Battery charge rate calculations

denverh
denverh Registered Users Posts: 4
Hello,

I've been reading as much as I can about how to plan an off-grid system, and I've found a huge amount of really good and helpful information here. But one thing still has me puzzled: battery charge rates. I've seen it expressed in a lot of places as something like C/8, which doesn't really tell me much, even when I know that C is supposed to be the amp-hour rating of the battery. Around here I usually see it as the number of amps charging the battery divided by the AH rating of the battery, and expressed as a percentage. I can almost make sense of that, except that amps divided by amp-hours gives you 1/hours, not a percentage. However, if you invert that, dividing amp-hours by amps instead, you get hours. So if you had 20 amps going into a 100 AH battery, the first method would give you 0.2/hour, but the inverse would give you 5 hours. That would represent the time it would take to charge the battery starting from a completely discharged condition. If you wanted to avoid charging faster than 8 hours for a complete charge then that 20 amps would be far too much.

When I began thinking about it that way, even the C/8 type expressions began to make more sense. I interpret them to mean the number of amps required for a complete charge in 8 hours. So C/10 would be the number of amps for a complete charge in 10 hours. Therefore the number under the C must be hours, and the result is amps, but that was never stated anywhere that I saw.

Am I completely out in the weeds with this, or does it actually make sense?

Regards,

Denver

Comments

  • BB.
    BB. Super Moderators, Administrators Posts: 33,431 admin
    Re: Battery charge rate calculations

    Welcome to the Forum Denver!
    denverh wrote: »
    Hello,

    I've been reading as much as I can about how to plan an off-grid system, and I've found a huge amount of really good and helpful information here. But one thing still has me puzzled: battery charge rates. I've seen it expressed in a lot of places as something like C/8, which doesn't really tell me much, even when I know that C is supposed to be the amp-hour rating of the battery. Around here I usually see it as the number of amps charging the battery divided by the AH rating of the battery, and expressed as a percentage. I can almost make sense of that, except that amps divided by amp-hours gives you 1/hours, not a percentage. However, if you invert that, dividing amp-hours by amps instead, you get hours. So if you had 20 amps going into a 100 AH battery, the first method would give you 0.2/hour, but the inverse would give you 5 hours. That would represent the time it would take to charge the battery starting from a completely discharged condition. If you wanted to avoid charging faster than 8 hours for a complete charge then that 20 amps would be far too much.

    C/8 = 0.125 = ~13%
    C/10 = 0.10 = 10%
    C/20 = 0.05 = 5%
    etc.

    And to be clear, we use Battery Capacity as defined as the C/20 or 20 Hour Rate... The rate to run a battery from 100% to dead in 20 hours:

    100 Amp*Hour capacity / 20 Hours = 5 amps

    If you discharge the battery faster -- Say C/8 hours, the "apparent capacity" of the battery is quite a bit less. Here are some numbers for a typical "Trojan brand Golf Cart Battery"--GC batteries are some of the best deals out there for smaller off grid cabin use:
    GC2 T-105 Trojan "golf cart" battery defined as 6 Volts at 225 AH--The detailed specifications:
    C/5 = 185 AH at 5 hour rate
    C/20 = 225 AH at 20 hour rate
    C/100 = 250 AH at 100 hour rate

    For our needs, we usually use the Capacity at 20 Hour rate--That is something 2 days of storage to 50% discharge (or 25% discharge per day--So, discharge the battery 1/4 per day). Or 20 hours / 4 hours = 5 hours of discharge per evening--That usually works pretty well for an off grid cabin or home (~5 hours of lights/TV/computer per night).

    There are other places that used different rules of thumbs with different discharge rates other than 20 hours... The numbers will be different, but when "translated" back to C/20 hour rate--It is usually "close enough"//
    When I began thinking about it that way, even the C/8 type expressions began to make more sense. I interpret them to mean the number of amps required for a complete charge in 8 hours. So C/10 would be the number of amps for a complete charge in 10 hours. Therefore the number under the C must be hours, and the result is amps, but that was never stated anywhere that I saw.

    So, these numbers really become estimates and short hand for "close enough" math... The faster you discharge the battery, the less efficient it is... For example, the amount of energy stored in that Golf Cart battery at different discharge rates:

    C/5 => 185 AH * 6 volts = 1,110 Watt*Hours
    C/20 => 225 AH * 6 volts = 1,350 Watts*Hours
    C/100 => 250 AH * 6 volts = 1,500 Watt*Hours

    So--you can see there is a huge difference in "efficiency" when discharge at different rates--Similar issues with charging--The higher the rate of charge, the less "efficient" the charging (and more energy that is turned into "wasted heat" and hydrogen/oxygen gases.

    We suggest 5% to 13% rate of charge ( C/20 to C/8 ) with 10% (C/10) as being a pretty "balanced system" that is being deeply cycled...
    Am I completely out in the weeds with this, or does it actually make sense?

    Even a battery bank's AH capacity can be off by as much as 20% from "factory rating" between high and low cells.... Trying to do 5% accuracy for all your calculations--It is not usually worth it... Just do nominal calculations and give your self a 10-20% buffer (minimum). This allows for variations and aging (you don't want it to "work well" when new--And two years later as things age and are not quite as efficient/bit lower battery capacity, etc...

    Technically, some Mfg. will call their batteries "end of life" when they are at 80% of capacity... And we have seen some mfg. try to get out of warranty claims on the forum (as I recall) if the battery has more than 50% of rated capacity.

    -Bill
    Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
  • denverh
    denverh Registered Users Posts: 4
    Re: Battery charge rate calculations

    Thanks Bill. I do understand about how the efficiency of a battery changes at different discharge rates, and how a lot of calculations are by necessity not exact but "close enough". I think much of my confusion has come from the same thing being represented in different ways, and different things being represented the same way. For example, in one book the amp-hour capacity, at a 20 hour discharge rate, would be referred to as C20. In another place it might be referred to as C/20. In a third place it might be referred to simply as C, with a note that it's the 20 hour rate. When you add in charging rates as related to the amp-hour capacity, it really gets confusing: one place might say C/8 - with a note that C is the 20 hour rate (which would expand to C20/8 or C/20/8, and another might simply say C20/8. At the same time they might also be talking about C/8 as the battery capacity at an 8 hour discharge rate. In these forums the charge rate is often represented as a percent, calculated by dividing the charging amps by the amp-hour capacity (at the 20 hour rate). The Rolls AGM battery manual explains charging rate as follows:
    "The initial charge current is recommended to be set at B = 0.25 X C20 (Imax = 0.35 X C20) in order to fully charge the batteries within a reasonable amount of time."
    Now 0.25 x C20 is the same as C20/4. I realize that different kinds of batteries tolerate different charge rates, and that the charging method changes as the battery approaches full charge, that's not what's confusing. The Rolls manual is about the only place where the calculation is actually fairly clear. C20 is amp-hours. Divide that by something, in this case 4, to get amps. Therefore, the something MUST be hours - but they don't say that. Other sources just say charge at some fraction of the amp-hour rating of the battery. But if I picture hooking up the battery to a charger that's equipped with a voltmeter and ammeter, how do I know when I'm charging at some specific fraction of amp-hours, which is what I get when I divide amp-hours by some dimensionless number? Perhaps I'm being overly pedantic, but I get uneasy with calculations that don't resolve to units that make some kind of sense.

    Let's take the bucket analogy, where the size of the bucket in gallons equates to the battery capacity (at the 20 hour rate) in amp-hours, and the rate we're filling the bucket in gallons per hour equates to amps from the charger. The time to fill the bucket is the size of the bucket divided by the fill rate. Equally, the time to charge a battery would be the size of the battery (amp-hours) divided by the fill rate (amps). And amp-hours divided by amps do indeed give a result in hours. If you wish to invert that and call it a percent, that's fine, as long as I understand that it's actually referring, in a way, to hours. And if a battery manufacturer specifies a maximum charge rate based on hours, then I can tell if I'm charging too fast or too slow. I know that I've ignored the fact that in reality the batteries won't be completely discharged, and that the actual rate of charge changes as the battery gets closer to fully charged.

    Going back to the Rolls manual: their C20/4 really means the amount of current that would be required to completely charge the battery from 100% discharged to 100% charged in 4 hours (assuming everything's perfect and ideal). Other battery manuals I've read might recommend charging at something like C/12 (where C is the amp-hour rating at a 20 hour discharge rate), which I would interpret as the amount of current required to go from 0% charge to 100% charge in 12 hours. It's really a way of saying how fast you can put back in what you took out - understanding that you'll always have to put more in than actually came out. If that's correct then I'm no longer confused.

    Thanks again,

    Denver
  • BB.
    BB. Super Moderators, Administrators Posts: 33,431 admin
    Re: Battery charge rate calculations

    Denver,

    Yep--You know what is going on... If we were being clear--Should probably write an equation like:

    C20/12 for 20 hour battery capacity and divide by 12 for a rate of charge (we only got sub/super-scripts in the last year or so in a forum software upgrade).

    But then, you would probably need to have a C20-discharge apparent capacity and a C12-charge apparent charging capacity... Where C12-charge is probably a bigger number than C20-discharge apparent capacity (battery bank is less efficient the faster it is charged) if you wanted to accurately predict the amount of AH needed to recharge the battery bank.

    Normally, close enough is C20 battery capacity * 1/10 (or 10% recharge rate) plus 2-4 hours (2 hours if battery is lightly cycled, 4+ hours of absorb time if deeply cycled)... So even if you got the Cxx/rate of charge accurate--There is still the 2-4-6 hours "extra time" (SWAG--Scientific Wild A$$ Guess) for the battery to "taper charge" time (absorb state--where battery voltage is held at a fixed voltage).

    Is this the best way to charge--Probably not--There are other ways (constant current to a voltage set point, the drop back to a lower voltage to finish, etc.)... However, with solar power, we are a slave to the sun--We cannot define a "nifty charging profile" like the industrial folks can--They have the (virtually) unlimited power from the grid to hold these charging profiles.

    In reality, a lead acid battery is near 100% efficient if you count electrons moving in/out of the battery (Amp*Hours). The only time it becomes less than 100% AH efficient is towards the end of the charging cycle when the battery starts to gas.

    But while Amp*Hours is a great tool and easy number to use--Because most of our loads these days (and even charging) is done with constant power devices...

    You draw 200 watts from an AC inverter:
    • 200 watts * 1/0.85 inverter eff * 1/14.5 volts = 16.22 amps
    • 200 watts * 1/0.85 inverter eff * 1/12.5 volts = 18.22 amps
    • 200 watts * 1/0.85 inverter eff * 1/10.5 volts = 22.41 amps

    So--our AH measurements are now longer fixed with the load, but vary because of battery bank voltage is changing--While the actual load is fixed (in terms of Watts). In fact, I have seen some UPS batteries are now also rated in Watt*Hours of storage (capacity) as well as AH capacity. Recognizing the fact that the UPS loads are AC inverters (constant power).

    Charging with a PWM controller--The maximum current from the solar array is just based on the amount of sun hitting the panel (constant current charging).

    With MPPT controllers, the battery charging current is also based on the battery voltage (constant power charging)
    • 200 watt array * 0.77 panel+controller losses * 1/14.5 volts = 10.62 amps
    • 200 watt array * 0.77 panel+controller losses * 1/12.5 volts = 12.32 amps
    • 200 watt array * 0.77 panel+controller losses * 1/11.5 volts = 13.39 amps

    Where was I going with this? :blush:

    I guess I was trying to say that taking into account all of the variables is a pain in the behind. Your battery bank is more energy efficient if you operate it in the 20-80% state of charge range--And a whole lot less efficient if operated in the 80-100% state of charge range (when charging voltage is high and the batteries are gassing during charging--and a lot of charging current is being turned into heat).

    The rules of thumb work pretty well... And being conservative with losses (assume worst case rather than best case)--Things usually work out pretty well... Trying to get to within 10% or better accuracy--Very difficult.

    -Bill
    Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
  • denverh
    denverh Registered Users Posts: 4
    Re: Battery charge rate calculations

    Thanks Bill. I understand what you're saying. If batteries really did behave just like buckets you could make exact calculations, but they don't. The bucket analogy is good only to illustrate the form of the calculations, not the substance. If you try to get too precise you find everything moving around. It's like what a machinist wrote in an article I read recently: "Everything is made of rubber." Meaning that no matter how rigid you think your materials and machine tools are, they actually do flex all the time. But usually not enough to matter. Knowing where and when it does matter is important, though. I guess that's where experience come in.

    Thanks again,

    Denver
  • inetdog
    inetdog Solar Expert Posts: 3,123 ✭✭✭✭
    Re: Battery charge rate calculations
    denverh wrote: »
    "Everything is made of rubber." Meaning that no matter how rigid you think your materials and machine tools are, they actually do flex all the time. But usually not enough to matter.

    FWIW, for things moving at a significant portion of the speed of light, relativity requires that even an object with arbitrarily high rigidity must flex by a very large amount during acceleration and deceleration. It is often referred to as relativistic elasticity and it is different from, although related to, the apparent static elongation and contraction familiar to those who enjoy analyzing purported paradoxes of relativity.
    SMA SB 3000, old BP panels.
  • denverh
    denverh Registered Users Posts: 4
    Re: Battery charge rate calculations
    inetdog wrote: »
    FWIW, for things moving at a significant portion of the speed of light, relativity requires that even an object with arbitrarily high rigidity must flex by a very large amount during acceleration and deceleration. It is often referred to as relativistic elasticity and it is different from, although related to, the apparent static elongation and contraction familiar to those who enjoy analyzing purported paradoxes of relativity.

    Yes, but doesn't that depend on your reference frame? It's possible that even stranger things could happen as you begin falling into a black hole. But let's not go there...
  • inetdog
    inetdog Solar Expert Posts: 3,123 ✭✭✭✭
    Re: Battery charge rate calculations
    denverh wrote: »
    Yes, but doesn't that depend on your reference frame? It's possible that even stranger things could happen as you begin falling into a black hole. But let's not go there...
    It has to depend on your reference frame. But to get two observers to agree on the outcome of events which either happen or do not happen, the only way to do it is to allow relativistic elasticity.
    On the other side of the analysis, you find that you cannot have infinite rigidity because it takes time for the forces involved to propagate over the distances between atoms.
    Also one of the little corners where Relativity and Quantum Mechanics rub rough edges.
    SMA SB 3000, old BP panels.