Impedance of a double submarine cable circuit using different types of cables within a single circuit

The interconnection between the Upper and Lower Peninsulas of Michigan has recently been upgraded from a single 138 kV circuit to a double 138 kV submarine power cable circuit. The original circuit consisted of four single-conductor cables, the fourth cable serving as a spare phase conductor. The second circuit was formed by adding two new single conductor cables and combining them with the spare cable from the original circuit. The use of two different types of cables in one circuit causes that circuit to be unbalanced. The series impedance and shunt admittance matrices of the circuits were studied to investigate the degree to which they were unbalanced, so that the impedance relays protecting the cable could be properly set. Measurements were made on the cables after they were installed and these were compared to calculations made with the ATP EMTP Cable Constants program