Physical model for space charge distribution measured by pressure wave propagation method in coaxial geometry

With the rapid development of the science and technology, the application of the high voltage power cable has become more and more extensive. Now, it is generally accepted that space charge has an important effect on the electrical properties of insulating material in a high voltage cable. The measurement of space charge is the research base for the behaviors and properties of space charge in the polymer dielectric. Actually, the pressure wave propagation (PWP) method and pulsed electroacoustic (PEA) method are two sophisticated methods of measuring the space charge. However, these two methods are based on a planar sample. For measuring the space charge in a real cable, it is necessary to need the correct and precise mathematical expressions for the PWP method and PEA method. According to the theoretical analysis of the space charge distributions in the plate samples, measured by the pressure wave propagation method, we propose a physical model and its mathematical method of treating space charge distribution data measured in a coaxial geometry. In terms of Poisson equation, the influences of pressure waves on coaxial samples can be divided into two parts, namely, sample deformation and particle displacement. These two parts take into consideration the variations of the sample electric field, dielectric constant and density of space charge disturbed by pressure waves. Therefore, the voltage and current equations about the space charge distribution in the coaxial structure are found. The mathematical expression for the current measured indicates that compared with the current measured in the planar structure, which is proportional to the space charge distribution, the current signal measured in the coaxial structure should be further corrected. This paper also shows the experimental results which are the induced current signals picked from the planar sample and coaxial sample respectively. The results indicate that the current measured in the planar sample is proportional to the space charge distribution. However, the current measured in the planar sample is related to the inner and outer diameter of the dielectric, which verifies the correctness of the mathematical expression. Due to the influence of the coaxial structure of the high voltage cable, the pressure wave focusing effect is obvious as the pressure wave propagates along the axis, which causes the measurement signal to increase gradually with the propagation of sound wave. As a consequence, the electric field and the space charge density will change apparently. Due to the influence of the pressure wave focusing effect, the current and voltage signal will be amplified more obviously in cable, and the current measured by the PWP method shows the distribution of space charge density in cable.