Analytical Thermal Cable Model for Bundles of Identical Single Wire Cables

Overcurrents may lead to critical temperatures in cable systems. Fuses can protect the cable insulation from damage. As the classically used melting fuses cannot fulfill the growing requirements concerning diagnosis, reset behavior, or fail safety, electronic fuses based on power transistors are more and more introduced in modern systems. As reliable temperature measurements are complex, the electronic fuses are often controlled by the electrical currents flowing through the semiconductor by, e.g., a microcontroller. On the microcontroller the cable temperature is estimated from the current based on an electrothermal cable model. When the temperature exceeds a given threshold the transistor interrupts the current flow. Therefore, accurate and computationally simple thermal cable models are necessary. Complex numerical solutions are inappropriate. For single wire cables several calculation methods are known already, for arrangements of several wires with insulation these methods are not accurate enough. This article presents an analytical thermoelectric calculation method for multiconductor cable arrangements consisting of several identical single wire cables. An approach for the determination of important model parameters is presented and the final model is validated for a power over data line application. The model is exemplarily applied for calculating the temperature developments and ampacities in cable bundles consisting of a different number of cables and for the comparison between a solid and a stranded cable.