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Could you help me with this problem?

I'm building a solar panel with these characteristics:

  • No. of Cells: 36

    Cell Type: Mono-crystalline 125x125mm 3.42w

    Max. P: 123W

    PTC Power Rating: 100W

    Voc: 18V

    Vop: 15V

    Working current (Iop) : 5.5A

And I want to charge with it my Lithium 48V 2.1 kWh battery

Dividing this capacity by the power delivered by the solar panel:

t=2100Wh/100W=21h

So it should take at least 21hrs at optimal conditions.

As I need to step up the voltage from 15V to 55V in order to be able to charge the battery, is that going to affect the calculations or add some loss? Is that easily doable with an mppt?

Thanks!

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    \$\begingroup\$ 30 years where I live \$\endgroup\$ – PlasmaHH Mar 29 '17 at 15:39
  • \$\begingroup\$ If the step-up circuitry has an efficiency of, say, 90%, i.e. 0.9, then the time taken will be 21h/0.9 = 23h20m. \$\endgroup\$ – Andrew Morton Mar 29 '17 at 15:58
  • \$\begingroup\$ efficiency drops in Stage 2 but for Stage 1 assuming good cells ESR= 10mΩ each*36 =360mΩ @5.5A I²ESR=11W or 11% loss. Then factor the avg solarity per day. \$\endgroup\$ – Sunnyskyguy EE75 Mar 29 '17 at 15:58
  • \$\begingroup\$ Another report in India suggested ~60% efficiency " Factors affecting the performance are internal heating, dust, mismatch+ wiring loss, DC-AC conversion, battery loss. The reduction factors for each of them are generally taken as 0.89, 0.93, 0.95, 0.90 and 0.9" \$\endgroup\$ – Sunnyskyguy EE75 Mar 29 '17 at 16:08
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It's easy if you're willing to buy a module to do it. It is horrendously difficult to design such an MPPT module yourself, and it will not perform nearly as well as the well-developed and extremely robust modules available on the market.

Fortunately, 48V lithium MPPT controllers are one of the standard variations, so they are readily available and very mature products. For example, this module can charge a 48V pack from as little as 5V input from a panel, and will constantly track the panel's maximum power point. Generally, these modules are less efficient the wider the voltage difference is, but they have minimum efficiency ratings which represent the 'worst case' scenario, whatever that may be. In the case of the module I linked, for a 48V battery pack, this worst case is 96%. Best case is 99%.

The massive amount of money and interest that has poured into photovoltaics have resulted in MPPT modules of excellent performance.

Now the bad news: It costs $240 USD. But you at least know what to look for, I am sure there are cheaper modules with poorer (but still quite good) performance available.

The losses in the MPPT module are frankly not going to be the primary contributor to your loss. Environmental effects are going to be the main worry here.

Solar panels put out less power the warmer they are, and more power the cooler they are. You can expect to charge your battery noticeably quicker in winter than in summer, for example. Also, mounting it in a field vs. the roof of a house (which will have heat from inside rising up, and a roof reflecting heat back at the panel) will potentially mean 10-15W of difference in the power your panel outputs.

The most important thing to note here, however, is that your panel has a PTC Power Rating of 100W. This is a good thing. PTC power ratings are meant to be 'real world' estimates, and, amongst other things, take into account things like heating and sun quality. PTC specifically assumes a panel will be heated to 45°C. Unfortunately, they usually will get even hotter, and how hot they actually get is highly dependent on the ambient temperature, how much breeze there is, etc.

The other important factor is the solar insolation of your geographic area. Most of India receives an average annual solar insolation of about ~6kWh/m^2/Day.

Pay attention to those units - its kilowatt hours per square meter per day, not kilowatt hours. Solar insolation is the most useful metric for solar panels because it factors in variation of sun through out the day, and the hours of sunlight per day.

If your area receives about 6kWh/m^2 per day, then you can view that as, averaged out, your panel will be receiving the standard 1000W/m^2 used to determine its PTC power rating for 6 hours a day. It of course is not constant like that, but that doesn't matter. For all intents and purposes, with everything else averaged out and accounted for, a solid estimate is that your panel will, on average for that year, provide it's PTC output power minus other inefficiencies for the equivalent of 6 hours a day.

This is of course going to vary depending on the day, the month, etc. But that 6 hours a day is everything averaged out for an entire year.

Using that average, and assuming you get a perfect 100W output power (which is unlikely, a safer estimate with thermal, converter, and wiring losses would be 80W), then you will be able to harvest 600Wh per day.

So it will take 2100Wh / 600Wh/Day, or 3.5 days or 84 hours to recharge your battery.

No, it will not take 2100Wh/100W = 21 hours. No where on this planet do you get high an average of 1000W/m^2 irradiance for 21 hours straight. Calculating charging time based on pure power capacity is a useless metric for anywhere on planet Earth.

So, given your location (somewhere in India, which is on planet Earth, and is subject to having sunlight for only part of the day), no matter what, it will wind up taking at least 3.5 solar cycles (days) to charge that battery. Sure, you can try to use some tricks, like start timing once light begins, and stop timing half way through the 4th day, and maybe it can, in isolation, seem like 70 something hours. But that's just fudging the numbers. Unless you're only going to use it once, 3.5 days is the number you have to go with.

However, it is best to be cautious. I would behooves me to say that no one can really say for sure how much power you'll get on average. My estimate of 80W is little better than wild speculation. It might be more, it might be less. It probably won't be much less, but you never know. The hard truth of the matter is you really can't estimate this with much accuracy. I think it is relatively save to assume you'll get a bit less than 100W, but not a huge amount less. Plan for the worst, then hopefully it isn't that bad, and so you have more power than you planned.

You're going to have to just set it up and measure the power you get yourself. And even then, you'll have to keep track day after day for a long time to build a reasonable average. If you end up getting closer to 80W from the panel, then it takes 4.375 days. And pushing it further, for worst case, and being very cautious, I think 5 days worst case to recharge the battery is reasonable. How did I get that number? I just made it up. It's arbitrary. I'm assuming worst case you'll get 70W from the panel. With very little reason. But a 30% hit would be more than one really tends to see, so I think its a fairly reasoned and cautious guess. You might decide on a different number - it's really up to you. It also doesn't really matter. The battery will charge in the time it charges and the time you or I planned it would charge has zero impact on that.

Again, 5 days is my arbitrary sort of 70W assumption as worst case. And beyond that, it is an average. There may be periods where it recharges days quicker, and periods where it takes days longer. That's the downside with solar power: it's wildly inconsistent, unpredictable, and you have no control over it at all. So plan accordingly.

Anyway, good luck! I know this answer probably just raised even more questions for you, but that's just how it is. Hopefully it was helpful, at least.

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