Modeling the high frequency behavior of the Rogowski-coil passive L/r integrator current transducer with analytical and finite element method

The Rogowski current transducers are widely used because they have several advantages over iron-cored devices: no saturation at high current, higher operating frequency and less error in wider measurement range. The main components of these current transducers are the measuring coil and integrator. Latter can be passive or active. The main advantage of passive integrator is the wider bandwidth. The simplest is the L/r integration method, where the coil itself makes the operation of integration. In this case the knowledge of the resistance and the inductance of the coil not enough to make a proper equivalent circuit model, because the upper limit of the frequency characteristic depends on the distributed capacitance of the winding. The paper of Tamus (2002) has showed a new analytical model, which takes the distributed capacitance of the windings into consideration. The knowledge of distributed capacitances enables to calculate the upper frequency bandwidth limit and can help to determine the phase error decrease at normal frequencies. This analytical model is based on the classical lumped parameter winding model in the work of Karsai et al. (1987), which originally designed for large power transformers and assumes continuous voltage distribution along the windings. In this paper, the authors present a finite element method for calculation of distributed capacitances of winding, where the discrete behavior of the turns is taken into consideration to make a novelty for the estimation of the upper frequency limit, which cannot be determined correctly from the analytical calculation.