Multi-scale formulation of admittance-based modeling of cables

•Modeling of cables using the nodal admittance representation exploiting the folded line equivalent.•Rational modeling with analytic signals or complex variables.•Development of a re-initialization scheme to allow variable time-step simulations.•Improvement of numerical efficiency of time-domain implementation of pole-residue representation of the nodal admittance matrix.•Multi-scale simulation of admittance-based models in phase coordinates that does not require interpolations of the propagation function as it relies on a rational approximation of the nodal admittance matrix based on the Folded Line Equivalent.•Extension of the FAST framework to include full frequency dependent cable models considering both underground and submarine cables. This paper proposes a novel multi-scale cable model in phase-coordinates exploiting the fully-coupled structure of the nodal admittance matrix instead of using the conventional approach based on the Method of Characteristics (MoC). The usage of the admittance modeling allows a straightforward representation of cables regardless of their lengths as it does not require a minimum time-step below the transient time associated with the fastest mode. In addition, some accuracy issues regarding the rational modeling of the nodal admittance matrix are overcome resorting to the Folded Line Equivalent (FLE) transformation. Following the so-called frequency-adaptive simulation of transients (FAST) concept, the trapezoidal rule and recursive convolution expressions are rewritten to perform computations using analytic signals or complex variables. This will allow the possibility to combine electromagnetic and electromechanical trasients phenomena in the same simulation environment with a unique mathematical model. A novel variable time-step algorithm is presented and its flexibility is so general that can be incorporated in Electromagnetic Transient (EMT) software such as EMTP-RV, PSCAD or Hypersim in straightforward way. Besides keeping the accuracy of the classic EMT-modeling, the proposed formulation provides a sensible gain in the overall computation time without significant loss of accuracy and also smooth transitions regardless of the time-step length.