Sequence impedances of insulated cables: measurements versus computations

The computation of the sequence impedances is a very important topic for insulated cable systems chiefly in HV and EHV levels. This highlights the importance of using reliable procedures in order to compute these impedances since, up to now, their computations are based on simplified formulae. In this paper, results of some measurement campaigns have been compared with both simplified IEC formulae and advanced matrix procedures based on Multiconductor Cell Analysis (MCA) [1, 2, 3, 4]. MCA considers the cable system in its real asymmetry without simplified and approximated hypotheses. One of the advantages of the MCA is the possibility of supplying the cable system with three sequence voltage phasors and of computing the ratios between voltage and current phasors for each phase. Both in planning and operating activities, power flow and short circuit studies are always based on the knowledge of the sequence impedances. Furthermore, the correct behaviour of network protection (mainly distance relays) is strictly depending upon their correct settings which are based on the positive-negative and zero sequence impedances. Moreover in the planning phase of a new underground cable (UGC) link the evaluation of its impact on the grid needs to know the sequence impedances. It is worth remembering that the use of zero, positive-negative sequence impedances Z0, Z1, Z2, is only exact if the system is symmetric since the application of voltage phasors of a sequence causes the circulation of current phasors only of the same sequence so that it is possible to compute the ratios between voltage and current phasors. For cable lines, this assumption is only true if the insulated cables are cross-bonded (CB) with phase transpositions (PTs) or if they are cross-bonded in trefoil arrangement. In all the other cases, the use of the sequence impedances Z0, Z1, Z2 would be theoretically mistaken. Even if an insulated cable is cross-bonded with PTs (or in trefoil arrangement) there could be causes of asymmetry:  minor sections with different lengths, so that the induced currents in the screens are not zeroed;  the presence of joint chambers and terminals which introduce a flat arrangement and a consequent asymmetry;  crossings of possible interfering services or natural obstacles usually overcome by means of directional drillings which can introduce a great spacing between the cables. If the line length is long enough, the presence of these installation differences can become less important but theoretically they would give always an asymmetric system. In this context, as already highlighted, it would not theoretically licit to refer to the sequence impedances.