Transmission models are dominated by lumped models, which describe the time dependence of transmission potentials (temperature, current and voltage). The space counterpart is not incorporated into the lumped model. To fill this gap, the present work proposes a distributed or coupled system of thermal and power equations, which depend on both space and time. The coupled system of equations were developed on the balance of thermal and power fluxes around a control volume representing the transmission lines. The Finite Difference Method is pivoted on the Crank Nicolson technique is used to solve the coupled system of equations. Transmission percentage losses ranged from 0.03 to 0.06%, which is consistent with the 5% recommended by the American Transmission Company. In addition, the simulated model results corresponded to field data obtained from the Uganda Electricity Transmission Company Limited (UETCL) on the Bujjagali - Kawanda transmission line. The coupled model system is useful for the simulation and estimation of the power losses in transmission lines respectively and could be implemented in other transmission lines.

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