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UBC Theses and Dissertations

Simulation of electromagnetic transients in underground cables with frequency-dependent modal transformation matrics Marti, Luis


This thesis presents a new model to simulate the behaviour of underground cable systems under transient conditions. The new cable model belongs to the class of time-domain, frequency-dependent models, and it is directly compatible with the solution algorithm of the EMTP (Electromagnetic Transients Program). The most important feature of the new model is that it takes into account the frequency dependence of the modal transformation matrices and cable parameters, thus overcoming the main limitation of currently-used transmission line and cable models, which assume that the modal transformation matrices are constant Conceptually, the new model is relatively simple. The system parameters which define the behaviour of an underground cable (namely the modal characteristic admittance matrix, the modal propagation matrix, and the modal transformation matrix), are expressed in closed form by approximating them with rational functions in the frequency domain. Therefore, in the time domain, all numerical convolutions can be expressed recursively. The host transients program (to which the model is interfaced) sees the new model as a constant, real admittance matrix, in parallel with a continuously-updated vector current source. The accurate approximation by rational functions of the modal transformation matrix is possible when its elements are continuous and smooth functions of frequency. Standard eigenvalue/eigenvector algorithms are not well suited for this purpose. Therefore, a new procedure to generate eigenvalues and eigenvectors has been developed. This procedure is based on the Jacobi method, and it produces the desired smooth functions of frequency. This manuscript presents a number of simulations where the performance of the new cable model is compared with exact analytical solutions. These simulations show an excellent agreement between analytical and numerical answers. The effects of not taking into account the frequency dependence of the modal transformation matrices is illustrated with the simulation of a line-to-ground fault on a three-phase cable. The response of the new cable model is also compared with results measured in a field test The new cable model is numerically stable. Its computational speed is comparable to that of frequency-dependent line models with constant transformation matrices. The new cable model is general. Its extension to the simulation of multiple-circuit overhead transmission lines should also be of considerable practical importance.

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