6. Size an inverter and module strings based on your array output.
Once you've determined your target array output size and selected your solar modules, you'll be ready to pick and size a central inverter. The different types of inverters, along with their specs and other features, are discussed in the main tutorial on this website. Like modules, inverters are commonly identified by their wattage output. But there are other specs to evaluate, particularly the array voltage range the inverter will accommodate. In this section, we'll discuss a typical grid-tied system that uses one central inverter.
Grid-tied inverters, like these products from SMA, come in a variety of shapes, sizes and specifications.
The first step in selecting and sizing an inverter model is to roughly match your target array watts to an inverter watt size. Standard inverter nameplates available for purchase include 2000 watts, 3000 watts, 3800 Watts, 4000 watts, 5000 watts, etc. If the main service panel for your home has a bus bar rated at 100 amps, the 3800 watt inverter is normally the largest inverter you can use, without a panel upgrade or other modifications made by an electrician.
An inverter with a slightly higher output wattage than the array watts is usually chosen, but that's not a hard and fast rule. After reading this section, you'll learn that the most optimum match for power efficiency may be an inverter rated at up to 25% less watts than your array. For instance, a 3,000-watt inverter might work for a 4,000-watt array. However, if you think you might like to add modules to your array in the future, you should buy the larger inverter. And if you live in a place that gets cold in the winter, you should also buy the larger inverter. (You'll see why in a moment.)
Two specs worth noting as you shop around and/or perform sizing calculations are module PTC ratings and inverter efficiency. Because modules are rated by their manufacturers using Standard Test Conditions, attentive PV designers wanting a more realistic appraisal of array output watts use another benchmark known as Practical Test Conditions. A PTC wattage estimate is invariably 10-15% less than the STC, or namplate, wattage. However, a PTC value is not always listed on the product spec sheet. You may have to search elsewhere to find the value, assuming the product has been tested and PTC certified. A California agency offering tax incentives maintains a database of PTC values for hundreds of modules, which you can access here. (If you plan to apply for a tax credit, low-interest loan or other incentive program, be sure to find out if PTC-rated equipment is mandatory before starting your module search.)
As for inverter efficiency, this value hovers at around 95-97%, which means that 3-5% of electricity from the array is lost due to heat, electricity needed to run the fan and operate the inverter display panel, etc. While a few percentage points difference between models may not sound like the sky is falling, over the course of ten or twenty years, it can mean a significant difference in kilowatt hours generated. Like a PTC rating, you may want to include inverter efficiency in your sizing calculations.
At any rate, once you have a wattage match between your array (i.e. module quantity mulitiplied by watts per module), and an inverter model, the next step is to figure out how many modules you should wire in series inside the array. Called string sizing, this is an electical calculation that determines the circuit's voltage. To create a string, you connect the positive lead of the first module to the negative lead of the next module, and the positive lead of that module to the negative lead of the next, and so on. For example, 10 modules of 30 volts each connected in series results in a 300-volt circuit. (If you don't know the difference between voltage and amps, click here for a quick intro.)
Diagram of a single series string of four modules connected to an inverter.
For home PV systems with no battery backup, the most common array configurations use 2 to 4 strings of 7 to 12 modules each. After the strings are wired, each string is connected to the next string in parallel. As shown in the graphic below, this means the positive lead (or circuit wire) at the end of String 1 is connected to the positive of String 2, and so on. Similarly, the negative wire at the end of each string is connected to its counterpart in all the other strings. A parallel connection involves no change in the circuit voltage. The module-rated current or amperage does change, however. If you have more than one string, you will need to multiply the current by the string quantity to determine the amps that will enter the inverter. (In a series string, current stays the same, which means it's exactly the amount identified on the module spec sheet.) Thus three strings of modules rated at 6 amps each will deliver 18 amps to the inverter. If there are two strings, then the inverter will see 12 amps.
This diagram represents multiple strings of modules connected in parallel. The dashed lines indicate there are more modules and strings in the array than pictured.
As a general rule, grid-tied PV designers configure arrays to generate a high DC voltage. A high voltage minimizes inevitable current losses as electricity flows downstream to the inverter. But there's a limit on how high you can go with DC voltage in your home. The National Electric Code (NEC) states that residential circuits are limited to a maximum of 600 volts. In Europe, it's 1,000 volts.
All grid-tied inverters are designed to handle a wide range of voltages, since sunlight across an array is rarely constant. A common range you'll see on spec sheets is 150 to 450 volts, which gives you wiggle room when sizing your module strings. Your goal in string sizing, therefore, is to hit the sweet spot inside the inverter's range, normally between the halfway point and two-thirds of the way to the upper limit, or the max voltage. Naturally, you don't want to get too close to the edge because that can tax the inverter's circuitry over the long haul.
Ideally, for a PV system of 3-5 kilowatts and the range just cited, a module series voltage between 250 and 400 volts should make an inverter hum like a kitten for ten years or more. But picking an inverter and string size is not the walk in the park that many PV students and new contractors initially think. Here's why you should pay close attention to voltage when deciding on a string size:
Fortunately, most inverter manufacturers provide an online sizing tool to help you get the job of string and inverter sizing done correctly. The free apps are a nice gesture, and you should use them if you don't speak directly with an experienced salesperson or technician. Just remember, all these tools come with the disclaimer that any mistake in sizing is your problem, not the manufacturer's. That's why you or your installer should read the spec sheets carefully and do at least some of the calculations on your own. This way, you can sleep tight knowing you've got the right array configuration and inverter size for your new PV system, even on the hottest and coldest days of the year. Also, a building inspector or permit application reviewer may ask to see some of these figures, especially the cold day voltage.
You can use the links provided on our Calculators page to access the manufacturer sizing tools. For more on choosing the right size of inverter, read this article from HomePower.com, and this sizing guide provided by SolarPro magazine .
So let's walk through the steps a PV designer or contractor takes in choosing and inverter and module string size. We'll use a sample 3.5 K array of 14 Sharp residential modules, the same model we used in the last step. Since the modules are each rated for 235 watts, the actually output is 3,290 STC watts under optimum conditions. We can set aside the derate factor that was used in the array sizing step, since that included shading and other conditions not generally applicable to string and inverter sizing. The other specs for the Sharp module are listed below:
We'll pair this module with a Fronius IG4000 grid-tied inverter that's rated to produce 4000 AC Watts. Here are its spec sheet details:
Notice the spec near the top, "Max. DC input voltage." It turns out this value, 500V, is 50 volts higher than the range of 150-450V provided in the previous spec. That translates to extra breathing room when you perform your cold day max voltage calculation below. Unfortunately, there's no spec on the sheet for Start-up voltage. You really shouldn't assume that any inverter will kick on in the morning as soon as it sees the low end of the operating range. More often than not, the start-up voltage is a bit higher. (It's a good idea to contact a company sales rep and ask for the actual value.)
The first set of equations identify the array wattage, voltage and current that the inverter will see when the PV system is operating under optimum conditions.
Array Watts = #Modules X Module STC Watts X .95 X Inverter Efficiency
Array Watts = #Modules X Module PTC Watts X Inverter Efficiency
On the Sharp spec sheet, the module's STC or nameplate watts are referred to as "Maximum Power". Hence, the first equation includes a modest derate of .95 to account for that. (Some designers will drop the factor to .90.)
Alternatively, if your module spec sheet provides a PTC watt rating (Practical Test Conditions), you can use that value and skip the .95 derate value altogether, as shown in the second equation. As for the Inverter Efficiency, this should always be listed on the inverter spec sheet, normally a value between 92% to 97%. Use the decimal version (e.g. ".96") when performing calculations.
Taking the first equation first, our sample 14-module array and IG4000 inverter produces the following math: 235 X .95 X 95.2 = 2975 watts. Since the result puts us under 3000 watts, it's possible to use an IG3000 model instead. However, since the inverter spec sheet indicates that 3,000 array watts will work for the IG 4000, and it would be nice to expand the array in the future, we'll stick with this inverter. If you check out its specs here, you'll see that the IG3000 has a peak power of 3300 watts, a lower maximum current (13.6 A), and exactly the same voltage range. So for a couple hundred dollars more, the IG 4000 seems like the smarter option. For now, at least...
System Voltage = String Size X Module Power Voltage (Vmp)
The Sharp module spec sheet lists the power voltage at 29.3 volts, so if you had one string of 14 modules, the array voltage would be 14 X 29.3 volts, which equals 410 volts. If you use two strings instead, the voltage is cut in half: 7 X 29.3 volts, which equals 205 volts. Since 205V is a relatively low voltage, the single string option is the preferable one. But while 410 volts is well below the 500-volt maximum list on the inverter spec sheet, we'll have to see what happens to the numbers in cold and hot weather.
System Current = #Strings X Module Current (Isc or Imp)
This calculation must be checked against the "Maximum AC Current" value listed on the spec sheet. If the spec value is exceeded, you should use fewer strings. You'll have to decide whether to use the short circuit or maximum power current for this equation. It's recommended that you use Isc if that spec is provided, since it provides a safety margin. So for one string, the math is 1 X 8.60, which equals 8.60 amps. For two strings, the amount doubles to 17.2 amps. This is a half amp higher than the maximum allowed by the inverter, 16.7 amps. which is a little irritating. If we use the Imp value of 8.02, then two strings would produce 16.04 amps. In a situation like this, you can always contact the manufacturer and ask for guidance. For now, we'll give the 2-string scenario a go and move on to the temperature equations.
Coldest Day Calculation
While it may sound counter-intutive, a cold ambient temperature raises the voltage of a PV array, regardless of the amount of sunlight shining on the modules. This issue is addressed in Article 690.7 of the NEC. Since solar designers must take into acccount the worst case scenario, they need to calculate the highest potential voltage on the coldest day of the century. The NEC provides a chart with voltage correction factors you can use to crunch the numbers for your city.
NEC Table 690.7
Luckily, for all but a few place in the United States, the correction factor is either 1.13 or 1.17. This corresponds to a low temperature between 31° and -4° Fahrenheit. In a few places, of course, it can get colder than that. At any rate, here's the formula to use It will determine the maximum voltage (Vmax) your inverter should ever see:
Vmax = Voc X #modules per string X low-temp voltage correction factor
Voc represents open-circuit voltage, which is listed on the module spec sheet. "Open circuit" theoretically means the highest voltage possible, which is not the same as rated voltage or power voltage. It's used for the cold day calculation to provide a greater margin of safety. Using the Sharp module and one strings of 14 modules mentioned above, the math looks like this: Vmax = 37.2 X 14 X 1.13, which is 588.5 volts. (So much for staying under the inverter's 500V max...) If two strings are used instead of one, the math is Vmax = 37.2 X 7 X 1.13, which is 294.25 volts.
Note: Vmax is not to be confused with Vmp, which is the normal optimum voltage your array will be delivering during peak sun hours each day. Vmax is the worst case scenario voltage.
In the meantime, there's a second method for computing your coldest day voltage calculation. This one uses the voltage temperature coefficient on the module spec sheet. According to the NEC, when a voltage coefficient spec is provided, you're supposed to use it in place of the chart above. A "coefficient" is similar to a correction or derate factor. You'll find several different coefficient values on a spec sheet, each representing a different unit of measure. Make sure you grab the right value, which depends on the equation in front of you.
For a cold day calculation, we want the coefficient listed for our Sharp module's Voc. It's 0.36% per degree Celsius. However, before you can use it, you have to determine the difference between your city's coldest recorded temperature, and the standard temperature (aka STC temp) that's used to generate module ratings, which is 25° Celsius. If our coldest day temperature is 14° Fahrenheit (-10 ° C), then you'll subtract the STC temperature from that. Thus:
Step 1: Temp Difference = Cold Temp - STC temp
In our example, -10 ° C - 25 ° C = -35 ° C. (Incidentally, to enter a negative number on some calculators, you should first type in the numeric part, then press the +/- key.) The next step determines a derate factor called the voltage percentage rise. According to the Sharp spec sheet, the temperature coefficient for short-circuit voltage (Voc) is -0.36, which now comes into play:
Step 2: Voltage Percentage Rise = Temp Difference X Voltage Coefficient (Voc)
The math translates to -35 ° C X -0.36 = 12.6% rise. Now that we have that value determined, it brings us to the final equation, which determines the maximum possible voltage on the coldest day of the year, Vmax:
Step 3: Vmax = Voc X #modules in series X (1 + Voltage Percentage Rise)
For one module string, the math is 37.2 volts X 14 modules X 1.126 = 586.42 volts. For two strings, it's 37.2 volts X 7 modules X 1.126 = 293.2 volts. These anwers are very close to the 588.5 and 294.25 volts calculated earlier using the NEC Table 690.7 correction factor method.
Inverter Sizing - Hottest Day Calculation
On the other extreme of worst case scenario, it's important to quantify how much the ambient heat arround an array will lower its voltage. Although it won't hurt the inverter, decreased voltage due to heat can cause the component to shut down at the height of summer, since the voltage value has dropped below the inverter's range.
To find out how much voltage will be lost on hot days, designers perform a slighly different calculation to the one for cold weather. Instead of open-circuit voltage, it's the power or operating voltage spec that's used. This also means a different temperature co-efficient, one that applies to power voltage or (if there's no coefficient listed Vmp), then the coefficient provided for power, or Pmp .
As for determing your highest local temperature, it's recommended that you use the ASHRAE 2% critical design temp. The acronym stands for the American Society of Heating, Refrigerating and Air Conditioning Engineers, which established these figures of the United States. But the best place to look up the temp for your region is the website Solar ABC's, The site provides a lookup feature based on your zip code. In addition, there's an assortment of values to choose one, especially including the likelihood that the array wiring will be running off the roof inside conduit. (This circumstance generates a higher ambient temperature.) Thus, based on the location and mounting of your array, pick the value that's the most applicable.
Here's an example of how to perform this math: For an array in Sacramento that's mounted six inches off the roof, the 2% high temp would be about 137 ° F, or 58 ° C. Meanwhile, the power voltage for the Sharp module is 29.3 volts, and the coefficient for power is 0.485 per degree Celsius. So for our sample array, here are the equations for the Hot Day Calculation:
Step 1: Temp Difference = STC temp - High Temp
So 25 ° - 58 ° = -33 °.
Step 2: Voltage Percentage Decrease = Temp Difference X Vmp (or Pmp) Coefficient
Thus, -33 ° X -.485 %/ ° C = 16%. (Remember to use Vmp.) Now you can work out the lowest possible voltage (Vmin) your array might experience due to heat. Be sure to convert the percentage to a decimal by dividing it by 100 , thus 16/100 = 0.16. Then you're ready for this last equation:
Step 3: Vmin = Vmp X #modules in series X (1 - Voltage Percentage Decrease)
The math looks like this: Vmin = 29.3 X 14 X (1 - 0.16) = 344.57 volts. For the scenario using two strings, Vmin = 29.3 X 7 X (1 - 0.16) = 172.28 volts Notice that unlike the Cold Temp calculation, you subtract the decrease percentage rather than add it.
To view a worksheet with module/inverter sizing for the scenario above, click here.
Now you can check the voltage window for the Fronius IG4000, which is 150-450 volts, with a maximum voltage of 500 volts and no listed Startup Voltage. Obviously, one string won't work because the series voltage for 14 modules will exceed the inverter's voltage max in extremely cold weather. Two strings, on the other hand, will do the job, because the cold day voltage here is only 294 volts, well below the 500V max, and its hot day minimum of 172 volts will keep it in the inverter's operating range. But the two-string operating voltage of 205V is pretty low for the inverter's 150-450 volt range, especially if the StartUp voltage (which we don't know) is higher than 150 volts. It's possible that this inverter may only operate for a few hours per day, even in summertime, because the array's operating voltage is low and the hot day voltage is really low. And that's not all the bad news, because you can expect the voltage to tank even further under the following conditions:
So while this module size and configuration might barely squeak by in the math marathon, a serious designer would probably find the low voltage scenario unacceptable. To try and get it higher without exceed the inverter max on a cold day, any of the following solutions might help out:
It's also not always possible to keep series strings even, due to shading, available space or other reasons. In some cases, you may even need to position your strings at different azimuth orientations or altitude angles relative to the sun. Since that affects the fluctuating voltage, it can complicate sizing calculations further. Regardless, you can still make such a configuration work by keeping each array or string separate from the others. Some types of inverters allow you to plug in four or more separate circuits, so the electrical characteristics of each string are isolated from the others.
When you can't match your series strings, or have to use more than one array, you have three options:
Some of these options will cost more money in equipment and/or wiring. The most popular solution nowadays, however, is to attach a microinverter on each module. As explained in our tutorial section on inverters, this device transforms DC to AC right there in the array and performs the MPPT function as well. A microinvert costs $175-$200 per module to get the job done, so for a 14-module array, expect to pay up to $2,800, as opposed to $1,750 for one central inverter. Also gaining traction in the United States is the transformerless inverter, which is widely used in Europe and more efficient in delivering energy . It's als many pounds lighter, since it dispenses with the heavy copper windings. However, a transformerless inverter requires ungrounded conductors, so the installer must implement special code requirements when wiring the PV system.
To remedy the voltage range situation for our sample circuit, let's look at the spec sheet for several SMA Sunny Boy transformerless inverters to see if one of these products will work:
Notice the Max DC voltage for all models is 600V. This should be enough to handle the max cold day calculation of 588 volts for a single string of 14 modules, but the slim 12-volt margin may be flirting with danger. The start up voltage for 240V models, meanwhile, is 150 volts. That's the same as the low-range voltage for the Fronius model above. Again, if you wanted to use two strings of 7 modules and a normal operating voltage of 205 volts, this voltage may be too low.
Incidentally, a slash mark ( / ) on the spec sheet indicates two different specs in one column. The value on the left side applies to 208V models, and the value to the right of the slash applies to 240V models. A 208V inverter represents the standard AC operating voltage for 3-phase commercial and industrial customers. Single-phase 240V is what residential customers receive from their utility company. Therefore, you can only buy a 240V model.
Incidentaly, these Sunny Boy TL inverters offer the added perk of a plug-in outlet on the unit. This you can use in the event of a grid power outage. When the sun is shining, you'll have 1500 watts available to power critical loads, at least until the utility restores power. No battery bank is needed.
SMA also sells a data monitoring system that works with all their transformerless models.
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