In my previous article on photovoltaic (PV) systems (“The Highs and Lows of Photovoltaic System Calculations” in the July 2012 issue), I went through methods to calculate the changes in voltage due to temperature changes, which are critical to system design. In terms of the electrical output of PV modules, the other set of calculations is based on the amount of current produced by the modules. In this article, I’ll review the different current ratings of PV modules and walk you through the process of how to properly calculate the current values as required by the NEC, as well as the resulting requirements on overcurrent protection devices (OCPDs) and conductor sizing.
One of the first things to realize is that the current produced by PV modules is both current limited and directly affected by the intensity of sunlight. PV modules are listed with two current values: short circuit current (Isc) and maximum power current (Imp ). As introduced and detailed in the July article, Fig. 1 is a representation of the current and voltage characteristics of a typical PV module. In this graph, known as an IV curve, the current is shown on the Y axis and the voltage across the X axis.
In terms of NEC compliance, let’s focus on the Isc value. Why? If there is a fault in the PV wiring, the modules can become shorted, and the conductors/overcurrent protection need to properly carry the current and interrupt the current. In addition, if the intensity of sunlight is in excess of the standard test condition (STC) value of 1,000 W/m2, then the amount of current produced by the module can actually exceed the listed values.
The size of the individual cells in the module directly impact the amount of current produced; the larger the cell, the more current that can be produced. In crystalline modules, the amount of voltage produced is ~0.5V per cell, regardless of size. Therefore, module manufacturers must place multiple cells in series to produce the desired voltage and current values from their modules. In addition to physical size, the amount of current produced from PV cells is dependent on the sunlight intensity. This means PV modules cannot provide an unlimited amount of current when a dead short scenario occurs, which is an important consideration when calculating conductor and OCPD sizes.
Maximum current calculations
To begin the process of sizing conductors and OCPDs, refer to Sec. 690.8 in the NEC. In 2011, this section was extensively revised in an attempt to clarify the required calculations. Although the section has been modified, the actual methodology used to calculate and apply the current values to PV systems remains consistent with previous Code cycles.
The first calculation covered is what the Code refers to as the PV maximum current value. Sec. 690.8(A) details the differences between the maximum source circuit and output circuit currents. Therefore, you need to determine what circuit you are dealing with to properly apply the calculations. The source circuit consists of the conductors that are connected directly to the modules before any parallel connections are made. A typical PV array will consist of multiple modules wired in series, making a string of modules. The conductors connected to such a string are the source circuit conductors. If multiple strings are present, they are placed in parallel in a combiner box — either at the array location or at the inverter location. The conductors leaving the combiner box are considered the output circuit conductors. Figure 2 (click here to see Figure 2) helps illustrate the conductor locations and designations.
To calculate the maximum source circuit current, Code requires you to multiply the rated Isc value by 125%. This multiplier takes into account increased irradiance values and the ability of the module to produce more than the rated current. Therefore, per 690.8(A)(1), a single string of PV modules that has an Isc value of 8.74A each would be calculated as follows: 8.7A × 1.25 = 10.9A.
If three strings of these modules were connected in parallel within a combiner box, the maximum output circuit current, as outlined in 690.8(A)(2), would be calculated by multiplying the modules’ Isc value by 1.25 times the number of strings placed in parallel: 8.7 × 1.25 × 3 = 32.7A.
690.98(A)(3) is the definition of the inverter’s maximum output current. Like PV modules, inverters used in PV systems are current limited. Thus, the maximum current is defined as the inverter manufacturer’s listed maximum current rating. This information is published by the manufacturers and does not require any additional correction factors, because the current is on the output side of the inverter and is not affected by changes in environmental conditions. The final maximum current defined in 690.8(A) is that for standalone (battery-based) inverter input circuits.
Those calculations are relatively straightforward and easy to follow. The next Code section, 690.8(B), is where most people start to get confused. Updated in 2011, this portion of the Code covers the requirements for overcurrent protection device and conductor sizing. The first portion of 690.8 determines the overcurrent device ratings. Before getting into those details, let’s make a quick jump into 690.9 to help define when OCPDs are required in PV systems.
When you look at 690.9, the general rule is that PV circuits are to be protected like any other electrical circuit, as required in Art. 240. When reading through the section, however, the Exception lists the scenarios where OCPDs aren’t required for PV source circuits. For grid direct systems, Exception (b) is the most applicable. To meet this exception, the source circuit conductors cannot be exposed to
external sources of current that exceed their ampacity or the maximum OCPD listed by the module manufacturer, known as the module’s series fuse rating. When you break this Exception down, the general rule of thumb is this: For grid direct PV installations (systems that do not incorporate batteries) that have only one or two strings in parallel, OCPDs are not required to protect the source circuits. The reason is PV modules are current-limited devices. Because the grid direct inverters cannot push current back into the modules, there isn’t a source of current to any set of conductors that would exceed the ampacity of the conductors. Even with two strings in parallel, it’s not possible for one string to backfeed into the other and exceed the maximum OCPD rating listed by the module manufacturer. Once you exceed two strings, you generally need OCPDs. This is because if there is a fault in any one string, the sources of current external to that string could exceed the series fuse rating and the conductor’s ampacity. There are exceptions to this rule, of course. However, the general rule can be safely applied to all grid-direct PV systems. If batteries are introduced to the system, then you will be required to have OCPDs on every string of modules. This is because the batteries are an external source of current that could be pushed back toward the modules in a fault scenario.
Given that set of conditions in 690.9, let’s return to 690.8 and evaluate the OCPD ratings with the understanding that they aren’t always necessary. For my examples, I will continue to use the PV array that has three strings placed in parallel to help illustrate the requirements in 690.8.
In 690.8(B), the NEC dictates that current within PV circuits is considered continuous. This means that the circuits are capable of delivering current for more than three hours. Therefore, to properly determine the ratings of these OCPDs, according to 690.8(B)(1)(a), you will need to multiply the maximum continuous current by 125% to ensure that the OCPD does not carry more than 80% of its rated value. This is the correction factor most electricians and electrical designers are familiar with and apply on a regular basis. It is worth pointing out that this second correction factor is on top of the first one applied in 690.8(A). When talking with individuals familiar with PV systems, this is often referred to as the 156% rule because 1.25 × 1.25 = 1.56. This is to say, the OCPD is required to be sized no less than 156% of the module’s rated Isc value.
690.8(B)(1) has three more requirements listed for OCPD sizing. You are required to follow the terminal temperature requirements as described in 110.14(C). This requires you to verify the terminal limitations for the fuse holders you connect the conductors to. Combiner boxes manufactured for PV systems will include terminals with a minimum of 75°C ratings. If the OCPDs are placed in environments exceeding 40°C (104°F), you are required to use the OCPD manufacturers’ listed correction factors to adjust the OCPD rating. 690.8(B)(1) concludes by permitting the OCPDs to be rated in accordance with 240.4(B), (C) and (D).
To determine the minimum OCPD required for the source circuits in the given example of three strings placed in parallel, you first need to realize that all three strings need to have OCPDs before they are placed in parallel. To determine the minimum OCPD rating, the maximum source circuit current, as calculated in 690.8(A)(1), must be multiplied by 125%: 10.9A x 1.25 = 13.6A.
By applying 690.8(B)(1)(d), the minimum OCPD can be a 14A fuse. The module manufacturer also lists the maximum series fuse rating. This value dictates the largest size OCPD that can be used — typically modules have 15A or 20A series fuse ratings. Thus, if the modules used in this system had 15A series fuse ratings, then the OCPDs placed in the combiner box could be either 14A or 15A. In 690.9(C), the standard values for OCPDs used in PV source circuits shall be considered in 1A increments up to 15A. In this scenario, most installers would choose the 15A option, given their ability to readily purchase that fuse rating.
If a combiner box that is external to the inverter is used, then the PV output circuit would also require OCPD, because the Exception in 690.9 only applies to PV module or source circuit conductors. Therefore, if three strings are placed in parallel, the output circuit OCPD’s rating would be calculated as: 32.7A × 1.25 = 40.8A.
Again, applying 690.8(B)(1)(d), this will result in a minimum OCPD rating of 45A. For combiner boxes internal to inverters, the output circuit wiring is considered part of the listed piece of equipment and is covered under the product’s listing.
The final portion of 690.8 is to determine the proper conductor size based on the maximum current, conditions of use, and the OCPD (as calculated earlier). This section of Code was also updated in 2011, greatly clarifying the requirements.
In the first portion, 690.8(B)(2)(a), you are to verify the conductor is sized such that its ampacity is at least 125% of the maximum current — or 156% of the rated short circuit current without any conditions of use applied. This is the same methodology used to determine the minimum OCPD. Another consideration when selecting the conductors is the terminal temperature limitations. PV systems are typically installed with 90°C conductors, but when those conductors are connected to terminals rated at 75°C, the conductor’s ampacity is limited to the value at the 75°C rating. This requires you to look at the 75°C column in Table 310.15(B)(16) to determine the minimum conductor size.
So in our example, for the PV source circuits connected to terminals rated at 75°C, the minimum conductor is determined by the same current value required by the OCPD — 13.6A. This would result in a minimum conductor size of 14AWG with the rating of 20A in the 75°C column and the ability to be placed on a 15A OCPD.
The PV output circuit would require a 75°C conductor rating of at least 40.8A or an 8AWG conductor.
The final check would be to look at the conductors’ ampacity against the maximum current value [Isc × 1.25 as defined in 690.8(A)] with conditions of use applied — correction factors for conduit fill and elevated temperatures. PV conductors can be subjected to extreme temperature conditions due to conductors running along rooftops, within attic spaces, and exposed on the exterior of buildings. All of these scenarios can greatly increase the temperature that the conductors are exposed to and reduce the overall ampacity.
Many PV designers use ASHRAE data to determine the temperatures to base the correction factors upon. A group called the Solar America Board for Codes and Standards (Solar ABCs) created an interactive map for the United States, which is in the Expedited Permit Process report found in the “Publications” section of its website (solarabcs.org).
To properly apply conditions of use, identify where the conductors will experience the greatest exposure to heat and the number of current-carrying conductors within a raceway. When the conductors are run in circular raceways exposed to sunlight on roofs, Code requires you to add to the ambient temperature value based on the height of the conductor from the roof surface as outlined in Table 310.15(B)(3)(c). This can add a significant amount of heat to the conductors, resulting in upsizing conductors to compensate for the lost ampacity. There are exceptions to this temperature adder, based on the length of the raceway exposed in relation to the total circuit.
In our example, if the PV source circuits were run in EMT along the rooftop before the combiner box, you would have to add to the ambient temperature as well as compensate for the additional rooftop temperatures. For an array located in Sacramento, Calif., that has all six current-carrying conductors in EMT 3 inches off the roof surface, you would use the following correction factors:
• Ambient temperature based on ASHRAE data: 37°C.
• 310.15(B)(3)(a), adjustment for more than three current-carrying
conductors in a raceway: 0.80.
• 310.15(B)(3)(c), ambient temperature adjustment for circular raceways exposed to sunlight: 22°C addition to ambient, resulting in a 59°C effective temperature.
• 310.15(B)(2)(a), ambient temperature correction factor for 90°C conductors exposed to 59°C temperatures: 0.71.
Applying these values to the 14AWG conductor selected in the beginning of this process, you get a conductor with the following ampacity:
25A × 0.8 × 0.71 = 14.2A.
Note: The example uses the 90°C ratings of the conductor because we are concerned with the ampacity of the actual conductor at this point — the terminal ratings do not come into play during this evaluation.
This ampacity must be greater than the maximum current calculated in 690.8(A), or Isc × 125%. In this case, the maximum current is 10.9A, and the conductor ampacity with conditions of use applied exceed that value. The final check is to verify the conductor size in 690.8(B)(2)(c), ensuring the conductor is properly protected by the OCPD. If 15A fuses are located in the combiner box, then the 15A fuse is allowed to protect the conductor with a corrected ampacity of 14.2A, per 690.8(B)(1)(d) and 240.4(B), as this is the next readily available OCPD.
The PV output circuits would be evaluated in a similar manner, applying specific conditions of use and verifying the resulting conductor ampacity is greater than the maximum current calculated.
As these examples show, conductor and OCPD sizing is no joke — this task needs special consideration. In addition, design decisions, such as where to place combiner boxes, affect conductor sizing and also have a ripple effect on items like disconnects and the installation requirements surrounding those components. In a future article, we’ll evaluate these situations and help identify the pros and cons of such design decisions.
Mayfield is a principal with Renewable Energy Associates, Corvallis, Ore. He can be reached at firstname.lastname@example.org.