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Abstract
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.
Highlights
Traditional methods for contact voltage measurements for transmission lines are limited in their application due to their large size, high price, and narrow frequency domain response [1,2,3]
Regardless of applying non-contact optical sensors or non-contact electric field coupling sensors [8,9,10,11,12], the transmission line voltage can be obtained by inverse calculation with the exact measurement data of the electric field
This paper proposes a unified error transfer model and uncertainty evaluation standard that can be applied to all the electric field numerical integration methods to improve the relevant discussion
Summary
Traditional methods for contact voltage measurements for transmission lines are limited in their application due to their large size, high price, and narrow frequency domain response [1,2,3]. Wang et al proposed inverse calculation of the transmission line voltage using a D-dot sensor and Gauss numerical integration in 2018, and their experimental test results were reliable, with a relative error size of below 0.5% [16,17] This measurement was carried out under relatively ideal conditions. The current research does not discuss the possible error sources in actual applications and the influence of error propagation on the final voltage measurement results, resulting in the inability to optimize the numerical integration method for calculating the transmission line voltage from the sources of error, and the difficulties in practical application. An error propagation model of the electric field numerical integration method for measuring the voltage of the transmission line is proposed to judge the accuracy of various methods, and the uncertainty evaluation criteria are established, based on the error, to measure the stability and reliability of the algorithm
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