Study of Harmonics in Cable-based Transmission Networks

SUMMARY The Danish electrical transmission network is currently going through major modifications. One of the main changes is the migration from a network based on overhead-lines (OHL) to a network based on underground cables. High voltage cable-based networks are a new reality that presents several interesting challenges for power engineers due to their differences to the more traditional OHL-based networks. The electrical differences between a cable and an equivalent OHL are many, the main one being the larger capacitance of the former. As a result, the behaviour of a cable-based network is also different from the behaviour of an OHL-based network. Some of the main differences are: electromagnetic transient waveforms, reactive power compensation techniques and harmonics issues. This paper focuses on harmonic studies of a cable-based transmission network, more specifically the transmission system of West Denmark as planned to 2030. This transmission network will have the entire 150kV level undergrounded, making it ideal for the study of harmonics in cable-based networks. A frequency spectrum can provide information about possible harmonic excitations and the voltage waveform during a transient. Therefore, it is necessary to assure that the model used in the digital simulation is adequate and that the accuracy of the results is sufficient. The paper focuses first on how the modelling depth and the modelling detail influence a simulation outcome. It compares two models, a first where an external equivalent network is used and a second where an extended network modelled by means of lumped-parameters models is used. The paper also describes the effect of the modelled area length, i.e., the modelling depth, in the results. The paper also addresses the influence of the cable bonding, both-ends bonding and cross-bonding, in the frequency spectrum and the impact that the number of cross-bond sections has in the frequency spectrum. The analysis is made for both positive-sequence and zero-sequence by means of simulations in the 2030 West Denmark transmission network and a meticulous mathematical analysis that is fully presented in appendix. It is demonstrated that a cross-bond cable has more resonant points than a cable bonded in both-ends. It is also proven that the magnitude of the parallel resonance points is larger for a cross-bonded cable than for a cable bonded in both-ends, whereas the magnitude of the series resonance points is lower. To finalise, the paper analyses how a deviation in the thickness of the different layers affects the frequency spectrum. It is demonstrated that the deviations allowed by the standard are sufficiently large to result in non-negligible changes in the frequency spectrum.