This study investigates the effects of mechanical strain on the surface roughness of copper conductors, focusing on the electrolyte-refined copper (Cu-ETP, CW004A) used in H07V-U 1.5 mm2 single-core cables. For the first time, the surface roughness evolution is characterized using the power spectral density (PSD) function, enabling a detailed roughness analysis across different spatial length scales. Conductors were subjected to mechanical stress, with measurements taken at multiple stages of service life. The study confirms the results from other studies that surface roughness increases significantly in the early stages of loading, with a plateau observed in 50 % - 75 % of cycles to failure. Micro crack formation and material extrusion are identified as key mechanisms driving roughness growth, especially at small length scales, with a shift towards larger length scales as strain intensifies. The increasing Hurst exponent suggests a transformation from a random to a more persistent and correlated surface. The results underscore the potential of power spectral density analysis in understanding surface behavior in copper conductors.