Diversity of load
Q:
I have tried to figure out the diversity of load formula in Appendix B of the 1999 Code, but haven't been able to figure out how the numbers or variables are arrived at. Could you please answer by showing several formulas as examples and use other than 50% load diversity and tell me how the diversity is deduced? Is it the average percentage of total ampacity per wire? I have contacted two electrical engineers who had no idea what I was talking about.
A:
It is important to understand that an appendix or a fine print note is not part of the requirements of the NEC. Mandatory terms are never used in an appendix or in a fine print note. The heading of Appendix B clearly states that the appendix is not a part of the requirements of the Code but is included for informational purposes only.
Section B31015(b)(1) is related to Section 31015(a)(1). This section allows ampacity to be determined through the use of Article 310 tables or under engineering supervision through the use of Section 31015(c). The formula for this calculation is given in Section 31015(c) along with a fine print note directing you to Appendix B for information.
Section B31015(b)(2) refers to IEEE paper 57660, “The Calculation of the Temperature Rise and Load Capability of Cable Systems,” by J. H. Neher and M.H. McGrath. The formula found in Section 31015(C) is based on this paper and is commonly known as the NeherMcGrath formula. The NeherMcGrath paper itself is 20 to 25 pages in length. If you intend to use this calculation, you should obtain a copy of this IEEE paper.
Application of the engineering calculation is far too complex to be covered in the Code Guide format. Over the years, a number of articles have been published on the subject in various trade journals. Most of the articles in my files offer only an outline of the application of the method.
Dann Strube
Termination ampacities
Q:
Could you please explain the use of dualtemperature rated wires in the ampacity Table 31016? I was under the impression that I could only use the 90°C values if the terminations, and devices, were rated for 90°C. In the McGrawHill handbook a section addresses derating wire for “more than three wires in a conduit” that indicated the advantage of using the higher 90°C value. In this case I am using six aluminum conductors in a 2in. conduit with a calculated load of 88A. These are two residential feeders 120V/208V singlephase threewire circuits, which come from a threephase system.
Because there are more than three wires I will have to adjust the ampacity of the wire to 80%. The breaker will be 100A or less. I have been told that it is permissible to use the 90°C rating for No. 1 aluminum at 15A and derate to 115 × 80% = 92A.
Is there any clear explanation as to the use of these dual temperature ratings? These feeders will be in a dry location, XHHW insulation.
I have also tried to understand the use of the load diversity formula and the examples in Appendix B to no avail.

The example in Appendix B is based on 50% load diversity. How is the load diversity calculated? Is it simply the total amperage divided by the number of conductors for an average amperage per conductor?

Is the 0.5 number in the Code book formula a static or given number and always the same in the formula or is it based on the 50% diversity and does it change with a different diversity?

In the formula, “N” and “E” are different, based on what? If my phase conductors are both loaded to 88A then my neutrals in this instance also carry 88A.
But more important than applying this formula to my specific situation I would like to understand the use of the formula.
A:
Termination ampacities and ampacities for conditions of use are two separate considerations. In your example, you have a conductor with a 90°C insulation rating. This means the conductor can operate at up to 90°C without damage to the insulation. According to Section 31015(B)(4)(b), the neutrals are currentcarrying because they are derived from a 208/120Y system. For your conditions of use, normal ambient and six currentcarrying conductors, the temperature correction factor is 1.00, and the adjustment factor is 0.80, so the ampacity of No. 1 Aluminum XHHW is 115 × 0.80=92A. Since your load is 88A, the conductor is big enough for the load. Rounding up from 92A in accordance with Section 2403(b) allows the feeder conductors to be protected by a 100A overcurrent device.
In this example we have considered the temperature factors explained in Section 31010 to be sure the conductors will not be overheated. However, we haven't considered whether the terminals would be overheated.
The 100A overcurrent device is assumed under Section 11014(c) to have 60°C terminals. For 60°C terminals, the maximum ampacity of the No. 1 XHHW conductors comes from the 60°C column of Table 31016. Therefore, the load on the conductors would be limited to 85A to avoid overheating the terminals, and the No. 1 conductors would not be big enough. However, if the terminals are actually 75°C, which is fairly likely, or if the feeders qualify for the special rules of Section 31015 (b)(6), the No. 1 conductors would be suitable for the terminals.
As for the information in Appendix B, three points must be understood before we try to use this optional method. First, Section 31015(c) requires that the NeherMcGrath formula shown be used only under engineering supervision. Second, Appendix B does not include the complete method for calculating ampacities, it only provides examples for underground duct banks. Third, in order to use this method, you will need the NeherMcGrath paper and perhaps some of the other information listed in Appendix B, Section B31015(b)(2). As to your specific question, the variables N and E are explained in the notes to the formula under Table B31011. The 0.5 in the formula is a constant for the stated 50% diversity. Example No. 1 shows an example of 50% diversity, that is N=24, and E=12, 24 conductors are in the raceway, but only 12 are currentcarrying. 12/24=50% diversity, which is the assumption in the table as indicated by the asterisk note.
Note that when diversity is 50%, the number under the radical is “1,” and the table factors work by themselves. The formula is for correcting the table values only when diversity is other than 50% and only when there are between 10 and 85 conductors, which was the reason for adding the formula and examples in the 1999 NEC. Example No. 2 shows a situation where N=24 and E=18. That is where there are 24 conductors but only 18 are currentcarrying. In this case, the ampacity limit for the No. 14 conductors is reduced to 11.5A rather than 14A.
There has been some disagreement, even among Code panel members, as to what “diversity” means. IEEE does not help. According to the IEEE Gray Book, a diversity factor is always 1 or greater. My interpretation is that in the second example, the diversity is 18/24=75%. If only six conductors were loaded out of 24 conductors, the diversity would be 6/24=25%. As the diversity goes up, the ampacity goes down, and as the diversity goes down, the ampacity goes up, as illustrated by the formula and examples of Table B31011, Fine Print Note.
Noel Williams
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