I'm wondering how to calculate the time it will take to charge my battery from a 20W solar panel. The battery is 12V/18Ah. The solar charger is a cheapo from Aliexpress so I'm assuming the efficiency is 50% max. Further I'm assuming the solar charger will only discharge the battery to 25% then shut off the load (13.5Ah removed). The battery capacity will last for three days of completely overcast sky. I know the charging rate is not constant throughout the day, but I just need to ball park the charge time for when the sun comes back out. Thanks.

I think the formula is something like one of these:

hours to charge = (Amp Hours removed / (Solar Watts - Load Watts) * efficiency / 12.0V)

hours to charge = (Amp Hours removed / ((Solar Watts *efficiency - Load Watts) / 12.0V)

 

You are pretty close to the mark there, the second one I think is the more accurate in as much as the efficiency applies to the panel & charger combination but not the load. The load will take the power it takes with 100% efficiency ;-)
Your other numbers however, may be a little misguided. Unless the charger is a MPPT type all it actually does is connect the panel to the battery until the battery voltage comes up to a specific voltage and then disconnects it until the battery voltage falls by a specific amount. A typical SLA charging voltage (assuming lead acid) would be around 14.7V for boost charging so the cut in / cut out voltages might be 14.6V and 14.7V (just for working numbers and a guide). So what you need to know is the current your panel will deliver at those voltages and that current will be a function of the insolation, the orientation of the panel with respect to the insolation etc etc and to some extent the temperature of the panel. Solar panel power is typically specified at the maximum power point which for a monocrystalline panel would be at around 19V to 21V or so and the current would be around 1A. But at 14.7V you might get a little better with maybe 1.1A or even 1.2A on a good day. If you are in Australia, we can get stronger insolation than most of the rest of the world peaking at around 1.4 sol so you may do better again.
From the panel current, subtract the load current and the remainder is your charging current. Battery charging efficiency varies with just about everything but typically lies between 60% and 80% for SLA batteries.
I wouldn't put too much faith in the 25% cut off either. If the cut off is voltage based and the typical threshold of less than 11V then it is more likely to be 5% or less otherwise high load currents (relative to the battery capacity) will cause premature load disconnection.
I don't think I have really answered your question but I hope I have given you useful information and an explanation of why the answer may not be so simple as you may have hoped.

 

The post above goes a long way to explain the intricacies of the problem.

In my experience, all these variables add up to the point where calculation becomes useless, following calculation typically leads to hopelessly optimistic predictions.

The true answer can only be found by testing - be prepared for disappointing results.

 

Thanks for the info. If I understand you correctly then the efficiency is not the charger output but the heat lost charging the battery? So its battery efficiency. If thats the case then if I use current instead of wattage then the first equation (not / 12V) should apply as the efficiency is applied to the current remaining:

hours to charge = (Amp Hours removed / (Solar Amps - Load Amps) * efficiency)
hours = 24Ah / ((1.0 - 0.6) *0.5) ~= 115

If I use a current of 1A solar current (20W panel) available with a 0.6A load current in the calculation then it triples my charge time I previously calculated, but that was assuming 20W out of the panel which was incorrect. I may need to go with a 40-60W (~2-3A available) panel to get my charge time to around 33 hours (3-4 days of sun) which is reasonable for my application. I'm designing this system to go in a location far away from me so I can't test out the rig under final conditions. I just need to design for worst possible case. Cheapest option looks to be to double up on 20W panels.

 

The post above goes a long way to explain the intricacies of the problem.

In my experience, all these variables add up to the point where calculation becomes useless, following calculation typically leads to hopelessly optimistic predictions.

The true answer can only be found by testing - be prepared for disappointing results.

You are absolutely correct. None of the specs of the components is going to be all that reliable and how it all comes together has a multitude of variables all conspiring to compromise the performance of the system.
You can only the know the useful battery capacity by testing it. It might say 18.5Ah on the box, but what you actually get could be something else entirely. Same goes for the solar panel, especially if it is something like a polycrystalline or amorphous panel. And then there is the charger which may work in any number of ways, many of them not so good. And then the load, linear or constant power and how does it react to the charging voltage or to the cut-off voltage.

Best you can do, is test as Sensacell suggested and keep the detailed information in mind to design the tests to get you the critical parameters you want. Be it the charging time independently of everything else or the charging time on a bright but cool day with typical load current applied for example. (I didn't mention it earlier but the battery temperature is also important and can take a battery days to thermally settle to around a constant ambient so overnight temperatures prior to testing may also be relevant.)

There is also that possibility that something, the charger maybe, just doesn't work properly so after all your careful test design the thing fails on the launch pad. "Houston, we have a dead duck" ;-)

 

Thanks for the info. If I understand you correctly then the efficiency is not the charger output but the heat lost charging the battery? So its battery efficiency. If thats the case then if I use current instead of wattage then the first equation (not / 12V) should apply as the efficiency is applied to the current remaining:

hours to charge = (Amp Hours removed / (Solar Amps - Load Amps) * efficiency)
hours = 24Ah / ((1.0 - 0.6) *0.5) ~= 115

If I use a current of 1A solar current (20W panel) available with a 0.6A load current in the calculation then it triples my charge time I previously calculated, but that was assuming 20W out of the panel which was incorrect. I may need to go with a 40-60W (~2-3A available) panel to get my charge time to around 33 hours (3-4 days of sun) which is reasonable for my application. I'm designing this system to go in a location far away from me so I can't test out the rig under final conditions. I just need to design for worst possible case. Cheapest option looks to be to double up on 20W panels.

That's a pretty fair statement I think and I think you are very likely in the ball park. I would add one caveat though; the battery will not accept a charging current simply because it is available. The battery will draw less current as it charges, assuming a constant charging voltage. Ideally, you would also have a temperature probe on one of the battery terminals as the charge voltage really should be modified to suit the battery temperature (not the outside of the case but the actual electrolyte which is best measured via a big thick lead battery terminal, but can't remember which one).

So to charge a battery from 20% to 60% is easier than 60% to 80% because it will naturally draw more current at the lower state of charge. To get upwards from 90% SOC to over 95% can take as long as it did to get from 50% to 90%. Usual thing is to assume a working range for SOC to be say a minimum of 30% (for long cycle life) and 80% as a practically achievable SOC after charging.

Given your load current of 0.6A and a charging current of around 1A it is clear the load cannot be a 24/7 thing anyway. But I would suggest you need to make sure that the load duty cycle and your minimum winters day length and your confidence that the solar panel(s) are correctly placed and at the correct angles be taken into account to avoid the disappointment of a dead battery.

The only way to get an idea of how quickly you can charge the battery is to test it, but keep in mind the temperature of the battery. It could lose, temporarily, anything up to 40% of its capacity at low temperature and probably should not be charged at all if it is over 40degC as it would likely be damaged permanently.

 

The load runs about 14 hours a day during daylight hours only. And yeah the batteries will have no shade protection at all. But with 2 x 40W panels the box could go behind them and be shaded somewhat. So I need to have about 2-2.5A average charging current. What is clear is that 1A is not enough. Adding the extra amp drops the charging time a lot. So now I just need to convince the client to reduce the overcast days run time to 2 x 14 hour days instead of 3. Just put it into the spreadsheet: 20AH will give me 26 hours run time and with 40W of solar charge in 22 hours. I'm angling my panel for winter as the worst case scenario. Also, maybe with the steeper angle the bird crap will slide off

 

The load runs about 14 hours a day during daylight hours only. And yeah the batteries will have no shade protection at all. But with 2 x 40W panels the box could go behind them and be shaded somewhat. So I need to have about 2-2.5A average charging current. What is clear is that 1A is not enough. Adding the extra amp drops the charging time a lot. So now I just need to convince the client to reduce the overcast days run time to 2 x 14 hour days instead of 3. Just put it into the spreadsheet: 20AH will give me 26 hours run time and with 40W of solar charge in 22 hours. I'm angling my panel for winter as the worst case scenario. Also, maybe with the steeper angle the bird crap will slide off

That is the usual setup for a fixed panel: angle and orientate for optimum winter performance. I will advise caution on the charging time calculations though. I think you are still assuming the battery will accept any amount of current you can present to it and that is just not true.

That said, since the load operates typically during daylight hours only your real concern is probably recovery after a couple of bad days. Keeping mind that overcast conditions don't impact solar energy all that badly and certain conditions, if you are near a body of water for example, can actually improve the conditions by reflecting extra light onto the panels.

So my only caution would be your estimates for recovery time. If you can get your hands on a copy of "Rechargeable Batteries - applications handbook" or "Handbook of Batteries" (Linden Reddy) they have information you can extract a mathematical model from and taylor to your battery with a few test results. You should also be able to make some aging projections of performance as well.

With 2 x 40W panels though, I'm not sure you need worry about any of it. That has to be plenty of power for the system I would think. A single 40W should probably be enough but modelling would be required to be sure of it.

 

I would add the calculations might be inaccurate but they will certainly give you an idea your in the ballpark. If you estimate 25% panel output for 6 hours you should get a good idea. I believe at lower power PWM controllers are more efficient as they are basically not pulse width modulating in that situation.

 

So I might split the load(s) between two panels/batteries and go up to a 35W solar panel. In my calculations I've been using a 75% max removable amp hours from the battery (of whatever capacity). From what I understand this is reasonable because the charge controller will only let the voltage drop to a certain point so I can't completely drain all the amps from the battery. I would like to because my load is a 5V voltage regulator which could handle down to about 6.5V probably. Is 75% a good number or too low? Thanks.

Doug

 

So the customer has agreed to in certain installations split the load(s) between two panels/batteries and go up to a 35W solar panel. In my calculations I've been using a 75% max removable amp hours from the battery (of whatever capacity). From what I understand this is reasonable because the charge controller will only let the voltage drop to a certain point so I can't completely drain all the amps from the battery. I would like to because my load is a 5V voltage regulator which could handle down to about 6.5V probably. Is 75% a good number or too low? Thanks.

Doug

In my opinion, 75% is quite high. If you discharge an SLA below 30% SOC to say 10% you will reduce its cycle life span by about 90%. So 30 cycles (say) instead of 300. It might be more like 300 instead of 3000, I don't know the battery you are using but you get the idea. There is also, As I have tried to explain to you before, a limit on the charging rate of the battery especially as it becomes charged above even 50% SOC it will not accept a charging current simply because you have it available. In any one day where the battery may start the day somewhat discharged, it would need to be a very long charging day to get the SOC up over 90% and unless the SOC was down to very low numbers, the size of the panel;s would make less difference as the battery would only accept very small currents anyway. So, an optimistic number might be 30% to 90% = 60% but the 30% is not something you are likely to be in any control of. Your controller that you say protects the battery from excessive discharge probably does not do that in fact for you. Typical controllers use a threshold of around 10.5V but an OC (relaxed) terminal voltage of around 12.0V indicates a totally dead battery. (around 12.9V to 13.0V indicates a SOC around 100%) Do you know the cut-off voltage and do you know if the load current makes any difference to that cut off voltage? (I'm not saying that simply modulating the cut off voltage with load current is the answer, but if there is no modulation then the extra steps required for the controller to estimate the SOC are probably not happening either. It might be using capacitance measurements to estimate SOC but that is doubtful too, or is it?).

Does the controller use a multiphase charging algorithm? Does it have a temperature probe to attach to one or other of the battery terminals?

I should have already asked this as well: what is the required life span of this system and is the battery a deep cycle type and what are the specs on discharge depth vs cycle life?

 

Thanks for your continued help in this. The system I am designing as a package will be deployed all over North America. My customer wants a standard package (eg fixed solar panel angle mount, battery size, panel wattage etc) The specs I've suggested are what the customer wants as ideal but he is willing to listen and compromise as required. However, one compromise that is going to be hard to push through is the charge controller. I've been given and told to use a $1.25 controller from Aliexpress:

By all accounts its actually pretty good, but frack no specs like you were talking about. However, your last point is what I've been thinking about for the past couple days.

I *was* wondering if a deep cycle / high cycle rate (same thing?) are the way to go for my application. Sounds like it might be a good idea for the extra couple of bucks. As for how long these are supposed to last in the field? Who knows? I'm thinking about three years before they get supplanted by newer tech. These are the two batteries I'm considering:

http://www.batteryspecialist.ca/12-volts-15ah-terminal-f2-sla-agm-battery-ub12150/

http://www.batteryspecialist.ca/12v-15ah-extended-run-high-cycle-csb-battery-evh12150/

Also, since this will be powering several cameras I'm designing a power control distribution board which will measure the power usage. So over time we will be able to model how much power the system uses in different parts of the country.

 

Thanks for your continued help in this. The system I am designing as a package will be deployed all over North America. My customer wants a standard package (eg fixed solar panel angle mount, battery size, panel wattage etc) The specs I've suggested are what the customer wants as ideal but he is willing to listen and compromise as required. However, one compromise that is going to be hard to push through is the charge controller. I've been given and told to use a $1.25 controller from Aliexpress:

By all accounts its actually pretty good, but frack no specs like you were talking about. However, your last point is what I've been thinking about for the past couple days.

I *was* wondering if a deep cycle / high cycle rate (same thing?) are the way to go for my application. Sounds like it might be a good idea for the extra couple of bucks. As for how long these are supposed to last in the field? Who knows? I'm thinking about three years before they get supplanted by newer tech. These are the two batteries I'm considering:

http://www.batteryspecialist.ca/12-volts-15ah-terminal-f2-sla-agm-battery-ub12150/

http://www.batteryspecialist.ca/12v-15ah-extended-run-high-cycle-csb-battery-evh12150/

Also, since this will be powering several cameras I'm designing a power control distribution board which will measure the power usage. So over time we will be able to model how much power the system uses in different parts of the country.

The first battery has a fairly good data sheet and appears to have reasonable characteristics for cyclic use. For a DOD (depth of discharge) of 50% you might expect 500 cycles before it drops to a 7.5AH battery or for 30% DOD that would be around 1200 cycles. The salient points with that though is that the data sheet assumes a full recharge each time and the battery is at a constant 25degC. In your application the DOD should be absolute, in other words, if you want the 50% DOD number to hold the battery should never be discharged below 50% SOC irrespective of what recharge the system can manage. So if the battery only gets up to 80% then you have only 30% to play with before the cycle life starts to drop and it will drop quite quickly.
The second battery has no data sheet and the instructions printed on the side of the battery don't quote cyclic use at all. I'd give it a miss. It might be the better battery but without data, how would you know?
The charger is likely to be a problem. I didn't watch the video as I don't have time. If it does not sense a depleted battery and go into a boost charge initially or even worse, goes into a boost charge and stays there your battery will have a short life span. The initial charge of a depleted 12V SLA battery should be up around 14.5V and fall back to float (13.8V) as the battery charges up. If the batteries are out in the wild (exposed to normal weather conditions, especially in North America -> huge temperature variations) the charge voltage must be modified to suit the temperature of the battery itself (not the ambient temperature). If the charge voltage is not reduced when the battery gets warm the battery could be seriously compromised in a matter of days. Float charging voltage is probably fairly safe but a boost charge voltage is definitely not and without a boost charge voltage applied the battery is unlikely to recover from a discharge in less than a week or two depending on temperatures and DOD.
Now I think you are becoming very aware of the issues. Your replies certainly indicate that to me and that is nice to know I'm not wasting my time on this. The data sheet for the first battery has lots of details you should probably mull over and keep temperature in mind as you look through it. I had a Sierra Nevada winter and a Mojave summer in mind when I read it. Very disturbing. ;-)

 

Some figures to formulas above:
Solar power flux in near space at orbit 1380 W/m2, at Africa midday - 600 W/m2, at 57 parallel bright summer cloudless day 350-400, bright day with minor clouds 150, average winter day 30-60 W/m2.
Solar joule thief efficiency 80-85%.
Solar cell efficiency - ultra-expensive 30-40%, average - 20-25%, cheap 10-15%.
Solar cell working without of joule thief - 25%.

 

Some figures to formulas above:
Solar power flux in near space at orbit 1380 W/m2, at Africa midday - 600 W/m2, at 57 parallel bright summer cloudless day 350-400, bright day with minor clouds 150, average winter day 30-60 W/m2.
Solar joule thief efficiency 80-85%.
Solar cell efficiency - ultra-expensive 30-40%, average - 20-25%, cheap 10-15%.
Solar cell working without of joule thief - 25%.

The irradiance figures don't gel with my experience which does not include the 57th parallel north so for those figures I have nothing to add. The numbers closer to the equator I think need some clarification though. In the northern half of Australia we get a full 1kW/m2 irradiance and in Sydney even with a tilt to suit Winter solar collection we would get at least 600W/m2 peak. Cloud cover makes a difference of course, but nothing like the numbers quoted. I saw drops of around 20 to 30% due to cloud cover during the peak of the day.

If a winters day was literally just 30 to 60 W/m2 compared to 350 to 400 W/m2 then there would be no autonomous solar powered system that could practically operate over the full year without being crazy over spec'd during the summer months. That might be true given it is quite an extreme latitude.

I have no idea what a Solar Joule Thief is nor how or why its efficiency is relevant. Do you mean a maximum power point tracker?

Unless there have been some monumental improvements in solar cell technology only military / satellite grade panels achieve 40%, the 'Professor Green' cells which are now fairly common place in the monocrystalline market achieve around 22% at last check and some polycrystalline / amorphous cells can get up to 17% but 7% is far more common. This is only broad category and commonly available type panels. There are way too many types to go into details which are beyond the scope / topic anyway.

To assist the OP, does anyone have to hand the optimum tilt angles and corresponding irradiance and insolation (integral of irradiance and daylight hours = total daily solar collection) figures at hand?