Discussion on modeling of voltage endurance

The model most widely used in voltage endurance to predict life of electrical insulation starting from the results of accelerated tests is the so-called inverse-power model, according to which the voltage endurance line is a straight line if plotted in bilog paper. However, the voltage endurance data very often do not fit a straight but a curved line in which we can distinguish three basic parts. The first, for short times for a few seconds to a few hours, has a smaller slope than the middle part, which is practically straight up to many hundreds or thousands of hours according to the insulating material. The slope of this line gives the value of the voltage endurance coefficent (or life exponent) which is fundamental in insulation design. In this range of voltage gradients breakdown is due to electrical trees developing from weak points in the insulation and thus statistics govern the process. In the design of actual insulators, starting from the results of tests on samples of smaller size, we must take into account the dimensional effect which consists of a reduction in the breakdown strength as the insulation size increases. After a certain time the life line begins to curve and the voltage gradient tends to a threshold below which electrical ageing no longer takes place in insulation. If the threshold appears at times shorter than the expected life in service, the insulating material must operate at or below the threshold. But in this way we no longer have weak points, because below the threshold we no longer have electrical ageing: Thus the dimensional effect disappears and statistics do not govern the process. If on the otherhand, the threshold is so low that we must choose a service stress higher than this, we accept a certain breakdown risk which can be calculated by means of statistical tools, starting from a given distribution of breakdown probabilities, usually the Weibull distribution. In this case the most convenient model for predicting life is the inverse-power one, not only because of better agreement with the experimental results but above all, because it is supported by statistical considerations. In the other case, when the service stress must be lower than the threshold in order to ensure a satisfactorily long life of insulation we can choose another model appropriate for this situation. This model is the exponential with the threshold, a simple equation which permits the threshold to be found in a rapid and accurate way from the results of normal voltage endurance tests. The first case is typical for cable insulation. The second is characteristic of epoxy resins and in general of electrical machine insulation, as shown by the results of tests on many insulating materials reported in the paper. The discussion above also explains the different philosophy by which the specialists in the two kinds of insulation approach the problem of voltage endurance.