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Solar & Wind Energy Calculations: The (very) Basics

This is a simplified, "lay persons'" overview of how solar energy systems calculations are made. The solar estimates provided via our solar estimators are much more complex and complete. This simplified overview is meant only to provide the reader with a very basic understanding of some solar energy system calculation methods.

In addition to the information provided below, try our Solar & Wind Estimator and here are some books we suggest you read to help you learn more ....

Photovoltaics
Solar Water heating
Wind Energy

General Terms

Photovoitaics (PV) is the direct conversion of light into electricity. Certain materials, like silicon, naturally release electrons when they are exposed to light, and these electrons can then be harnessed to produce an electric current. Several thin wafers of silicon are wired together and enclosed in a rugged protective casing or panel. PV panels produce direct current (DC) electricity, which must be converted to alternating current (AC) electricity to run standard household appliances. An inverter connected to the PV panels is used to convert the DC electricity into AC electricity. The amount of electricity produced Ąs measured in watts (W). A kilowatt (kW) is equal to 1,000 watts. A Megawatt (MW) is equal to 1,000,000 Watts or 1,000 Kilowatts. The amount of electricity used over a given period of time is measured in kilowatt-hours (KWh). For a more in depth overview, please see our General Overview: About Solar Energy & Solar Power

What is a solar rating?

The solar rating is a measure of the average solar energy (also called "Solar Irradiance") available at a location in an average year. Radiant power is expressed in power per unit area: usually Watts/sq-meter, or kW/sq-meter.

The total daily Irradiation (Wh/sq-meter) is calculated by the integration of the irradiance values (W/sq-meter). Click here for the Solar Radiance map of the USA.

Shading: If your solar collectors or solar panels experience any shading during the day the output of your solar energy system can be dramatically reduced. This is especially true of photovoltaic (PV) solar panels since a partially shaded PV panel can result in a loss of power across the PV array. Some solar incentive programs, such as the California Solar Initiative (CSI) reduce the incentive available to you if your solar system is impacted by any shading.

Solar Electric (Photovoltaic) System Calculations

Estimating Solar Electric (PV) System Size: Are of Solar Panels

On average (as a general "rule of thumb") modern photovoltaics (PV) solar panels will produce 8 - 10 watts per square foot of solar panel area. For example, a roof area of 20 feet by 10 feet is 200 square-feet (20 ft x 10 ft). This would produce, roughly, 9 watts per sq-foot, or 200 sq-ft x 9 watts/sq-ft = 1,800 watts (1.8 kW) of electric power.

Converting Power (watts or kW) to Energy (kWh)

One kilowatt-hour (1 kWh) means an energy source supplies 1,000 watts (1 kW) of energy for one hour. Generally, a solar energy system will provide output for about 5 hours per day. So, if you have a 1.8 kW system size and it produces for 5 hours a day, 365 days a year: This solar energy system will produce 3,285 kWh in a year (1.8 kW x 5 hours x 365 days).

If the PV panels are shaded for part of the day, the output would be reduced in accordance to the shading percentage. For example, if the PV panels receive 4 hours of direct sun shine a day (versus the standard 5 hours), the panels are shaded 1 divided by 5 = 20% of the time (80% of assumed direct sun shine hours received). In this case, the output of a 200 square-foot PV panel system would be 3,285 kWh per year x 80% = 2,628 kWh per year.

Estimating Solar Electric (PV) System Size to Replace a Specified Amount of Utility (grid) electricity

PV System Capacity Required (kW of PV) can be roughly calculated as follows:

Annual electricity usage = Monthly Usage x 12 months. Electricity usage is express in kilowatt hours (kWH)

KW of PV = (Annual Usage) / (78% x kWh/kW-year from Solar Radiance chart below)

solar kwh per kw year map US

Energy production from a solar electric (PV) system is a function of several factors, including the following ... the "78%  used above assumes the following losses across the PV system:

FactorAssumption
Solar resources Assumed solar availability: As per PV Watts
Soiling or contamination of the PV panels Clean, washed frequently: 98% design sunlight transmission
Temperature 25C, calm wind
System configuration (battery or non-battery) Non-battery
Orientation to the sun tilted at your latitude, South facing
Shading None
PV Energy delivered as % of manufacturers rating 95%
Wiring & power point tracking losses 9% (91% delivered)
Inverter Efficiency 90%
Total Energy Delivered 95% x 91% x 90% = 78%

Solar Thermal System Calculations for Water Heating

Solar thermal collectors come in many types and sizes. For a more in depth overview, please see our General Overview: About Solar Energy & Solar Power

Most typically, a solar water heating system for a home or small building will use "glazed" flat-plate collectors. Each collector will have a rated output, usually expressed in thousands of BTU's per day (kBTU/Day). For example, a typical solar collector about 100 sq-ft in area will produce about 32 kBTU on a clear (no shade) day. The kBTU units can be converted to kWh, a typical unit of measure for electricity. A typical solar thermal collector will produce about 10 kWh per day. Or, over the course of a year (365 days) about 3,650 kWh.

There are many other factors which affect the performance of a solar thermal collector, including ambient air temperature, water temperatures, the volume of water being heated, and the thermal losses (efficiencies) inherent in the solar thermal system.

Solar Rating & Certification Corporation (SRCC) is generally used as a reference for solar thermal system performance ratings. You might want to visit their web site to learn more.

Wind Turbines: How Much Power and Energy Does a Wind Turbine Generate

Only a fraction of the wind`s power can be actually extracted out of the wind; there is no way to harvest all of the wind`s power. If all of the wind's energy was transfered to the wind turbine, then the air that hits the blades would have to come to a complete stop (i.e. all the wind`s energy was absorbed in the blades). This is not possible because continuous operation of a wind turbine requires that the air that hit the blades then "get out of the way" to let the air that is behind also hit the blades. If all the energy from the wind was transferred to the blades, the air would stack up in front of the turbine. Then the wind would have to blow around the turbine, rather than through it. In reality, the air that hits the blades keeps some speed allowing the air to move out of the way, thus allowing continuous flow of the air into the turbine.

According to the laws of physics, the theoretical limit of wind energy that can be converted to rotational energy at the turbine`s shaft is about 59%. This value is known as the Betz Limit. In practice, the collection efficiency of commercially-manufactured wind rotors is typically 25% to 45%. Small wind turbines tend to have efficiencies at the lower end of this range.

Wind Example:

If you have a small wind turbine with a blade diameter of 1 m (about 3 ft) and an operating efficiency of 20% at a wind speed of 6 m/sec (about 13.4 mph). Then, to calculate how much power the turbine can generate at this wind speed:

Rotor swept area: Area = Π × (Diameter/2)2 = 3.14 × (1/2)2 = 0.785 m2

Available power in the wind: Pwind= Air Density × Area × v3/2 = 1.2 × 0.785 × 63/2 = 101.7 watt

Then the power that can be extracted from the wind assuming 20% turbine efficiency is:
Pturbine=0.20 × 101.7 = 20.3 watts

If this ran continuously for a year (about 8,750 hours) then it would produce: 20.3 watts × 8,750 hours = 177,625 watt-hours, or about 177 kWh in a year.

(Note: we used the density of air at sea level, which is about 1.2 kg/m3)

wind turbine swept area diameter
Wind Turbine Metrics 		wind energy curve
Wind Energy Curve of a typical wind turbine

 
Tip: Measure the wind characteristics at your location.
 
If you are thinking of installing a wind turbine, you might want to monitor the wind speed at your location, first. There are several weather stations and wind speed meters (anemometer) available that can provide this information to you at a reasonable price. And, you'll probably have some fun doing it.
 
The one pictured to the right is about $100 at Amazon.com: La Crosse Technology WS-1612AL-IT Professional Weather Station, White

Wind Resource Maps are available from http://www.windpoweringamerica.gov


Suggested Books to Help You Learn More

Photovoltaics
Solar Water heating
Wind Energy