A Fourier transform technique for calculating cable and pipe temperatures for periodic and transient conditions

An underground pipe-type cable system is represented by a thermal impedance network. A ladder network of resistances/capacitances represents the cable out to the outer surface of the pipe. The earth, adjacent pipe-type cables, and cable images are modeled by a frequency dependent thermal impedance found by solving the heat transfer differential equation. The heat input to the system is conductor I² R loss. The heat input can be a periodic signal or a transient of up to 300 h. A fast Fourier transform (FFT) is used to obtain heat input in the frequency domain. The frequency domain thermal input at the conductor is divided by the thermal admittance seen by the conductor and an inverse FFT is used to obtain conductor temperature as a function of time. A similar procedure obtains shield and pipe temperature. Iteration is used to model conductor electrical resistance change with temperature. The ambient temperature and temperature due to dielectric loss is added in to obtain final values