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  • Sizing Math Questions

    Hi Everyone :

    First time here for me and new to PV technology. After going through various tutorials/forum posts, some things are not readily apparent to me. Thought I should post some of the issues confounding me here - maybe, I can pick up nuggets of knowledge here and there!

    Assuming I have a system like this in mind:
    • total energy demand for one day = 21,177 wh/day
    • nominal system voltage = 48v
    • days of autonomy = 5 days
    • average operating time per day = 4.1 hrs.
    • Depth of battery discharge = 80%
    • insolation for critical design month = 4.5 hrs/day
    • max rated module current = 5.76
    • max rated module voltage = 54.7
    • max module power = 315


    Questions I can't figure out ( cross eyed starring at this spreadsheet for awhile now):
    1. I came up with a required battery capacity of 3,064 ah. How long will the array take to charge this from the 20% level to 100% ?
    2. Does the array sizing take into account the need to charge the batteries whilst meeting load requirements? This is a system in a country where the grid supply is erratic during the day so the panels might be pulling double duty charging batteries used the previous night and also driving critical loads during the day. Looking at the calculation for array sizing, I only see an adjustment for battery charging efficiency. but not anything that accounts for meeting load requirements and charging batteries? Or maybe I am looking at this all wrong?
    3. Is it absolutely important to keep the number of batteries in parallel less than or equal to 3? For PV systems designed for relatively large load requirements - like 21,177 wh/day, I can't get this down to 3 without some ridiculous battery capacity selected.
    4. Using the figures above, i came up with a nominal array output of 8,190 w. What does this number mean? How does it jive with the daily energy demand of 21,177 wh/day and the battery capacity of 3,064 ah ? I guess I am looking to validate if this is enough? Do you guys have a way of checking to ensure the battery and array sizes are optimal and not over or under sized?


    That's it! Many thanks!!

  • #2
    Hi & Welcome.

    comments:
    * days of autonomy = 5 days

    5 days is for a cell tower site, not a house.

    Try with 3 days, and plan to use a generator to fill in the gaps. If you bleed your batteries down for 4 days and get a sunny afternoon on the 5th, your harvest won't do much to the huge battery that is way low.

    Off grid systems need to have a generator (or 2) designed into the system. This allows you to size an array for the next to worse month, budget for 15 gallons of fuel, and save a bunch of money. You don't need a huge generator, something in the 2 - 5 KW class is generally enough.

    *total energy demand for one day = 21,177 wh/day
    This is HUGE and you need to figure how to reduce it, or install a huge 10KW PV array to support your loads.
    Powerfab top of pole PV mount (2) | Listeroid 6/1 w/st5 gen head | XW6048 inverter/chgr | Iota 48V/15A charger | Morningstar 60A MPPT | 48V, 800A NiFe Battery (in series)| 15, Evergreen 205w "12V" PV array on pole | Midnight ePanel | Grundfos 10 SO5-9 with 3 wire Franklin Electric motor (1/2hp 240V 1ph ) on a timer for 3 hr noontime run - Runs off PV ||
    || Midnight Classic 200 | 10, Evergreen 200w in a 160VOC array ||
    || VEC1093 12V Charger | Maha C401 aa/aaa Charger | SureSine | Sunsaver MPPT 15A

    solar: http://tinyurl.com/LMR-Solar
    gen: http://tinyurl.com/LMR-Lister

    Comment


    • #3
      Originally posted by Mike90250 View Post
      Hi & Welcome.

      Off grid systems need to have a generator (or 2) designed into the system. This allows you to size an array for the next to worse month, budget for 15 gallons of fuel, and save a bunch of money. You don't need a huge generator, something in the 2 - 5 KW class is generally enough.

      I can drop the days of autonomy to even lower than 3 if required. However, this is in a country where people are looking for alternatives to using a generator. The price of gas and maintenance is a factor too. So proposing a PV system which still uses an existing genset it is supposed to replace is a bit of a tough sell. But I get the argument. The best bet then is to explore how to reduce the daily energy demand to a point where an offgrid system without a gen backup makes sense - even with erratic utility supplies.


      Originally posted by Mike90250 View Post
      *total energy demand for one day = 21,177 wh/day
      This is HUGE and you need to figure how to reduce it, or install a huge 10KW PV array to support your loads.
      As a newbie to PV tech, I am wondering what the average load requirements for a full size offgrid house is? My daily requirement is compounded by the fact that the PV system needs to support loads even in daytime hours, when the grid is on the fritz. I sized this based on the number of load drawing appliances , lights etc . The biggest culprits of course are AC units ( wall mount types, not central ) , a refrigerator, freezer and the usual stuff - lights around the house, PCs, household appliances etc. So I am thinking of a system that can run the whole house with this new PV system. Seems this will be an expensive proposition. We will have to decide what is critical and what is not.

      Comment


      • #4
        Originally posted by juju View Post
        Questions I can't figure out ( cross eyed starring at this spreadsheet for awhile now):

        1. I came up with a required battery capacity of 3,064 ah. How long will the array take to charge this from the 20% level to 100% ?
        2. Does the array sizing take into account the need to charge the batteries whilst meeting load requirements? This is a system in a country where the grid supply is erratic during the day so the panels might be pulling double duty charging batteries used the previous night and also driving critical loads during the day. Looking at the calculation for array sizing, I only see an adjustment for battery charging efficiency. but not anything that accounts for meeting load requirements and charging batteries? Or maybe I am looking at this all wrong?
        3. Is it absolutely important to keep the number of batteries in parallel less than or equal to 3? For PV systems designed for relatively large load requirements - like 21,177 wh/day, I can't get this down to 3 without some ridiculous battery capacity selected.
        4. Using the figures above, i came up with a nominal array output of 8,190 w. What does this number mean? How does it jive with the daily energy demand of 21,177 wh/day and the battery capacity of 3,064 ah ? I guess I am looking to validate if this is enough? Do you guys have a way of checking to ensure the battery and array sizes are optimal and not over or under sized?
        A1. Last thing you want to do is take your battery down to 20% SOC. On a properly sized system it would take 4 or more days to recharge. Discharge 20 to 30% a day and you get 5 years out of a battery. Discharge 80% and you get a year.

        A2. You are looking at it wrong. The size of the PV array is designed to generate your daily 24 hour usage. You only get a few hours of sun and in that time muct generate enough power for 24 hours and then some.

        A3. No its important to keep them to a single string. You simple use 24-2 volt batteries of 3000 AH capacity. Keep in mind once you have over 500 pounds of toxic acid is going to require an EPA permit, tracking them from the factory to grave, yearly inspections, spill containment, and you will be held liable for any spills.

        A4. Simple 5th grade math. You came up with 21,000 watt hours per day or 21 Kwh.

        For battery you size it to supply you 5 days reserve capacity which actually only give you 3 days of reserve to CYA for cloudy days and maximizing battery life. 5 days x 21 Kwh = 105,000 watt hours or 105 Kwh. To find the battery capacity you choose a voltage. You chose to use 48 volts. AH = Watt Hours / Battery Voltage. So 105,000 wh / 48 volts = 2,187 AH so you got that part wrong. Lets just call it 2200 Amp Hours @ 48 volts. Now here is the really fun part of the math a 3rd grader can figure out. How much does it cost and weigh? Well a good 5 year battery cost $225 per Kwh x 105 Kwh = $23,625 every 5 years. It weighs 65 pounds per Kwh x 105 = 6825 pounds. Here is your battery, you need 24 of them.

        For panel wattage you take your daily watt hours usage x 1.5 correction factor to account for all the losses system. So with 21,000 wh x 1.5 = 31,500 way hours is what the panels must generate to replace 21,000 watt hours. Now all we have to do is simple 5th grade math and factor out the time element hours so we are left with watts. Watts = Watt Hours / Hours. Now you said 4.1 Sun Hours average but for battery systems you do not use yearly average. You have to use worse case month which is usually December/January. If you 4.1 like you did every month under 4.1 Sun Hours means you go dark or run off generator every day to make up for the shortage. Let's pretend in December you have 3.15 Sun Hours. Do the math. 31,500 watt hours / 3.15 hours = 10,000 watts.

        At 10,000 watts of panels operating into a 48 volt battery the controller size is Panel Wattage / Battery Voltage = Amps. So 10,000 watts / 48 volts = 208 amps. That will be two or 3 charge controllers meaning you will have 2 or 3 solar panel systems. Each with its own charge controller charging a common battery.

        Pretty simple stuff.
        MSEE, PE

        Comment


        • #5
          Originally posted by Sunking View Post
          A1. Last thing you want to do is take your battery down to 20% SOC. On a properly sized system it would take 4 or more days to recharge. Discharge 20 to 30% a day and you get 5 years out of a battery. Discharge 80% and you get a year.
          What about deep cycle batteries?


          Originally posted by Sunking View Post
          A3. No its important to keep them to a single string.
          One string always?

          Originally posted by Sunking View Post
          A4. Simple 5th grade math.

          Pretty simple stuff.
          Ha! Simple for you! Anyway, I am assuming that your correction factor of 1.5 accounts for all possible system losses. What about methodologies that account for specific losses in detail - e.g. losses due to temperature will be different in different climates, say East coast US vs Arizona? Soiling losses in climates with heavy rainfall vs those without e.t.c When looking at all this, how close does your correction factor get to an average? Many thanks for helping out here.

          Comment


          • #6
            Originally posted by juju View Post
            What about deep cycle batteries?
            That is all we talk about here. SLI batteries cannot even be shallow cycled.

            Originally posted by juju View Post
            One string always?
            You will if you want to protect your battery investment of $25,000 and make them last as long as possible.

            Originally posted by juju View Post
            Ha! Simple for you! Anyway, I am assuming that your correction factor of 1.5 accounts for all possible system losses. What about methodologies that account for specific losses in detail - e.g. losses due to temperature will be different in different climates, say East coast US vs Arizona? Soiling losses in climates with heavy rainfall vs those without e.t.c When looking at all this, how close does your correction factor get to an average?
            That is what a professional does and after 35 year doing it professionally comes within a few percentage points.
            MSEE, PE

            Comment


            • #7
              Originally posted by Sunking View Post
              That is all we talk about here. SLI batteries cannot even be shallow cycled.
              Interesting. Some textbooks ( a few of them ) mention that the benefit of deep cycle batteries is, they can go down to 20% without any repercussions. I guess there is a gap between academic theories and reality! Having 3 or less series connections for batteries is another one.

              Another question for you - why is it unusual to have something close to 21K wh/day? After playing with various load sizing sheets and taking into account what types of loads I will be running, I can't get it any lower than this - sure, I can reduce it by using energy efficient loads but my question is, what is the typical energy demand for a whole house that is completely off the grid, using all the usual loads they would have been using if the grid were available?

              It goes to the question if solar should be purely regarded as a backup system of sorts, only able to drive a few critical loads or has the technology and economics evolved to a point where it can completely power a whole house without paying through the nose for it? For instance, what will a 5kW system support ? Seems its a reasonably large system for a house. I'd be happy to post a typical load sizing sheet I am looking at here so you can poke holes at it. Thanks

              ps my project is in an area where this PV system is potentially going to serve as the main source of power due to erratic power supplies from the grid - hence my questions. it is almost synonymous with a totally offgrid house but not using solar as a backup but sized to be the main source.

              Comment


              • #8
                Originally posted by juju View Post
                Another question for you - why is it unusual to have something close to 21K wh/day? After playing with various load sizing sheets and taking into account what types of loads I will be running, I can't get it any lower than this - sure, I can reduce it by using energy efficient loads but my question is, what is the typical energy demand for a whole house that is completely off the grid, using all the usual loads they would have been using if the grid were available?
                Almost unheard of with respect to Off-Grid. Very rarely do you here of real off grid folks using more than 8 to 10 Kwh per day. Living off-grid is a minimalist life style of hermits, hippies, recluse and fringe lunatics like Preppers and Survivalist.

                Due to equipment limitations the largest Off-Grid system is 5000 watts on a 48 volt @ 800 AH battery. Such a system wil provide roughly 10 Kwh of usable energy per day, but also requires a generator to maintain batteries and provide power during cloudy days.
                MSEE, PE

                Comment


                • #9
                  I am still on the grid, but I built my system for off grid with grid and generator backup. I also use 20 to 22kwh daily, I don't have AC, That is no no for off grid, It draw too much power. I do have water pumps, refrigerator and freezer, also the regular appliance like microwave oven, toaster and blender etc. I change all my lights to LED and use most of my heavy load during the sun hours.

                  I live in Jamaica, one sunny island in the Caribbean. But I live in Mandeville town where clouds always passing especially during the 4 most critical sun hours that is 11am to 2pm. I have 6920watts name plate PV panels, but most of the time I only get 4000 to 5000 watts during the sun hours to the charge controller, I don't know how much more lost when it reach to the battery bank.

                  I have 1 refrigerator use around 250 to 300 watts when it is running, I use a timer switch turn the refrigerator on every 8am in the morning and of 8 pm in the night and give 2 more hours during the night from 11pm to 12am and 3am to 4am in the early morning. I also have a freezer that store the meat. I turn it on 8:30am to 4pm in the afternoon. and one hour during the night from 9pm to 10 pm.

                  I make sure all the wash machine and cloths iron is use during the sun hours.

                  I have 2 strings of Rolls 6 volts at 48 volt bank. total 750 amps hours, I don't have any reserve capacity. The off sun hours consumption is around 10 to 11kwh. Any day I have rain or overcast I have to turn on the grid or generator to charge the battery banks.

                  Comment


                  • #10
                    Originally posted by Sunking View Post
                    Living off-grid is a minimalist life style of hermits, hippies, recluse and fringe lunatics like Preppers and Survivalist.
                    .
                    You brought a smile to my face! I'd fit in to this crowd perfectly. But not sure i want to be minimalist. I just want to size the system to be my main feed.

                    Comment


                    • #11
                      Originally posted by paulcheung View Post
                      I am still on the grid, but I built my system for off grid with grid and generator backup. I also use 20 to 22kwh daily, I don't have AC, That is no no for off grid, It draw too much power. I do have water pumps, refrigerator and freezer, also the regular appliance like microwave oven, toaster and blender etc. I change all my lights to LED and use most of my heavy load during the sun hours.

                      I live in Jamaica, one sunny island in the Caribbean. But I live in Mandeville town where clouds always passing especially during the 4 most critical sun hours that is 11am to 2pm. I have 6920watts name plate PV panels, but most of the time I only get 4000 to 5000 watts during the sun hours to the charge controller, I don't know how much more lost when it reach to the battery bank.

                      I have 1 refrigerator use around 250 to 300 watts when it is running, I use a timer switch turn the refrigerator on every 8am in the morning and of 8 pm in the night and give 2 more hours during the night from 11pm to 12am and 3am to 4am in the early morning. I also have a freezer that store the meat. I turn it on 8:30am to 4pm in the afternoon. and one hour during the night from 9pm to 10 pm.

                      I make sure all the wash machine and cloths iron is use during the sun hours.

                      I have 2 strings of Rolls 6 volts at 48 volt bank. total 750 amps hours, I don't have any reserve capacity. The off sun hours consumption is around 10 to 11kwh. Any day I have rain or overcast I have to turn on the grid or generator to charge the battery banks.
                      This is almost exactly how my system might look and work. I am also sizing this system for a home in Africa. The 21 - 22 kwh reflects my expectation of daily consumption. So perhaps, i should get a bit more detail about your system. I am particularly interested in how you are managing the daily use ( if its automated in a way ) e.t.c, reliability of the equipment you have, long term cost e.t.c That Rolls battery seems to be a favorite of most people here?

                      Comment


                      • #12
                        In the scale like 20KWH, the daily use is about the same every day, from 18 KWH to 22KWH. Sometime it do go over that when I use the grid to full charge the battery bank after a day or two of bad weather. But the consumption on the grid is not calculated in the solar consumption, it is in a different circuit. I use a KWH meter to monitor the solar usage.

                        My system has no reserve capacity as I mention before, I have 750 amp hour at 48 volt, that give me about 36KWH power, I calculate use about 30% DOD, that is about 12KWH, come right back to my daily off sun hour usage 10 to 12KWH. So any day I have bad weather I have to use the grid or the generator to fill the gap.

                        I have 2 bank of Rolls 4000 series batteries. I will be more to get a new bank of Trojan battery for replacement when the time comes for the reason of Smart Carbon Technology. For the PSOC. unless Rolls introduce the same technology.

                        For the single string compare to 2 or 3 strings in a battery bank, it is the best just to use a single string, unless you don't have any choice at all. I sorry that I have two strings as it start to give me problems right now. may be it is because the two strings are different capacity even though they are close, 350 amp hour and 400 amp hour. The 350 AH has less resistance compare to the 400AH bank, when it come to absorb charging, the 400AH going to less amperes before the 350AH, at 62 volt the 400AH take only 13 amps charge current after 2 hours absorb but the 350 AH still taking 29 amps charging current. so the 350AH run very hot like 115 degree F. so it is best to use only ONE string.

                        Comment


                        • #13
                          To get your daily use down to what solar is manageable, you have to look back at living 100 years ago, and see what you can do without. Fridge, air conditioning, motors, pumps, spa heaters, septic grinders, laptop computer or desktop, ceiling fans. All the loads add up, and what changes you can do to the house (insulate, shade awnings......) will be a great help elsewhere.
                          Powerfab top of pole PV mount (2) | Listeroid 6/1 w/st5 gen head | XW6048 inverter/chgr | Iota 48V/15A charger | Morningstar 60A MPPT | 48V, 800A NiFe Battery (in series)| 15, Evergreen 205w "12V" PV array on pole | Midnight ePanel | Grundfos 10 SO5-9 with 3 wire Franklin Electric motor (1/2hp 240V 1ph ) on a timer for 3 hr noontime run - Runs off PV ||
                          || Midnight Classic 200 | 10, Evergreen 200w in a 160VOC array ||
                          || VEC1093 12V Charger | Maha C401 aa/aaa Charger | SureSine | Sunsaver MPPT 15A

                          solar: http://tinyurl.com/LMR-Solar
                          gen: http://tinyurl.com/LMR-Lister

                          Comment


                          • #14
                            System details

                            Originally posted by paulcheung View Post
                            In the scale like 20KWH, the daily use is about the same every day, from 18 KWH to 22KWH. Sometime it do go over that when I use the grid to full charge the battery bank after a day or two of bad weather. But the consumption on the grid is not calculated in the solar consumption, it is in a different circuit. I use a KWH meter to monitor the solar usage.

                            My system has no reserve capacity as I mention before, I have 750 amp hour at 48 volt, that give me about 36KWH power, I calculate use about 30% DOD, that is about 12KWH, come right back to my daily off sun hour usage 10 to 12KWH. So any day I have bad weather I have to use the grid or the generator to fill the gap.

                            I have 2 bank of Rolls 4000 series batteries. I will be more to get a new bank of Trojan battery for replacement when the time comes for the reason of Smart Carbon Technology. For the PSOC. unless Rolls introduce the same technology.

                            For the single string compare to 2 or 3 strings in a battery bank, it is the best just to use a single string, unless you don't have any choice at all. I sorry that I have two strings as it start to give me problems right now. may be it is because the two strings are different capacity even though they are close, 350 amp hour and 400 amp hour. The 350 AH has less resistance compare to the 400AH bank, when it come to absorb charging, the 400AH going to less amperes before the 350AH, at 62 volt the 400AH take only 13 amps charge current after 2 hours absorb but the 350 AH still taking 29 amps charging current. so the 350AH run very hot like 115 degree F. so it is best to use only ONE string.
                            Thanks for sharing your experience. I am trying to size a similar system as well. Would you specify the equipment you have currently?

                            Comment

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