A method for the evaluation of the sea return impedance and application of the stochastic collocation technique to take into account the uncertainty of input parameters

We present a method for the evaluation of the sea return impedance term to be employed in the construction of the per-unit-length parameter matrix which is required to describe submarine cables in Electromagnetic Transient software. We evaluate the sea return impedance using the quasi Monte Carlo technique, and an adapted sequence of pseudo-random variables to get a faster convergence. In the calculation of the impedance integral we employ a change of variable in order to reduce its oscillatory behavior and allow it to converge. We also introduce the stochastic collocation technique in order to analyze the impact of uncertainties on the knowledge of the input parameters. This technique is well adapted to numerical calculations; it gives results similar to those obtained with a standard Monte Carlo method, but requires a minor number of computations, some units, instead of the thousands needed with the Monte Carlo method; this is an advantage because the computation time with the latter method would be too long. Furthermore this technique is non intrusive and thus does not necessitate a modification of the function. We show that for the evaluation of the sea return impedance a certain inaccuracy in the knowledge of the cables laying configuration and of the conductivities of the soil can be tolerated in some cases.