Calculating the Electrical Energy Output of a 100W Rooftop Solar Panel
Note: This blog-post is from my book titled, “The Energy Equation: Requirements, Resources, and Projections”. This book provides a comprehensive analysis of our energy-future.
When choosing a rooftop solar panel, estimating the average daily electrical energy output is always a challenge. Data sheet of a solar panel specifies only the power output while it is the energy output that is required for sizing most applications. The purpose of this blog-post is to describe some basic principles that will help with the estimation of energy output. Once you know the expected average energy output, it is possible to size the panel for a particular application. This blog-post uses locations in India and USA as examples for calculating the energy output. Similar calculations can be made for virtually any location in the world.
Power output of a solar panel is specified in Watts for Standard Test Conditions (STC). The STC corresponds to a solar insolation (radiation) of 1000 W/m2 and a cell temperature of of 25º Celsius. For instance, the Kyocera KD215GX-LPU panel is rated to produce 215W as the maximum power when solar insolation is 1000 W/m2 and solar-cell temperature is limited to 25º Celsius. This output power is rarely achieved in practice. There are several reasons for the reduction in output. Each of these reasons correspond to a down-rating factor to apply to the published power output:
- Solar insolation: An insolation of 1000 W/m2 is probably achieved in a desert when the sun is directly overhead! In practice, insolation varies considerably across the globe. Absorption of sunlight in air varies, depending on the volume of air through which the sunlight passes. The volume depends on the latitude and the season. At latitudes far away from the equator, sun never comes directly overhead and the sunlight must pass through a larger volume of air. During the winter season, there is a further increase in the volume of air through which the sunlight must pass as the declination of sun in the sky increases. Absorption in the atmosphere also depends upon factors such as humidity, dust particles and aerosols present in the air. Moreover, there are cloudy days, during which the insolation reduces significantly. Given these variables, how do we estimate the amount of energy that a solar panel will deliver? Thankfully, NASA has gathered data for solar insolation for almost every part of the globe and averaged it over the past 22 years. This data was gathered using satellites. Analysis of this data reveals that for many cities in India, the average insolation is only a little over 700W/m2 for a panel that is tilted at an angle of latitude degrees towards south. For instance, for the city of Pune, India, the average solar insolation is calculated to be 708W/m2 for a panel that is tilted at an angle of 18 degrees towards south. The main reason for this deviation, as compared to the test condition of 1000W/m2, is the impact of the monsoon season. During the months of July and August the amount of sunlight reaching the ground is just over half of that in the months of March and April, in spite of more daylight hours! Hence, a calculation for energy output needs to down-rate the solar panel wattage based on the insolation data for the location of installation. Average insolation for multiple cities in India is calculated to be 717 W/m2 as compared to the STC specification of 1000 W/m2. Thus, we arrive at a down-rating multiplicand of 0.717 to down-rate the power output from the solar panel.
- Operating Temperature: A solar panel rarely operates at a cell temperature of 25º Celsius. In a tropical country like India, it is more common for the cell temperature to rise to more than 50º Celsius. At this temperature, power output from a solar panel is less compared to that at 25º Celsius. For the Kyocera panel, about 10% drop in power output is expected at the cell temperature of 50º Celsius. Hence, the down-rating factor due to the operating temperature is calculated to be 0.9.
- Electronics associated with using the energy produced by the solar panel can’t operate at 100% efficiency. However, well designed inverters operate at a very high efficiency; with many inverters claiming even 98% efficiency. This includes the fact that it may not always be possible to operate the panel exactly at the peak power point. Thus, down-rating factor due to efficiency of associated electronics is 0.98.
- Cabling Losses: Several solar panels are connected in series to form a system that operates at high voltage and (relatively) low current. Lower current implies a lower power loss in the cables. For the purpose of this document, the cabling loss is assumed to be 5%, implying a down-rating factor of 0.95. The length and diameter of cables and configuration of a given system will decide the actual loss; but a down-rating factor of 0.95 should be achievable.
- Ageing and Cell Mismatch.: Output of solar panels reduces with age. The panels generally come with a guarantee of 90% output after 10 years and 80% output after 25 years. Secondly, solar panels collect a lot of dust and bird droppings on the glass surface. This too reduces the output from the panel. Even when the panels are cleaned periodically, some residue remains. Reduction in output of even a single solar cell affects the power output from the entire panel. Remember, all the solar cells within the panel are connected in series. This means that the cell with lowest current output dictates the current output from the solar panel. Reduction in current output causes a corresponding reduction in power and energy output of the solar panel. The reduction in output of a solar panel due to these factors is mostly a guess! It is assumed that there will be a 5% reduction in power output of a panel that is 5 years old, owing to the factors explained above. Thus, down-rating factor on this account will be 0.95. Older panels will have a lower output.
- COS(θ) Effect: During the course of the day, as the sun traverses the sky, angle of incidence of sunlight on the solar panel keeps changing. Take a look at the figure TBD. Early in the morning and late in the evening, the angle of incidence is maximum. Near noon, this angle is 0 and maximum solar radiation in incident on the panel. The direct solar radiation incident on the panel early in the morning and late in the evening is close to 0. The radiation incident on the panel when the angle of incidence is, say 60 degrees will be half of that when the angle is 0 degrees. Thus, the 100W panel does not output 100W throughout the day, simply because sun is moving in the sky! Using some simple mathematics, the average radiation incident on the panel in a day is calculated to be about 0.64. This is called the COS(θ) effect. The performance degradation due to the COS(θ) effect is separate from the degradation caused by the lower average insolation. There is one more factor that results in another COS(θ) effect. Throughout the year, as seasons change, the declination of sun in the sky changes. This results in another angle of incidence as shown in figure TBD. The COS(θ) effect of this is relatively little and is calculated to be 0.97. Thus, the down-rating factors due to the two COS(θ) effects will be, 0.64, and 0.97.
- Daylight Hours: The most obvious factor is the number of hours of daylight. On the average, sun shines for 12 hours per day. This results in a down-rating factor of 0.5 for obtaining the average power available from the solar panel.
Output Calculation for India:
Multiplying all the down-rating factors, we get 0.177 as the net down-rating factor. Thus, the energy delivered by a 100W panel in a day is actually equivalent to the energy produced by a 17.7W power source throughout the day. Thus, in a day, on the average, a 100W solar panel will deliver 424 Wh of energy and in one year it will deliver 155 kWh of energy. This calculation is an average for India, taking into account many major cities. Quite obviously, these numbers will vary depending on the location. Secondly, even for a given location, there will be days when the energy output will be significantly larger or smaller. However, for most cities in India, the average energy delivered will be close to this number. The exceptions will be the locations in the far north-east and northern most parts of India where solar insolation is much lower. At certain locations in Rajasthan, eastern Gujrat, and north-west Maharashtra, the energy output It will be higher than 424 Wh per day.
Output Calculation for USA:
It will be interesting to calculate the corresponding numbers for some of the locations in the USA. For instance, at Seattle, WA, the expected energy output from a 100W panel is calculated to be only about 279 Wh/day while at Bakersfield, CA, the same panel will output about 450 Wh/day. On the east cost, output at Orlando, FL, is expected to be about 382 Wh/day, while at Boston, MA, the output is expected to be only about 326 Wh/day. In Phoenix, AZ, the energy output is expected to be 457 Wh/day, While there is a wide variation in the energy output across the USA, there exists a vast expanse of land in the eastern parts of southern California, Arizona, Nevada, New Mexico, and Texas where there is ample sunshine. The daily output at these locations will match that at Phoenix. Such locations are ideal for solar photovoltaic electricity generation.
In summary, at most locations in India, the average energy output of a 100 W solar panel is expected to be around 424 Wh/day. The output in USA will vary a great deal depending on the location. At the best locations, output can be expected to be around 457Wh/day while there are locations where output will be as low as 279 Wh/day.