UBC Theses and Dissertations
Full frequency-dependent modelling of underground cables for electromagnetic transient analysis Yu, Ting-Chung
A major difficulty in multiphase cable modelling with traditional electromagnetic transient program like the EMTP is the synthesis of the frequency-dependent transformation matrices that relate modal and phase domain variables. Although much effort has been devoted in the last several decades to solve this problem, we believe that the best solution is to completely eliminate the necessity of the frequency-dependent transformation matrices. The purpose of this thesis is to develop an accurate and stable model to simulate the behavior of underground cable systems under transient conditions. This thesis presents a new cable model (zCable model), which separates the representation of the wave propagation into two parts: a constant ideal propagation, which parameters depend only on the geometry of the cable configurations, and a frequency-dependent distortion, which depends on the skin effect. This approach permits the representation of the frequency.-dependent part of the parameters directly in phase coordinates and avoids the difficulties related to frequencydependent transformation matrices. A simultaneous curve-fitting procedure is introduced to synthesize each element of the phase-domain frequency-dependent loss impedance matrix with rational function approximations in the frequency domain. After synthesizing each element of the loss impedance matrix by the proposed procedure, the fitted functions show a very good agreement with the original ones. By synthesizing each element of the impedance matrix simultaneously, the new technique avoids the numerical stability issues of traditional procedures. A "pi-circuit" correction is proposed to solve the problem of different travelling times in the ideal line propagation. This approach makes the travelling times of all modes identical to one another in the modal domain and avoids the linear interpolation process used in the traditional multiphase line and cable models; By avoiding this interpolation process, a much larger integration time step At can be used without loss of accuracy, which results in considerable savings in computational time. The thesis presents a number of simulations where the behavior of the new zCable model is compared with that of the established JMARTI (FD line) and LMARTI (FDQ cable) models. These simulations show a very good agreement between the zCable model and the very accurate cable model - LMARTI model. The main advantage of the proposed model compared to existing full frequency-dependent transformation matrix models is the new model's absolute numerical stability for any kind of asymmetrical cable configurations and for arbitrary fault conditions. In addition, the new model parameters can be obtained with robust algorithms and the model can be efficiently implemented in the context of the realtime PC-cluster simulator developed by the power systems research group at UBC.
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