Chapter 11

Sizing a Grid-Direct System

IN THIS CHAPTER

Bullet Understanding the role budget and space play in limiting an array’s size

Bullet Evaluating energy production and consumption

Bullet Calculating power values and temperature-adjusted voltages

Bullet Checking the maximum current input as the final piece of the puzzle

So you’ve used the information in Chapter 2 to determine that a grid-direct system is the best fit for your client, and you’ve familiarized yourself with the elements of such a system in Part 2. Now the fun really starts — it’s time to size the system! By that, I mean it’s time to match the array to the customer’s needs and to the inverter and associated safety equipment.

When you set off on the task of sizing a grid-direct PV system you need to account for many variables. As you find out in this chapter, the overall process results in a PV system that’s based on the client’s budget, the available area, the annual energy production and consumption at the site, and your choice of materials for the job (notably, the array and the inverter).

Remember In comparison to stand-alone PV systems (which I show you how to size in Chapter 12), grid-direct sizing is much less complicated. You also don’t have to make nearly as many assumptions and leaps of faith. Because the utility grid is always (well, almost always) present, and because a grid-direct inverter operates in parallel with the utility, you don’t have to size the array to meet electrical consumption at any given time. If the loads within the building require more power than the array can provide, the utility can supply the difference. And even though the PV system goes down when the utility goes down, the system automatically restarts when the grid comes back to life. A grid-direct system, therefore, should be viewed as a way to supplement (rather than replace) the utility grid.

Note: Sizing a grid-direct PV system requires you to know a few temperatures and be able to make calculations with those temperatures. The calculations get pretty messy when you try throwing Fahrenheit into the mix, which is why all the temperature-related calculations presented in this chapter use Celsius.

First Things First: Evaluating the Budget and the Available Array Area

Whenever you’re looking to install a grid-direct PV system, the overall system size will generally be limited by one or more factors, but the first two you need to consider are your client’s budget and the amount of space available for the PV array. People with unlimited budgets and unlimited space for a PV system are out there, but those clients are few and far between.

Remember Before you establish anything else, find out what your client’s budget is. Of course, everyone would love to offset 100 percent of their electrical energy consumption with solar power, but most people simply can’t do that. So before you spend too much time sizing the best-possible system for your client’s desires, find out what his budgetary realities are first and work from there. By establishing your client’s budget in the beginning of the process, you can prevent yourself from wasting a lot of time and energy designing a system that never has a chance of being installed.

The next limitation to consider is the area available for mounting the array. For the majority of grid-direct PV systems, this area is the roof of the house or business. (Other options include the ground outside of a building or the top of a pole.) To determine the amount of space available for the system, you need to perform a site survey; Chapter 5 goes over the site-survey process and the major considerations, such as shading issues and various roof obstacles, you need to make when evaluating where to place the array.

After you conduct a site survey, you can calculate the available square footage by measuring the length and width of the array area and multiplying those two values together. You can then take that area and multiply it by the module’s power density, or the number of watts per square foot for the module you’re thinking about using based on the client’s budget and what’s available from your suppliers (Chapter 6 has details on power density and different types of modules). The resulting number gives you an idea of the total power in watts (W) that can be placed in the available area.

Warning I recommend you don’t attempt to use every last square inch of a roof surface when installing an array. Squeezing a few more modules up there whenever possible is tempting, but don’t do it! Cramming the roof will not only make the installation more difficult but it’ll also make it tricky (and possibly downright dangerous) to try and maneuver on the roof when the system needs maintenance. Also, wind loading at the edge of the roof is much greater (requiring more mechanical support), and some jurisdictions have requirements based on access for firefighters and other safety personnel. (The same goes for array sites other than roofs — when it comes to placing PV modules in a given spot, less is definitely more.)

Be sure to consider “dead” spaces (the areas around the array that can’t be used due to shading or the need to maintain sufficient paths for access) as well as the small spaces between the modules when determining the overall area available for the PV array. Suddenly that decent-sized roof may be very limited to account for all of these issues. To account for dead spaces, simply subtract the area needed for the access paths from the overall area and use one of the shading-analysis tools in Chapter 5 to determine the area that’s unavailable due to shading. By taking these areas out of the picture, you can establish a realistic idea of the total power rating of the potential array.

Remember The size of the PV array may change over the course of your design process. For example, you may estimate that you can fit 24 modules on a roof, but as you progress, you may realize that the string configuration requirements (covered later in this chapter) won’t allow that many modules. Or perhaps you have to consider a different module type entirely. Consider your initial estimate of the available space a starting point and use it only for reference.

Estimating the Site’s Annual Energy Production

When you know roughly how much space you have for the array, you can begin to estimate the annual energy production for that site. This estimate is helpful to have when designing grid-direct PV systems because you need to evaluate the type of agreement the utility will be willing to enter into. (I review some common agreements and how they affect your decision-making process in the later “Looking at contract options with the utility” section.)

You can estimate the annual energy production in a variety of ways. For larger commercial systems or in situations where advanced techniques are required, you can use modeling programs to evaluate multiple scenarios and change parameters to estimate the energy production (PV*Sol and PVsyst are two popular programs). For residential and small commercial systems, one of the best ways to estimate energy production is to use the PV Watts tool (available at www.nrel.gov/rredc/pvwatts).

PV Watts is a free Web-based tool provided by the National Renewable Energy Laboratory. Many people in the solar industry use PV Watts on a regular basis. To use it correctly, you need to know

  • The amount of power the PV array you're thinking of using can potentially produce (in kilowatts [kW])
  • The tilt, orientation, and shading effects of the array (see Chapter 5)
  • Some basic information about the equipment you’re thinking about using (the PV Watts program makes some good assumptions about the performance of the equipment)

The PV Watts tool takes the information you enter and creates a total solar resource factor (TSRF), the percentage of the solar resource available for that specific site in relation to a perfectly oriented and shade-free array, as I describe in Chapter 5. It then provides a simple report that estimates monthly and annual energy production values measured in kilowatt-hours (kWh). It also calculates the dollar value for that energy, which is nice because this is a value everyone can relate too (unlike peak sun hours or system efficiencies).

Tip I suggest you use the first version of the PV Watts calculator until you become familiar with the program. Then you can move on to Version 2 if you like. (I rarely use Version 2 because Version 1 gets me all the information I generally need.) Either way, PV Watts is relatively self-explanatory; it even has helpful links for commonly asked questions and ways to manipulate the program based on your needs.

Remember The annual energy production you calculate at this point is only an estimate. Don’t treat it (or let your client treat it) as the promised production value. The energy produced from the array will be affected by installation methods to an extent, but ultimately, the available solar resource dictates how much energy is produced. So if your client experiences an abnormally cloudy or sunny season, the energy-production number you gave him will be off.

Sizing the Array to Meet Your Client’s Energy Consumption

I promise that if you’re in the PV industry for more than two weeks, you’ll be asked this question before you finish telling someone what you do for a living: “How big of a PV array do I need to power my average-size house?” My favorite response: “Gosh, I’m not sure. What color is your house?”

Neither question makes much sense, does it? Sure, I can figure out what the average American household’s energy consumption was two years ago, but that number rarely means much to anyone individually. The energy consumption of an individual, family, or business has little to do with the size of a house or commercial building and more to do with people’s lifestyles. Does your client have all-electric heating? How does he heat his water? Does he have an electric car hidden in the garage, just charging away? Is his business home to a welding shop or a number of refrigerators?

After you establish the maximum array size and estimate the site’s annual energy production, you need to look at some utility bills (preferably all 12 bills from the previous year) to get a sense of how much energy the house or business consumes and what the impact of a rooftop or yard-based PV system will be. You also want to guarantee that the energy the system produces provides the maximum financial benefit for your client based on the agreement with the utility. I explain what you need to know in this section.

Determining annual energy consumption

Grid-direct PV systems have the advantage of built-in energy record keeping from the utility provider. To determine the annual energy consumption for the household or business in question, simply collect the last 12 months’ worth of bills from the utility. This snapshot will give you a great idea of the amount of energy consumed annually (so long as you look at the total kilowatt-hours consumed). Of course, if you have access to more than one year’s worth of utility bills, go ahead and take a look at them all. The extra information can only add to your knowledge of your customer’s energy habits.

Tip One thing to ask is whether there are any recent changes to the electrical consumption. For example, did your client install a solar hot-water system a few months ago? Or did he just put an electric water heater in the master bedroom suite? Such changes affect future electrical consumption, which is why you should always base your estimates on the most recent information.

Note: If you can’t obtain the energy records for the client’s current home or past home because the current electrical consumption is dramatically different, you may have to estimate the annual energy consumption by using the same process I describe in Chapter 12 for sizing battery-based systems.

Looking at contract options with the utility

Your client has a few options for entering into a contract with the utility, but the most common approach is net metering. In a net-metering agreement, the utility agrees to “pay” your client the exact amount it charges him for energy — given that your client doesn’t produce more energy than he uses in a given time period (typically a year). The exact restrictions are included in the interconnection agreement provided by the utility. Usually, if a PV user produces more energy than he consumes in a year under a net-metering agreement, the utility can say thanks very much for the extra energy and move on. The PV user (in this case, your client) doesn’t get any extra accolades or cash for producing more energy than he consumes.

Remember Many utilities allow customers to essentially bank up their kilowatt-hours when they produce more than they consume — kind of like when your extra calling-plan minutes roll over. At some point, though, the utility will start over; this is known as the true-up period. Some utilities make this true-up period occur monthly, which means your client doesn’t get the full benefit of the energy produced in any month that he doesn’t use that same amount of energy. As the installer and designer, be sure to confirm with the utility how its true-up period works before getting too far into the design process.

Another component of net metering to consider is the time-of-use metering option (TOU). With TOU, the utility charges your client different rates based on the time of day he uses energy. Typically, TOU rates are highest during the middle of the day when overall consumption peaks. This means that for a PV system installed under a net-metering agreement that uses TOU, the times of the day when the PV array is producing the greatest amount of energy correspond to the times when the utility rates are at their highest. If your client can maximize PV production and minimize consumption to correspond to peak energy rates, say he’s at work all day with as many appliances powered down as possible, the overall effect can be beneficial financially.

The other contracting system that may be available is the feed-in tariff system (FIT). With a FIT contract, your client doesn’t really care about annual energy consumption because there’s no direct relationship between his PV array size and his energy consumption due to the fact that he receives more money per kilowatt-hour generated from the PV array than he’s charged from the utility. So if your client signs a FIT contract with the utility, you want to design the PV system so it maximizes the amount of energy the array produces regardless of your client’s energy appetite.

Note: Regardless of the utility contract, I encourage you to advise your client to conserve energy as much as possible even though he doesn’t really have to worry about comparing his energy consumption to the size of the array. Energy conservation should be the mantra of anyone installing a PV system. Besides, conserving energy helps your client financially — the less energy he consumes, the less he has to buy.

Using consumption and contract options to select an array’s needed power value

At this point, you’ve collected data about how much energy your client consumes and established a starting point for the total amount of energy the proposed PV array will produce annually. Now you can begin comparing the two numbers and working with your client to establish the best option based on the utility agreement he has to enter into.

If your client consumes less energy annually than the PV array will likely produce, he’s in great shape. He can either reduce the overall wattage of the array or be prepared to overproduce annually and not receive full financial credit for every kilowatt-hour produced by his system.

A more likely scenario is that the energy produced by the PV array is less than the energy consumption of the people in the building. In this case, you can work with your client to help him reduce his overall energy consumption (common techniques for this include changing to compact fluorescent light bulbs and installing better insulation). You can then compare the estimated production to the assumed reduced energy consumption and establish the percentage of electrical energy that will be provided by solar power and the associated dollar savings. For example, if your client’s PV system can produce 2,000 kWh but the client consumes 5,000 kWh annually, the PV array will offset 40 percent of his total energy consumption.

Remember Keep the true-up period that the utility uses in mind (see the preceding section for the scoop on this). If the utility looks at the values monthly, you need to evaluate the production and consumption ratio on a monthly, rather than annual, basis. Make sure your client is aware of how the interconnection agreement works so he isn’t surprised if he doesn’t get full credit from the utility because he produced twice as much energy as he consumed.

Applying the right consumption numbers and contract options may seem like a lot of upfront work, but after you go through the process a few times, you can establish some good working numbers based on the equipment you like to use, local utility requirements, and the site-specific information you gather. Having these numbers in mind helps you finalize the proposed array’s design, including its size.

Getting Ready to Match an Inverter to an Array

After you nail down the right PV array wattage for a client’s grid-direct system, you’re ready to establish the relationship between the inverter and the PV array. To do so, plan to look at all the electrical characteristics — power, voltage, and current.

Tip I suggest looking at power, voltage, and current in that order so you can narrow down your inverter choices with each step. Another benefit to following this sequence? The final check, current levels, typically becomes a simple verification.

Remember Every inverter manufacturer has online PV sizing calculators to help you with matching an inverter to a PV array. Even though I use them on a regular basis, I do so as a check of my calculations, not the source of my calculations. As a PV system designer and installer, it’s vital that you perform your own calculations instead of relying on the online calculators. Here’s why:

  • The potential for error: The data plugged into the online calculators is entered by humans who’re fully capable of making mistakes. Trust me; I’ve seen some of these mistakes firsthand.
  • The inevitable disclaimer: Every inverter manufacturer requires you to accept a disclaimer before you can access its tool. In essence, the disclaimers all say the same thing: The information here may or may not be accurate, and if you use the tool, we (the manufacturer) aren’t responsible for any problems.
  • The National Electrical Code® (NEC®): One section of the NEC® says that “you shall do the calculations.” At some point, the local electrical inspector may ask you to show him these calculations. If you can’t, you run the risk of having your system fail inspection. (Shall in NEC® terms is pretty strong language. It’s equivalent to the sideways look you used to get from mom and grandma — something not worth messing with.)

Remember Occasionally, you may want (or need) to use multiple inverters in a system. In grid-direct systems, the most common reason for having multiple inverters is that the desired PV array wattage is greater than a single inverter can handle. Many of today’s inverters are rated at less than 10 kW, but fewer options exist between 10 kW and 30 kW, so if the PV array wattage falls into this range, you may need to design for multiple inverters. Another popular reason for having more than one inverter in a grid-direct system is that sometimes the PV modules are installed in different locations or sometimes they’re all on a roof but pointing in different directions.

Matching Power Values for an Array and an Inverter

As I note in Chapter 9, all inverters are rated by their maximum continuous power output, which is measured in watts or kilowatts. (More often than not, this number is incorporated into the inverter’s model number, giving you a quick idea of the inverter’s rating.) This value is the AC power output. Inverters actually limit their power output, so you can use this value to figure out the maximum power input coming into the inverter from the PV array.

When you look at PV module ratings, you find that the power output ratings are based on standard test conditions (STC) where the cell temperature is 25 degrees Celsius and the intensity of the sun is equal to 1,000 W/m2. PV modules rarely operate in these conditions due to the motion of the sun across the sky and increased PV operating temperatures (see Chapter 6). So, the power output from the array (in other words, the power input coming into the inverter) is typically considerably less than the rated values.

Tip On top of that, both the inverter and the array (along with all the other equipment in a grid-direct system) have efficiency losses that must be taken into account. Fortunately, you can quickly estimate all of these system inefficiencies by adopting the industry standard that any PV system will operate at approximately 80 percent overall system efficiency, which means that about 80 percent of the array’s rated value will be “processed” by the inverter and pushed on to the load center. Even though a PV system as a whole can be more efficient or less efficient at times, approximately 80 percent is a good industry standard to use when relating the PV array output power to the inverter’s output power.

So how do you get started? Well, because you’ve already established the approximate wattage of the PV array you want to install (if you haven’t, refer to the earlier “Sizing the Array to Meet Your Client’s Energy Consumption” section), you can now take that array wattage and relate it to the inverter’s rated output power. Because inverters are limited in the amount of power they can process, it doesn’t make a lot of sense to try and make an inverter work any harder than it can. You therefore need to put enough, but not too much, PV power into the inverter in order to have the inverter efficiently produce AC power on the output side.

The industry standard for turning PV-rated DC power into AC output power is 80 percent. You can use this value to help determine the size of the inverter based on the array you’re working with. For example, if you go through the process I describe in the beginning of this chapter and decide that your client is a good candidate for a 5 kW array, you can use that array size to narrow down your inverter choices. Because the overall system efficiency will be around 80 percent, you can multiply the 5 kW array size by the 80-percent efficiency rating to calculate the minimum inverter rating.

5 kW array × 80% efficiency = 4 kW minimum inverter rating

This calculation tells you that for a 5 kW array, you should have at least a 4 kW inverter. This inverter-sizing methodology is within the specifications of most inverters. Of course, you should confirm with the inverter’s manufacturer that it supports this sizing method.

Remember To find the maximum rated input power from the PV array, refer to the inverter’s specification (spec) sheet. You can put less power on an inverter than what the calculated maximum array size suggests, but you should put on more only in very rare circumstances (and only after careful consideration of the effects). If you were to put on more power, the inverter would limit the output to its rated value, so your client wouldn’t get any benefit from the extra modules anyway.

Believe it or not, I encourage you to put fewer modules on inverters than what they can handle. If you think about the last example, if you went ahead and put 5,000 W on that 4,000 W inverter, you’d be limiting the overall system efficiency to 80 percent. On days when the efficiencies are higher than normal (say, a cool day with high irradiance conditions), the inverter would have to limit its output, resulting in a lost opportunity. Also, I don’t like to see inverters pushed so hard for long-term reliability. An inverter’s internal temperature rises as the number of watts out of the inverter rises. As with all electronics, the hotter an inverter runs, the shorter its life will be.

Tip When I design a PV system, one of my first goals is to multiply the PV array’s power value by 87 percent rather than the 80-percent maximum value. Doing so gives me a larger inverter wattage that’s closer to the PV array’s wattage. By keeping the PV array size closer to the inverter’s rating, you keep the inverter cooler, increase its life, and allow the array to operate at maximum efficiency values at all times.

So in the earlier example, the minimum-size inverter for a 5,000 W array would be:

5,000 W × 87% = 5,000 W × 0.87 = 4,350 W

However, a 4,350 W inverter isn’t an option (because inverters come in nice round numbers like 4 kW or 4.5 kW), which means you need to look for an inverter that’s close to this value. You may be able to find a 4,500 W inverter, or you may need to jump all the way up to a 5,000 W inverter. (Note that this efficiency level allows the system to operate at approximately 87 percent, a value that won’t limit the array’s power output. The real world may of course interfere, but the 87-percent efficiency level is still a solid starting point.)

Coming Up with the Right Voltage Values for Your Array and Inverter

After you know the necessary power values for the PV array and the inverter, you can look at operating voltages in real-world conditions to further narrow your search for an inverter.

  • On the inverter’s DC side (which is connected to the array), there’s a minimum number of volts required to allow the inverter to produce the maximum amount of power from the array and a maximum voltage that can be applied without damaging the inverter.
  • On the inverter’s AC side (which is connected to the loads), a minimum and maximum voltage value is dictated by testing requirements and anti-islanding values (see Chapter 9 for details on anti-islanding).

Remember The minimum to maximum voltage values on both the AC and DC sides define the inverter’s two voltage windows (a voltage window is a range of allowed voltages). If the voltage values fall outside of these windows, the inverter won’t work; in the case of too much DC voltage, the inverter can actually be damaged. Keeping the voltages inside these windows is an important design consideration. After all, it’s your job to keep the PV array operating and maximizing your client’s investment.

To keep the voltage values within the inverter’s voltage window on the DC side, you must define the adjusted voltage values of the PV array and the DC voltage window based on temperature. In Chapter 6, I explain how PV modules are affected by temperature, so head there if you need to see those relationships. (You also need to remember the relationships between open circuit voltage, Voc, and maximum power voltage, Vmp, for this portion of the design; I cover these in Chapter 6 as well.) For the inverter’s AC voltage, you must choose an inverter that matches the available AC voltages. I explain what you need to know in the sections that follow.

Establishing the inverter’s AC voltage

On the AC side, you need to determine the nominal AC voltage that the utility power is operating at (and which you’ll be interconnecting to) and make sure you specify (choose) an inverter that operates at that same voltage. A qualified person (such as an electrician), should verify this voltage, preferably during your initial site survey (covered in Chapter 5).

Tip The nominal AC voltage for residential systems is usually 120/240 VAC. For commercial systems it’s either 120/208 VAC or 277/480 VAC. (Note: You should still check with the individual utility, just to be safe.)

Remember Many inverters allow you to field select (change the voltage settings on-site) the nominal AC voltage, but not all do. For those that operate at a specific nominal voltage, you need to make sure you specify the correct inverter for the voltage present. For example, if you’re installing an inverter at a residential location where the voltage is 120/240 VAC, you can’t install an inverter that’s meant for a 120/208 VAC system. You can’t mix up the inverters and expect the inverter to ever work.

Completing this step of matching the inverter to the AC voltage present helps reduce the pool of eligible inverters even further. Now you can evaluate your PV array in relation to very specific models of inverters and the DC requirements for those units.

Defining the inverter’s DC voltage window

In Chapter 9, I introduce you to the concept of an inverter’s voltage window. This window consists of a maximum input voltage that you must stay under if you want to avoid damaging the inverter and a minimum voltage you must stay above to keep the inverter operating at the array’s maximum power point. As a PV system designer, you need to identify these values from a spec sheet and make sure the array can operate within this window throughout the year. If you allow the array to move outside this window, you risk damaging the inverter or shutting down the system for the day.

As you can see in Figure 11-1, the DC voltage window can be viewed in relation to the PV array in an IV curve (refer to Chapter 6 for an explanation of these curves). The goal is to keep the Voc portion of the IV curve below the maximum inverter voltage value and the Vmp portion within the operating voltage range. Each of the voltages gets adjusted based on temperature, so this window can actually become very narrow very quickly.

Illustration depicting a DC voltage window in relation to the PV array in an IV curve In the MPPT voltage range.

FIGURE 11-1: The DC voltage window in an IV curve.

Remember The minimum and maximum DC voltage values dictate the number of modules that can be placed in any string that’s connected to an inverter. Typically, the calculations I show you in the next two sections result in multiple string lengths — different numbers of modules you can place in series for proper inverter operation.

Warning Most inverters have just a single maximum power point tracker installed. Unless you’re using an inverter that has multiple built-in maximum power point trackers, you must keep the strings of PV modules equal in size. Therefore, if you calculate that an inverter can accept multiple strings of 11 modules or strings of 12 modules, all the strings must be either 11 or 12 modules in length. In other words, the string lengths must remain equal, or else the inverter can’t operate correctly.

Calculating the modules’ maximum DC voltage contribution

When working with the DC side of an inverter, I like to consider the inverter’s maximum DC voltage input first because providing too much voltage to the inverter can cause damage. You see, all inverters have capacitors inside them that act as shock absorbers. They accept the array’s power and are able to smooth out any bumps along the way, which means the capacitors are one of the very first things connected to the PV array. If too much voltage is connected to these capacitors, they’ll eventually become compromised and fail, meaning the inverter can’t operate.

Warning You should also know that all inverters record the maximum voltage values ever seen by the inverter. So if you design or install your client’s system incorrectly and apply too much voltage to the inverter, that information will be recorded. If your client sends the inverter in for a warranty repair, the manufacturer will check the stored data, see that the voltage was too high, and void your client’s warranty. This is an expensive mistake that can be easily avoided in both the design and installation processes.

Remember As I explain in Chapter 6, as the temperature decreases, a PV module’s voltage actually increases (voltage and temperature therefore have an inverse relationship). To make sure an array’s voltage never exceeds the inverter’s input value, you need to adjust the modules’ STC open circuit voltage value (Voc) for cold temperatures; this value is reported on spec sheets.

The most common way to approach this problem is to look at the record cold temperature wherever the array is to be placed and adjust the modules’ open circuit voltage based on that temperature. By using the record cold temperature, you’re accounting for the fact that it takes very little irradiance to produce voltage from a module (irradiance is the intensity of the solar radiation striking the earth). And because current won’t be flowing immediately (because the irradiance value is very small when the sun breaks over the horizon), the inverter will be connected to this initial high voltage.

In reality, this is a conservative approach because, as I note in Chapter 6, a PV module reaches approximately 90 percent of its full voltage at 200 W/m2. By the time the module is producing full voltage, the array has sufficient irradiance to produce current, and the voltage will automatically drop to maximum power voltage values. The exact values are difficult to calculate accurately, so in all the calculations I show you in the following sections, I use the record cold temperatures and say that the voltage will jump to full open circuit voltage as soon as the sun breaks over the horizon each morning.

With that in mind, you’re ready to calculate a PV module’s adjusted open circuit voltage based on temperature. First things first: Keep the big picture in mind. You must determine the maximum voltage produced by the module based on the record cold temperatures and then use this adjusted voltage to determine the maximum number of modules you can place in a series string without exceeding the inverter manufacturer’s requirements for the maximum DC voltage input. I walk you through the process in the sections that follow.

Talking about temperature coefficients

In order to accurately calculate a PV module’s adjusted open circuit voltage, you need to know how the module’s manufacturer measures how its modules’ voltage values will react at temperatures less than and greater than the STC of 25 degrees Celsius. This number is known as a temperature coefficient, and it can be reported for both Voc and Vmp. (Note: The two different voltage values have two different temperature coefficients, but many PV module manufacturers report only the temperature coefficient for Voc. When I get to adjusting the Vmp in the later “Crunching the numbers” section, I show you how to estimate this rarely provided coefficient fairly accurately.)

Remember A typical Voc temperature coefficient value for crystalline modules is –0.35%/°C. This value indicates that for every degree change in the PV module’s temperature, the voltage changes by slightly more than a third of a percent. The negative number in the coefficient is very important; it shows the inverse relationship between temperature and voltage. (Keep in mind that –0.35%/°C is a close approximation for all crystalline PV modules, but it’s by no means an absolute value. As for thin film modules, the temperature coefficient values vary widely among technologies.)

According to STC, the base temperature for all PV modules is 25 degrees Celsius, so you have to look at the change in temperature as it relates to 25 degrees Celsius. For example, if the module is on a rooftop and the temperature at dawn is 15 degrees Celsius, the module’s voltage will be 10 degrees Celsius less than STC: 15°C – 25°C = –10°C (the negative sign indicates a temperature less than STC). So if you were asked what the percentage change in voltage is due to temperature, you could run the numbers like so:

–10°C × –0.35%/°C = +3.5%, or a rise of 3.5%

Another way you may see temperature coefficients reported is as a certain number of volts per degree Celsius. The exact number is dependent on the Voc for a particular module and should only be used for that module. To see what I mean, suppose an array was in a 15 degrees Celsius environment. If I told you that the temperature coefficient for the module was –0.158 V/°C, you could take that information and tell me how many volts the module would be reading off of the STC of 25 degrees Celsius:

  • 15°C – 25°C = –10°C

    –10°C × –0.158 V/°C = +1.58 V, or a rise of 1.58 V

Tip You can use either value reported as long as you use them correctly in the equations. However, the second temperature coefficient mentioned, the number of volts per degree, is generally easier to visualize because you can imagine the numbers of a meter changing.

Working the steps

Remember To determine the change in voltage due to temperature, you need to apply the temperature-adjustment equation. Here’s how to do just that:

  1. Collect the temperature coefficient for the PV module.

    You can find this information on the manufacturer-provided spec sheet that comes with the module.

  2. Collect the record cold temperature for your client’s location in degrees Celsius.

    The Web site weather.com is a great resource for this data.

  3. Calculate how many degrees Celsius less than STC the site will be on that record cold day.

  4. Multiply the temperature coefficient for the module by the number of degrees calculated in Step 3.

    The result of this equation is the change in voltage the module will produce.

  5. Add the number of volts calculated in Step 4 to the Voc for the module at STC.

    What you’re left with is the adjusted maximum module voltage based on the area’s record cold temperature.

To help you grow more at ease with the temperature-adjustment equation, try the following example. The PV module in question is a typical crystalline module located in a place that has a record cold temperature of –5° Celsius. The module specifications you need to collect are as follows:

  • Voc = 45.0 V
  • Temperature coefficient = –0.158 V/°C

At this point, you have all the information you need to determine the maximum voltage for this module at the area’s record cold temperature. Follow the previously outlined steps to find that

  1. The given temperature coefficient is –0.158 V/°C.
  2. The lowest recorded site temperature is –5°C.
  3. The number of degrees this temperature is from STC is –5°C – 25°C = –30°C.
  4. The voltage change is therefore –30°C × –0.158v/°C = +4.7 V.
  5. The adjusted module voltage is thus 45.0 V + 4.7 V = 49.7 V.

Tip But what if the module manufacturer gives you the temperature coefficient in the percent per degree Celsius? The easiest thing to do is convert that percentage into a number of volts per degree Celsius by multiplying the percent per degree Celsius by the open circuit voltage. For example, if the module you’re using is rated at 45 Voc and the temperature coefficient is given as –0.35%/°C:

45 Voc × –0.35%/°C = 45 Voc × –0.0035/°C = –0.158 Voc/°C

Remember The steps for working the temperature-adjustment equation can be used with any PV module so long as you find the temperature-adjustment data specific to the module manufacturer — the PV technology (crystalline versus thin film) doesn’t matter.

Warning The different PV module technologies all have their own temperature-adjustment factors, which means you can’t swap the values of a crystalline module for those of a thin film module just because the manufacturer doesn’t supply the information. If you do, you’ll wind up with false information that may cause you to design and install a PV system that’ll damage the inverter on the first cold morning.

Using NEC® info in a pinch

If you’re using a crystalline PV module, either single or multicrystalline, and the module manufacturer doesn’t supply a temperature coefficient, the NEC® states that you can use the values presented in Table 690.7 (see Figure 11-2). This table allows you to look up a multiplier based on a temperature range and use that to determine the temperature-adjusted voltage.

Tabular illustration presenting the voltage correction factors for both cyrstalline and multicrystalline silicon modules at ambient temperatures below 25 °C.

Reprinted with permission from NFPA 70®, National Electrical Code®, Copyright © 2007, National Fire Protection Association, Quincy, MA 02169. This reprinted material is not the complete and official position of the NFPA on the referenced subject, which is represented only by the standard in its entirety.

FIGURE 11-2: NEC® Table 690.7.

If, for example, you’re using a crystalline PV module with a Voc value of 45 V and the manufacturer doesn’t supply a temperature coefficient, you can turn to Table 690.7 in the NEC®. If the record cold temperature is –5 degrees Celsius, just find –5 degrees Celsius in the table and look straight across to find the appropriate multiplier, which is 1.12. To determine the temperature-adjusted maximum voltage, simply multiply the module Voc value at STC by the multiplier. Here’s what the equation looks like:

45 V × 1.12 = 50.4 V

Remember Obviously, using the NEC® table is a lot easier than performing the temperature-adjustment equation yourself. So why would you ever want to take the time to run the calculations when you can easily find what you need in the NEC® table? Well, there are a few reasons:

  • First off, Article 690.7 of the NEC® has a requirement that when the information is provided from the manufacturer, “you shall calculate the new voltage.”
  • Second, you may want to use thin film technology in the PV system you’re designing, in which case the table doesn’t even apply. If you’re using any PV technology other than crystalline, you have to use the calculations I show in the previous sections to determine the maximum voltage.
  • Finally, the NEC® will always be more conservative in its method. Therefore, relying solely on the table may result in a maximum voltage that doesn’t work well in the system you want to install.

Applying the adjusted open circuit voltage to come up with the right number of modules in a string

After you calculate the module’s temperature-adjusted voltage, you need to see how that temperature-adjusted voltage will affect the number of modules you can place in any one string that will connect to your grid-direct inverter.

Remember As I explain earlier in this chapter, every inverter has a maximum allowable voltage it can receive from the array. For grid-direct inverters, this value typically ranges from 500 VDC to 600 VDC, although it can be even lower than that (the maximum allowable voltage really depends on the components used by the inverter manufacturer). To determine the maximum number of modules you can place in a series string, you need to look up the maximum input voltage from the spec sheet of an inverter you’re thinking about using and divide that value by the module’s maximum Voc value (which you calculated based on the record cold temperature in the area).

Say you want to use an inverter that has a 600 VDC maximum input value and you select the temperature-adjusted module Voc from the earlier “Working the steps” section. You can calculate the maximum number of modules like so:

600 VDC ÷ 49.7 V = 12.07

This equation tells you that you can place 12.07 modules in a string without exceeding the 600 V rating of the inverter. But because you can’t buy fractions of a module, you have to round this number down to the nearest whole number, which is 12 modules.

Note: I used the maximum voltage I calculated in this example, but you can also run the numbers by using the maximum voltage you find with the help of the NEC® table in the earlier “Using NEC® info in a pinch” section. To save you flipping some pages, that voltage was 50.4 V. If 50.4 V was in fact the correct adjusted voltage, the maximum number of modules you could place in a series string would be

600 VDC ÷ 50.4 V = 11.9

In this case, you have to round down to 11 modules in a string. If you were to round up to 12, the 600 V value would be exceeded, and you’d run the risk of killing the inverter. This is an example of why taking the time to perform all the calculations can be beneficial: The array using 11 modules in a string may not be the best scenario for your client’s installation, and having the ability to add an extra module could make a big difference.

At this point, all you’ve done is define the maximum number of modules you can place in a string. You haven’t necessarily determined the right number of modules for the system because the number of modules in a string doesn’t need to exactly match the physical layout of any one row or column of modules. Therefore, you must repeat this process for voltage loss due to high temperatures (see the next section) and then use that info, combined with the initial criteria you established — the client’s budget, the available area, and so on (see the earlier sections in this chapter) — to define the whole array.

Figuring out the modules’ minimum DC voltage contribution

On the other end of the voltage window is the minimum power point tracking voltage. If the voltage from the array ever drops below this value — usually due to high heat conditions that occur on the sunniest days (as in the days system owners expect their arrays to produce the maximum amount of energy possible) — the inverter won’t be able to continue operating and will shut down. Although this scenario won’t damage the inverter, it may damage your reputation. If your client sees his inverter shut down on a bright, sunny day because the voltage isn’t high enough, expect to have a not-so-pleasant conversation with him (and possibly lose recommended business from your client if you can’t salvage his opinion of your work).

A PV module’s voltage decreases as the temperature increases (see Chapter 6 for more on this), which means that in the heat of the day — while the array is operating — the modules’ voltage will be reduced. In this situation, you need to look at the maximum power voltage, Vmp, and make adjustments from there because the array will be operating and the voltage will be reduced from the Vmp value. I explain what you need to do in the next sections.

Keeping long-term performance considerations in mind

PV modules are great and can perform for many years, but they aren’t perfect. The typical power output warranty for a module says that the manufacturer guarantees that the module will produce at least 80 percent of its original power output in 25 years. This verbiage means that over the course of 25 years, the module’s power output will be reduced by less than 1 percent per year — at the expense of both voltage and current over the course of the module’s life. Being aware of this voltage loss is critical because voltage is so important when matching PV arrays to inverters.

Remember So what does long-term voltage loss mean to you as you go about sizing systems? Simple. You don’t want to design a PV array for connection to an inverter that barely fits inside the voltage window today. For example, if an inverter needs 250 VDC to operate, you don’t want to design your PV array to operate at 255 VDC at the hottest time of the year starting in the first year. If you do, you’re not allowing for much voltage degradation before the array can’t keep up with the inverter’s requirements.

Tip In the next few sections, I show you how to calculate the minimum number of modules you need to place in a string to allow the inverter to operate when the module temperature is elevated. When you go through these steps and arrive at the minimum number of modules needed, add one module to that value and consider that your minimum (unless of course adding one module makes you have too many modules in a string; see the previous section for more on that). By adding just one module, you build in protection against falling out of the inverter’s voltage window due to natural degradation, thereby preserving the long-term performance of the system.

Picking the temperature to use in your math

Just like you need to calculate the adjusted Voc for the record cold temperatures, you need to calculate the adjusted Vmp for hot temperatures. But which hot temperature should you use? After all, the NEC® doesn’t have any requirements when it comes to keeping an array above an inverter’s minimum voltage because you can’t cause any damage with a low-voltage scenario like you can when too much voltage is applied. You also can’t rely on a table to tell you the multiplier value because no such table exists.

Here’s what to do: Start by defining the ambient summertime temperature, which is the high temperature at the array location during the summer. Then increase the estimated module voltage above the ambient temperature based on the method used to hold the PV array.

You have to know how to use the temperature-adjustment equation I present in the earlier “Working the steps” section. The method used to calculate an array’s voltage in hot weather is exactly the same as for cold weather; you merely use different numbers. Here are your ambient temperature options:

  • The average high summertime temperature for the array’s location: If you use the average high summertime temperature for the array’s location, you’ll design around a realistic value that’ll be reached often. Then again, there’ll be many days of the year that the average high temperature is exceeded. If you use the average high temperature and don’t allow for those extremely hot days, the array may just turn off on those record hot days.
  • The record high temperature: By designing with the record high temperature in mind, you ensure that the PV array will operate in all conditions, which isn’t a bad situation in my opinion. On the other hand, using the record high temperature can lead to overly conservative arrays because the calculated voltage loss is on the extreme end and doesn’t really happen on a regular basis.

  • Remember The American Society of Heating, Refrigerating, and Air-Conditioning Engineers’ (ASHRAE) 2-percent design temperature: This is the value that I like to use. ASHRAE’s 2-percent design temperature says that for the given site, the temperature rises above the reported value only 2 percent of the time. In other words, 98 percent of the time, the temperature is less than or equal to the number given. Using this value allows you to design for nearly every situation without requiring excessive calculations.

    Tip In 2009, Solar ABCs, a group that advocates for the solar industry on a wide variety of topics, released a document titled “Expedited Permit Process for PV Systems.” In this document, Solar ABCs publishes the average 2-percent temperature data for June through August for a number of cities across the United States. This resource (found at www.solarabcs.org/permitting/Expermitprocess.pdf) gives you a quick reference for the 2-percent data.

Accounting for mounting in your math

After you know which hot temperature you intend to use for your calculations, you need to consider how you plan to mount the PV array because the mounting method affects the module’s temperature. To account for the mounting method, add a certain number of degrees to the ambient temperature based on the array’s proximity to a mounting surface. The values shown in this section are estimates based on measurements made at multiple locations over a number of years. They can be used in the design process and represent rises in a PV module’s temperature at the hottest time of the year.

Remember To estimate a PV module’s temperature at the hottest time of the year, you should add one of the following temperatures to the ambient temperature:

  • 35 degrees Celsius for arrays with fewer than 6 inches between the backs of the modules and the mounting surface
  • 30 degrees Celsius for arrays with more than 6 inches between the back of the array and the mounting surface
  • 25 degrees Celsius for arrays that are mounted on top of a pole

By adding these values to the ambient temperature, you can arrive at a best estimate for your array’s operating temperature — the temperature you expect to see at the module level if you were to measure the temperature in the middle of the summer.

Crunching the numbers

When you know the temperature you’re going to estimate for the modules when they’re operating in the summer, you can begin the process of adjusting the Vmp value. To do so, you need to apply a specific temperature coefficient to the Vmp as the array grows hotter.

Tip PV module manufacturers often report the temperature coefficient for Voc, but they rarely provide it for Vmp. Also, they almost all universally report the temperature coefficient for power. Although voltage isn’t the only factor affecting the temperature coefficient for power, it’s what affects it the most. Therefore, if the module manufacturer doesn’t supply a temperature coefficient for voltage, I suggest taking the value reported for power and substituting it for the voltage coefficient. Doing so results in slightly more conservative values when it comes to the adjusted voltage, but your numbers will be reasonably close to the exact answer (and in most scenarios, the end result will be exactly the same).

Remember For crystalline modules, the coefficient for power (and unless specified otherwise, for voltage) is very close to –0.5%/°C, which is a slightly greater change when compared to the coefficient that applies to Voc.

Here’s how to apply all the factors when calculating the adjusted Vmp values for your modules:

  1. Collect the temperature coefficient for your PV module in volts per degrees Celsius.
  2. Collect the 2-percent design temperature for your client’s location in degrees Celsius.
  3. Determine how many degrees Celsius to add to the ambient temperature based on how you plan to mount the array.
  4. Add the ambient and mounting method temperatures to estimate the operating temperature of the array in the summertime.
  5. Calculate how many degrees Celsius greater than STC the modules will be on 98 percent of the days.

  6. Multiply the temperature coefficient for the module by the number of degrees calculated in Step 5.

    The result of this equation is the change in voltage that the module will produce.

  7. Add the number of volts calculated in Step 6 to the Vmp for the module at STC.

    Because the Step 6 number will always be negative, you must subtract the calculated value instead of adding it in order to find the adjusted maximum module voltage based on that temperature.

Suppose the Vmp for a particular module is 37.2 V and the manufacturer reports that the temperature coefficient for power is –0.5%/°C. Because the manufacturer doesn’t provide the temperature coefficient for voltage, you must apply the power coefficient to the voltage. To calculate the number of volts per degree Celsius, multiply the coefficient by the Vmp.

37.2 V × –0.5%/°C = 37.2 V × –0.005/°C = –0.186 V/°C

The array location has an ASHRAE 2-percent design temperature of 33 degrees Celsius, and the array will be mounted parallel to a roof with only 4 inches of space between the roof and the backs of the modules. Apply this information to the preceding steps to get the following:

  1. The reported temperature coefficient is –0.5%/°C.
  2. The ambient design temperature is 33°C.
  3. The altered ambient temperature (to accommodate the mounting method, which calls for fewer than 6 inches between the backs of the modules and the mounting surface) is 68°C (33°C + 35°C = 68°C), the estimated module temperature when the array is operating.
  4. The number of degrees off of STC is therefore 68°C – 25°C = 43°C.
  5. The voltage loss due to temperature is thus 43°C × –0.186 V/° = –8.0 V.
  6. The new adjusted voltage for the module at the design temperature is therefore 37.2 V + –8.0 V = 37.2 V – 8.0 V = 29.2 V.

As you can see, the loss of voltage will be 29.2 V in the summertime — that’s pretty significant. If you continue to look at how the voltage will be reduced as the module ages, you’ll soon recognize the importance of keeping an eye on this calculation in the design process.

Totaling the minimum number of modules needed in a string

After you have the adjusted Vmp value, you can calculate the minimum number of modules needed in any string in order to operate the inverter. Continuing with the earlier example, if the inverter you’re thinking about using has a minimum input of 250 VDC, the minimum number of modules necessary will be that minimum voltage divided by the temperature-adjusted module voltage.

250 VDC ÷ 29.2 V = 8.56, or 9 modules minimum

Tip Although this calculation defines the absolute minimum number of modules needed to keep the inverter running, a good practice is to make your minimum number of modules be the calculated number plus one. This practice gives you plenty of room for degradation and allows for the array to operate significantly hotter than anticipated and still keep the inverter running. So I’d want to use at least 10 modules in the strings for the earlier example.

Bringing It All Together: Combining Your Power and Voltage Information

This section is your chance to put all the information you’ve acquired (specifically, matching the array’s power to the inverter and defining the string length based on the maximum and minimum number of modules allowed in each string) and put it to use for your client’s site.

Earlier in the sizing process, you determined the number of modules you can fit on the roof and possible inverter sizes (see the earlier “Matching Power Values for an Array and an Inverter” section). Now, with the string lengths defined, you can see whether that array size is a real possibility. For example, in the earlier “First Things First: Evaluating the Budget and the Available Array Area” section, you determined that the roof (or ground, the physical site isn’t crucial, just the space limitations) could hold 24 of the modules and that the inverter you based your calculations on can handle the power from 24 modules. Can you really fit all 24? The minimum string length was 9 modules (or 10, if you follow my advice), and the maximum was either 11 or 12, depending on how you calculated the temperature adjustment (see the earlier “Working the steps” and “Using NEC® info in a pinch” sections).

If you took the time to calculate the adjusted Voc by hand instead of using Table 690.7 from the NEC®, then yes, you can fit all 24 modules on the roof by placing two strings of 12 modules in parallel. If, however, you only used Table 690.7 and calculated a maximum of 11 modules in series, then no, you could place only 22 modules on the roof because you’d be limited to strings of 11 modules (because the space is limited to 24 modules or less, two strings of 11 is the closest you can get).

Remember Unless you’re using an inverter that can handle different maximum power point inputs, the strings must be the same length and face the same direction. Otherwise, they’ll have different maximum power points, and the inverter won’t be able to harvest all the potential power.

What if the roof could hold only 18 modules? In that case, the array and inverter relationship in this example will work, but you can probably do better. I suggest finding a different inverter that has a lower DC input voltage than 250 VDC, just to make sure the system doesn’t shut off in high heat conditions or in a number of years as the modules degrade.

One Last Check: The Inverter’s Maximum Current Input

The maximum amount of power input and the DC voltage window are generally the only considerations you need to make when sizing a PV array to the DC side of the inverter. One final check to make, though, is the maximum current input from the array to the inverter.

All inverter manufacturers list the maximum current input allowable on their inverters, but this value isn’t always the easiest specification to find because the manufacturers tend to list it in the backs of their installation manuals. Be sure to find out the maximum current input value so you can make sure the array size you’ve calculated doesn’t exceed it.

To verify that the array you’ve sized doesn’t exceed the inverter’s maximum current input, divide the value reported by the inverter manufacturer by the short circuit current rating of the array at STC.