Commercial transient simulation packages which include frequency dependent transmission line (FDTL) elements rely on the use of either the J. Marti method or the Universal Line Modeling (ULM) method. The advantage of the J. Marti method is that the N-phase FDTL can be modeled by N-independent single-phase FDTL circuits which is very robust for transposed or nearly transposed FDTLs. The disadvantages of this method become evident as one deviates from the transposed-line assumption such as in the case of asymmetric-lines or underground cables. The Universal Line Modeling (ULM) method is a generalization of the J. Marti method and opts to model the FDTL directly in the phase-domain. This method is capable of modeling arbitrary FDTLs, not limited to the transposed and nearly transposed cases as opposed to the J. Marti method. The disadvantages of this method however are increased computational complexity as well as numerical considerations due to high-order rational function approximation (RFA) modeling.
This dissertation introduces a procedure for modelling a network of frequency-dependent transmission lines (FDTL) by means of a perfect-reconstruction filter-bank (PR-FB), which allows us to decompose the transient simulation problem into independent narrow-band (subband) problems. This allows us to: (i) obtain insights regarding the behavior of the transients within frequency-bands of interest (ii) use low order approximations to reduce the complexity of the overall system, (iii) improve numerical stability, (iv) leverage parallel processing capability of modern computers to increase simulation speed, and (v) employ distributed computing frameworks such as Hadoop MapReduce to increase simulation speed. We use several examples to demonstrate the utility of our subband-ULM method, including a single-phase FDTL, a three-phase FDTL, and a single-phase FDTL network based on the IEEE 5-bus grid.
- Professor Hanoch Lev-Ari
- Professor Ali Abur
- Professor Aleksandar Stankovic