# Two Strings in Parallel with Unequal String Voltages

Solar Expert Posts: 316 ✭✭✭
I'm now ready to tackle trying to understand how an array behaves, with respect to its Vmp, that consists of 2 strings of unequal string voltages, connected in parallel.

For example, let's say I have 26 diode-protected panels connected as 2 strings, in parallel, of 13 panels each. And each panel is 225 Pmax, 7.86 Imp, and 28.66 Vmp at a standard 1000 W/m2 irradiance.

My fundamental question I could use some help with, is, how does the array behave (i.e. at the DC disconnect switch) with respect to the array's Vmp?

I understand the answer if all 26 panels have the same irradiation. At the DC disconnect switch, where the 2 strings connect together in paralell, assuming theoretical conditions, the array will be at 2925 Pmax, 15.7 Imp (2 parallel strings * 7.86 A), and 372.6 Vmp (13 panels * 28.66 V).

Now let's assume 2 panels in one of the strings are in shade. The array's current will still be 15.7 A (I understand the concept of constant current sourcing).

But what will the array's Vmp be? One string, the string with 2 shaded panels, before connecting in parallel with the other, would be at 372.6 - 28.66 - 28.66 = 315.3 V. The other would be at 372.6 V.

So what happens to a 2 string array's voltage when strings at 315 and 373 V are parallel connected to each other?

Many thanks!

Best regards,

Bill

Re: Two Strings in Parallel with Unequal String Voltages

And that is the rub of the problem... What happens to the MPPT calculations.

Just as an FYI, I use this data sheet for a crystalline silicon panel that includes a couple of graphs/curves that you don't see on most specifications such as cell temperature vs I/V/Power (other Si products should behave pretty much identically).

You could pretty much print it out and add your own I/V scales (even for an array of 13 panels) and it will pretty much show the panels will behave in differing conditions.

Note that the power peaks for Crystalline-Si panels is fairly flat... As long as you are within 10% of the of Vmp, Power is probably within 10% of peak output too...

So, now, you take add the second string with Vmp-2 panels and graph that composite array out and you will probably see something like:
```[B]Made-up Power (vertical) vs Varray / Pmax plot with two array Vmp's[/B]

[FONT=Fixedsys]  Vmplow Vmpmix Vmphigh
/^\
p    /^\  /   \/^\
o   /   \/        \
w  /               \
e  |drop where      \
r  |vlow drops       \
/below Vin-min     \
/                    \
/                      \
/                        \
array voltage at xxxx watts per sq.meter.
[/FONT]
```
Which one will the MPPT circuit track on? Don't know. Different vendors may find different peaks. As temperature and power levels change, points will move.

Note the crest of the peaks is wider/less sharp that I did in my ASCII drawing.

And note that the total Power Max of the combined string paralleled on one MPPT controller will be less than if each string had its own MPPT tracking inverter.

And the shoulder on the left when Vmp of the lower voltage/shaded array drops below the inverter's minimum input voltage requirements.

The above is all just a guess... I am sure Solar Guppy can give you much more interesting answers--but it still probably all boils down to "it depends" on a lot of different issues (including the inverter's performance/tracking capabilities).

To do a generic solution is probably not possible and to document special cases becomes hopelessly data intensive (13/11 panels, 13/13, 14/12, etc.)...

To a degree, do the worst case planning and if that is acceptable for you--then you may be pleasantly surprised if it exceeds your minimum expectations.

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Solar Expert Posts: 316 ✭✭✭
Re: Two Strings in Parallel with Unequal String Voltages

Bill, thanks. I'll spend some time now digesting your note above. Much appreciated.

Let me step backwards a moment to ask a question that perhaps I should have asked first, that may accelerate my learning process:

If panel Voc is 37.33 V, what is an array's Voc with 2 strings connected in parallel as described in my example (1 string with 2 shaded panels)?

I.e., the array's Voc at the DC disconnect switch, where there's no inverter connected to the switch?

Does the array operate at:
(1) the higher of the two string Vocs (i.e. 37.33 *13)?
(2) the lower of the 2 string Vocs (i.e., (37.33 * 13) - (37.33 * 2)?
(3) the average of the 2 string Vocs?
(4) something else?

Or does this question not make any sense because at open connection the shaded panel bypass diodes don't operate?

Thanks.

Bill
Re: Two Strings in Parallel with Unequal String Voltages

Voc only makes sense when there is no load on the array (oc=open circuit). So, this is the very worst case open circuit voltage an array/cell can achieve with minimal amount of sun light (more or less, the Voc is achieved once there is a minimal amount of sun on the panel--in theory, even in deep shade).

The amount of current from a panel is pretty much directly proportional to the amount of sunlight on the panel (from ~0 to 1,000 watts per sq.meter -- where 1,000 watts per meter is roughly the maximum average sun strength at noon on a clear day).

Solar cells do have some, non-infinite, dark resistance... So any voltage developed by a minimal amount of sun light is going to charge the panel's capacitance and be drained off by the resistance of the panel.

So, now you have some Voc that is developed in weak sunlight (or even sky-shine/back-scatter from deep shade). In the case where you have shadows on a two parallel string array, unless that shadow is from a black sheet of plastic directly on the panels, I would guess that even the shaded portion of the array will still develop some sort of near-normal amount of Voc... So the entire array will have near normal Voc (even if partially shaded.

Even my GT array (3.5 kW DC) will generate some 10's of watts of power when in deep shade (sun in west, clear blue sky-shine).

Next when do we see Voc? Most likely if the inverter shuts down during an AC power hit (out of frequency and/or out of voltage) and during the morning and evening times when the inverter to trying to get MPPT voltage right--and there is enough current/power to run the inverter (my 3kW array seems to need about 50 watts minimum to output a stable "zero" watt output/no array fault or about 0.2 amps between 250 and 300 volts for my Vmp=320 volt nominal array).

Assuming that the input state voltage limit for a GT inverter is set by Vmax--it does not take very much current at all to damage the input silicon. Typically the silicon is damaged by very small over voltage punch-through and/or by very heavy I^2*R self heating losses.

So, my theory is that Voc in dim light and cold temperatures (little available current) are going to just about as damaging as a Voc in bright light and cold temperatures (high available current).

Since you are designing your system for worst case conditions (minimal power input, cold weather--typically first sun after a cold night) the fact there may or may not be shading on one string is almost irrelevant. You have to assume there is enough light for the array in weak sun to supply the any leakage current in the "shaded array" and because you don't know when the shade will be there or not (Voc because of power line hit could spike later in the day when their is no shade).

In the end, it is fair amount of hand waving. From the graph / PDF I posted to the generic Si-Panel--you could see that Voc=44.4 (at 77F or 25C and 1,000 w/sq.mtr) and that Voc approaches ~42 volts (near 0 watt/sqmtr).

For a 444 volt Voc array, that would mean "dim sun" could save you ~24 volts... Significant--but do you want to trust that?

But, temperature has a greater effect anyway, moving down towards -25C (same pdf spec.) we are seeing a +20% increase in Voc due to temperature--So a 5% drop based on low sunlight is not what we should probably focus on.

And since Voc (regardless of available current) is the damage limit for the inverter (and some devices will log Vmax and if exceeded, will automatically void your warranty)--Then trying to play too close to the limit may burn us anyway (even if the fault was something completely unrelated to the Voc over voltage).

I have thought about, in the past, of doing something to limit Voc... A temperature controlled relay that clicked on a 10% load at low temperatures (10% load can drop Voc by 10%--for a GT system, that is a 60 volt drop).

I also thought about adding a Zener / Electronic voltage clamp... But all of that seemed like a lot of work/expense/issues for little gain (150-600 VDC voltage clamps/zener diodes have lots of issues--Zeners are not rated that high, need to dissipate 30 watts on a 3kW array, etc.). Just easier to pick the right panel and string sizing in the first place.

Is this the type of discussion you were looking for? I may be wandering here. :roll:

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Solar Expert Posts: 1,989 ✭✭✭
Re: Two Strings in Parallel with Unequal String Voltages

When you parallel two arrays with different vmp's you have two concerns

With two different VMP points, both strings will be operating at a loss, the shaded array due to bypassed panels and the good array as its pulled down by the inverter to match the lower vmp, you get a double loss. In real world, the shaded array can run a few volts higher but the good array get yanked down, it works out roughly to about two thirds of a four panel loss.

Second and this is VERY important, your relying on the inverters software to not get stuck some where in tracking as BB points out it not simple to find the merged vmp of the strings. manufactures don't test for this from my experience and most dynamic P&O tracking will fail to work as the multi humps fool the tracking

If you know your going to have shading, DO NOT PARALLEL THE STRINGS, otherwise you might have some very large performance issues

In your picture of the chimney, the best thing to do is lower the rails, I see at least what I thought was a panels length the rails could be towards the soffit
• Solar Expert Posts: 316 ✭✭✭
Re: Two Strings in Parallel with Unequal String Voltages
If you know your going to have shading, DO NOT PARALLEL THE STRINGS, otherwise you might have some very large performance issues

Thanks to everyone here. I think I finally figured out what the behavior is for a 2x13 array, where just 1 module in 1 string (4% of total modules) is shaded.

For a 1x13 array, with only 1 (8% of total) module shaded: 12% array power loss during the shading period (see material I just published in my other thread that's focused on just one string).

For a 2x13 array, with only 1 (4% of total) module in just 1 string shaded: 31% array power loss during the shading period.

While this is specific to the 225 W Astronergy modules, my guess is the theory applies regardless of module size or manufacturer.

It looks to be pretty sizable power hit, if shading exists, and if strings are in parallel. Certainly worthy of Mr. Guppy's capitalization above.

I'll publish a quantification of the numbers tomorrow, for this parallel strings example.

Best regards,

Bill
• Solar Expert Posts: 316 ✭✭✭
Re: Two Strings in Parallel with Unequal String Voltages

Here's the analysis for how shading on one panel of a 26 panel array (4% of the panels) can lead to a 31% loss of array producing power, when the panel strings are connected in parallel.

First, the entire array in full sun:
• String 1: 13 panels, all in full sunlight, operating at Pm = 2928 W (7.86 A * 28.66 V * 13 = 373 V)
• String 2 (connected in parallel): 13 panels, also all in full sunlight, also operating at Pm = 2928 W
• Total array Pm = 2928 * 2 = 5856. It's operating at 15.7 A and 373 V.
Now assume one panel in String 2 goes partially shaded, to a 0.4 Sun level (not low enough for bypass diodes to 'kick in.')
• String 1 still operates at Pm=2928 W, Imp=7.86 A, Vmp=28.66 * 13 = 373 V
• Each panel in String 2 is forced to operate at 28.66 V, the same as String 1. Thus, String 2 current reduces to 3.0 A to stay on each panel's I-V curve.
• String 2 Pm = 28.66 V * 13 panels * 3.0A = 1119 W.
• Array power is reduced from 2928 W + 2928 W = 5856 W to 2928 W + 1119 W = 4047 W. It's operating at 10.9 A and 373 V.
• This is 31% reduction in array power.
Now assume one panel in String 2 goes fully unshaded (low enough for the bypass diodes to 'kick in,' making the string in essence a 12, not 13 panel string.
• String 1 is still operating at Pm=2928 W (7.86 A and 373 V)
• Each panel in String 2 is forced to operate at a voltage such that the aggregate is 373; i.e., 373 V / 12 = 31.1 V.
• From the panel's I-V curve, at 1.0 Sun, current is reduced to 7.5 A.
• String 2 Pm = 373 V * 7.5 A = 2798 W.
• Array power is reduced from 5856 W to 2928 + 2798 = 5726 W, a 2% reduction.

Conclusions if you have shading challenges with a two strings connected in parallel:
1. Greatest impact (and quite significant) occurs with light shading, such that bypass diodes don't 'kick in.' If you're going to have shade, you want it to be significant enough to cause the bypass diodes to 'kick in.'
2. An array with strings consisting of a a large number of serially connected panels will 'hold up' better than strings with a less number of serially connected panels.

Thanks for everyone's contributions on this - I learned a lot!

Best regards,

Bill
• Registered Users Posts: 5
Re: Two Strings in Parallel with Unequal String Voltages
If you know your going to have shading, DO NOT PARALLEL THE STRINGS, otherwise you might have some very large performance issues

I've posted similar questions about "unequal series strings wired in parallel" on a different thread, and am following up here.

Background: I have room for 27 modules (210W Kyoceras) on my roof. Could I wire this array these as two series strings, one of 14 modules (Voc=465V, Isc=8.6A), and one of 13 modules (Voc=432V, Isc=8.6A). It sounds like wiring these two series strings in parallel on the roof, and running the single circuit back to the inverter would result in a performance penalty, just like shading a single module of a 28 module array would.

My final question is: Does running each of the two (unequal) series strings directly to two different inverter inputs (Fronius IG5100) constitute paralleling the strings? (as opposed to wiring two series strings in parallel in a rooftop combiner, and then one circuit back to a single inverter input). That is, how does the inverter treat the two different input connections?

• Solar Expert Posts: 316 ✭✭✭
Re: Two Strings in Parallel with Unequal String Voltages
cfcf463 wrote: »
... 27 modules (210W Kyoceras) on my roof. Could I wire this array these as two series strings, one of 14 modules (Voc=465V, Isc=8.6A), and one of 13 modules (Voc=432V, Isc=8.6A). It sounds like wiring these two series strings in parallel on the roof, and running the single circuit back to the inverter would result in a performance penalty, just like shading a single module of a 28 module array would. ...

In summary, I think you'll see somewhere between a 2.4 to 5.5% decrease (reduction) in power output solely due to having unequal string sizes, noting the particulars offered, and the assumptions I made (below). Where the decrease ends up in this range depends on the inverter's MPPT capability.

Here are the details.

Assume 1.0 Sun irradiance and a GT only inverter, with MPPT capable of finding Pmax. Further assume the panels are similar to Kyocera KD210GX (which have Voc and Isc specs that match the numbers quoted above). For these panels, Vmpp=26.6 V and Impp=7.90 A (and Pmax=210 W).

Since both strings are connected in parallel, each string's operating voltage must be identical.

There's 2 possible operating points an MPPT inverter can choose from here.

Scenario 1: String voltage is set at 372 V by the inverter. This is the 14 panel string's Vmpp (26.6 V * 14 panels).

The 14 panel string will operate at its Impp, 7.90 A, and power output is 372 V * 7.90 = 2942 W.

The 13 panel string must operate at the same 372 voltage in this scenario. Each panel is thus operating at 372 V / 13 panels = 28.6 V. From the panel's I-V curve, I'll guess the current is 6.5 A. This string's power output is thus 372 * 6.5 A = 2421 W.

The total power of the 2 strings is 2942 + 2421 = 5363 W.

Scenario 2: String voltage is set at 346 V by the inverter. This is the 13 panel string's Vmpp (26.6 V * 13 panels).

The 13 panel string will operate at its Impp, 7.90 A, and power output is 346 V * 7.90 = 2732 W.

The 14 panel string must operate at the same 346 voltage in this scenario. Each panel is thus operating at 346 V / 14 panels = 24.7 V. From the panel's I-V curve, I'll guess the current is 8.1 A. This string's power output is thus 346 V * 8.1 A = 2803 W.

The total power of the 2 strings is 2732 + 2803 = 5536 W.

Possible Operating Conclusion: If the inverter's MPPT can find the higher of the 2 scenario power points, the total panels will operate at 5536 W, since this is greater than 5363 W.

If you figure the theoretical max power of 27 panels, at 26.6 V * 7.9 A * 27 panels = 5674 W, then the 'penalty' for having an unequal number of panels per string is (5536 - 5674) / 5674 = -2.4%.

If the inverter instead locks on to the lower of the 2 scenarios, at 5363 W, then the 'penalty' increases to -5.5%.

Hope this helps.

Best regards,

Bill
• Solar Expert Posts: 316 ✭✭✭
Re: Two Strings in Parallel with Unequal String Voltages
cfcf463 wrote: »
...Does running each of the two (unequal) series strings directly to two different inverter inputs (Fronius IG5100) constitute paralleling the strings? (as opposed to wiring two series strings in parallel in a rooftop combiner, and then one circuit back to a single inverter input). That is, how does the inverter treat the two different input connections?

I think it's the same. From a connectivity point of view, you're either combining the 2 strings in parallel at a roof top combiner box, or you're combining the 2 strings in parallel at the inverter input terminals.

I think there are only a few GT only inverters that offer more than one independent MPPT circuit (i.e., Power-One).

Best regards,

Bill
• Registered Users Posts: 5
Re: Two Strings in Parallel with Unequal String Voltages

Bill,
Sorry it's taken so long for me to reply, but thanks for the detailed, clearly articulated answers to my questions. You've been a great help.
• Solar Expert Posts: 713 ✭✭
Re: Two Strings in Parallel with Unequal String Voltages

This is a systems level problem and is one of the reasons I'm liking the new Solaredge inverter that puts a mppt converter on each solar module. The complexities of optimizing a number of possibly shaded modules is hard to do perfectly for a central inverter. Solaredge says that they have a few percent efficiency improvement in each of 4 areas that add up to a significant advantage.
* No module mismatch losses
* No under voltage losses
* Improved MPP tracking performance
• Registered Users Posts: 22 ✭✭
a0128958 said:
Re: Two Strings in Parallel with Unequal String Voltages

Here's the analysis for how shading on one panel of a 26 panel array (4% of the panels) can lead to a 31% loss of array producing power, when the panel strings are connected in parallel.

First, the entire array in full sun:
• String 1: 13 panels, all in full sunlight, operating at Pm = 2928 W (7.86 A * 28.66 V * 13 = 373 V)
• String 2 (connected in parallel): 13 panels, also all in full sunlight, also operating at Pm = 2928 W
• Total array Pm = 2928 * 2 = 5856. It's operating at 15.7 A and 373 V.
Now assume one panel in String 2 goes partially shaded, to a 0.4 Sun level (not low enough for bypass diodes to 'kick in.')
• String 1 still operates at Pm=2928 W, Imp=7.86 A, Vmp=28.66 * 13 = 373 V
• Each panel in String 2 is forced to operate at 28.66 V, the same as String 1. Thus, String 2 current reduces to 3.0 A to stay on each panel's I-V curve.
• String 2 Pm = 28.66 V * 13 panels * 3.0A = 1119 W.
• Array power is reduced from 2928 W + 2928 W = 5856 W to 2928 W + 1119 W = 4047 W. It's operating at 10.9 A and 373 V.
• This is 31% reduction in array power.
Now assume one panel in String 2 goes fully unshaded (low enough for the bypass diodes to 'kick in,' making the string in essence a 12, not 13 panel string.
• String 1 is still operating at Pm=2928 W (7.86 A and 373 V)
• Each panel in String 2 is forced to operate at a voltage such that the aggregate is 373; i.e., 373 V / 12 = 31.1 V.
• From the panel's I-V curve, at 1.0 Sun, current is reduced to 7.5 A.
• String 2 Pm = 373 V * 7.5 A = 2798 W.
• Array power is reduced from 5856 W to 2928 + 2798 = 5726 W, a 2% reduction.

Conclusions if you have shading challenges with a two strings connected in parallel:
1. Greatest impact (and quite significant) occurs with light shading, such that bypass diodes don't 'kick in.' If you're going to have shade, you want it to be significant enough to cause the bypass diodes to 'kick in.'
2. An array with strings consisting of a a large number of serially connected panels will 'hold up' better than strings with a less number of serially connected panels.

Thanks for everyone's contributions on this - I learned a lot!

Best regards,

Bill
dear bill

you said
" Now assume one panel in String 2 goes partially shaded, to a 0.4 Sun level (not low enough for bypass diodes to 'kick in.')
• String 1 still operates at Pm=2928 W, Imp=7.86 A, Vmp=28.66 * 13 = 373 V
• Each panel in String 2 is forced to operate at 28.66 V, the same as String 1. Thus, String 2 current reduces to 3.0 A to stay on each panel's I-V curve. "
can you share the pic of I V curve so i can understand better because i want to know how current of string 2 reduces to 3.0

Thanks bill
It is getting difficult to find "real" IV cures for solar panels these days (original link is now dead).

Here is a generic curve.

You can see that when the voltage of the solar panel rises over Vmp, that Imp starts to fall dramatically.

And here is another curve with V*I (power) plotted on the same curve. If you are on the left side of the curve a little bit, the power produced by panel will change very quickly (with little change in current value). To the "left" of the Pmax point (where V*I = Vmp*Imp) the solar panel acts like a "current source" and this is how the power transfer function will behave. To the right of Pmax, current quickly collapses because the solar cell is not able to generate any more voltage--And all that can happen is current is reduced.

And here is a plot that shows you how the IV curve responds to different levels of sunlight (note that Vmp does not move very much). And there is a plot on how the curve varies according to cell temperature.

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
I did find a copy of the orginal PDF that I used for discussion, and here are the IV curves:

http://www.solarsourcepower.com/STP175S_24Ab-1BLK.pdf

You can "rescale" this drawings to any crystalline solar panel/cell and be close enough for modeling overall behavior.

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Solar Expert Posts: 316 ✭✭✭

Nice to see the IV curves used for the tutorial above to be found and preserved in this thread.

Best regards,

Bill

• Solar Expert Posts: 3,123 ✭✭✭✭
The difference between ten and eleven panels is going to be a problem, as noted, but will still produce more power than either string alone and roughly the power of the two combined strings less one panel.
A good rule of thumb is that if there is no uneven partial shade a difference of Vmp of less than 5% will not be a problem.
SMA SB 3000, old BP panels.
• Solar Expert Posts: 6,352 ✭✭✭✭✭
I will add on to rules of thumb from my experience with virtual and and many cases of dynamic tracking.
same number and exact model of panels per string on virtual.
same angle/direction. due east and due west for virtual on same mppt.
Clouds will really mess up virtual tracking on one mppt.
Use multiple mppts and all is well. Dynamic tracking  (multiple arrays,  multiple single axis trackers) will do fine on one mppt most of the time. However, they can be affected by shading, clouds, and different models of panels also. Use multiple mppts!
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