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Unformatted text preview: IEEE Transactions on Electrical Insulation Vol. EI-20 No.3, June 1985 519 APROBABILISTIC INSULATION LIFEMODEL FOR COMBINED THERMAL-ELECTRICAL STRESSES G. C. Montanari and M. Cacciari Istituto di Elettrotecnica Industriale University of Bologna Italy ABSTRACT The Weibull distribution is widely used in statistical problems related to aging of solid insulating materials subjected to electrical stress. The main object of this paper is to explain the Weibull probability function in such a way that it can be applied to the statistical analysis of the risk of failure for solid insulating materials or structures subjected to single or combined (in particular thermal-electrical) stress situations. For this purpose, appropriate expressions for the scale and shape parameters of the two-parameter Weibull function are proposed, starting from a model for combined-life, based on the inverse power model for electrical life and the Arrhenius relationship for thermal life. The agree- ment of the statistical model thus obtained has been verified by means of experimental tests carried out on Low-Density Polyethylene. INTRODUCTION order to study, from a statistical point ofview, the aging phenomenon iCn an insulating material subjected Many problems related to the statistical treatment to combined thermal-electrical stress. In particular, of times to failure of solid insulating specimens sub- the case of materials having life times followingthe jected to ac voltage are usually solved byusing the inverse power model (ipm) will be examined, and the Weibull probability function. This function, in its agreement of the proposed expression of the cumulative commonly used two-parameter form, has the following probability function with experimental results ob- expression [1-5]: tained for a Low-DensityPolyethylene (LDPE), will be tested. F(t) = 1 - exp[ (a)] (1) L ~'J DETERMINATION OF THE WEIBULL CUMULATIVE MODEL The scale and shape parameters, a and S, are obvious- FOR COMBINED THERMAL-ELECTRICAL STRESS ly not constant, but functions of the applied stresses. In order to obtain appropriateexpressionsfor the In particular, in the case of an insulating material coefficientsof Eq. (1), a reparametrization of the subjected to combined electrical-thermal stress, the Weibull function is required. scale and shape parameters are functions of voltage and temperature, e.g. =c=a(E,T) and S=B(E,T). Since a is the time to failure for 63.2% probability, a(E,t) can beexplained once appropriate expressions for Hence, it is important to find an appropriate expres- electrIcal and combinedstresses are assumed. In par- sion for these functions to solve problems related to tclr flf ie olwteivrepwrmdl the reliability of electrical apparatus and products, th folwn eqain.o obne i e c n b sd where limiting values for the failure probability must often be considered....
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