The Problem - Consider this hypothetical example: an XHHW-2 circuit is designed for operation at 90°C. The engineer or designer believes they have all the information they need to maximize the usage of this conductor, loading it at that maximum operating temperature. Unfortunately, they've made a mistake and neglected some additional temperature derating that lowers the conductor's ampacity. Now, the installed conductor operates at a steady-state temperature of 95°C, 5°C more than its operating temperature limit.
What happens now? Does the cable melt?
No. Although this situation is far from ideal, it's not uncommon. Conductors are typically designed for annual peak conditions, not all-time worst-case conditions. If an intense, historically-high heat wave passes through an area, it's sure to wreak some havoc on the electrical system but the result won't be every insulated conductor melting, even if they were previously operating at or near their maximum operating temperature. In reality, the melting temperature of conductor insulation is much higher than the insulation's steady-state temperature limit.
The Arrhenius Equation - Nevertheless, the lifespan of cables subjected to these enhanced ambient conditions will be shortened. The reason why comes from chemistry, The Arrhenius Equation:
Where:
k is the rate constant, a value that describes the rate of change of concentration of a chemical reactant as part of any reaction. The rate constant is inversely proportional to the half-life of a chemical reaction.
A is a constant value that must be determined for any reaction
E is the activation energy of the reaction in J
R is the ideal gas constant in J/K
T is the absolute temperature in K
Applying this equation in detail requires a lot of knowledge about the cable itself and could only reasonably be obtained from the manufacturer. Fortunately, actual application of this equation is seldom required. It's more important to understand it at a conceptual level.
In the Arrhenius Equation, A, E, and R are all constants. The only thing that impacts the rate of the equation is the temperature T. As the temperature increases, the rate constant will also increase. The effect is nonlinear since the rate constant is proportional to e^-T. In other words, a small increase in the operating temperature can lead to a substantial change in the rate constant.
Application - How does all of this apply to conductor lifespans? If we neglect damage from mechanical stresses, then conductor insulation will only fail after some period of time due to chemical reactions. The insulation will react with the air, soil, or water around it. This reaction will be driven by the rate constants k for each reaction.
Conductor insulation is generally designed to last 20-30 years. This means that a conductor loaded to its operating temperature will last this long in the absence of physical damage. Of course, all kinds of projects have wiring much older than this installed with no problems.
The reason conductors can last so long is twofold:
Conductors are typically loaded well below their operating temperature. It is common for conductors that are loaded continuously to be operated at no more than 80% of their ampacity. This significant reduction in temperature can drastically improve lifespans because of the nonlinearity in the Arrhenius equation.
Effects are cumulative. Even if a conductor operates near or slightly over its operating temperature for a few hours each year, there are likely many more times where the conductors will be operated significantly below its operating temperature. The chemical equations governing decomposition of the insulation are always ongoing, so negative effects from slight overtemperature can theoretically be overcome with colder periods.
Conclusion - A bit of chemistry knowledge can go a long way in electrical engineering. Although the Arrhenius equation will rarely be applied in practice, we need to understand it to truly get what "ampacity" means. Conductors don't immediately melt when they exceed their operating temperature, which is why designers don't rely on all-time worst-case temperatures for design. However, predicting the impacts of overtemperature on lifespans can be very challenging and should never be utilized to justify a design.
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