Unbalanced Strings - loss calculation

[So Cal]

An SB 6000 has 3 strings of 11 Upsolar 225s. One upsolar panel needed replacement, its output was zero. So the system was operating essentially with two strings of 11 and one string of 10.

The strings of 11 measured 363V, while the string of 10 measured 330V. Paralled in the inverter we get 352V for the three strings combined.

The amps are 5.5 x 3 strings parallel = 16.5

3 strings of 11; 363 x 16.5 = 5,989.5 W x 5.5 x 365 = 12,023.9 yearly kWh (roughly)

2 strings of 11 = 1 string of 10; 352 x 16.5 = 5,808 x 5.5 x 365 = 11,659.9 yearly kWh

Applying percent difference equation:

	(12,023.9 - 11,659.9)			? 100%
[(12,023.9 + 11,659.9)/2]

= 3.1%

The difference in production according to these figures is the same % of non producing (or missing) solar modules (3%). My understanding has always been that unbalanced strings have a bigger effect than this. Which leads me to believe that there is some factor that I am not taking into account.

 

[SolarPro]

You're taking a snapshot in time and applying it across an entire year. But that snapshot may not represent normal operating conditions, for any number of reasons.

FWIW: using default values, PV Watts estimates that a 7.4 kW array in LA will generate 10,900 kWh annually. That assumes a shade factor on 1.0 (no shade). Since you've lost 1/33rd of the array, your best case shade factor is now 0.97. Plus you have mismatch between the PV source circuits. So instead of .77 default derate, you might be looking at something like 0.70. If you run PV Watts using a 0.70 derate, you new production estimate is around 9,900 kWh, which is roughly 90.8% of optimal.

http://rredc.nrel.gov/solar/calculators/pvwatts/version1/US/California/Los_Angeles.html

The losses could be worse than that. A more powerful production modeling tool, like PVsyst, might be able to generate a more accurate result. If you can, you should find an identical or an electrically similar replacement module and restore the string symmetry.

http://solarprofessional.com/articl...ng-term-module-replacement-and-serviceability

 

[GoldDigger]

The difference in production according to these figures is the same % of non producing (or missing) solar modules (3%). My understanding has always been that unbalanced strings have a bigger effect than this. Which leads me to believe that there is some factor that I am not taking into account.

Your calculation did not take into account that the current in the string of 10 will be lower than in the other two strings.
Neither the string voltages at Vmp nor the string currents at identical voltages are equal. That means that you will end up with the Vmp of the entire array somewhere between Vmp10 and Vmp11. Since the strings are long, that difference is not too large proportionally.
But you will be getting operating the 10 panel string at less than full current since the combined voltage will be higher than Vmp10. And you will be operating the two strings of 11 at a lower voltage than Vmp11 but at a slightly higher current.
Since the nature of the Maximum Power Point is that for small deviations in either direction the the loss in power will be small, the additional power loss will not be more than a few percent. But the output will definitely be lower than what you would get just by subtracting the power of one panel.

All this is assuming that the failed panel is either shorted internally or the bypass diodes are conducting. Otherwise you will lose the entire output of the string of 10. There will also be a few (5-10) watts reduction in the power output of the string of 10 because there will be drop of 1 or 2 volts across the bypass diodes.

If the voltage difference among the strings gets larger than 5-10%, the power loss will be high enough to consider adding a second MPPT input for the short string. Making the three strings balanced by dropping one panel from each of the strings of 11 will cost you more power than just living with the mismatch.
A replacement panel with an Imp of 5.5 or higher and a Vmp anywhere from 20 to 40 volts will return you to very near original production.

 

[jaggedben]

An SB 6000 has 3 strings of 11 Upsolar 225s. One upsolar panel needed replacement, its output was zero. So the system was operating essentially with two strings of 11 and one string of 10.

The strings of 11 measured 363V, while the string of 10 measured 330V. Paralled in the inverter we get 352V for the three strings combined.

Those are open circuit voltages, right? If so, they really tell you nothing about how the inverter's MPPT is going to operate on that array.

The SMA will show voltage and current readings on its display while operating. What does it say then?

I would generally assume that 2 strings of 11 and 1 string of 10 will deliver not much more power than 3 strings of 10.

 

[GoldDigger]

Those are open circuit voltages, right? If so, they really tell you nothing about how the inverter's MPPT is going to operate on that array.

The SMA will show voltage and current readings on its display while operating. What does it say then?


I would generally assume that 2 strings of 11 and 1 string of 10 will deliver not much more power than 3 strings of 10.

Since the OP stated that the parallel voltage was 352, I suspect that is not Voc but Vmp, but I will wait for the answer to confirm that.

In any case, the mismatched strings should deliver very close to (although lower than) the power of 32 panels. Certainly more than 30 or 31 panels.
When the voltage mismatch of the strings gets larger than roughly 10% you will start to get a noticeable reduction below the power for the same number of panels all operating at their individual MPP.
But unless the short string is back biased to the point where it shorts out the longer strings, you will not see the power of the longer strings completely lost.

For example, a string of 1 in parallel with two string of 11 will not contribute anything at all. And if the Voc of the short string is below the Vmp of the longer strings, then the MPPT control algorithm may not find the voltage point where the shorter string contributes at all, even though that would produce more total power from the array.

 

[SolarPro]

I would generally assume that 2 strings of 11 and 1 string of 10 will deliver not much more power than 3 strings of 10.

Yeah, that's a good bet.

Plug that into PV Watts using default values for LA and it spits out 9,921 kWh.

 

[jaggedben]

Since the OP stated that the parallel voltage was 352, I suspect that is not Voc but Vmp, but I will wait for the answer to confirm that.

If it's Vmp then how did he measure separate voltages for the different strings? The separate voltages would have to be Voc measurements before the strings were paralleled. Then the paralleled voltages are in between so it makes sense that's also a Voc.

Also, I looked up the Upsolar 225 specs and the voltages make the most sense for Voc at somewhat hot temperatures.

 

[GoldDigger]

If it's Vmp then how did he measure separate voltages for the different strings?

Well, I hoped that he disconnected just one (10 panel) or two (11 panel) strings from the GTI input and then measured the voltage during operation.
However, if the voltages are a better match for the Voc than the Vmp, maybe he did not.

Also:

Paralled [sic] in the inverter we get 352V

Not "paralleled but not connected to the inverter we get...."

 

[So Cal]

It was Voc measurements

 

[SolarPro]

Since there's no power output at Voc, that's not a reading that you want to extrapolate out as an indicator of system performance over time. Voc is mostly useful as an indicator of whether modules are connected properly in a source circuit.

FWIW: here's a link to an article about PV system commissioning:

http://solarprofessional.com/articles/design-installation/pv-system-commissioning

And here's a link to a separate article about production modeling:

http://solarprofessional.com/articl.../production-modeling-for-grid-tied-pv-systems

 

[So Cal]

I certainly do understand Voc measurements aren't what you project forward for system production.
The real reason for my origonal post was more academic than anything else. I do plan to replace the non functioning panel. Again, academically I had figured that the panel replacement wasn't too critical as to matching electrical characteristics, as long as Imp & Vmp are equal or greater,and the same basic setup,IE neg ground etc.. I thought greater would be a tiny advantage?

I was curious and went back to the site to get Vmp measurements;

string of 11 - 288Vmp
string of 11 - 288Vmp
string of 10 - 260Vmp
combined - 280Vmp
These measurements are averages of the displayed readouts that fluctuated continuosly.

The inverter readouts Were a little higher than my tester.

So according to this limited test of a moment out of the year, and following the simple formula of V x A = W, having an unbalance of the strings doesn't seem to adversly affect efficiency very much in this case.

 

[SolarPro]

Yes, not surprisingly the combined Vmp is closer to that of the intact source circuits. The MPPT algorithm is going to lock in on a Vmp that is set by those longer strings. The systemic inefficiency results from the fact that Vmp of the string of 10 modules does not equal the Vmp of the of two other source circuits, as you have measured.

So what happens when you operate a source circuit off of its Vmp?

The answer is that that source circuit no longer outputs its maximum power.

In this case, something like 30% of the array is being operated off of its maximum power point under all operating conditions. What does that mean at the end of the year? The effects of this are not easily quantifiable, but you can estimate it in a number of ways.

Jaggedben's suggested approach is the simplest. But it is also the most conservative. With one module missing, the system will perform better than if you simply had three source circuits of 10 modules each. However, the losses will definitely be more than 1/33rd of the estimated annual production; the losses are not linear?because that source circuit with the missing module will never be operated at its Vmp.

 

[GoldDigger]

However, the losses will definitely be more than 1/33rd of the estimated annual production; the losses are not linear?because that source circuit with the missing module will never be operated at its Vmp.

But since by the very nature of a Maximum, the slope of the power graph is zero at that point, you can move a little bit either way without changing the output by nearly the same percentage.
So the two strings of 11 operate a little lower than MPP, but within 1%, and the string of 10 operates at a little higher than Vmp, but within 1%. Net result:within 1% of 32 panels full output.

 

[SolarPro]

That's optimistic. There's a 9% difference between the Vmp of the 10-module string and that of the 11-module strings.

 

[SolarPro]

Put another way: If your analysis is correct, why do inverter manufacturers bother providing string inverters with multiple MPPT inputs?

 

[GoldDigger]

That's optimistic. There's a 9% difference between the Vmp of the 10-module string and that of the 11-module strings.

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.

 

[GoldDigger]

Put another way: If your analysis is correct, why do inverter manufacturers bother providing string inverters with multiple MPPT inputs?

Partial shading, vastly different numbers or types of panels, very different temperatures at a time when both strings are producing high power, etc.....
If you have matching panel types and numbers, and no partial shading within a string, you can even parallel panels facing in totally different directions without any power loss.
Part of the reason that multiple MPPT inputs were provided is that people do not understand this and so it became a sales point.
Part of the reason is people who have a lot of really different panel types or array sizes because they are upgrading an existing smaller system. Or are planning to do that someday.

As long as there is a good voltage match (at Vmp) you can parallel different Imp strings with no problem.
As long as there is a good current match (at Imp) you can put different individual panel types in series to create comparable Vmp strings to be paralleled.

Last but not least, if two same-length strings of comparable panels are facing in different directions, the Vmp of both strings in isolation will be so close as to be insignificantly different, even when the corresponding current, Imp varies by a factor of 10 or more between the strings.

 

[ggunn]

But since by the very nature of a Maximum, the slope of the power graph is zero at that point, you can move a little bit either way without changing the output by nearly the same percentage.
So the two strings of 11 operate a little lower than MPP, but within 1%, and the string of 10 operates at a little higher than Vmp, but within 1%. Net result:within 1% of 32 panels full output.

One thing to consider is that the power graph is not symmetrical. A string that is operating at lower than its MPP voltage won't be affected as much as a string that is operating at higher than its MPP voltage.

With a good meter with clamp current capability on site, someone could settle this bar bet.

 

[jaggedben]

I certainly do understand Voc measurements aren't what you project forward for system production.
The real reason for my origonal post was more academic than anything else. I do plan to replace the non functioning panel. Again, academically I had figured that the panel replacement wasn't too critical as to matching electrical characteristics, as long as Imp & Vmp are equal or greater,and the same basic setup,IE neg ground etc.. I thought greater would be a tiny advantage?

I think we all agree, given a system of 33 panels, that one loses far less production by temporarily leaving one non-functioning panel out of a string than by leaving out the whole string. But I can think of situations where the question is less academic. Suppose more than one panel starts to malfunction. At what number of dead panels is it better to disconnect the whole string? If there are dead panels removed from multiple strings, at what point is it better to take live panels out of the good string(s) to match the others?

I was curious and went back to the site to get Vmp measurements;

string of 11 - 288Vmp
string of 11 - 288Vmp
string of 10 - 260Vmp
combined - 280Vmp
These measurements are averages of the displayed readouts that fluctuated continuosly.

The inverter readouts Were a little higher than my tester.

Hm, no current readings? That would tell us what the real difference was.

 

[jaggedben]

Last but not least, if two same-length strings of comparable panels are facing in different directions, the Vmp of both strings in isolation will be so close as to be insignificantly different, even when the corresponding current, Imp varies by a factor of 10 or more between the strings.

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. On a recent job, I measured a 40V difference between identical east and west strings. That was at 10am, and the house only had about a 20deg pitch. The east string was more than one panel Voc lower. After scratching my head for a bit I realized it was all due to temperature, since the sun at that time had been hitting the east string directly for a couple hours, but not the west string.