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A8D14916d01 - 148 IEEE TRANSACTIONS ON ELECTRICAL...

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IEEE TRANSACTIONS ON ELECTRICAL INSULATION, VOL. EI-6, NO. 4, DECEMBER 1971 Computation of Electric Field Distributions in High-Voltage Equipment HUGH M. RYAN, MEMBER, IEEE, JOHN M. MATTINGLEY, AND MALCOLM F. SCOTT Abstract-In an earlier paper two of the authors described a general-purpose digital computer program suitable for solving, with considerable precision, multidielectric fields in two dimensions or in three dimensions with at least one axis of symmetry. The program, after being rigorously checked, has been extensively used for several years to solve many practical multidielectric field problems; on all occasions it has been completely satisfactory. This paper, in addition to presenting supplementary program details, presents a few applications of the numerical method to high-voltage equipment design. INTRODUCTION C< ONSIDERABLE interest has recently been shown in developing numerical techniques for solving practical electric fields [1]-[13]. In a previous paper [1] a general-purpose digital computer program was described that is suitable for solving practical multi- dielectric field problems in two dimensions and in three dimensions with one axis of symmetry. For several years, extensive use has been made of this program in insulation design and development studies for bushings, circuit breakers and control equipment, transformers, and fields associated with high-voltage laboratory equipment. Further, with the aid of supple- mentary digital computer programs, developed to facili- tate detailed determination of potential gradients, this general purpose program has been extremely useful when predicting breakdown voltages in gases, for gas-insulated equipment, and for a wide range of electrode configura- tions and test conditions, using either the empirical ap- proach [13]-[15] or the semiempirical method [16] sug- gested by Pedersen [17], [18]. Rigorous early validation studies have confirmed that a high degree of precision is attainable for both closed- and open-type multidielectric field systems; errors in computed potentials can generally be kept to less than 1 percent in any region of interest. Certain practical fields do not possess, nor can they be assumed to possess, symmetry. Although such problems are not yet amenable to direct solution using this pro- gram, an approximate two-dimensional technique, shortly to be reported, based on Boag's simple approach [18], is often useful. The present paper gives a few typical examples that demonstrate the application of the computer program to Mantuscript received November 16, 1970; revised June 7, 1971. The authors are with A. Reyrolle and Company, Ltd., Heb- burn, County Durham, England. practical power frequency multidielectric fields amenable to direct solution. DIGITAL COMPUTER PROGRAM The general-purpose digital computer program de- scribed by Galloway et al., [1] and outlined in Fig. 1 has been developed to solve the Laplace equation V24 = 0 in two dimensions or in three dimensions with at least one axis of symmetry. A system of rectangular grids of unequal size is used to set up finite difference
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