Designing a Rogowski Coil with Particle Swarm Optimization

Abstract

Rogowski coils are inductive sensors based on Faraday’s and Ampère’s Laws to measure currents through conductors without galvanic contact. The main advantage of Rogowski coils when compared with current transformers is the fact that the core is air so they never saturate and the upper cut-off current can be higher. These characteristics make Rogowski coils ideal candidates to measure high-amplitude pulsed currents. However, there are two main drawbacks. On the one hand, the output voltage is the derivative of the primary current so it has to be integrated to measure the original signal; on the other hand, the transfer function is resonant as a result of the capacitance and the self-inductance of the coil. The solution is the use of a passive integration with a terminating resistor at the output of the sensor that splits the two complex poles and gives a constant transfer function for a determined bandwidth. The downside is a loss of sensitivity. Since it is possible to calculate the electrical parameters of the coil based on its geometrical dimensions, the geometry can be adapted to design sensors for different applications depending on the time characteristics of the input current. This paper proposes the design of Rogowski coils based on their geometric characteristics maximizing the gain-bandwidth product using particle swarm optimization and adapting the coils to the specific requirements of the application.