Not sure about (*)

simagic
simagic Solar Expert Posts: 100 ✭✭✭✭
in Solar Beginners Corner #1
So I've been reading, reading and reading. I've "got it" on some things and didn't get it on others. On thing that I find confusing is the use of this symbol in some of the math calculations (*)........ Does it mean (X) multiplied by........Does it mean (/) divided by......Does it mean (=) equals. . . Does it mean ("so therefore it means").
I've tried using it several ways to figure out some calculations, but it appears that if I use it one way, it doesn't work that way all the time. ( OR ) , that's where I'm just not getting it.

Also, about the "ideal" charge rate of 5-13% of the AH capacity of the battery. Is that based on the "sticker" specs. I have read several places that the sticker specs are not the real life specs. So I have (2) 100w panels running to (2) separate controllers (reason being that when (1) is in the sun, the other is in the shade, and vise versa). The sticker specs are about 5.5amps per panel equaling about 11amps.. I have a 220AH battery (2 6v in series).....So, 5% would be 11amps. this is based on the sticker specs.......Is this OK ??.
I also read "somewhere" that if you have AGM batteries, you could charge with 3% and it would be OK.....Is that right??.........
Thanks
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  • ggunn
    ggunn Solar Expert Posts: 1,973 ✭✭✭
    #2
    Re: Not sure about (*)
    simagic wrote: »
    So I've been reading, reading and reading. I've "got it" on some things and didn't get it on others. On thing that I find confusing is the use of this symbol in some of the math calculations (*)........ Does it mean (X) multiplied by........Does it mean (/) divided by......Does it mean (=) equals. . . Does it mean ("so therefore it means").
    I've tried using it several ways to figure out some calculations, but it appears that if I use it one way, it doesn't work that way all the time. ( OR ) , that's where I'm just not getting it.

    Most of the time, it is a symbol for multiplication (V = I*R), but it may indicate a caveat, as in:

    The voltage from solar modules is virtually constant*


    *except when it is dark.
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  • Cariboocoot
    Cariboocoot Banned Posts: 17,615 ✭✭✭
    #3
    Re: Not sure about (*)

    Welcome to the forum.

    The asterisk (*) is a standard algebraic symbol for multiplication. As in: Watts * hours = Watt hours.

    The 5-13% charge rate is based on the Amp hour capacity of the battery at the "20 hour rate" (some batteries may list capacity a different rates). So a 100 Amp hour battery wants a peak charge current of 5 to 13 Amps. Some (like AGM's) can handle more. What works for a particular system is subject to a lot of variables.

    How you get that charge rate is another story. No, you can't rely on a solar panel's "nameplate" rating. That is derived under "ideal" laboratory conditions that rarely occur in the real world. It is necessary to use a derating factor. Typically we us 77% (multpily the nameplate rating by 0.77) to account for average panel output during hours of "equivalent good sun" plus losses from wiring and charge controller. So a 100 Watt panel will deliver approximately an average 77 Watts at the battery over the course of the expected good sun (which is typically 4 hours).

    These are all just starting points; the sort of performance you might expect on average. When it comes to "dialing in" any particular system you have to take into account the large number of variables that affect power production. This includes ambient temperature, elevation, length of day, length of wire runs, et cetera.

    But you have to start somewhere. The short beginning-to-end formula is: panel nameplate rating * hours of good sun / 2 (the famous "Icarus Formula" :D ). So for every 100 Watts of panel you can expect 200 Watt hours of AC power: 100 * 4 / 2.

    Does that help?
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  • simagic
    simagic Solar Expert Posts: 100 ✭✭✭✭
    #4
    Re: Not sure about (*)

    So as i now understand, these (about) 11 amps (from the 2, 100w panels ) with the .77 factor injected, will now, of course be producing less than (about) 11 amps, therefore if 11amps is 5% of my 220ah battery, then I will not be giving my batteries the needed 5%. Is this correct. And i mentioned that I read somewhere about AGM's only needing 3%...Do you know about that? thanks
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  • Cariboocoot
    Cariboocoot Banned Posts: 17,615 ✭✭✭
    #5
    Re: Not sure about (*)
    simagic wrote: »
    So as i now understand, these (about) 11 amps (from the 2, 100w panels ) with the .77 factor injected, will now, of course be producing less than (about) 11 amps, therefore if 11amps is 5% of my 220ah battery, then I will not be giving my batteries the needed 5%. Is this correct. And i mentioned that I read somewhere about AGM's only needing 3%...Do you know about that? thanks

    Actually the derating factor should be applied to the Watts, not the Amps. The reason being that panels are a current source: they will produce their rated Amps, but the Voltage may not be the Vmp expected. You have to plan on 11 Amps in terms of wiring and fusing. In fact there will be to current ratings: Imp and Isc. The last one is the short circuit current and should be used for planning.

    So 200 Watts * 0.77 = 154 Watts. Divide this by the charging Voltage to get the expected current to the battery. On a 12 Volt system that's usually 14.4, which gives (154/14.4) 10.6 Amps or 4.8% - which is below the 5% minimum by just a bit. (To determine percentage, multiply the charge current by 100 then divide by the Amp hour rating). If your conditions are a bit better than average it might just work. Most likely it won't; better to have more than you need and not use it than have less and dead batteries. I will also mention that we do it this way so that the formula works for both PWM and MPPT charge controllers, as the MPPT type can turn "extra" array Voltage into more charge current.

    AGM's are more efficient than FLA's - and more expensive. They can take more curren, but not more Voltage (FLA's will withstand overcharging better). As for using only 3% charge current on an AGM ... not recommended by me. Others may disagree.

    And always remember that is a target net peak current. Meaning: it won't be maintained through the whole charge cycle and it is the output of the charge controller less the draw of any loads. More or less something to be used for planning, not an absolute. I always recommend "shooting for" 10% to make sure you get at least 5%. Furthermore, you have to examine the Amp hours used and how well the panels will replenish them. With lower depth of discharge this is easy, but if you go for the maximum 50% DOD you may need even more panel than the current calculation would indicate.
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  • BB.
    BB. Super Moderators, Administrators Posts: 33,591 admin
    #6
    Re: Not sure about (*)

    When doing the calculations, there is also a dependency on the order that the calculations are performed.

    I am not a math nut-- but I try to use a lot of fairly simple math to help people size their system. And while I try to be clear, I have fallen into a non-standard short hand. And, depending on the type of calculator you use, you could get different results.

    For example, here are some basic equations. Say you want a small emergency system with two golf car type batteries that are each 6 volts and 225 Amp*Hours (at 20 Hour Rate).

    Note, we choose 20 Hour Rate because that usually maps pretty well to the average off-grid system use of power--I.e., roughly the average cabin load will discharge the batteries in about 20 hours. A 100 Hour Rate would give you a higher capacity (maybe 250 AH), and a 5 Hour Rate would give a smaller AH number (maybe 180 AH).

    Now the example, two 6 volt 225 AH batteries connected in series which gives us a 12 volts (14.5 volt charging) and 225 AH battery bank (connecting batteries in series adds voltage. Connecting batteries in parallel adds AH capacity). How much solar panel will we need. Using the 5% to 13% charge rate and 0.77 panel+charge controller derating gives us:
    • 225 AH * 14.5 volts charging * 1/0.77 derating * 0.05 rate of charge = 212 watts of solar panels minimum
    • 225 AH * 14.5 volts charging * 1/0.77 derating * 0.13 rate of charge = 551 watts of solar panels rough cost effective maximum
    Now, lets look at my equation closely:
    • 225 AH * 14.5 volts charging * 1/0.77 derating * 0.05 rate of charge = 212 watts of solar panels minimum
    I should actually write it as:
    • 225 AH * 14.5 volts charging * (1/0.77 derating) * 0.05 rate of charge = 212 watts of solar panels minimum
    The 1/0.77 is actually 1.2987, so one way to write the equation as all multiplications is:
    • 225 AH * 14.5 volts charging * 1.2987 derating * 0.05 rate of charge = 212 watts of solar panels minimum
    Another way to write the equation is:
    • (225 AH * 14.5 volts charging * 0.05 rate of charge) / (0.77 derating) = 212 watts of solar panels minimum
    The wrong way to write/process the equation would be:
    • (225 AH * 14.5 volts charging) / (0.77 derating * 0.05 rate of charge) = wrong answer
    My short hand has been:
    • 225 AH * 14.5 volts charging * 1/0.77 derating * 0.05 rate of charge = 212 watts of solar panels minimum
    Note that write "225 AH * 14.5 volts charging" and I have spaces before and after the "*" (multiplication sign). But I wrote "1/0.77 derating" without spaces... I have been doing that (no spaces) as a short hand for "(1/0.77)"--I.e., do the division "first", then do the rest of the numbers.

    For most calculators, if you perform the equation from right to left it will evaluate the equation correctly.

    Regarding symbols:
    • * is multiply
    • x is multiply
    • / is divide (or fraction)
    • Amp*Hours is Amps times Hours
    • AmpHours = AH = Amps * Hours (two variables next to each other is multiply)
    • ^ is raise to the power (2^3 = 2*2*@ = 8)
    • ** is sometimes used as ^ (2**3 = 2^3 = 8)
    • spaces are used like parens: Power = I^2 R = (I^2)*R = (I^2)R
    • If it gets more complex, then should write I^(2i) or I raised to power of (2i)
    • 2 * 1/0.77 * 0.05 is not equal to (2*1)/(0.77*0.05)
    • 2 * 1/0.77 * 0.05 is equal to (2*(1/0.77))*0.05
    -Bill
    Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
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  • Cariboocoot
    Cariboocoot Banned Posts: 17,615 ✭✭✭
    #7
    Re: Not sure about (*)

    Footnote to Bill's post:

    There is a standard procedure in mathematics called "order of operations" which fixes which function should be applied first in complex formulas. It is known as "PEMDAS" for : Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. Unfortunately not all calculators use it. Especially not the human ones. We tend to write our intended order as we go along. :blush:

    Okay, school's out! :D
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