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Calculating your Required Battery CapacityFactors

The primary and certainly the most important factor is the load you anticipate your batteries

will have to store. Using the watts of load you calculated for your daily electrical loads,convert this into the measure of how storage batteries are measured. Storage batteries aremeasured in Ampere hours (AHr.).Ampere HoursUsing the example of 157.42857 Watt hours per day from our getting started page and

assuming the battery array will be 12 volts you will arrive at 13.1 Ampere hours

required. The math is the same as before, this time we divide Watt hours by the batteryvoltage ( 157.42857 12V = 13.1 Ampere hours)System OverheadsEach time you convert electricity as from solar voltaic panels to battery voltage and thenfrom electricity to chemical storage (battery) and transport low voltage electricity over

connections and through wire you lose some power. Using experience, a bit of math andindustry hearsay we use a 20% loss factor. This loss factor must be taken into account

within your battery storage. We call this portion of the calculation the Loaded Daily AHrrequired. If we use 20% we now require 15.7 AHr ( 13.1 AHr X (1+20%) = 15.7 AHr.)Reserve DaysAll would be fine if the sun were guaranteed to shine equally every day. We now need to

factor how many days of capacity you want your batteries to hold up until the sun comesout from the clouds or you need to turn on your generator. Lets assume you want 2 and a

half days of reserve time. This will bring your requirement up to 39.4 Ampere hours ofbattery (15.7 Ampere hours X 2.5 days = 39.4 Ampere hours) of battery with reservecalculated.Battery AgingYour batteries if well taken care of will have many years of life. However, batteries will ageover time and lose some of their potential. Because a battery array will work at the level ofthe weakest battery placing new batteries into an old battery array is a waste (seeadding

batteries). We use best to account for the loss now as it also helps you keep the DOD

(soon! read on to the next point!) down. It is not unreasonable to use a factor of 20% toaccount for battery aging so your battery requirement now comes to 47.2 AHr. (39.4 AHr X

(1+20%) = 47.2)Battery TemperatureBecause they are a based on an electro chemical process batteries lose power in the cold. If

you are going to use your system during the winter or shoulder seasons and store them

outside or in an unheated area, your batteries will need to be de-rated. If you use yourbatteries all year, this is an important factor. Most battery manufacturers supply de-rating

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tables based on battery temperature. We'll leave this factor out of our example for now

because many of you use your systems only in the summer and shoulder seasons (seetemperature de-rating).Depth of Discharge (DOD) this is very important!DOD a measure of how deeply a battery is discharged. When a battery is 100% full, theDOD is 0%. Ampere hours removed from a fully charged cell or battery, is expressed as apercentage of rated capacity. For example if 25 Ah are removed from a 100 Ah battery, it'sdepth of discharge is 25% and the battery is at a 75% state of charge.OK, with the definition taken care of, why is DOD an important part of calculating batterycapacity? First another definition:A Cycle is a period of discharge and recharge is called one cycle. A battery cycle is one

complete discharge and recharge cycle. It is usually considered to be discharging from100% to 20% DOD, and then back to 100%. One of a Battery's performance indicators isthe measure of the expected number of cycles it may deliver.

The greater the average depth-of-discharge, the shorter the cycle life. Be careful whenlooking at ratings that list how many cycles a battery is rated for unless it also states how

far down it is being discharged. A battery that is rated for a 20 year life expectancy ifdischarged by only 15% may have a 5 year life expectancy if discharged to 50%. Typicallybatteries ratings are in AHr are published to 100% discharge. (Careful again! The longer

the discharge time e.g. 100 hr the more Ampere hours that can be squeezed from abattery. Ratings should be compared at 20 hrdischarge ratefor off-grid purposes.)Here's the crunch; If say a 100 AHr battery that is discharged to 100% will last 100 cycles,however, it will last 400 cycles if discharged to 50% and longer yet if discharged to35%. Before we go further with your battery sizing lets do the math for DOD.

100 cycles at 100% = 10,000 AHr discharge over the life of the battery. (100 cycles of100AHr = 10,000AHr.)400 cycles at 50% = 20,000 AHr discharge over the life of the battery (400 cycles of

50AHr = 20,000 AHr.)

At 400 cycles the battery lasts 4X as long an produces 2X as much power over its life!back to battery sizing...Size Calculation at 50% DODAt 50% discharge the battery size required is 94.5 AHr. (47.2 AHr 50% = 94.5 Ahr.)CALCULATION SUMMARY

We started off with a daily usage of 157 Watts or 13.1 AHr @ 12V and ended up with a

requirement of 94.5 AHr. capacity. I hope by this you appreciate how many systems aresized to people's pocket books not to the system configuration requirement.

A Cynical Aside: Too many clerks tend to sell what a client is be able to afford, knowing full

well you'll be back later with your wallet open to buy more. It's easy to blame client

electrical usage, the weather or any number of things, then sell you more. ...or they just

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don't know. Remember,you cannot add new or different batteries to you existing batterybank. The new ones will fail before your existing batteries.

Saving you from Battery MathWe have developed a MS EXCEL spreadsheet to assist our NORTH AMERICAN clients withthese calculations. Contact us by emailand we'll help you with your calculations.

http://www.enviroharvest.ca/batteries1.htm#Adding%20Batterieshttp://www.enviroharvest.ca/batteries1.htm#Adding%20Batteriesmailto:info@enviroharvest.ca?subject=Off%20grid%20Power%20calculations-%20Battery%20mathmailto:info@enviroharvest.ca?subject=Off%20grid%20Power%20calculations-%20Battery%20mathmailto:info@enviroharvest.ca?subject=Off%20grid%20Power%20calculations-%20Battery%20mathhttp://www.enviroharvest.ca/batteries1.htm#Adding%20Batteries