This paper proposes a method for the quick estimation of the average voltages at terminal loads when the transmission line translate randomly and analyzes the sensitivities of the loads' voltages to the translation. Because nonuniform transmission lines can be approximated as n-cascaded uniform lines, the study of uniform lines is the basis. Based on the transmission-line equations, the equations are derived to estimate the average voltages, the voltage variations, and the sensitivity of the voltage to the random translation when transmission lines have random translation in their cross sections. With these equations, the average voltages at the loads, the probability distributions of the voltage variations, and the sensitivity of the voltage to the random translation can be obtained quickly. A two-wire line over the ground is studied by using the proposed method. The average voltages and the voltage variations' probability distributions agree well with those via the Monte Carlo (MC) method and the proposed method is more efficient. The results show that the sensitivities of the voltages at the loads to the random height increase with the terminal sources but decrease with the height.
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