I am no math expert, this is a blog for the average person who is curious about what goes into designing a solar energy system. I welcome all comments and discussion about the calculations here. The basic formulas are:
Volts = I (current)R(resistance) = I = V/R or R = V/I
Power (watts) = VI = V2/R = I2R
Energy = VIH
Next entry we will also have to calculate the voltage drop in a line, which we will use:
Designing a PV power generation system is not as hard as installing one, or so my experience so far leads me to believe. Days 27 and 28 will be devoted to the action project for the solar energy week; designing and instaling a real-world system for one of the structures on the farm. Chef Keith will be introduced in more detail next week, slow foods module, but he gets to play a role in this weeks project by being the lucky recipient of lights and a stereo system in his yurt.
The YurtKeith's yurt is standing on a platform made of "lumber" from recycled plastic. It was all built many years ago during the early construction phase of the farm. Even Ben Jones, the founder of the farm, lived in the yurt for three years. It has running water and has been a useful structure for many inhabitants, but other than some old extension cords run from who knows where, it's dark.
Here are the steps we went through for determining our solar array for the yurt. The array consists of: panels, charge controller, battery bank, and inverter (to run AC appliances as well as DC).
Step 1: Determing the Power Consumption
This is a tricky step. None of the calculations are "easy" but this one requires some soul searching. How much power do you use? When? How much power do you need? What does your curling iron take up, 1500W? Can you get a DC fridge?
Consider your AC and DC power requirements separately. We made a simple chart so that we could organize our data and reference back when we needed to adjust.
Appliance, Watts, Quantity, Hours run per day. Total that up the daily needs and then multiply by the number of days per week that you will use that particular appliance to get your watt hours per week. Total up the number or watt hours for all DC appliances then multiply by 1.2 (to compensate for system losses). Then do the same for AC appliances.
Add up the AC WH/Week and DC WH/Week. To determing the number of Amp-hours of energy required for week, divide this number by the voltage of battery you are using (usually 12 or 24V). Then divide that number by 7 to determine the average requirement per day. Here is what our totals were if Keith is running a DC Fan, two types of DC lights (efficient), charging a laptop, running a laptop off the wall power, charging a cellphone, and running an iHome stereo (very efficient):
DC WH/Week: 1831
+ AC WH/WK: 1370
= 3201 WH/WK
x 12V (we are using a 12V battery bank)
= 267 AH/WK
So the average amp-hour requirement per day = 38.1 AH.
Step 2: Size the Battery Bank
When determining how much energy we need to store, the first big question is how long does he need to be able to last without any sunshine. If a hurricane were to come through he could expect to be without direct sun for a few days. We decided that three days of using everything full blast would be enough, assuming that if he really needed to run his stereo or charge his cell phone he could do so at the community center. Also, you need to determine how much charge you want to remain in the batteries at all times. We chose 20% capacity as a reasonable amount of depletion that would not damage the batteries for long-time use.
AH requirement for day: 38
x Days of autonomy: 3
= amp hours needed to store: 114
+ 20% to remain in the batteries
= 136AH is needed to be stored at 12V in the Battery Bank.
It's not a cold-weather climate so we don't have to worry about the ambient temperature multiplier, but we do need to look at what batteries we already have.
Because we already had four 6V batteries with 220AH it made most sense for us to use those. However, because of their age they are about 50% depleated of their total storage capacity. Assuming it's exactly 50% depleated we should calculate that each of the 6V batteries actually holds 110 AH. We need 136 AH at 12V.
2 6V batteries run in series adds the AH over the series making the total 6V and 220 AH. We need at least 136AH, so if we run those two strings in parallel, then we add the voltages toether to make 12V and the AH stay constant, bringing us to 220AH at 12V, enough to give us some room to breathe.
Step 3: Determine the hours of sun available per day and size the array
Now, how many panels do you need? First, available on-farm we have 4 180W/24V panels that we can't use (12V system), 4 100W/12V panels, and 4 75W/12V or 24V panels.
Determine the Power requirement per day
Daily AH requirement: 38.1
= 457.2 WH/day
OK, we need 457.2WH, how many WH does each panel give off? Multiply the wattage by the number of hours of sun per day. In St. Croix the average is about six.
1 75W panel x 6 hours of sun = 450WH/day (not enough)
1 100W panel x 6 hours of sun = 600 WH/day
= perfect. We need one 100W panel at 12V to fill our power needs and contraints.
The other items in the array? The charge controller, the inverter, the wires, and the fun of installing it in the rain.
Tomorrow I'll complete the package..