A smoothing algorithm for frequency-dependent transformation matrix calculation

Difficulty in performing rational approximation arises from the discontinuities in the elements of transformation matrices obtained with conventional algorithms. To resolve the problem, a new algorithm for evaluating the transformation matrices as smooth functions of frequency is presented. Firstly, the new algorithm calculates the transformation matrices at each frequency point using a conventional algorithm; a special smoothing procedure is then used to eliminate the discontinuities in the transformation matrices. Furthermore, the new algorithm is implemented and compared with the Newton-Raphson algorithm with a double-circuit three-phase untransposed transmission line example. Experimental results and theoretical analysis demonstrate that the new algorithm is more efficient than the NR algorithm and has better tracing ability.