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Understanding the Neher-McGrath Calculation and the Ampacity of Conductors


Heat Transfer

The key to understanding ampacity is to learn about heat transfer. The definition of ampacity is given in the National Electrical Code (NEC) as "the current in amperes a conductor can carry continuously under the conditions of use without exceeding its temperature rating." To better understand ampacity we need to examine how heat is transferred and thermal circuits in respect to a current carrying conductor.

When current is carried by a conductor it must pass through the electrical resistance of the conductor. When this happens heat is generated. One unit of heat, watts, can be calculated by I squared times R, where R equals the electrical resistance of the conductor in ohms and I equals the current in amperes. The heat generated in the conductor passes through several thermal barriers by convection, conduction, and radiation and dissipates into the air. Possible thermal barriers are the conductor insulation, the air inside a duct, the duct wall, the soil surrounding an underground duct, and any additional thermal insulation applied such as polyurethane.

The transfer of heat follows a fundamental law in physics, and heat always flows from the warmer object to the colder object, much like heat flowing from the inside of a house through the walls to the outside on a cold day. The rate of heat transfer is dependent on several variables and can be described by a thermal equation that closely resembles ohms law (E=IxR), substituting heat for current and thermal resistance for electrical resistance. In a heat transfer equation the rate of heat transfer is directly dependent on the difference in temperature between the conductor called TC and the ambient temperature called TA. In a heat transfer equation TC-TA = (IxIxR) x RCA, where I is current in amperes, R is electrical resistance in ohms, and RCA is thermal resistance in degrees Centigrade-cm/watt usually called thermal-ohm-feet. TC is the maximum permissible operating temperature in degrees Centigrade of the conductor. TA is the ambient temperature of the air or soil for underground installations. Solving for I:

Letting heat, IxIxR in this case, be represented by W and thermal resistance, RCA, by R with a line over it, we can draw a thermal circuit that is similar to an electrical circuit.

Neher-McGrath equation

Founded by a man named Fourier in the 1850's, Equation No. 1 is sometimes called the Fourier heat transfer equation. The equation in section 310-15(b) of the NEC, called the Neher-McGrath equation, is a more complex version of the Fourier heat transfer equation. The Neher-McGrath equation was discovered by two cable engineers in 1957. In the Neher-McGrath (NM) equation, Delta TD, is a term added to the ambient temperature, TA, to compensate for heat generated in the jacket and insulation for higher voltages. Delta TD is called the dielectric loss temperature rise and is insignificant for voltages below 2000. Another term in the NM equation, (1+YC), is a multiplier used to convert direct current resistance (RDC) to alternating current resistance or impedance. For wire sizes smaller than No. 2 this term becomes insignificant. Of course, we must remember that the NM equation was developed using the standard power frequency of 60 hertz and sinusoidal wave forms for current and voltage.

There are many equations used to calculate the various thermal resistances for the conductor insulation, the air space between a conductor and the inside of a conduit, the conduit or duct wall, and the thermal resistance outside the conduit. Like electrical resistors, thermal resistances in series are added and the total equals RCA.

Ambient temperature, TA, varies but usually 30 or 40 degrees Centigrade is used for above ground installations. For underground installations TA is universally 20 degrees Centigrade. Civil engineers working for the State of Alaska Department of Transportation state that the actual measured temperature 30 inches beneath the surface is 19.3 degrees Centigrade near Fairbanks, Alaska. This of course, is during the summer months. The conductor temperature, TC, for most 600 volt building wire is 60, 75, or 90 degrees Centigrade. The maximum insulation temperature for conductors is determined by conducting aging and enlongation tests in environmental chambers.

In the NM calculation there are many variables in the 30 to 40 equations used to account for the number of conductors, number and size of adjacent conduits, number and size of adjacent duct banks, coefficient of surface emissivity, number of cables, axial spacing between cables, extraneous heat sources, and wind velocity. All these factors and more effect the calculation of ampacity. An analysis of the NM calculation reveals many details about ampacity: for instance, the ampacity of conductors in a bright and shiny conduit in free air is higher then the ampacity in a dull and dark conduit because of the coefficient of surface emissivity and its effect on the radiation of heat. Also, one of the most criticized faults of the NM calculation is revealed: The calculation is based on one single linear foot of a conductor that may be several hundred feet long where the conditions vary dramatically along the entire length.

There are ampacity tables in the National Electrical Code that are sufficient for most installations. However, the tables in the NEC are very crude approximations and therefore include a substantial safety margin. There are instances where the application of the ampacity tables including the safety margins are insufficient requiring engineers, installers, and inspectors to perform actual NM calculations using one of the several software packages available. For instance, there are no requirements in the NEC to address the problem of excessive thermal insulation around cables and conduits. What happens if there are several inches of polyurethane foam around a conduit? There are no derating tables in the NEC for this kind of situation. Yet, the addition of excessive thermal insulation will effect the ampacity of a conductor, especially polyurethane foam that has three times the insulation value of fiberglass. To address this problem we must remember that the NM equation is a radial heat transfer equation and that the NM calculation is performed on one typical foot of an installation that may be several hundred feet long. Radial heat transfer means that heat flows outward at ninety degrees to the length of the conductor as opposed to axial heat transfer where heat flows along the length of the conductor. In the real world there is axial and radial heat transfer. But the NM equation and the NEC assume that a conductor and surrounding thermal barriers are infinitely long and uniform where no axial heat transfer takes place. There are, however, some allowances in the NEC for axial heat transfer. For instance, there are no derating for over three current carrying conductors in a nipple if the nipple is not over 24 inches long. Also, bundled cables are not required to be derated if the bundles are not longer than 24 inches. There is also the ten per cent rule given in section 310-15(c). These are situations where there is enough axial heat transfer to prevent the conductors from overheating. It would also be prudent to assume that where there is excessive thermal insulation not over 24 inches long, the ampacity of the applicable conductors would not be effected because of axial heat transfer.

© 1996 Gerald Newton. All rights reserved.