Matrix methods for the evaluation of simultaneous faults in three-phase systems

The paper illustrates two methods whereby the steady-state impedance matrix in terms of symmetrical component parameters may be obtained for a 3-phase system with multiple unsymmetrical faults. In the first method all faults are replaced by a balanced condition for which the symmetrical component impedance matrix is easily obtained using Stigant´s rule. This matrix is then transformed to that of the faulted network by means of a connection matrix and relationships developed by Kron. The second method shows how Stigant´s rule may be used to write down the impedance matrix of the symmetrical component network representing the unsymmetrical system.