Analysis of Magnetic Flux Density of Rogowski Coil for Full Harmonic and Lightning Channel-Base-Current Measurements

The Rogowski coil (RC) is most prevalent device for the measurement of harmonic currents and surge currents. This coil is also measuring the currents across wide range of frequencies which are ranging up to $\mathbf{G H z}$. In this paper, magnetic flux density (B) inside of RC is analyzed using Ampere’s law and full current theory. In this work MATLAB based coding was utilized to calculate $\boldsymbol{B}$ for both conduction and displacement currents. The effectiveness of the radius ‘ r ‘ from the current carrying conductor to center of the coil on B is evaluated for the range from 0.1 m to 0.5 m. Magnetic flux density (B) is evaluated for different full harmonic high current peaks with frequencies range between 1 kHz and 1 GHz. From the results it is observed that the dominating magnetic field due to conduction ($B_{a}$) and displacement current ($B_{f}$) are for smaller and larger radius respectively. The error between $B_{a}$ and $B_{f}$ is calculated and reported. From the results it is observed that, irrespective of current peak, for frequencies up to 1 MHz the error is 0%. Additionally, full current theory-based B evaluation is attempted for different peaks of lightning channel base current (CBC), same CBC peak with different maximum front steepness $\left((\mathrm{di} / \mathrm{dt})_{\mathrm{max}}\right)$ and its results are reported. From the study, it is noticed that for 12 kA peak CBC, with front steepness from 12 to $120 \mathrm{kA} / \mu \mathrm{s}$, a maximum of 251% error on B is observed within RC under study.