Solar Calculations Math Tutorial

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-HoursUsed 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-HoursUsed 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 freezersfor 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.

Successful Off Grid Solar

Successful Off Grid Solar 

So You Think You Want to Go Off Grid?
The common question asked by the uninitiated, without providing any other significant details, is “What will it cost to take my house (cabin, cottage, etc.) off grid?”
There is no pat answer to the question. From my own experience of living off grid for more than 5 years, my advice is to think very carefully about your willingness to adapt your energy consuming behavior to the variables of being dependent on sun, wind and in some cases moving water for your energy needs rather than being connected to a seemingly endless supply of grid electricity created by burning the remains of dinosaurs and their ancient habitat (oil and coal) or the fission of radioactive materials that leave waste with a nasty half-life of 50,000 years or more.
Even the best designed off grid system will experience variables that will require occasional behavior modification whether you like it or not. Sticker shock typically occurs for those who want things to be off grid and just like they have always been. Things are not going to be like they have always been. Reliability of the grid as evidenced by the recent events in India that left 600 million people without electricity is an insight into our energy future.
This being said, as far as I can tell, unless you are a Wall Street robber baron or a banker with friends at the Federal Reserve and Treasury Department, there is no better return on investment in today’s uncertain times than being your own power company. Grid power is not going to get any cheaper as fossil fuel supplies decline. The US solar tax credit and other local incentives help to defray initial investment. Your future cost of electricity is now known, with the main future expense being the replacement of batteries which you can cover through a monthly sinking fund contribution to your savings account that will be significantly less than your current utility bills.
Success is in the DETAILS!
The success of an off grid solar system design begins with details. The size of an off grid solar electric system depends on the amount of power that is required (measured in watts), the amount of time it is used (measured in hours)and the amount of energy available from the sun in available in the location where the system will be installed (measured in solar insolation (sun) hours per day).
As a prospective off grid solar system owner and user, you have control of the first two of these variables. The third variable depends on your location and the weather.
Conservation Saves the Day
Conservation plays a highly important role in keeping down the cost of an off grid solar system. The use of energy efficient appliances and lighting, as well as non-electric alternatives wherever possible, can significantly reduce the size and cost of the system.
There are very few exceptions where conservation is less cost effective than the alternative. Anything that you can operate on low voltage direct current (DC) rather than 115 or 230 volt alternating current
(AC) will make a big difference. 230 volt single phase AC in parts of the world that use 115 volts requires two inverters to make the two legs of 115 that make 230 single phase.
Cooking, Heating, & Cooling
Conventional electric cooking, space heating and water heating equipment use a prohibitive amount of electricity. Electric ranges use 1500 watts or more per burner, so bottled propane or natural gas is a popular alternative to electricity for off grid cooking. A microwave oven has about the same power draw, but since food cooks more quickly, the amount of kilowatt hours used may not be large. Propane, natural gas and wood are better alternatives for space heating.
Good passive solar design and proper insulation can reduce the need for winter heating. Evaporative cooling is a more reasonable load than air conditioning and in locations with low humidity; the results are almost as good. One plus for cooling-the largest amount of solar energy is usually available when the temperature is the highest.
Low voltage ceiling fans, ventilating fans and whole house fans do a remarkable job of creating comfort during both warm and cool weather. We have lived off grid for over 5 years without air conditioning. The ceiling fan over the bed works wonders. Ceiling fans running on low speed circulate heat from the wood stove during the heating seasons.
Lighting
Lighting requires the most study since many options exist in type, size, voltage and placement. The type of lighting that is best for one system may not be right for another. The first decision is whether your lights will be run on low voltage direct current (DC) or conventional 110 volt alternating current (AC). In a small home, an RV, or a boat, low voltage DC lighting is often the best choice. DC wiring runs can be kept short, allowing the use of fairly small gauge wire. Since an inverter is not required, the system cost is lower.
When an inverter is part of the system, a home will not be dark if the inverter fails and the lights are powered directly by the battery. In addition to conventional-size medium-base low voltage bulbs, the user can choose from a large selection of DC LED lights, which have 3 to 6 times the light output per watt of power used compared with incandescent types.
Halogen bulbs are 30% more efficient and actually seem almost twice as bright as similar wattage incandescents given the spectrum of light they produce. High quality LED lights are available for 12 and 24 volt systems.
In a large installation or one with many lights, the use of an inverter to supply AC power for conventional lighting is cost effective. AC LED lights will save a tremendous amount of energy. It is a good idea to have a DC-powered light in the room where the inverter and batteries are in case there is a problem with the inverter.
AC light dimmers will only function properly on AC power from inverters that have pure sine wave output.
Refrigeration
Natural gas or propane powered absorption refrigerators are a good choice in small systems if natural or bottled gas is available. Modem absorption refrigerators consume 5-10 gallons of LP gas per month. They also create heat, good in the winter, not so good in the summer. If an electric refrigerator will be used in a stand-alone system, it should be a high-efficiency type. Some high-efficiency conventional AC refrigerators use as little as 1200 watt-hours of electricity per day at a 70° average air temperature.
A comparably sized Sun Frost refrigerator/freezer uses half that amount of energy and the smallest SunDanzer refrigerator (without a freezer) uses less than 200 watt-hours per day. The higher cost of good quality DC refrigerators is made up by savings in the number of solar modules and batteries required to operate the alternatives.
Major Appliances
Standard AC electric motors in washing machines, larger shop machinery and tools, swamp coolers, pumps, etc. (usually 1/4 to 3/4 horsepower) require a large inverter. Often, a 2000 watt or larger inverter will be required. These electric motors are sometimes hard to start on inverter power, they consume relatively large amounts of electricity, and they are very wasteful compared to high-efficiency motors, which use 50% to 75% less electricity.
A standard washing machine uses between 300 and 500 watt-hours per load, but new front-loading models use less than 1/2 as much power. If the appliance is used more than a few hours per week, it is often cheaper to pay more for a high-efficiency appliance rather than make your electrical system larger to support a low-efficiency load. Vacuum cleaners usually consume 600 to 1,000 watts, depending on how powerful they are, about twice what a washer uses, but most vacuum cleaners will operate on inverters larger than 1,000 watts since they have low-surge motors. There are also battery powered low voltage vacuums that can now be purchased at places like Wal-Mart.
Small Appliances
Many small appliances such as irons, toasters and hair dryers consume a very large amount of power when they are used but by their nature require very short or infrequent use periods. If the system inverter and batteries are large enough, they will be usable. Electronic equipment, such as stereos, televisions, VCR's and computers have a fairly small power draw. Many of these are available in low voltage DC as well as conventional AC versions. In general, DC models use less power than their AC counterparts.
Standby Loads
Electrical appliances and hardware that are “instant on” use electricity whether they are actually on or not.
Looking Back in Time
Before the electrification of North America and elsewhere, there were mechanical alternatives to most of the common appliances used today. Do you really need an appliance for every little thing in your kitchen and your life?
Calculate Your Loads
The last page of this document is a typical loads listing for conventional appliances. This is helpful but not as good as the real thing from your own situation. Details!
Included in the ZIP file is an Excel workbook you can use to determine the total energy in watt-hours per day used by all the AC and DC loads in your system. Save a copy of the original and then use a copy to do your work. Send back the workbook and I will finish the calculations for you.
Calculate Your AC Loads
If there are no AC loads, go to the DC loads section.
1. List all AC loads, amps, watts and hours of use per week in the spaces provided. Multiply watts by hours per day to get watt-hours per day. Add up all the watt hours to determine AC watt-hours per day. Insert more lines if you need to list more loads than the space allows.
2. NOTE: Wattage of appliances can usually be determined from tags on the back of the appliance or from the owner's manual. If an appliance is rated in amps, multiply amps by operating voltage (120 or 240) to find watts.
3. Convert to DC watt-hours per week. Multiply the total AC watt-hours by 1.15 to correct for inverter loss.
4. Inverter DC input voltage; usually 12, 24 or 48 volts. This is DC system voltage. Usually, the bigger the system the higher the system voltage.
5. Divide the product of the watt-hours by the system voltage. This is total DC amp-hours per day used by the AC loads.
Calculate Your DC Loads
1. List all DC loads in the space provided. If you have no DC loads, skip this section.
2. DC system voltage. Usually 12, 24, or 48 volts. Usually, the bigger the system the higher the system voltage.
3. Find total watt-hours per week used by DC loads. Divide the total watt-hours by the system voltage.
4. Add the AC and DC loads; this is your total amp-hours per day for your system.
POWER CONSUMPTION:
Items listed by watts per hour unless otherwise stated. Remember that some items are used for shorter durations.
Coffee Maker 800
Blow Dryer 1000-1500
Hot Water kettle 1500
Shaver 15
Toaster 800-1500
LTV 950 Ventilator 66
Blender 300
CPAP 30-50
Microwave 600-1700
Home Dialysis Machine (600 starting surge) 100
Hot Plate 1200
Oxygen Concentrator 350
Juicer 85-1000
Computer 200-600
Refrigerator/Freezer 1500-2000/day
Laptop 75- 100
Freezer Conventional 14 cu Ft 440
Printer 100-500
Vacuum Cleaner 200-1500
Fax 40
Hand held vacuum 100
Cordless Phone 50-150
Iron 1000
TV 25’ Color 150+
Table fan 10-50
TV 42’ LCD 210
Fan 100-200
Xbox360 185
Personal AC 240
DVD/ Radio/ CD 25-100 each
Room AC 1500
Satellite/Internet 30-85
Garage Door Opener 350+
Clock radio 10
Alarm/ Security equipment 150+
Lights 100W equiv. CFL 30
High eff. Gas furnace 250+
Lights 100W Incandescent 100
Furnace Blower 300-1000+
Washing machine – automatic 500
Furnace (oil/forced air) 250+
Dishwasher 1200-1500
Hedge trimmer 450
12” chain saw 1100
¼’ drill 250
7 ¼” circular saw 900
1” drill 1000
Aquariums 300+
3” belt sander 1000
Water Pump (300gpd) 3000+/day
* NOTE: the watts listed by an appliance type are averages – makes/ models/ years made can drastically alter the watts used. Some appliances have a starting surge much higher than the watts they use to run.