The application of length dependent external transmission line impedances to power system analysis

This thesis presents the derivation, evaluation and application of the length dependent external impedance to typical transmission line configurations in power systems. In particular, this thesis is concerned with improving the accuracy of power frequency studies in the design phase for distribution networks. Existing methods for calculating the external impedance are generally based on the per unit methodology, which assumes that the source conductor is of infinite length. For short transmission line lengths, which are typical in distribution networks, this assumption may not hold. This has the implication of artificially increasing the external impedance for short lines. This can have adverse effects on typical studies such as public safety analysis (step and touch potentials) and induction into adjacent third party infrastructure. This can result in excessive mitigation costs post design. To evaluate the resulting length dependent external impedance expressions, a novel method, the length dependent matrix pencil method, is implemented in this thesis. The method leverages of the matrix pencil method, which facilitates approximations of the integral kernels by sums of complex exponential terms. This in turn allows the resulting expressions to be evaluated analytically, removing the need for time consuming numerical integration routines. The proposed evaluation technique is applied to the three most typical configurations encountered on a power system. These are the overhead, underground and mixed overhead and underground transmission line systems. The performance of this algorithm, for each of these configurations is tested over a wide range of parameters to ensure accuracy in typical power system operating conditions. The results of the evaluation inform designers under what conditions a length dependent approach is beneficial. Finally, the length dependent method is validated through field testing a 4.6km long dual circuit transmission line. The results of the experiment highlight the increased accuracy obtained for voltages and currents measured on the transmission line using a length dependent approach versus the per unit methodology.