Application and error analysis of the quadrature methods in the voltage transformer

The distribution of the electrical field between the two electrodes under 1 kV DC voltage was simulated with the Ansoft software, and then the voltage value was deduced by the quadrature formula with limited electrical field sensors. To compare the inherent error of different quadrature methods on the voltage measurement, three kinds of the typical quadrature methods were conducted: Gauss, Simpson, and Gauss-Legrendre quadrature. It was revealed that more accurate value could be achieved with the Gaussian quadrature. The relative error of the Gaussian method with three samples was below 0.2% in the condition without outer interference. The additional error caused by outer interference and the misplacement of the electrical field sensors was also given with the further calculation. When the interference was kept away from the quadrature route, the influence could be reduced. From the simulations and the calculations, it was concluded that the Gaussian quadrature could meet the same accuracy with fewer sensors, so it could be more efficient on the high voltage measurement.