Neher-McGrath Method

In electrical engineering, NeherMcGrath is a method of estimating the steady-state temperature of electrical power cables for some commonly encountered configurations. By estimating the temperature of the cables, the safe long-term current-carrying capacity of the cables can be calculated.

NEC Tabels 310-15 Some history?

Starting in 1889, many attempts we made to find the correct ampacity for conductors in order to prevent conductor temperatures that exceed the insulation rating.

A paper published in 1889 Arthur Edwin Kennelly provided tables listing 46 Amps rating for #10 copper conductor.
The following year  H.W. Fisher listed 19 Amps, and in 1894 the Underwriters' Electrical Bureau listed 20 Amps for the same conductor.
By the end of 1937 various organizations listed at least 14 different ampacities for the same size conductor.

In 1938 Samuel J. Rosch, a member of the American Institute of Electrical Engineers (AIEE) and head of products development for the Anaconda Wire and Cable Company, conducted an investigation to determine the correct ampacities for all the standard size conductors used at that time.

The first step was to establish the maximum continuous operating temperature for insulations, and he performed deterioration tests in Environmental Test Chambers.

Taking wire and connecting thermocouples, he then applied voltages and measured the ampacities and temperatures.
The result was published, "The Current-Carrying Capacity of Rubber-Insulated Conductors" in March of 1937.

This publication became the bassline of  Table 310-15 of the National Electrical Code. Rosch's original table was based on an ambient temperature of 30°C and a conductor temperature of 50°C for industry-standard rubber of the time.
If we convert the ampacities in The Current-Carrying Capacity of Rubber-Insulated Conductors publication to 60°C  using the formula given in NEC, and set the delta TD equal to 0 for <600V and rounding off to the nearest 5 Amps, we can calculate the ampacities for 60°C  insulations as found in the first column of Table 310-15.
The same calculation was used to determine the ampacities in the 75°C  and 90°C  columns in table 310- 15.

Issues with Table 310-15
There are some limitations to Rosch's paper.

  1. He did not investigate the effects of mutual heating from adjacent heat sources.
  2. His paper only considered above ground installations.
  3. Voltages higher than 600 were not investigated. For most, when a load is calculations are performed according to Article 220, there is enough safety margin built in to prevent any issues.


To clarify this, a fine print note was added to the NEC for determining conductor sizes on loads calculated in accordance with Article 220.
In the 1950s when the industry began to see very large and continuous loads on systems, utilizing underground feeder runs in underground duct banks and the issues in Rosch's paper surfaced.

In cases where load calculations using engineering methods in place of Article 220, and used Table 310-15 to determine the conductor size, conductors overheated. This problem was particularly evident in the conductors located nearest the center of the ductbanks.


Rosch used Fourier heat transfer equation, adding the variable "n" for the number of conductors in the same raceway.
But that modified equation had no variable to adjust the ampacity for heat that came from adjacent sources, or for the differences in the thermal insulation of the soil or concrete an underground installation.

In 1957  J. H. Neher and M. H. McGrath published a paper that solved these issues. The paper titled "The Calculation of the Temperature Rise and Load Capability of Cable Systems" now simply know as Neher-McGrath, showed that center conductors in a three by three duct bank would need to be derated to almost 60% because of the mutual heating effect from adjacent ducts in duct banks.

Tc = conductor temperature (°C)
Ta = ambient temperature (°C)
ΔTd = dielectric loss temperature rise
Rdc = dc resistance of conductor at temperature Tc
Yc = component ac resistance resulting from skin effect and proximity effect
Rca = effective thermal resistance between conductor and surrounding ambient

However, this single equation masks the great complexity involved in these procedures. There are scores of complicated equations involved in developing the terms in this equation and those required for temperature calculations. (The paper defines over 80 variables and contains in excess of 70 formulas excluding appendices.) To solve for unique ampacities or temperatures at each cable position, a multiple set of equations must be developed to take into account interference heating from every position in the system, and a matrix solution technique for simultaneous equations utilized.

There are many software packages sold today that will perform this complex calculation. Some of these systems are very good, and some are weak or poorly designed. The package you buy is dependent on the complexity of the calculation you need to perform and how much tolerance you have for a steep learning curve and your budget. As discussed above, there are numerous variables that you need to know and understand fully before you can even start the calculation. Let's say you have the software and the required system variable, and you do a calculation. Now you have the results, and you are halfway home.  Much like an X-Ray, the information is only as good as the Dr. who analyzes it. It takes years to truly understand all the results and find the most cost-effective solution. There are numerous ways to mitigate heat in an underground installation. Some are easy and may have little or no cost, and some can be extremely expensive and time consuming for the Project.

We are constantly being asked to fix issues caused by engineers that are not truly qualified to interpret the calculation results or caused by contractors that did not understand how to install the underground system per the engineer's specifications
We are also involved in litigation as expert witnesses where there were failures in the underground electrical installation.