With the increasing use of switch controlled devices within power systems, it has become necessary to have a detailed knowledge of the harmonic currents and resonant overvoltages occurring throughout a power system, so that measures can be taken to avoid harmonic associated problems such as motor overheating, capacitor and cable overloading, telecommunications interference and maloperation of protection, metering and control equipment. To obtain this information, it is necessary to use analysis techniques and models which are capable of describing the system in detail.
This thesis examines various methods used for the analysis of power systems. The methods which are investigated, progress from those based on the frequency domain techniques, through to those based on state space and time varying Norton equivalent techniques. Particular emphasis is given to the application of these methods for the harmonic analysis of autotransformer traction systems.
Following the description of various types of alternating current traction systems, the requirements of a harmonic analysis technique are defined for autotransformer traction systems. Investigation of the properties of various two-port network descriptions then leads to the development of a frequency domain power system analysis procedure called. Modified Cascading. Modified Cascading is a numerically stable procedure which permits detailed modelling of branches which contain passive linear elements, changes in the number of phases, phase transpositions and independent sources. Because of its numerical stability properties. Modified Cascading is particularly useful for analysing systems which have detailed earthing networks and contain large shunt admittance components. Voltages and line currents can be determined anywhere within the power system network. Following the development of Modified Cascading, it is shown how it may be simplified for tree structured power systems.
Modified Cascading is used for the analysis of various autotransformer traction systems, from which the resonant characteristics are determined. The results of field tests on an operational autotransformer traction system indicate that the analysis technique and models can accurately determine the resonant frequency. The resonant level and the exact phase of the resonant component are more difficult to match. This is due to the inherent assumptions of frequency domain methods, which exclude the effects of time domain interactions between non-linear devices and the rest of the power system.
An alternative analysis philosophy is proposed to include the dynamic interactions between the supply system and the non-linear loads. This analysis technique is based on state space methods and uses weighted linear least squares to estimate single-input multi-output state equation models from frequency domain responses. Existing methods are used to model the non-linear devices. This analysis procedure is implemented for an autotransformer traction system.
The continuous time state equation models may also be used within nodal conductance matrix programs, such as the Electromagnetic Transient Analysis Program (EMTP). This is achieved by discretizing the state equations and forming time varying Norton equivalents of the models. The trapezoidal and single-step state transition matrix (STM) methods are investigated for discretizing the state equations. It is shown that the single-step STM methods are generally more accurate than the trapezoidal method when the system order is two or higher. The trapezoidal method is generally more accurate for first order systems. It is also shown that the single-step STM methods have damping adjustment procedures similar to the critical damping adjustment procedure, recently developed for the trapezoidal method. These procedures effectively eliminate the numerical oscillations that, can occur when disturbances or changes occur within the system. From these findings a hybrid approach is proposed, which incorporates both state space and nodal conductance methods. The objective of this approach is to increase subsystem accuracy, so that larger time steps may be used without degrading the overall system accuracy.