Appendix II: Photovoltaic String Sizing:
A string refers to a collection of PV modules connected either in series or parallel wiring. There is a worksheet on wiring as a file to download on the Photovoltaic group on Mahara. The following link from Heatspring Learning Institute also provides a solid overview of PV sizing. At first, this may seem overwhelming, as though there are too many elements to consider. However, with practice and a better understanding of the basic concepts, I'm confident that anyone with a basic knowledge of algebra and construction can become a PV designer & installer.
The following is basic DC theory: In series wiring (+-,+-,+-) voltage adds while amperage stays the same. In parallel wiring (++,- -,++,- -) amperage adds while voltage remains the same. It is standard for residential PV systems to be comprised of 2 strings in series, connected in parallel. This creates a high voltage, low amperage environment. I will provide a few examples to make this concept graspable.
A solar module is technically a collection of columns of solar cells all wired in series with blocking diodes at the top of each row. Thus, the electrical output rating of a solar module is high voltage and low amperage. The columns themselves wired in series, and then wired in parallel to each other. Each individual module has a distinct rating. As the columns are separated by blocking diodes, therefore, if 2 of 6 colums are shaded, then the module will only put out 2/3 of it's maximum possible voltage. As this is an interconnected DC system, the downgrade of one module will bring down the voltage of the entire system.
I will walk through the sizing of the system outlined in the electrical analysis on the previous page. I have chosen the Sunpower X21 modules. Sunpower is known in the industry as the company that makes the most efficient modules, that also have a sleek look on rooftops. Modules of the same size from other manufacturers are rated at 250W, while Sunpower's are rated at 345W.
What is essential to understand is what all the codes on the table to the right signify as pertaining to designing a functional system. I will cover the module on the right, the X21-345W.
Open Circuit Voltage (Voc) refers to the voltage that the module puts out under Standard Test Conditions (STC). Standard Test Conditions are defined as 1,000W/m2 @ 25C (77F) @ 1.5 Air Mass. Standard test conditions do not reflect reality, but rather a module being blasted by artificial light in an artificial environment in a laboratory. Because of this, the STC rating does not include derates. The STC numbers cannot be used to explain the kWh cost benefit to clients, however a designer may not use anything but the STC for the maximum voltage rating for safety. Likewise, the Isc (or Current Short-Circuit) is the lab based STC rating.
Notice that if you multiply the STC voltage and amperage you get 435.79 Watts, yet this is a 345W panel. This is because the more realistic rating that includes derate values is what the module rating is based off of. There are various tests that include wind speed, different air mass and different derate values for inverter efficiency etc. The subscript MPP refers to Maximum Power Point, which is the highest wattage point on the I-V curve. Remember that volts times amps equals watts, so if we plot these numbers on an XY axis we can represent the 3 values working together. To learn more about I-V curves, please watch the video on the right.
This means that the string voltage is based on the coldest ever temperature recorded for the site location, which provides us with a temperature coefficient. To learn more about the temperature coefficient, please watch the video on the right. In essence, photovoltaics put out more power when it is colder outside and the wiring and inverter must be able to handle the maximum amount of voltage output that the system could possible create.
The residential grid in the United States is 60 hertz and 600 volts maximum. This means that a PV system cannot create more than 600 volts output under STC rating and that the AC sine wave that comes out of the inverter must be at a frequency of 60hz.
The equation to size a string is as follows:
(Voc) x (# of Modules) x (Temperature Coefficient)
e.g. (68.2Voc) x (10 modules) x (1.14 temp-coeff.) = 777 volts
This means that we cannot create a string of 10 Sunpower X21-345W modules wired in series in a residential PV system in the USA because it could potentially put out more than 600 volts.
Remember that the household electrical consumption on the previous page was 2.74kWh/day. This is the AC usage that we need to design for.
In order to size the system, we need to divide the daily kWh energy needs by the power output of each module. The power output of the X21 Sunpower modules is 345W.
2.74kWh/day x 1,000 = 2,740Wh/day AC ÷ 345W/module = 7.9
Therefore, this house would require 8 X21-345W Sunpower Modules in order to account for it's energy needs. The design would consist of 2 strings of 4 modules each wired in series. As voltage adds in series, we would then have two strings producing 57.3Vmp x 4 modules per string = 229.2 Vmp/string. Since there are 2 strings, the Vmp of the system is doubled and becomes 458.2Vmp. These 2 strings are wired in parallel making a 458.2Vmp and 12.04Imp PV system. Remember that voltage remains and amperage adds when wiring in parallel. Most residential PV systems consist of 2 strings of modules wired in series, that are themselves wired together in parallel. This wiring method creates a high voltage yet low amperage system. Please refer to the images from the Sunny Web Design software and an example design of this system on the right.
Equation for Annual kWh rating of solar system
Remember to follow the variables through the equation, and that the derate value is the part of the equation that switches from AC/DC electricity. This equation answers: What is the annual kWh rating of a 2,760W DC system?
First, we have already converted W into kW by dividing by 1,000.
2,760W ÷ 1,000 = 2.76kW DC
Next, we multiply by the industry standard 77% derate value.
2.76kW x .77 derate = 2.13kW AC (AC output of a 2.76kW PV system)
Next, we multiply the kWh/day AC by the peak sun hours per day.
2.13kW/day AC x 5 peak sun hours/day = 10.65kWh/day AC
For annual usage, we multiply this by 365 days/year.
10.65kWh/day x 365 days/year = 3,887.25kWh/year
When this number is multiplied by the cost per kWh from your local utility company, you will have the annual payback that a 2.76kW solar system will provide the client. In California, the cost per kWh is very high at around 13cents/kWh. This means that this 2.76kW system will pay back an average of $500/year in California. Take the difference of this annual number from the net cost of the system to obtain the payback period for the entire system.