Mutual inductances between crossing three-phase power lines and communication line both with earth return

The mutual inductances between crossing three-phase power lines and communication lines, both with earth return, are studied. Infinitely and finitely long power lines are both considered, and the terminal effect from the earth is taken into account. By applying the complex image theory and superposition principle, analytical solutions to the mutual inductances are derived. The solutions are valid for both oblique and parallel proximity. Comparison made with experimental results shows that the derived formulas are sufficiently accurate. In practical applications, the measured value of the earth conductivity should be used in order to obtain a higher accuracy