## Non-contact voltage measurement of three-phase overhead transmission line based on electric field inverse calculation

With the development of smart grid, the demand for voltage measurement along the overhead transmission lines is increasing. However, the installation of voltage transformers in the existing lines entails numerous difficulties. This study proposes a new non-contact measurement method by inversely calculating the voltages on AC overhead transmission lines based on the power-frequency electric field measurement data. To improve the calculation accuracy, the 3D model of transmission lines is built, and the relations between the 3D electric fields and voltages are presented. An improved algorithm that intermingles with the particle swarm algorithm and genetic algorithm is developed to ascertain optimal inverse solutions, meanwhile to improve the convergence speed and calculation stability. To further reduce the computational complexity, the constraint relations between the voltages and electric fields are derived, thereby the simplification from three decision variables to one is achieved. Then, some simulation cases with different measurement errors and voltage running states are conducted to show the good robustness and high accuracy of the proposed inversion method. Finally, a three-phase experimental system is built and the actual measured data are used to inversely calculate, which verifies the practicability of the proposed non-contact voltage measurement method.