ABSTRACT
Uncertainty is a major issue facing electric utilities in planning and decision making.
Modeling uncertainty can be based on two general approaches. The first is a probabilistic
approach where probability distributions for all of the uncertainties are assumed. The second
approach is called “Unknown but Bounded" in which upper and lower limits on the
uncertainties are assumed without probability distributions. Interval mathematics provides a
tool for the practical implementation and extension of the unknown but bounded concept. The
calculation of HVDC transmission lines fields is used as an example to illustrate the use of
interval mathematics. Ground- level electric field values are calculated using the traditional
single point numbers as well as interval numbers. Various geometries for monopolar and
bipolar dc lines are considered. The values from the two methods are compared to prove the
validity of interval analysis to, practically, model uncertainties associated with HVDC
transmission lines field analysis. Procedures devised to reduce the width of the resulting
interval bounds either through rearranging the governing expressions or through derivation of
interval probability are discussed.