.

    It will be interesting to try to detect the temperature effect after we have more data -- I wonder if that accounts for the morning output appearing slightly highly than the afternoon.


    Douglas M Okamoto wrote:

    In the photo of the solar farm, the length of the shadows cast by the fence posts in the foreground is indicative of early afternoon. If Array B solar panels are those nearest the camera, they will continue to generate electricity as these shadows lengthen and the sun sets in the west. This would explain the blip I observed at dusk when I differenced the power output curves for the two arrays. If Array A solar panels are shaded by the tree-line visible in the background, their power output will lag the power output by Array B when the sun rises in the east, as Anil suspected and Xan confirmed via email yesterday.


    Daniel wrote:

    Is heat a factor? Again, according to Wikipedia, "Most crystalline silicon solar cells decline in efficiency by 0.50%/°C and most amorphous cells decline by 0.15-0.25%/°C."


    A. Evangelista wrote:

    Excellent blog topic and presentation! Here is a theory to consider regarding the relatively small dip at midday. The solar panels at midday are at or near horizontal, thereby obstructing wind and warm/hot airflow underneath the panels. In other words, there's a slightly greater tendency for hot air to accumulate underneath the panels when they are all laying in a near-perfect plane to one another. Also, at midday, the solar irradiation is at its peak maximum. Hence, panel temperatures should be at a maximum peak for the day.

    Manufacturer and solar PV literature clearly demonstrate that solar panels exhibit a loss in efficiency that is inversely proportional to panel temperature - the hotter the solar panel, the lower the output. This difference is fairly small to be sure - on the order of -0.10-0.35 watt/delta T (results in negative watts; delta Tempeerature is in deg C) for a 160-195 watt panel.

    It would be interesting to plot the output against array temperature, windspeed. Better yet, consider gathering seasonal data to identify the magnitude of this midday dip.


    Douglas M Okamoto wrote:

    Differencing power output data by subtracting Array A from Array B, shows a spike of up to 100 kilowatts as the sun rises in the morning on sunny days. However, there is a blip of 10-20 kilowatts as the sun sets around six oâ clock in the evening.

    If the solar panels in Array B are aligned on the east side of the farm, then their exposure to the rising sun before those in Array A explains the early morning lag in power output. East-west alignment does not explain the lag in the evening.

    With regard to the mid-day sag in power output for both arrays, I agree with Anil that horizontal tracking is sub-optimal around noon because Cary is 35 degrees north of the equator.

    Here's Wikipedia on the subject of Solar Tracking:

    â Several manufacturers [including SunPower] can deliver single axis horizontal trackers which may be oriented by either passive or active mechanisms, depending upon manufacturer. In these, a long horizontal tube is supported on bearings mounted upon pylons or frames. The axis of the tube is on a North-South line. Panels are mounted upon the tube, and the tube will rotate on its axis to track the apparent motion of the sun through the day. Since these do not tilt toward the equator they are not especially effective during winter mid day (unless located near the equator), but add a substantial amount of productivity during the spring and summer seasons when the solar path is high in the sky. These devices are less effective at higher latitudes.â

    Thanks for providing the interesting data visualization problem (and the JMP exchange file) .


    Anli wrote:

    I assume array A lags B because it close on the east side and there must be some shadow in the morning.

    The noon dip is surprising. My guess is that since there's only one axis (NS) the angle of the arrays against the ground is optimized for morning and evening hours, i.e. it's too steep, and the Sun at its highest point is at a disadvantage. The mid-June data should have a more pronounced dip.


    Solar Array Data, January Through August - JMP Blog wrote:

    [...] my Solar Array Surprises post about the SAS solar farm, one of the surprises was a midday dip in the power output, for which [...]


    Solar Panel Output Versus Temperature - JMP Blog wrote:

    [...] 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 [...]


    GM wrote:

    Although there are many different factors that can influence the production of a solar site, there is one purely geometrical reason to explain the dip at noon in clear Winter days. These are the facts:

    1. The incidence angle is maximum at noon, and therefore

    2. The effective area collecting solar rays is bigger at, say, 10am than at 12pm

    The above happens for every day of the year at a latitude of 35deg. However:

    3. The incidence angle (or, more meaningfully, its cosine -inversely-) is greater during Winter (about 60 degrees) than during Summer (about 14 degrees).

    This means that:

    4. The effect is more visible on clear Winter days and practically negligible on clear Summer days

    So, the above can be summarize as:

    5. There is an effect that tends to "push down" the production at noon

    6. The "push down" effect is more visible in clear Winter days

    On the other hand:

    7. The radiation in clear days is greater at noon than, say, at 10am.

    This means that:

    8. There is an effect that tends to "pull up" the production at noon in clear days

    This analysis shows that there are two "effects" in opposite directions (pulling up or pushing down) the production curve at around midday hours. How both effects interact will define the shape of the curve. For Winter days, it can be shown on normalized radiation curves that the "push down" effect "wins" over the "pull up" effect (due to 3.).