Distribution of non-sinusoidal currents in parallel conductors used in three-phase four-wire networks

This paper presents an analysis of the distribution of non-sinusoidal currents among parallel-connected cables in low-voltage, three-phase TN–S systems. The cables are assumed to be laid on metallic cable trays in free space, which means that the influence of earth is neglected. An iterative algorithm is developed which can accurately estimate the distribution of line and neutral currents among parallel-connected cables at various harmonic frequencies provided that the impedance matrix of the whole cable system is given.The impedance matrices of the cable systems are calculated by a Finite Element Method (FEM) model, because – as shown – the approximate analytical equations presented in the literature introduce significant errors at frequencies above the 7th harmonic. On the contrary, a FEM model can take into account the variation with frequency of the ohmic resistance, self and mutual inductance of a cable system. The FEM model is further used to estimate the temperature at the surface of the cables.It is shown that the non-uniform distribution of the current among parallel-connected cables can be very high and that it increases with frequency and with the number of parallel cables. The proposed model is used to estimate the cable arrangement that yields almost uniform current distribution without having to transpose the cables. Examples of the distribution of the current of two common non-sinusoidal loads are presented for various cable configurations.The proposed calculation method is validated through comparison with the measured distribution of the current among eighteen 300 mm2 single-core cables in an industrial distribution substation. Measurements and calculations of the surface temperature of the individual cables showed also very good agreement which further validates the method.