With an increase in population of the country day by day and with high growing speed of geographical residential plots, the demand by the public for new set up of electrical power transmission system has become a common mandate. Therefore it is the responsibility of the concerned authority to protect the interests of common man in a smart manner and develop solutions for the growth of country in an intelligent way keeping safety of public as prime importance. This paper proposes an Affine Arithmetic approach of mathematical modelling to estimate the safety parameters of AC transmission line leading to sag, like, temperature, wind loading, ice loading, weight of the conductor, stress, tension, pressure etc., taking into account the uncertainty conditions so that the solutions developed address in real time. The proposed model is executed in MATLAB integrated development environment and gives the complete behavior of sag in transmission lines with respect to each of the safety parameters individually and closely ascertains the safety threshold limits considering 50% factor of safety and 5m ground clearance. The critical safety threshold limit for wind loading is found to be about 3.02 kg/m and the typical value is about 1.51 kg/m. Similarly, the critical safety threshold limit for weight of ice is found to be about 1.45 kg/m, whereas its typical value is about 0.7 kg/m. Extending further, the critical safety threshold limit for conductor weight is found to be about 3.07 kg/m, whereas its typical value is about 1.6 kg/m, which is a close approximation to the typical weight per unit length of industry-grade conductors like Aluminum Conductor Steel Reinforced (ACSR). The critical safety threshold limit for tension in the conductor and the span lengths are found to be 1850 kg and 230m respectively.