| Abstract |
The evaluation of harmonic distortions in electrical power systems leads to extensive parameter studies of periodically switched systems of high order. Usually these studies are carried out by means of rather general simulation programs. This may result in high computation times, especially for networks with a great difference in the time constants, and even in numerical problems. In this contribution a direct evaluation method for the steady state is presented, by which periodical harmonic distortions can be computed with lesser effort and moreover with greater accuracy. Starting from a piecewise description by state equations and from the continuity conditions of the state vector at the switching points, from the corresponding difference equation a first condition for the steady state is immediately obtained. Together with the switching equations a complete problem description in the form of non-linear equations results, which can be solved by an analytically based Newton-method. Apart from asymmetries in the net or in the converter even non-linear elements can be taken into account. For the practically most relevant case of a symmetrical operation, by taking advantage of the cyclical symmetry, an especially high reduction in the computation times follows. |
