Analysis of Capacitance to Ground Formulas for Different High-Voltage Electrodes

Abstract

Stray capacitance can seriously affect the behavior of high-voltage devices, including voltage dividers, insulator strings, modular power supplies, or measuring instruments, among others. Therefore its effects must be considered when designing high-voltage projects and tests. Due to the difficulty in measuring the effects of stray capacitance, there is a lack of available experimental data. Therefore, for engineers and researchers there is a need to revise and update the available information, as well as to have useful and reliable data to estimate the stray capacitance in the initial designs. Although there are some analytical formulas to calculate the capacitance of some simple geometries, they have a limited scope. However, since such formulas can deal with different geometries and operating conditions, it is necessary to assess their consistency and applicability. This work calculates the stray capacitance to ground for geometries commonly found in high-voltage laboratories and facilities, including wires or rods of different lengths, spheres and circular rings, the latter ones being commonly applied as corona protections. This is carried out by comparing the results provided by the available analytical formulas with those obtained from finite element method (FEM) simulation, since field simulation methods allow solving such problem. The results of this work prove the suitability and flexibility of the FEM approach, because FEM models can deal with wider range of electrodes, configurations and operating conditions. power supplies composed of several modules in series, since in [9] it is proved that the stray capacitance to ground has a significant impact on the individual voltage of each module. In other high-voltage applications, including high-voltage transformers [10] or high-voltage motors, parasitic capacitances have a key role to predict the frequency behavior of such machines.Accurate methods to calculate the capacitance are based on the calculation of the electrostatic field generated by the system of charged objects under consideration [3]. The capacitance of basic isolated geometries, such as very long horizontal cylindrical conductors, coaxial cylindrical conductors, concentric spheres, or spheres well above ground, can be easily deduced theoretically. However, such formulas have very restricted practical use. The calculation of the capacitance of conductive objects which are close to ground leads to challenging mathematical problems, even for simple geometries. Therefore, analytical solutions for capacitance only exist for a limited number of electrode geometries and configurations, which have almost no practical applications [11], and often only contemplate the stray capacitance to ground, thus disregarding the effects of nearby grounded electrodes, structures or walls [3].As a consequence, computational methods are increasingly being applied to solve such problem, although most of the published works deal with very particular problems, such as insulator strings [4,5,7], transformer windings [10]...

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