Studies on long lines of power transmission remain a controversial subject up to this day in view of the unsatisfactory results. These studies often address cases where the line is connected to a node which is perfectly voltage regulated. Likewise, the telegraph equations, reflecting how these lines work, express the voltage and current of the source as a function of the voltage and current along the line. Thus, our study examines the case of a line connected to an unregulated node. Regarding the telegraph equations dedicated to long lines, we will take care to express the voltage, the current and the joule losses according to the length of the line considered as variable while the voltage and the current of the source constitute constant. This way of approaching the study allows us to design an optimal compensation plan in order to maintain an ideal voltage profile.
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