Calculation of earthing and screening effects of compensation conductor laid alongside underground multi-cable power lines

Power substations in an urban area are interconnected by high voltage underground power cables, resulting also in interconnections of their earthing grids through cable metallic screens/sheaths. Most modem power cables with XLPE insulated core have metallic screens which are practically insulated from ground. These screens can only be (and usually are) grounded at cable ends and therefore do not act like extra earth electrodes extending from a station. In this case, almost the same positive earthing effects of an extended electrode can be obtained only by extending an auxiliary wire in the same trench and routing it closely parallel to the power line. This bare conductor also provides better screening for nearby telecommunication circuits against inductive interference. This paper presents an analytical method to determine the line-to-ground fault current distribution and related voltages in the earthing system which consists of two substation earthings interconnected by insulated metal sheaths of modern XLPE cables and one bare earthing wire laid in parallel in the same cable trench. The analytical expressions, derived by solving a set of differential equations, are based on the assumption of uniformly distributed conductance between the earthing wire and earth. The proposed mathematical model takes into account mutual inductive couplings between all conductors (phases, cable sheaths and the bare conductor). In addition the paper presents a procedure for computing the resulting nominal screening factor of multi-conductor connection between two substations. The earthing and screening effects of one bare conductor laid parallel to double cable power line are numerically illustrated and outlined. As differences in numerical results show, the calculations with individual line reduction factors should not be used if more than one power line exist in the same trench.