05_deconv - IEEE Transactions on Dielectrics and Electrical...

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Novel Numerical Methods for Measuring Distributions of Space Charge and Electric Field in Solid Dielectrics with Deconvolution Algorithm Luoquan Hu, Yewen Zhang and Feihu Zheng Pohl Institute of Solid State Physics Tongji University Shanghai 200092, China ABSTRACT The deconvolution algorithm for measuring the distribution of space charge under ( ) dc by the pressure wave propagation PWP method is studied in this paper. A new Fredholm integral equation of the first kind, including a space charge distribution without a partial differential operator is presented. Numerical methods based on Tikhonov regularization for solving this integral equation and the original PWP equation are studied. Numerical simulation is studied for the effect of signal-to- ( ) noise ratio SNR , and comparison with other algorithms is discussed. The numer - ical solution of an electric field distribution from measurements of a LDPE speci - men is obtained successfully. Index Terms — Space charge, deconvolution, Tikhonov regularization, solid dielectrics. 1 INTRODUCTION PACE charge in solid dielectrics plays a very S important role in the insulation properties of polymers w x under high voltage 1, 2 . Since the 1980’s, many re- searchers have worked on the space charge distribution measurement in solid dielectrics, and studied the behavior of space charge within. The pressure wave propagation Ž . PWP method is an important method measuring space charge distribution in solid dielectrics. This method has been widely used in space charge research for understand- ing the charge behavior in solid dielectrics. However when using the PWP measurement method, the electric field, Ž . E z , in a specimen, is included in an integral equation named Fredholm integral equations of the first kind Ž . w x FIEFK 3 . In order to get the real electric field distribu- tion, a deconvolution algorithm should be utilized. How- ever, it is relatively difficult due to an ill-posed problem in FIEFK. There are already several types of deconvolution w x methods to solve FIEFK 4, 5, 6 . They can generally be w x divided into two groups, Tikhonov regularization 7, 8 , and w x iterative regularization 9, 10 . Abou-Dakka used a modi- fied inverse matrix method to treat high signal-to-noise Ž . ratio SNR data, but the result of this method is not steady w x 11 . If the voltage of an open circuit is measured, the Ž . electric field, E z is included in a standard FIEFK. From this equation, a direct deconvolution method can be Manuscript recei ® ed on 26 May 2004, in final form 11 October 2004. adopted. Ditchi has studied this problem in detail by w x means introduced by Philips 12, 13, 14 . However, the re- sults are not perfect. If the short circuit current is mea- sured, a differential form of pressure wave is included in a standard FIEFK. Because the differential form of pres- sure wave can only be determined appropriately, this equation is more complex for a direct deconvolution method, unless some special methods are adopted. This paper introduces a new FIEFK through the mathematical transformation of the original integral equation. With
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