The Formula
Yes Martha there is a formula for designing solar power systems.
There has been a lot of controversy in these groups about this formula
for system sizing so let’s take a close look at the formula.
Step 1) Is the system volts. Usually 12, 24, 48 volts. See note (A) below.
Step 2) Is the battery volts. Now to be perfectly clear you may be using
a battery (several cells in one container) or a series of individual
cells to make a battery. See note (A) below.
Step 3) Is your daily load for the AC side of your system. This is in
Watt hours. See note (B) below.
Step 4) Is the inverters efficiency. This is needed because the
inverter, as well as providing AC for your use also consumes DC energy.
This is expressed as 0.9 for 90% - 0.85 for 85% etc.. See note (C) below
Step 5) Is where you account for the inverters inefficiency. The
calculation is (step 3 / step 4)
Step 6) Is the daily load for the DC side of your use if any.
Step 7) Is the total Ah demand for the day. The calculation is (step 5
+ step 4 / step 1) What we have done here is to add the AC Watt hours
(adjusted for the inverters inefficiency) to the DC watt hours (if
any)divided by the system voltage to produce the Amp hours these loads
will consume from our batteries.
Step 8) Is where we enter the number of days of autonomy required from
our system. This is the numbers of days the system must run without
input. Five days is common. See note (D) below.
9) Is the maximum depth of discharge for our battery. This is
expressed as 0.7 for 70% - 0.8 for 80% etc.. See note (E) below.
Step 10) Is where the basic battery capacity is calculated. The formula
is (step 7 x step 8 / step 9). What we have done here is to multiply the
total Amp hour demand per day by the days of autonomy and dividing the
result by the maximum allowable depth of discharge. See note (C) below.
Step 11) Is the lowest 24 hour average temperature in degrees Celsius.
Step 12) Is the correction factor. See note (F) below.
Step 13) Is where we adjust the battery capacity for the lowest 24 hour
average temperature. The formula is (step 10 / step 12).
Step 14) Is the Amp hour capacity of the battery chosen. See note (G) below.
Step 15) Is the number of batteries in parallel. The formula is (step 13
/ step 14) This is rounded up or down to a whole number. See note (A) below
Step 16) Is the number of batteries in series. This is rounded up or
down to a whole number. The formula is (step 1 / step 2)
Step 17) Is our daily Depth of Discharge. The formula is (100 x {step 7
/ step 14}) This is expressed as a percentage. The daily DoD should not
be confused with the Maximum DOD used at step 9.
Step 18) Battery effciency. A battery in good condition will be close to
90% so we will use 0.9 here. If you know that your battery is more or
less efficient than 90%, adjust this number accordingly.
Step 19) Is where we work out the array output required to for the
system to operate correctly. The formula is (step 7 /step 18)
Step 20) Is the Peak Sun Hours for the tilt of your panels for the month
that corresponds to mid winter where you are. This is the worst case.
Step 21) Is where we select a PV module. We look at the spec sheet and
find the module's Amps at 14V NOCT (Normal Operating Cell Temperature)
See note (H) below.
Step 22) Is the selected module's nominal voltage. Usually 12 or 24 Volts.
Step 23) Is the guaranteed current. The formula for this is (step 22 x 0.9)
Step 24) Is the number of panels in series. The formula is (step 1 /
step 20)
Step 25) Is the output per module. The formula for this is (step 23 x
step 20)
Step 26) Is the number of panels in parallel. The formula for this is
(step 19 / step 25)
NOTES:
A. Given that you should avoid the use of parallel strings of batteries
if possible you might find it advisable to go to a higher battery
voltage. Example; if If you size your system at 12V and find that the
only way to achieve the required Amp hour capacity is to use parallel
strings of batteries you may find that opting for a 24V system will
allow you to use a single string of batteries in series. This would be
the better option.
B. Why not use an average of week/month/year? Because an average is
lower than what you could/might use in a day. Average numbers = average
systems and average performance. The formula was written for daily load.
You can average separate loads. i.e. Dishwasher used every second day,
this load could be divided by 2 for daily load.
C. Not all inverters are 90% efficient. Many of the cheaper brands can
be as low as 60% efficient. A lot of inverters may only be 90% efficient
for a narrow part of their output. Get the full specs when ever
possible. Query the manufacturer for the efficiency curve. Beware the
words, "This twenty-nine dollar inverter is just as good as the one
costing three times more". Do your homework.
D. If you want to use 50% of your batteries capacity in a single day, as
has been suggested by some in these groups, then you will need to put
"1" as your days of autonomy. You will also need to replace 50% of your
batteries capacity + at least 10% every day. This means lots of panels
or a generator. There are people here who have convinced themselves that
they have a generator as a back up for charging. What they really have
is a generator system with solar boost.
This is a good point to talk about reality.
People have the amazing ability to lie to themselves. They do this as an
ego boosting exercise. Take the person who wants what their neighbour
has, but is too much of a cheap ass to buy it. He goes to Wall Mart and
pays a tenth of the price for a copy made in China.
The product has a tenth of the quality of the product the neighbour
has but our wanker can only see that his sad copy is better than the
real item his neighbour owns. Beware of falling into this trap. If you
can't afford to buy the best quality, accept the fact. Buy the best you
can. But you have lost the plot when you build a system that is based on
a generator with solar backup and start telling people that you live on
solar energy.
E. Many people get confused about "Maximum Depth Of Discharge" and daily
"Depth of Discharge". These are not the same thing. The Maximum Depth Of
Discharge is the absolute minimum state of charge you will allow your
batteries to reach. Some here will tell you that 50% is the limit, they
claim that discharging below this point will shorten the life of your
batteries.
These people fail to take into account that even if you set the limit at
80% a properly designed system will only reach this point a couple of
times a year.
They will also have you believe that discharging your batteries 50%
daily will give a longer battery life or more energy storage or some
other miraculous benefit.
The thing is though, is that you are designing a system to provide a
daily load with a certain number of Days of Autonomy from batteries of a
defined capacity.
If you set the Max DOD to a limit of 50% then you will be drawing your
Days of Autonomy from only 50% of your batteries capacity.
What difference does that make?
Well if we start with 12V system and a 2 kWh daily load and use 70% as
the max DOD with 5 days autonomy you will need a battery bank with a
capacity of 1377 Amp hours.
The same system with a maximum DOD of 50% would require a battery bank
with a capacity of 1929 Amp hours. And if we take it to the extreme, as
one person has suggested, of 20% DOD the battery capacity jumps to 4822
Amp hours.
So what these people will say.
I say cash, your cash to be more precise. 1377 Amp hours in L16 Trojans
would cost $3300 here in OZ.
1929 Ah in L16 Trojans adds another $1000 to the cost,
4822 Ah in L16 Trojans would cost $12100.
The life time difference between a Maximum Depth Of Discharge of 70% and
a Maximum Depth Of Discharge of 50%, given that this level of discharge
will only happen a couple of times a year in a properly designed system,
just might be measured in a days if not in hours.
The question is "Is an extra couple days of battery life worth an extra
$1000 for batteries?"
F. TEMP. Conversion factors
-10 .85criteria
-5 .88
0 .91
5 .94
10 .96
15 .97
20 .99
25 1.00
G. Yes, you have to choose a battery at this point. This means doing
your home work. Battery specs vary a lot between manufacturers. The
advertising is not the same as a spec sheet. Collect as many spec sheets
as you can. Try all your batteries in the formula. Keep copies of all
your trial calculations for comparison. Cost all your copies.
H. Yes, you have to choose a solar panel at this point. This means doing
your home work. Panel specs vary a lot between manufacturers. The
advertising is not the same as a spec sheet. Collect as many spec sheets
as you can. Try all your panels in the formula. Keep copies of all
your trial calculations for comparison. Cost all your copies.
This formula has been around for at least 25 years and has been used to
design working, balanced solar power systems for all this time.
There are any number of people in these NGs that think that because they
have managed to get batteries to charge from a solar panel that they
have designed a system.
The truth is that it is almost impossible to fail. But true design means
that the system will fulfill a set of criteria. Anything else is just
playing with solar.
Some just resort to copying a system. Then brag about their "Design".
Some just guess. Then brag about their "Design".
Some will buy some batteries and panels, but don't believe solar works
so they rely on a generator to make it work. Then brag about their
"Design".
The one thing they all have in common is a complete lack of
understanding of what they are doing.
They all say that this formula is only good for playing "what if" with
the numbers. It is true that you can play what if with this formula. But
it is also true that this formula will correctly size a solar power
system to meet your needs. There is no magic, no black art, just the
information you put into the blanks. It is entirely in your hands. You
can "Play" with solar or you can get serious about it.
If you are serious about it, if you want a system that will provide
your energy needs for many years, you need correct information for the
formula. It has to be the correct information.
Not correct because you want it to be correct. Not correct because it's
cheaper. Not correct because it makes you feel good. Not correct because
anything else will show the world that you are a complete git.
It has to be correct because it's true.
Now the usual suspects will flood you with reasons why this formula will
not work, or tell you that their system is so revolutionary that it is
beyond this formula and your comprehension.
They are wrong.
You can prove it yourself.
Want a nice clean spreadsheet of this formula?
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