Electric field numerical integration algorithms can realize the non-contact measurement of transmission line voltage effectively. Although there are many electric field numerical integration algorithms, lack of a comprehensive comparison of accuracy and stability among various algorithms results in difficulties in evaluating the measurement results of various algorithms. Therefore, this paper presents the G-L (Gauss-Legendre) algorithm, the I-G-L (improved Gauss-Legendre) algorithm, and the I-G-C (improved Gauss-Chebyshev) algorithm and proposes a unified error propagation model of the derived algorithms to assess the accuracy of each integration method by considering multiple error sources. Moreover, evaluation criteria for the uncertainty of transmission line voltage measurement are proposed to analyze the stability and reliability of these algorithms. A simulation model and experiment platform were then constructed to conduct error propagation and uncertainty analyses. The results show that the G-L algorithm had the highest accuracy and stability in the scheme with five integral nodes, for which the simulation error was 0.603% and the relative uncertainty was 2.130%. The I-G-L algorithm was more applicable due to the smaller number of integral nodes required, yet the algorithm was less stable in achieving the same accuracy as the G-L algorithm. In addition, the I-G-C algorithm was relatively less accurate and stable in voltage measurement.
Keywords: error transmission; numerical integration of electric field; transmission line voltage measurement; uncertainty evaluation.