A Quasi-Monte Carlo Integration Method Applied to the Computation of the Pollaczek Integral

Abstract—This paper presents an effective numeric method to compute Pollaczek integral. This integral is widely used in transmission-line theory when computing the mutual impedance between an overhead conductor and another overhead or un-derground conductor and the earth-return impedance of an underground cable. At first, we present mutual expressions pro-posed by Pollaczek and underline the numerical complexities that often lead to the adoption of alternative simplified methods. Then a brief review of the so called “quasi-Monte Carlo ” integration method along with its advantages is given. Such an approach is then applied to compute numerically Pollaczek expressions. Com-parison between our numerical procedure and an algorithm that has already been published proves both the procedure accuracy, one of its main advantages along with its ease of implementation, and its relatively low time consumption, independent of the input parameters. Finally, as an application example, quasi-Monte Carlo method is used to assess the adequacy, for several study cases, of the simplified formula by Lucca, which is a widely used approximate expression of interest. Index Terms—Coupled transmission lines, mutual coupling, power cables, power system transients. I