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This paper presents a new method for computing internal voltages and currents along transmission lines. The approach is an extension to the existing method of characteristics (MoC)-based line models and computes the voltage at internal points as a superposition of forward and backward waves. These waves are obtained by convolution between the reflected wave and the propagation function from the line end to the considered position. This voltage profile component (VPC) permits computing the voltage at arbitrary points along the line while avoiding the error accumulation that can result when cascading line models. The VPC can be utilized with any MoC-based approach and has been used in this paper together with the universal line model in order to obtain a model of very high accuracy. The VPC approach is demonstrated to give more accurate results than a cascade of regular line models in the case of fast front transients.