Solar 101: How the output of a solar system is calculated

If you are looking into solar and have reached the point of obtaining a Solar Estimate from an installer, you would have noticed that your system’s output is measured in kWh (kilowatt-hours). Or, kilo…what…’s this mean? Apart from being subjected to bad solar puns, kWh is a term that will no doubt cause some confusion for the first-time solar inquirer. If you have been studying up on solar, then you may be wondering how the output is actually calculated. As we said in our first Solar 101, Solar Panel Technologies – what’s the difference?, we’re here to de-bunk some one the lingo used in the industry (and the calculations behind it), to help you make informed decisions when looking into solar.

Before we get into the details of how the output of a solar system is calculated, let’s just refresh your memory of the basics. Below are some of the key terms and their definitions, relative to you – the solar inquirer.

• Watts – A term usually used to describe the size of an individual solar panel, it is a unit of electrical power that indicates the rate at which energy is produced.
• Kilowatts – One thousand watts
• Kilowatt Hours – The number of watts produced (or used) per hour. E.g. a solar panel that is 185W, will produce 185W in 1 hour (max), or 0.185kWh.
• DC – Direct Current, measured in Volts. This type of electricity is produced by the solar panels, but cannot be used in your home just yet.
• AC – Alternating Current, measured in Volts. The type of electricity is produced by a solar system’s inverter, which converts DC to AC, suitable for use in your home or business.
• Peak Sunlight Hours (PSH) – The sum of each sunlight hour’s rate of solar insolation, divided by the maximum rate of solar insolation. In other words, if we squashed all the sunlight hours in a day together, how many of the absolute best sunlight hours would it create? E.g. 10 sunlight hours may equal 4 peak sunlight hours.
• Pitch – The longitudinal angle of the solar panel in relation to the sun. 0 degrees would be mean a solar panel is laying flat, whereas a pitch of 39 degrees would mean it is facing directly at the sun.
• Azimuth – The latitudinal direction of the solar panel in relation to the sun. As the latitude of the sun at the equator is 0 degrees, solar panels in the northern hemisphere should face south, or 180 degrees.

A little confused? Not to worry. It is not until we apply these terms and measurements to a system, that they actually become easy to understand and relevant. So first, let’s get started on sizing a system!

Step 1. Calculate the System Size

Lets say you would like 20 x 200W solar panels. To calculate the system’s basic DC output, we simply multiply the number of panels by the panel size (W).

20 x 200W = 4000W / 4kW

This is typically how an installer will describe the size of the system to you. This output figure (4000W) is also the answer to a hypothetical question: How much energy could the system produce per hour, if it received the maximum amount of sunlight possible, as the optimal temperature? In other words, an unrealistic scenario. So how do we work out the DC output for a more realistic scenario?

Step 2. Applying Peak Sunlight Hours

As you can appreciate, different locations receive different levels of sunlight. A property in Northern WA won’t receive the same, high level of sunlight compared to say, TX. So the first step in calculating the DC output of a system, is using sunlight data relative to the area that it is being installed. Let’s use an example of Philadelphia:

Average Peak Sunlight Hours/ Day: 4.6

4.6 PSH x 4000W = 18400Wh

The output figure is now the daily amount of energy produced by the solar panels. Now we need to factor in Pitch and Azimuth.

Step 3. Factoring in Pitch and Azimuth

The pitch and azimuth are the two most important factors to consider when calculating the output of a solar system in a particular area. The reason for this is because solar is most efficient when the panels are angled to the latitude of an area (39 degrees for Philadelphia), and facing due South (180 degrees).

When solar panels (on fixed arrays) deviate from the aforementioned pitch and azimuth, efficiency loss is incurred. This is due to a reduction in Peak Sunlight Hours, meaning that less sunlight is hitting the panels directly. For this example, we’ll assume that the roof is facing South West, and pitched at 30 degrees.

225 degrees (SW) @ 30 degrees pitch = 4.34 PSH

Now, we just recalculate Step 2 with the new PSH

4.34 PSH x 4000W = 17222Wh

Step 4. Factoring in Temperature

It may surprise you to know that temperature can play a major part in determining the output of a solar system. This is because solar panels operate most efficiently at 25C cell temperature, or around 55F ambient – a temperature much lower than that found in many areas across the US, particularly in summer.

For this reason, most US-Certified panels now come with a PTC rating, which is the output (wattage) of a particular solar panel in average US conditions (20C/ 60F), measured in ambient temperature. For this particular system, we will assume an efficiency of 91% (9% loss due to temperature).

17222W – 9% = 15672W

For a more accurate efficiency loss, a more complex equation, accompanied by area-specific data needs to be used. This figure is simply an average to demonstrate that there is a loss incurred by temperature. Certain types of technology perform better in higher temperatures. You can read more about different panels here.

Step 5. Factoring in Other Losses

Last but not least, we must consider a number of other factors when calculating the output of a solar system. These include inverter and transformer efficiencies, diode and connection losses, wiring loss, soiling (dirt build up), shade, just to name a few. Each of these factors is given a rating, usually between .95 and 1. Each of these are them multiplied by each other to calculate a “Derate Factor”, which is used to calculate the final system output figure. For example, after calculating the amount of loss for each factor, we get a Derate Factor of .94, or 94%.

15672W x .94 = 14731W

Step 6. Calculating the Daily, Monthly and Annual Output

Now that we have factored in all the potential losses for the system, we can now calculate some relative output figures. Because hey, what does 14731W actually mean?

To calculate the daily output of the system , we simply use the following equation:

14731 / 1000 = 14.73kWh

To calculate the monthly output of the system, the following calculation is used:

14731 / 1000 x 30 = 441 kWh

To calculate the annual output, we simply use the following calculation:

14731 / 1000 x 365 = 5376 kWh

And there you have it, a simplified process of how a solar system output is calculated. However, we have only scratched the surface! It may be hard to believe, but there are even more factors to consider when calculating the output of a system, which we will touch on in future 101′s, so stay tuned!

*Image credits: step 3 a., step 3 b., step 5.