Unbalanced Strings - loss calculation

[SolarPro]

Which means that the composite value is not much more than 5% away from either of them.
If the slope of the power versus voltage were 45degrees, that would make a 5% difference. But since the slope of the power curve is close to zero, a 5% change in voltage will not cause anywhere near a 5% difference in power compared to the MPP value.

If there were two strings in the system, then sure the array Vmp would be found roughly in the middle, in between that of the Vmp of the 10- and 11-module string. But this system has three source circuits, which means that the overall array Vmp is going to be weighted toward the Vmp of the 11-module source circuit.

If the slope of the power versus voltage were 45degrees, that would make a 5% difference. But since the slope of the power curve is close to zero, a 5% change in voltage will not cause anywhere near a 5% difference in power compared to the MPP value.

If ifs and buts were candy and nuts, we'd all have a very merry christmas. But if you look at the slope of a power curve between Pmp and Poc, you'll notice that it is not 45?. Power falls off a cliff as you start operating the source circuit above it's Vmp. I understand that a 9% Vmp delta does not extrapolate to a 9% delta in kWh, but it's not 1% either.

And yes, I do understand how unshaded east and west facing source circuits operate on a single MPPT. But those strings have identical I-V curves. Imbalanced strings do not. It doesn't really matter if that imbalance is the result of shading, orientation or a failed module.

 

[SolarPro]

Except that two same-length strings facing different directions are likely to be very different temperatures for much of the day, at least in a typical example where it's east and west on a pitched roof house.

Correct, but the difference in temperature is generally counteracted by a difference in irradiance with the net result of these differences do tend to balance out as far as power is concerned. If inverter manufacturers were the only ones claiming this, that would be one thing. But Bill Brooks says the same thing.

Part of the equation, though is that if you want to track an east- and a west-facing string precisely, then you either need an inverter with two MPPT channels or two inverters. But all else being equal, inverter or system efficiency takes a hit when you add a second MPPT or use smaller capacity inverters.

So part of the reason it can make sense to put identical unshaded source circuits with different orientations on an inverter with a single MPPT is because you are going to take an efficiency hit one way or the other. It's not so much that there isn't an efficiency loss inherent in having different array orientations, but that those losses are not much greater than the losses incurred via other means.

 

[GoldDigger]

Correct, but the difference in temperature is generally counteracted by a difference in irradiance with the net result of these differences do tend to balance out as far as power is concerned.

The Voc and Vmp are both affected by the temperature, in pretty much the same proportion.
What some people do not realize is that both the Voc and Vmp values are almost completely independent of irradiance over the whole range from full direct sun to moonlight. The Imp and Isc value change almost linearly with irradiance, but the V values change only because of the effect of internal shunt resistance in the PV cells.

What is a major real factor is that if one subarray is getting low light, it is also producing little power, and so even if there is a difference in the Vmp between the two subarrays it will only cause a loss of a small fraction of what is already a small fraction of the total power at that time.

The ability to collect output monitoring data for the subarrays separately is the main real justification for using two MPPT inputs. And even that could be resolved by two inputs which share the same MPPT operating point, not that that would be likely to get into a product for cost/benefit reasons

 

[ggunn]

What some people do not realize is that both the Voc and Vmp values are almost completely independent of irradiance over the whole range from full direct sun to moonlight.

I have a visceral understanding of that. I was troubleshooting an array mounted on a mockup of a roof in an indoor lab lit only by dim fluorescent lighting and got a 485VDC shock when I did something stupid.

 

[GoldDigger]

I have a visceral understanding of that. I was troubleshooting an array mounted on a mockup of a roof in an indoor lab lit only by dim fluorescent lighting and got a 485VDC shock when I did something stupid.

Visceral understandings do have a tendency to stay with us more effectively than "book learning"!
Hope you did not end up falling off the mock roof as a result.

 

[ggunn]

Visceral understandings do have a tendency to stay with us more effectively than "book learning"!
Hope you did not end up falling off the mock roof as a result.

As a matter of fact I did fall off. Luckily the fall was only a foot or two. If it had been a real roof in full sunlight, I might not be here to write this.

 

[SolarPro]

The Voc and Vmp are both affected by the temperature, in pretty much the same proportion.
What some people do not realize is that both the Voc and Vmp values are almost completely independent of irradiance over the whole range from full direct sun to moonlight.

Yes, you get most of the voltage even in low light conditions. But if you study the curves—or just put a meter on an array as the sun rises—you will see that the voltage is still dependent on irradiance. However, the half of the array that is getting more sun will also be operating hotter—and we all know what temperature does to voltage. So even as irradiance is increasing voltage on one side of the roof, cell temperature effects will reduce the voltage. The net effect is that both source circuits will tend to have more or less same Vmp. (Plus, as you point out, the stronger string will always drive the Pmp of the array.)