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  • Battery Sizing Calculator

    The how is really a simple formula. Watt-Hours / Battery Voltage = AH

    The first and most crucial step is to determine how many watt hours you will need in a 24 hour period. The second step is to determine how many days of reserve capacity are required (autonomy). The minimum is 2.5 days and up to 14 days. Then multiply this by 2 (for 50% depth of discharge as you never ever want to discharge more than 50%). So let’s select the minimum of 2.5 days. 2.5 days x 2 = 5 days.

    Third step is to take the number of days determined from step two, and multiply by the daily watt hour usage. So in this example 4500 wh x 5 = 22,500 wh or 22.5 Kwh.

    The last step is to dived the watt hour figure in step three by the battery system voltage. So now we must decide on a battery voltage of 12, 12, 36, 48, 60 and so on with multiples of 12 volts. For consumer grade applications the highest voltage (limited by equipment available to the public) is around 48 to 60 volts. Commercial applications can go as high as 500 volts and higher with special exemptions by limiting access to only qualified personnel. The voltage you choose is restricted mainly by the charge controller current capacity vs the solar panel wattage. Basically you want to use as high of voltage as you can afford to minimize power losses on the wring, and to keep the wiring as small as possible to minimize cost. For example the largest charge controller current available today to consumers is 80 amps. These controllers can be used on 12, 24, 36, and 48 volt systems. So a typical MPPT charge controller of 80 amps will have solar panel wattage limitations. For example at:

    * 12 Volts max panel wattage = 1000 watts
    * 24 Volts = 2000 watts
    * 36 Volts = 3000 watts
    * 48 volts = 4000 watts


    So for this example let’s assume we live in Kansas City which has a winter Sun Hour Insolation of 3.3 Sun Hours. So from another calculation (found elsewhere) we know we have to have minimum solar panel wattage of 1400 watts. So in this example the minimum battery voltage we can use is 24 volts. Now we have all the information we need to determine the battery Amp Hour Capacity needed. The formula is Watt Hour Capacity / Battery Voltage so using the numbers from previous steps AH = 22,500 / 24 volts = 938 Amp Hours.

    Fourth step is to select a battery. If possible we want to only have one single string of batteries wired in series to obtain the voltage needed. We only want to use true deep cycle batteries made for renewable energy. This limits manufactures, and you will not find them at Walmart. A very good manufacture with the best warranty is Rolls-Surrette. They have a very good selection tool you can use. Check the RE battery option, input Desired AH, input +/- Percentage (10 to 15%), and 20 Hour Rate. Then you will see your choices to the right. Select a battery with enough AH capacity to construct with 1 string if possible. In this case the Rolls S1380 is the right choice. It is a 2 volt @ 1050 AH battery so you would need 12 of them wired in series to make 24 volts. The battery carries a 7 year warranty, with 2 years free replacement and last 5 prorated. You can expect 5 years of life out of it with excellent care.

    Finally you might be asking why do I need so may batteries and reserve capacity. Well the answer is batteries only have so many cycles (discharge/charge) in them and the number of cycles depends on the depth of discharge. Generically the Cycles vs Depth of Discharges (DOD) look like this:

    * 50% = 200 cycles
    * 40% = 500 cycles
    * 30% = 1000 cycles
    * 20% = 2000 cycles
    * 10% = 4000 cycles

    Hope this helps.

    SK
    MSEE, PE

  • #2
    Originally posted by Bentley
    So then you would divide amp hour needs by amp hour rating on battery to determine how many batteries to get right? Just wondering
    No all batteries already have an Amp Hour rating. For example a popular battery used by RE folks is a 6 volt golf cart battery and it is rated 6 volts @ 225 AH. So let' say you need 12 volts at 225 AH. You would buy 2-6 volt batteries @ 225 AH and wire the two batteries in series to obtain 12 volts @ 225 AH.

    In any event the preference is to use only 1 single string of batteries so as to avoid parallel strings. Rather than try to list all combination, that would take a book, most of the better battery manufactures have APPLICATION SELECTION tools where you enter the AH capacity and it will select the closest match.

    Here is a site that can help out:
    Rolls Surrette Battery Selector
    MSEE, PE

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    • #3
      @ Sunking - Great information - thanks from everyone!

      Russ
      [SIGPIC][/SIGPIC]

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      • #4
        Please more explaining

        As I understood it Ah means Ampers per Hour, isn't it? That (for me) means how many ampers can battery can battery give. But you counted capacity time day, not hours.
        More confusing for me was, when I tried to understand, there is different rating - 20, 72 and 100 hours. I have some thoughts, but is quite uncertain for me. Can explain it to me please?
        s pozdravom, best regards, mit freundlichen Grussen, cordialement, Pavel

        Pavel

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        • #5
          Originally posted by P.S. View Post
          As I understood it Ah means Ampers per Hour, isn't it?
          No not at all. It means Amp Hours at a specified discharge rate. Most battery manufactures use the 20 hour discharge rate. So lets say you have a 100 AH battery rated at the 20 hour discharge rate. That means the battery can deliver 5 amps for 20 hours. T = AH/A


          Originally posted by P.S. View Post
          That (for me) means how many ampers can battery can battery give. But you counted capacity time day, not hours.
          More confusing for me was, when I tried to understand, there is different rating - 20, 72 and 100 hours. I have some thoughts, but is quite uncertain for me. Can explain it to me please?
          Lets start with the TIME element of HOURS. When working with a battery AMP Hours is some what meaningless unless you are working in AMP units. It can be done but makes for a lot of conversions. What is easier to work with is Watt Hours, and how many WH per day you use. The formula for Watt Hours is as the term suggest = watts x hours = watt hours. So if you have a 100 watt light bulb and turn it on for 5 hours it uses 100 watts x 5 hours = 500 watt hours.

          With a battery say 12 volts @ 100 AH we can determine the watt hours by taking the battery voltage x the Amp Hours, so 12 volts x 100 amps hours = 1200 watt hours. So if we take 500 wh from the 1200, that leaves us with 700 watt hours capacity left, or 700 wh / 12 volts = 58.3 amp hours

          As for the 20, 72 and 100 hour discharge rate go back to the first example. Batteries are rated at 20 hour discharge rates. so a 100 AH battery at 20 hour rate = 5 amps for 20 hours, 1.38 amps for 72 hours, or 1 amp for 100 hours. But there is a catch called Peukert Law which means the capacity changes depending on the discharge rate. I will try to explain this with an example. Lets say you have a 100 AH battery at the 20 hour discharge rate or 5 amps for 20 hours. Greedy Mr Peukert will rob you if you discharge at a higher rate. For example you discharge at the 10 hour rate (10 amps) and that battery will only last for 7 hours, not 10 so it now becomes a 70 AH battery. Drop down to the 5 hour rate of 20 amps and it will only last 2.5 hours making the battery a 50 AH battery. On the flip side if you discharge at the 100 hour rate or 1 amp and it will last 140 hours making it a 140 AH battery.

          OK as to the
          MSEE, PE

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          • #6
            Originally posted by Sunking View Post
            Battery sizing is really a pretty simple straight forward process and is crucial to get right for an Stand Alone Off-Grid Battery systems. In the past I have used a default KISS approach (Keep It Simple Stupid) to make things really easy. The formula for the KISS method is:
            • (Daily Watt Hour Usage x 5) / Battery Voltage

            This works in most applications in moderate climates where winters are fairly mild, and uses a default 2.5 consecutive Cloudy Days to the 50 % Depth of Discharge threshold cutoff point. So as an example let
            I think this formula is a little light on battery capacity.

            The formula I have been using for 25 years is:

            Daily watt-hour usage
            X
            days of automony (usually 4-7, depending on climate)
            /
            maximum depth of discharge (I use .75, I think .50 is a little high for lead acid batteries, they can take it)
            =
            desired battery capacity in watt-hours
            / (220 x 6) if golf cart batteries or (350 x 6) if L16
            =
            number of batteries needed.
            Driver of the Solar Bus

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            • #7
              Originally posted by garybeck View Post
              I think this formula is a little light on battery capacity.

              The formula I have been using for 25 years is:
              Light on what? Autonomy I use 5 days for non critical systems , and 10 days for mission critical systems. DOD is just an end result of how many days of autonomy you have. DOD is 20% for a 5 day capacity and 10% for 10 days.
              MSEE, PE

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              • #8
                Originally posted by garybeck View Post
                desired battery capacity in watt-hours
                / (220 x 6) if golf cart batteries or (350 x 6) if L16
                =
                number of batteries needed.
                This I have no idea what you are talking about as it nonsense. Battery capacity is 3rd grade math. AH = WH / Battery Voltage
                MSEE, PE

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                • #9
                  Originally posted by Sunking View Post
                  This I have no idea what you are talking about as it nonsense. Battery capacity is 3rd grade math. AH = WH / Battery Voltage
                  It took me awhile to figure this out.
                  The key is that having gotten the WH number he divided by the WH/battery (= AH x 6) of two different battery types to get the number of batteries.
                  However his AH figures are only approximate for the two battery types he mentions and real battery models from different manufacturers may be somewhat different.
                  Not the best way to make it understandable, but as he writes it out it is sort of correct.

                  It is frustrating to have to spend the time to figure out what somebody means when it is poorly stated, but I like to play around that way by choice.
                  SunnyBoy 3000 US, 18 BP Solar 175B panels.

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                  • #10
                    Math looks right on both, just trying to decide whether to multiply something by (6x4) or (24) situation, both come out the same if you use the same autonomy, with the only real difference being the adjustment to DOD. SK's version seems simpler to me, but maybe that is because I have been looking at it longer?

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                    • #11
                      Originally posted by inetdog View Post
                      It took me awhile to figure this out.
                      The key is that having gotten the WH number he divided by the WH/battery (= AH x 6) of two different battery types to get the number of batteries.
                      However his AH figures are only approximate for the two battery types he mentions and real battery models from different manufacturers may be somewhat different.
                      Not the best way to make it understandable, but as he writes it out it is sort of correct.
                      Well OK but what battery is used is the last step and of no concern when determining capacity. Do that and you get stuck in a box like using 12 volt 100 AH batteries for everything. That does not work. If you need 1000 AH battery, then buy 1000 AH cells and avoid parallel batteries.

                      Lock the thread down so no one else can muck it up.
                      MSEE, PE

                      Comment


                      • #12
                        Originally posted by garybeck View Post
                        I think this formula is a little light on battery capacity.

                        The formula I have been using for 25 years is:

                        Daily watt-hour usage
                        X
                        days of automony (usually 4-7, depending on climate)
                        /
                        maximum depth of discharge (I use .75, I think .50 is a little high for lead acid batteries, they can take it)
                        =
                        desired battery capacity in watt-hours
                        / (220 x 6) if golf cart batteries or (350 x 6) if L16
                        =
                        number of batteries needed.
                        I think the misunderstanding may be that you are interpreting the "5" in Sunking's formula:
                        • (Daily Watt Hour Usage x 5) / Battery Voltage

                        as Day's autonomy. However if you read his larger explanation above it is actually the minimum 2.5 days autonomy multiplied by 2 for 50% days autonomy. He makes it clear that his acceptable range for autonomy is 2.5 days minimum up to 14 days for mission critical.

                        You consider an acceptable range for autonomy to be 4-7, based upon climate, but not taking into consideration a mission critical application which is what Sunking did. (eg Telco - you want your cell service in an emergency, right?) but also take your batteries down to 75% instead of the more conservative 50%.

                        So it is either a matter of misinterpretation of terms or apples and oranges. I am curious if you have somewhere identified which climates you consider a '4' and which you consider a '7'. That seems more subjective than "mission critical" since one could have high insolation but larger potential for cloudy days or storms vs low insolation with clear skies most of the time.

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