**Solar
Calculations Math Tutorial **
for Solar Energy Power Systems
Electricity can be a mystery to folks
who have never had any experience working with it, or for
folks who took physics in high school (that's me) and can't
remember much of anything other than that the battery made
the light bulb glow.
Basic electric calculations for off
grid solar applications are not that hard, but you have to
know the terminology. Here it is. Don't quit
now, it's really pretty easy, but you have to learn the
vocabulary for it to make sense.
Amps
Amps is a measure of energy flow,
measured in electrons moving per second. The
amount of Amps represents the amount of charge flowing past
a point in a particular time period.
Volts
Volts is a measure of the force of
the moving electrons. It's the pressure which
causes electrical current to flow.
It is also used to describe the
amount of energy stored, like a 12 volt
battery.
Watts
Watts is a measure
of power. It describes the amount of energy
converted by an electrical circuit.
Ohms
Ohms is a measure of electrical
resistance. It you have a wire with
two conductors, like a lamp cord, and connect one conductor
to the positive and the other to the negative pole of a 12
volt battery (like jump starting a car), the smaller the
wire diameter and the longer length of the wire the greater
the Ohms, which causes the Volts delivered to decrease.
An increased resistance measured in Ohms causes
a reduction in current aka Volts.
The Good Old Garden
Hose Example
Get your garden hose and turn on the
water so that it is flowing at the rate of a couple of
gallons a minute, so that you could fill up a 5 gallon
bucket in 2-3 minutes.
The rate of flow of the water, which
is pretty slow, is equivalent to
**Amps**. The lower the flow the lower the amps.
The force of the water coming out of
the hose is the **Volts**. The lower the force, the
lower the volts.
The power (energy) of the water coming out of
the hose is **Watts**. Put your thumb over the end
of the hose and see how far you can squirt. The harder
you squeeze the farther you can squirt? The water flow
is still a couple of gallons per minute. In the same
way, if you increase the Volts, a small amount of Amps can
turn into a lot of Watts.
If you link together 2 or 3 or 4
garden hoses without changing the setting on the faucet,
what you will see is that the rate of flow goes down because
the resistance of the water passing though the hose reduces
the flow. This same effect is measured in **Ohms**
in electrical circuits.
Solar Calculations Math
All of these electrical units of
measure are used together to determine the Volts, Amps and
Watts for any particular solar electric application. I
am not going to talk about Ohms or Ohms Law. Ohms is
not important for calculating solar component sizing.
Ohms IS important when you start looking at the available
Volts and wire sizes and
the distances between components like batteries, solar
panels, charge controllers and inverters. The lower
the Volts and the greater the distance traveled, the bigger
the wire that is needed.
Volts x
Amps = Watts
This is the starting
point for doing the math.
**Convert Watts
to Amps**: Amps = Watts / Volts (slash =
divide)
12 Watts / 12
Volts = 1 Amp
**Convert Amps
to Watts**: Watts = Amps x Volts
1 Amp x 12
Volts = 12 Watts
**Convert Watts
to Volts**: Volts = Watts
/ Amps
120
Watts /
10 Amps = 12
Volts
**Convert Volts
to Watts**: Watts = Amps x Volts
12
Amps x 12
Volts = 144
Watts
Energy
Measurements Over Time
When you are trying to
figure out what size solar panels you need, and how much
battery storage, and what size charge controller or inverter
you need for any particular solar energy application, the
time that the sun shines on your panels, the time between
sunny days (cloudy weather), the time that you what to be
able to operate whatever you are going to power with your
solar energy - everything is about time.
So, watts and amps are
measured by time for any given voltage. The voltage of
your off grid system is a given based on what you decide - you are going to have a 12
volt system, or a 24 volt system, or a 48 volt system based
on the batteries you decide to use.
Watt-Hours
Used to measure energy inflow from
your solar panel
and outflow from the devices you are powering
Watt-Hours per day or other time period
Amp-Hours
Used to measure energy storage and
outflow in batteries
and energy inflow from your solar panel.
A Simple
Load Analysis
I have two
10 watt 12 volt LED
lights I want to operate for 4 hours per night. 10
watts x 2 x 4 hours = 80 watt-hours.
80 watt-hours divided by
12 volts = 6.67 amp hours. Because we can only use
half the energy in a lead acid battery without harming the
battery, the minimum battery size is 6.67 amps x 2 = 13.34
amp hours.
I want my system to be
reliable if we have four consecutive days of cloudy weather,
4 days of autonomy x 13.34 = 53.36 amp hours for the
battery.
Sun Xtender
makes a 56 amp hour AGM battery, PXV-560T.
This installation is in a
location that gets 5 hours of full sun (insolation) per day.
To recharge the battery for one day of use we need 13.34
amps in 5 hours = 2.67 amps from a 12 volt solar panel.
Most load calculations include a discount factor for the
inefficiency of recharging the battery. 20 percent is
typical. 2.67 / 0.8 = 3.34 amps.
We have a 60
watt solar panel that has an Imp (amps maximum power point)
of 3.49. Look at the 60 watt panel top of the
page.
The 60 watt solar panel
has a short circuit amp rating (Isc) of 3.86 amps.
3.86 x 1.25 = 4.83. I can use a 5 amp or larger charge
controller with this panel to charge the battery. If I
want to make sure I am getting the best efficiency available
for charging the battery, I would use a
small MPPT
charge controller like the Genasun 5 amp for lead acid.
Summary
Solar energy math
calculations for system sizing can be done with a simple
calculator using the basic formulas shown here.
If you want to see an
example already in the website, read my page about
CPAP
battery backup emergency solar power.
When you calculate your
loads, you will quickly see the advantage of using the most
energy efficient devices you can find, like our SunDanzer
solar
refrigerators and freezers for example. High
efficiency refrigerators and other appliances like
Vari-Cyclone super energy efficient ceiling fans,
Pico portable
LED lights and
other electrical devices used around the house are less
expensive than solar electric components. If you can
downsize your loads through efficiency, your solar system
will be less costly and easier to justify from a return on
investment perspective.
Learn more, download the
Successful Off Grid System Design Primer. Or,
download the
Successful Off Grid System Design Primer with Excel Workbook
in a ZIP file.
Please contact us today for
more information or assistance with your solar applications.
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