Transfer Function Derivation in an Easily Scalable Two-Port Network as Basis for Filter Design

The connection of voltage source converters (VSC) to the power grid needs filters to satisfy the relevant grid code. If connected to machines, these can be protected by filters from unwanted frequency components and high voltage gradients, e.g to improve lifetime of insulation and bearings. In order to design those filters, numerical time domain simulations are a well known method with limited implementation effort, but high computational effort. Transfer functions describe a linear time-invariant system as complete as the systems impulse response, so time domain simulations can be built on their basis as well. Their application also provides additional advantages such as fast calculation of steady state values and straightforward filtering in the frequency domain. The calculation of a transfer function itself, although based on simple rules, is laborious, especially for higher order filters. This paper gives a solution based on the definition of an electrical network suitable for many types of filters, which is fully scalable. On the basis of this network, algorithms are developed to derive any transfer function in this network. The algorithm is then extended to enable the calculation of quantities in a scaled two-port network with superposed sources. The algorithm is implemented in Matlab. The proposed method is compared to a time domain simulation with PLECS Blockset. The results are evaluated regarding their deviation from each other as well as the computational effort.