By Paul Grana, co-founder of Folsom Labs
Shade leads to mismatch. Simple, right? Not so fast. This relationship is one of the most commonly discussed in solar design—and was a big factor in propelling microinverters & optimizers to their early market adoption. But precisely how much mismatch should you expect from shading on an array?
On one hand, some will say that shade on a single module can take down an entire string, implying a multiplier effect of 10 to 15 times. In reality, that would depend on the system wiring, and often the string would have the option to bypass that shaded module and run the remaining modules at a higher voltage (still mismatch loss, but not 15 times the shade). On the other end of the spectrum, if all modules are shaded at the same time, then there would technically be no mismatch, since each of the modules in the array would be perfectly balanced.
Either of those thought experiments are just one moment in time. In reality, we need to understand the losses over a full year, factoring in the exact locations of the modules and obstructions, the location of the sun and the corresponding shadows that will be cast each hour, and the exact shape of the resulting I/V curves of the array. So the right answer to how much mismatch will result is, it depends. Let’s look at a few scenarios to see how all of these factors play out in a real array.
We can start with a commercial system with a variety of sources of shade: HVAC units on the roof, nearby trees and a large, tall building in the next lot (and 0° tilt, so the only shade on the modules is from the obstructions, not the row in front).
Running an initial simulation, we find that the system gets 6.1% shade loss, with a corresponding mismatch loss of 4.6%. In other words, the mismatch losses are roughly similar to the shade losses.
We can then isolate each of the different objects to see how that relationship between shade and mismatch can change. For example, the HVAC units produce 4.1% shade loss and 3.5% mismatch loss—fairly similar levels. The nearby building creates 3.3% shade loss, but 1.8% mismatch loss—just half as much mismatch as shade. On the other end of the spectrum, a flagpole (with a long, skinny shadow) would create just 0.6% shade loss, but 1.8% mismatch loss—a 300% difference between shade and mismatch.
The type of object can have a big impact on the amount of mismatch in an array, so clearly the shape of the shadow is playing a role here.
Looking deeper into the shade/mismatch relationship, we can look into the hourly simulation with a scatter plot where each point represents an hour of the system’s operation.
We see that the shade-mismatch relationship is by no means consistent. There are a number of hours of the year where shading losses are greater than the mismatch losses, and a number of hours of the year where the mismatch losses are greater than the shading losses. In fact, they often cluster into “zones” of operation where there are specific loss profiles. We can isolate a few of these to get a better sense of what causes them:
- Zone 1: High mismatch: These hours (for example, 3 p.m. in June) are times where the sun is still strong, and shade from obstructions is just starting to hit the modules. In these hours, there are many strings with just one module shaded, which tends to maximize the mismatch effect.
- Zone 2: Equal shade-mismatch: In these hours (e.g. 4 p.m. in the summertime) the shadow is covering more modules in each row, bringing the shade and mismatch losses more in line with each other
- Zone 3: Greater shade, less mismatch: At these times (for example, late afternoon), large swaths of modules are shaded by the nearby obstructions. This creates situations where entire strings (or even entire inverter blocks) are shaded—which will lead to high shade losses, but very low mismatch loss since they are all equally shaded.
To understand how shade leads to mismatch, we need to understand the type of shade that hits the array: Are the shadows narrow and only hit a few modules? Or are they wide and sweeping across many modules at once? Ultimately, it’s a good reminder to use real simulation programs rather than general rules of thumb.