PurposeThe purpose of this study is to obtain the optimal frequency for low-frequency transmission lines while minimizing losses and maintaining the voltage stability of low-frequency systems. This study also emphasizes a reduction in calculations based on mathematical approaches.Design/methodology/approachTelegrapher’s method has been used to reduce large calculations in low-frequency high-voltage alternating current (LF-HVac) lines. The static compensator (STATCOM) has been used to maintain voltage stability. For optimal frequency selection, a modified Jaya algorithm (MJAYA) for optimal load flow analysis was implemented.FindingsThe MJAYA algorithm performed better than other conventional algorithms and determined the optimum frequency selection while minimizing losses. Voltage stability was also achieved with the proposed optimal load flow (OLF), and statistical analysis showed that the proposed OLF reduces the frequency deviation and standard error of the LF-HVac lines.Originality/valueThe optimal frequency for LF-HVac lines has been achieved, Telegrapher’s method has been used in OLF, and STATCOM has been used in LF-HVac transmission lines.