**6. Discussion**

With regard to the ±500 kV line, it is observed that this line presents an RI level (53.85 dB) below the maximum tolerable limit recommended by the relevant standards, which is usually 60 dB in the reference measuring point [18]. Nevertheless, optimization studies, such as the one applied in this case, allow for maintaining an acceptable RI performance of the line at even higher altitude regions. Considering an RI altitude correction factor of 1 dB/300 [19], the initial HVDC line design would exceed 60 dB at an altitude of 1900 m above the sea level; however, with the optimization applied, this line would present an acceptable RI performance (59.23 dB) until 2700 m above the sea level. On the other hand, even though the number of sub-conductors was reduced from 4 to 3, because of the increment in the sub-conductor radius, the total mass of the bundle increased from 8540 kg/km to 10,293 kg/km. This increment of 1753 kg/km (20.5%) in the total mass of the bundle should be evaluated from an economic point of view as well as from the strength of the tower to support this new load [20,21].

Regarding the ±600 kV HVDC transmission line, the RI value computed at the reference point (23 m, 1.0 m) is 61.27 dB, exceeding the limit of 60 dB for this voltage level. With the adjustments in the sub-conductor radius and bundle spacing derived from the optimization study, the RI value was reduced to 58.88 dB. This optimal case involves the use of larger conductors, increasing the total mass of the conductors by 5184 kg/km (60.7%), therefore, for this option, the adjustments derived from the optimization study seem to be feasible only in those cases that consist in the conversion of an AC line to DC operation, where one of the phases is removed.

In future work, it would be interesting to consider other variables, such as the height and the distance between the poles, a comparison of di fferent configurations of the line (horizontal and vertical), and the inclusion of shielding wires in the model. Also, to determine the feasibility of the increment of the sub-conductor radius, it is necessary to consider the maximum mass that the towers can support as a constraint in the optimization study.
