15 Section 1 EMC OF ELECTRICAL POWER EQUIPMENT MUTUAL INDUCTANCE BETWEEN WIRES IN HELICALLY TWISTED POWER CABLES BERND W JAEKEL GERMANY Siemens AG Automation and Drives Germany e mail bernd jaekel Abstract The arrangement of the conductors in a multi core power cable leads to a situation where various conductor loops are built up One or several loops are formed by the phase and neutral conductors with the operational current flowing in these conductors A further loop is built up by the protective earth conductor which is connected to the equipotential bonding system at several locations The area of this loop is essentially arranged outside of the power cable The inductive coupling from the phase conductor loops into that loop causes common mode voltages in the protective earth system with consequent common mode currents It can be demonstrated that this effect even takes place in the case of balanced phase currents in the cable Numerical simulations and parameter studies were carried out in order to describe this effect quantitatively and to investigate the influence of different cable parameters onto the resulting common mode voltages Introduction Power cables represent components of an entire power supply network which can be carried out in different types If an earthed system is required i e a system which is connected to the local reference earth mainly two types of supply networks can be distinguished TN C and TN S From an EMC point of view a TN S power network should definitely be preferred 1 In this type of network the neutral and protective earth PE conductors are strictly separated except at one net point where both conductors are connected normally at the transformer or the switchgear This type of installation prevents that any operational currents flow outside of the phase and neutral conductors No cable net currents should exist and therefore the equipotential bonding system is generally assumed to be free of any operational currents But when looking in more detail at this type of network and at the physical structure of power cables some physical mechanisms can be identified which nevertheless lead to the generation of common mode voltages and common mode currents even in the case of balanced loaded TN S power net systems Low Voltage Power Cables Multi core low voltage power cables consist of the phase conductors and depending on the grounding arrangement of the power supply network of a neutral conductor and or a PE conductor An example for the structure of a power cable is shown in Fig 1 for a cable of type NYY Each of the conductors as well as the entire conductor arrangement are covered by an insulation for which a material is chosen depending on the specific requirements and fields of applications 2 The n individual insulated conductors are twisted together and each conductor can be represented by a helical line An appropriate cylindrical coordinate system for describing the spatial arrangement of a conductor is shown in Fig 2 together with the relevant parameters such as a as the radius of the helical line with respect to the centre line of the cable and the pitch distance p as the twist length of the cable i e the length of the cable per rotation of the conductors For simplicity reasons only one conductor is shown The further n 1 conductors can be represented as similar lines and they are rotated by an angle 3600 n with respect to that one shown in Fig 2 Fig 1 Multi core power cable of type NYY Common Mode Voltages in Power Cables The magnetic flux density B caused by the currents in the individual conductors can be calculated by means of the Biot Savart law as long as the situation at the power frequency range is considered C r d 3 0 4 rrrI B 1 I represents the phasor of the exciting alternating current r with its cylindrical coordinates r z denotes the observation point and r with its cylindrical coordinates r z means a variable point on the line current Though this expression can be easily solved in the case of straight wires the situation is relatively complex in the case of power cables where the various conductors are twisted and each conductor can be represented by a helical solenoid see Fig 2 PE conductor phase conductors 16 In power cables where a protective earth conductor PE conductor is twisted along with the phase conductors an inductive coupling exists between the phase conductor loops and a loop built up by the PE conductor and its connecting structures to the equipotential bonding system This effect can be explained by means of a schematic sketch of a 4 conductor cable as shown in Fig 3 For reasons of clarity the twisting of the conductors is not shown in the figure Fig 2 A twisted conductor helical line in a cylindrical coordinate system 3 The conductors L1 L2 for example form a spatial loop in which the phase current IL1 L2 flows Corresponding loops are built up by the arrangement of conductors L1 L3 and L2 L3 with the loop currents IL1 L3 and IL2 L3 respectively A furth