# Adding a real tracking algorithm to PVWatts

The web version of PVWatts doesn’t take into account the effect of one row of panels/trackers casting a shadow on another, and neither does it account for backtracking in the morning and evening to avoid shading. Essentially, you are modeling the performance of a single tracker.

NREL has a page devoted to derate factors here which provides a rough approximation for a shading derate based on GCR (ground coverage ratio), but in reality the affect of backtracking is dependent on location.

With this in mind, I modified the PVWatts source to calculate the correct incident angle (function incident2) for a horizontal single axis tracker given a GCR, and ran the simulation for a number of GCR’s and locations. Here is a sample result: Derate factor versus GCR for 3 different locations

This shows the actual derate factor you can expect as a function of GCR for 3 different locations. Clearly, they are NOT all the same! At a GCR of 40%, there’s a 1.4% difference in energy lost between San Diego and Salt Lake City.

With small changes like this I’m getting closer to a model that accurately predicts real world performance.

# WolframAlpha sucks at math

Either that or I’m doing it wrong: WolframAlpha can't do subtraction.

# Measured inverter efficiency curves

Thanks to the California Energy Commission we can see what a real inverter efficiency curve looks like, and compare it to the pvwatts model.

It turns out that the pvwatts model doesn’t match reality very well. The pvwatts nominal efficiency of 92% is well below the average of current inverters, and the 4th order polynomial is a rather poor fit to the shape of the efficiency curve.

The plot below shows the measured efficiency curve for a SatCon PVS-135 (green) and the pvwatts model (blue). Clearly there’s quite a bit of room improvement.

I’ve created a log function to model the inverter and plotted that in red. Substituting the improved model in pvwatts calculations results in about a 4.5% increase in annual energy.

Even if you don’t know what inverter will be used in a particular case, just increasing the nominal efficiency inside pvwatts from 92% to something around 95% seems reasonable given the test data on the CEC site. Inverter Efficiency Curves

# pvwatts inverter model

This is a plot of the pvwatts inverter model. Nominal efficiency is 92%, but if the input power is between 10 and 100%, a 4th order polynomial is used to calculate efficiency, and convert dc power to ac. If this is accurate (I haven’t yet found any efficiency curves published by inverter manufacturers), then there are some clear implications for string sizing. pvwatts inverter model

# Under the hood of pvwatts

One of the projects I’m working on right now involves getting under the hood of pvwatts, the solar performance prediction software from the National Renewable Energy Laboratory.

Just about everyone in the solar energy world is familiar with pvwatts, but how many of them have actually had a chance to examine the source code? I’m just digging into it now, and I’ve already found several areas that could use some improvement. Considering how widely accepted this calculator is, the code is quite a shock. The algorithms make sense, but the implementation is a bit frightening.

More to come.