The conventional formula used to estimate the electricity generated in annual output of a photovoltaic system is: Energy (kWh) = A × r × H × PR
Where:
A = Total solar panel Area (m2)
r = Solar panel yield (percent)
H = Annual average solar radiation on tilted panels (zero shading)
PR = Performance Ratio: provides a coefficient for energy losses (see details below)
In the above equation, r is the yield of the solar panel, given in terms of the ratio of electrical power (in kWp) of one solar panel to the glass surface area (in m2) of the panel or module covering the solar cells. For example, the solar panel yield r of a PV module of 250 Wp with an area of 1.6 m2 is 0.250 / 1.6 = 15.6 percent.
This nominal ratio is given for standard test conditions (STC): solar radiation equal to 1000 W/m2, a cell temperature of 25°C, and a wind speed of 1 m/s. The nominal power of a photovoltaic panel under these standard test conditions is referred to as “watts peak” (Wp). All PV solar panels are rated in this way. For example, a Wp rating of 250 indicates the theoretical, rather than the actual, amount of power that will be produced by a given PV panel, because Wp does not account for the losses that can occur. See “Performance Ratio” below.
H refers to the solar radiation or insolation value. You do not need to calculate this value yourself. You can find the solar radiation value for any location worldwide free of charge on several web sites, or from the above table for North America. For more extensive coverage of many other locations and countries, you can visit: http://www.photovoltaic-software.com/solar-radiation-database.php.
You’ll have to find the global annual radiation incident on your PV panels, which is determined by your specific location (see tables above). Sometimes this needs to be modified with respect to your specific installation data, including the inclination (slope or tilt) and orientation or compass alignment (azimuth) of your panels. However, most of the major solar radiation websites will provide the solar radiation values for any given location, already taking into account the optimal inclination (number of degrees from the equator), and optimal orientation (i.e. due south).
PR (performance ratio): Knowing the PR is an important part of evaluating the quality of a photovoltaic installation, because it indicates how well the installation will perform independent of its orientation or inclination. It includes all losses. Factors that could cause energy losses that would affect the PR value include: the site; the PV technology; the type of inverter to be used; the sizing of the system; and the weather conditions determined by geographical location, as summarized below:
The following analysis of solar module performance factors will help explain the conversion from the solar module power rating (watts peak DC STC) to the energy (kilowatt-hours AC) produced by the PV solar system you propose to install at your home.
The “Performance Factors” for PV solar modules are summarized and quantified as follows:
Modules are rated in DC watts at STC by all manufacturers. For example: manufacturer rating 100 watts STC DC. All solar module manufacturers test the power of their solar modules under specific standard test conditions in the factory. The test results are used to rate the modules according to the tested power output. For example, a factory-test module that produces 100W of DC power would be rated and labeled as a 100W STC DC solar module.
The operating temperature of PV modules increases when the modules come in contact with the rays of the sun. As the operating temperature increases, the power output decreases slightly due to the properties of the solar cell conversion materials. This applies to all solar modules. The PV USA Test Condition (PTC) ratings, which are based primarily on the specific module temperature characteristics, take this into consideration. The PTC ratings are different for each module and can vary from approximately 87 percent to 92 percent of the STC rating. A typical decrease in power output is approximately 12 percent for crystalline-based solar modules. This decrease would result, for example, in a STC rated 100-watt DC solar module being PTC rated at approximately 88 watts DC.
When a PV solar module is mounted on a rooftop, airborne particulates such as dust settle and accumulate over time on the glass surface of the module, just as dust settles on the glass windshield of your car wherever it may be parked. These particulates prevent a certain amount of light from reaching the module and therefore reduce the power produced by the module. As you know by now, modules produce more power when exposed to more light. Depending on local conditions and on the maintenance provided by the homeowner, the reduction in power from particulate build-up can be anywhere from 2 percent to 14 percent. A typical value for this factor can be estimated at 7 percent, giving a particulate loss multiplier of 93 percent. A module installed in a wet weather climate would have less “soiling” than a module installed in a drier climate, due to rainwater rinsing off the module’s glass surface. Particulate build-up results in the power decreasing from 88 watts to approximately 82 watts (88W × 0.93 = 82W).
Typical solar electric systems require that modules be connected to one another. The wires used to connect the modules create a slight resistance in the electrical flow, decreasing the total power output of the system, a phenomenon similar to what happens when low-pressure water flows through a long hose. In addition, slight differences in power output from module to module reduce the maximum power output available from each module. The system AC and DC wiring losses and individual module power output differences could reduce the total system-rated energy output by 3 percent to 7 percent. A typical value for these losses is 5 percent. This results in the estimated power output decreasing from 82 watts DC to 78 watts DC (82 W × 0.95 = 78W).
In order for the DC power from the solar modules to be converted to standard utility AC power, a power inverter (DC to AC) is installed along with the PV solar system. The conversion from DC power to AC power results in an energy loss of between approximately 6 percent and 8 percent. This is mainly due to energy losses in the form of heat, but this can vary between different inverters. A typical value used for these losses is 6 percent. This gives a loss multiplier of 0.94. This results in the estimated power output decreasing from 78 watts DC to 73 watts AC (78 W DC × 0.94 = 73 W AC). Now we have the power in alternating current after the inverter.
First of all, not every roof has the optimal orientation or “angle of inclination” to take full advantage of the sun’s energy. Non-tracking PV systems in the northern hemisphere should ideally point toward true south, although orientations that face in more easterly or westerly directions can work too, albeit by sacrificing varying amounts of efficiency.
Solar panels should also be inclined at an angle as close to the area’s latitude as possible to absorb the maximum amount of energy year-round. A different orientation and/or inclination could be used if you want to maximize energy production for the morning or afternoon, and/or the summer or winter. Of course, the modules should never be shaded by nearby trees or buildings, no matter the time of day or the time of year. In a PV module, if even just one of its cells is shaded, power production can be significantly reduced (slightly more for central inverters or somewhat less if micro-inverters are used).
The module installation angle in relation to the sun affects the module energy output. The module produces more power (watts) and, as a result, energy (watt-hours), when the light source is perpendicular to the surface of the module. For this reason, solar module installations are often tilted towards the sun to maximize the amount and intensity of light exposure.
As the sun angle changes throughout the year (higher in the sky during summer and lower in the sky during winter), the amount of light falling directly on the module changes, as does the energy output. In southern California, a typical optimum tilt angle for average module power production over the course of a year in a fixed-tilt system is approximately 30 degrees. The typical southern California residential roof is tilted approximately 15 degrees. The reduction in the average annual energy output for a module, which is mounted at a south-facing, 15-degree tilt, is approximately 3 percent when compared to the optimal tilt angle of approximately 30 degrees.
This 3 percent reduction gives us a loss multiplier of 0.97 and results in a power reduction from 73 watts AC down to 71 watts AC (97 percent × 73 = 71).
For flat-mounted systems (zero tilt), the reduction in average annual energy output for a module is approximately 11 percent when compared to the optimal tilt of approximately 30 degrees.
The amount of sunlight shining on the module is partially dependent on the direction the PV system array is facing relative to the equator. As the sun moves across the sky throughout the day, from the east in the morning to the west in the afternoon, the compass direction (south, southwest, east, etc.) of the module affects the cumulative energy output. Assuming you’re in the Northern Hemisphere, it’s best to install a south-facing module in order to obtain the maximum amount of direct sunlight exposure on your PV modules. If the module is facing east or west, it will be exposed to less direct sunlight as the sun moves across the sky.
There is no loss factor for south-facing modules, so the estimated energy output (from one hour of exposure) for this particular example will remain at 71 watt hours AC.
If the module was not facing south, the estimated energy output would have been reduced. For example, the estimated energy output for a southwest-facing module would be reduced by approximately 3 percent.
The amount of sunshine on your modules is determined to a great degree by the extent of the sun’s year-round intensity at your particular location, known as the solar irradiation index or solar insolation index.
Refer to the Solar Irradiance Map in Chapter 4, which illustrates and explains the different solar irradiance levels measured in average peak sun hours/day for any location in North America. The map accompanies the long table showing the “Sun Hours” for approximately 100 cities in the United States and Canada.
Every location on earth has a different amount of sunlight exposure throughout the year, referred to as solar irradiation, which is measured in kWh/M2 expressed as “sun hours.” For example, a coastal California city like Malibu or San Francisco will have a lower average amount of yearly sun hours compared with desert cities like Palm Springs or Phoenix because of fog and moisture in the air in coastal locations. Since solar modules produce power and energy when exposed to sunlight, the more sun hours a location receives, the more energy will be produced from a PV solar module installed at that location.
“One sun” refers to the peak noon sunlight power intensity in the middle of summer. “One sun hour” is the energy produced by the peak noon sunlight intensity in the middle of summer, over one hour. Because the sun’s energy is converted by a solar module, recorded sun hour data for particular locations is used to help approximate the energy produced by a solar PV module.
The amount of sun hours for a particular location differs from day to day. There are multiple sun hour data sources, which differ slightly from one another. The US Department of Energy and NASA have calculated average daily sun hour data for most locations for over 20 years, which helps predict yearly energy output. This recorded data shows an approximate daily sun hour average of 5.5 hours throughout the year for many southern California locations.
SUN HOURS
(Southern California = 5.5 daily sun hours), 391 watt hours AC per Day (71 watt hours AC × 5.5 h/day), equivalent to 142 kWh/year (391 Wh/day × 365 days divided by 1,000 W/kW).
A table in Chapter 4 specifies the average yearly sun hours available for more than 120 cities in the United States and Canada. This table also provides the average summer and winter sun hours, or irradiation index, for each city. In southern California, for example, there are approximately 7.1 sun hours per day during the summer and approximately 3.9 sun hours per day during the winter. These seasonal averages result in a yearly average of approximately 5.5 sun hours per day ((7.1 + 3.9) / 2 = 5.5).
In order to estimate the yearly energy production of a solar module, simply multiply the estimated module energy output (from exposure to one sun hour, 1000W/m2 over one hour), 71 watt hours AC (remember we used a PV panel of 100Wp adjusted by all the power-loss factors), by the number of sun hours for the particular location: 5.5 per day, in our example. This produces approximately 71W × 5.5h/day = 391 watt hours AC per day. Expressed in kilowatts, this is 0.391 kWh/day per panel. When estimating yearly energy production, the estimated daily energy production, .391 kWh AC, is multiplied by 365, the total number of days in a year. This results in approximately 142 kWh/yr AC energy production. Therefore, one 100-watt (100 Wp) DC module will produce approximately 142 kilowatt hours/year AC of electric energy under the specified conditions in this example.
If the module rating were higher than 100 Wp DC—for example, many polycrystalline modules have a rating of 250 Wp DC—you would simply multiply 142 by the ratio 250/100 (142 × 2.5) = 355 kWh/yr of AC power for one PV panel rated at 250 Wp.
The key figure to remember in all of this is the estimated module energy output, which is 0.71 watt hours AC for every 1.0 Wp DC of rated module power. This is equivalent to 29 percent total energy losses.
Once you make the commitment to go solar, the next step is to determine how big your solar PV system must be to meet the electricity needs of your home and to see if the total net cost is within your budget, taking into account any government financial incentives and subsidies, and then adjusting the size of your proposed system if necessary.
Start by reviewing your electricity bills over the past year to get an idea of your typical electricity usage measured in kilowatt hours. For example, in recent years the average American household used about 11,000 kilowatt hours of electricity per year, according to the US Energy Information Administration (EIA). Using the calculations above, to obtain 11,000 kWh of power over the course of one year in an average California city, we would need 31 modules rated at 250 Wp DC. The calculation is: 11,000 kWh/yr divided by 355 kWh/yr/panel = 30.9 panels (for PV panels rated at 250 Wp DC).
Of course, the above calculations were based on the solar irradiation index of an imaginary California city, and you will want to recalculate using the irradiation index in your particular location, which you can obtain from the table and map in Chapter 4.
Many utility companies also offer complimentary energy audits, and this can provide greater insight into your family’s energy use habits and the basic requirements for your proposed PV solar system.
Some arid regions of the US Southwest can receive more than six hours of peak sun, while in the northeastern states it would be only about four hours. The process of comparing your power needs to your sunlight availability is known as your load calculation, and this simple calculation is critically important for planning the size of your PV solar system.
Let’s take another, simpler example to understand how you may calculate the required size of your solar array. Let’s use the typical North American family’s monthly consumption figure of 900 kWh. To arrive at a daily consumption figure we divide the monthly figure by 30, the average number of days in one month. 900 kWh/month divided by 30 days/month = 30 kWh/day AC.
Now we want to calculate the size at which a solar array will produce 30kWh/day. We know this depends on peak sun hours available, and we’ll use for this example five peak sun hours. Depending on your location, 30 kWh/day divided by five peak sun hours = 6 kW/day AC.
We need to remember to convert this back to DC power because all PV panels are rated in Wp DC. As detailed above, we learned the DC/AC conversion factor, allowing for all normal losses in 1.0 Wp DC = 0.71 W AC. Therefore, 6 kW/day AC divided by 0.71 = 8.45 kW/day DC.
| Number of PV Panels of Different Ratings Required to Produce Specified Levels of Daily Power Consumption | |||||
| DAILY CONSUMPTION AC | EQUIVALENT DC POWER | NUMBER OF PANELS REQUIRED USING 200WP PANELS | NUMBER OF PANELS RE-QUIRED USING 240WP PANELS | NUMBER OF PANELS REQUIRED USING 285WP PANELS | |
| 4,000 W/d AC | 5,634 W/d DC | 28 | 24 | 20 | |
| 5,000 W/d AC | 7,042 W/d DC | 35 | 29 | 25 | |
| 6,000 W/d AC | 8,450 W/d DC | 42 | 35 | 30 | |
| 7,000 W/d AC | 9,859 W/d DC | 49 | 41 | 35 | |
| 8,000 W/d AC | 11,267 W/d DC | 56 | 47 | 40 | |
| Note: The number of panels is rounded off to the nearest whole number. | |||||
Therefore, for a 6,000 W/d AC (8,450 W/d DC), you would need forty-two 200Wp panels (8,450 / 200 = 42), or thirty-five 240Wp panels (8,450 / 240 = 35), or thirty 285Wp panels (8,450 / 285 = 30). This calculation is included in the table below.
Those of you with three-or four-bedroom homes who are putting in solar PV systems will want to offset most of your electrical requirements with a PV solar array that is between 4kW/d and 8kW/d (daily consumption AC). Using this simple formula provided above, we can calculate the number of panels for different power levels as described below
If your monthly average consumption figure varies much from the 900 kWh/month example, or if you receive fewer than five peak sun hours on average, then it’s simple math to calculate your own daily consumption figure and the number of panels in accordance with their rated capacity. The basic formula is as follows:
Monthly consumption _________ kWh/month, divided by (30 d/m × 1,000 W/kW) = _________ W/d, divided by number of peak sun hours _________ h/d, divided by the capacity of each solar panel _________ Wp DC = _________, the total number of panels required for your system. (Note: To be practical, we round up or down to the nearest whole number.)
The National Renewable Energy Laboratory (NREL) developed the world’s most widely used computer model to estimate the energy production and energy cost of grid-connected photovoltaic solar energy systems. It can be used for existing or proposed PV solar systems anywhere in the world. This service, and specifically their PVWatts calculator, enables homeowners, small building owners, installers, and others to quickly develop estimates of performance for potential PV solar installations. The calculator can be accessed here: http://pvwatts.nrel.gov
In the UK, Scotland, and Wales, there’s a quality solar energy calculator that estimates the income and savings the homeowner can receive from the domestic feed-in tariff scheme, which is available for eligible PV installations of up to 4kWp. The calculator uses the latest tariff rates and is available here: www.energysavingtrust.org.uk/domestic/solar-energy-calculator.
A site for an easy-to-use online solar energy calculator for US and Canadian PV solar customers that computes how many tons of CO2 emissions any proposed PV solar rooftop system will avoid can be reached through this web address: www.solarenergy.org/solar-calculator.
The following website is for the USA-Canada market, and it provides some useful programs that can calculate the size of the PV solar rooftop you need, as well as system costs. It also helps you determine the government financial incentives you may qualify for.
Here is a link to the calculator in reference:
www.solar-estimate.org/?page=solar-calculator
The following links to solar calculators each enable you to build your own customized calculator to match your particular desired conditions or energy consumption level:
www.findsolar.com/Content/SolarCalculator.aspx (USA–Canada)
www.energymatters.com.au/climate-data (Australia)
www.affordable-solar.com/residential-solar-home/Residential-Calculator (USA)
The last website above also provides a national map of peak sun hours summarized by state.
Chapter 10 contains information about numerous websites that provide reputable cost savings calculators, which can automatically compute the annual cost savings of your proposed PV solar rooftop system as compared to your future yearly electricity bills if you don’t install a solar system.
Finally, it’s important to note that the figures generated by online solar calculators should only be used as a rough estimate. Some calculators may not include data on federal, state, or local solar incentives and rebates. Site-specific factors may also influence designs and output that an online calculator would not factor into the computations. A solar contractor will usually be able to provide you with a more accurate estimate.