Circular Array of Magnetic Sensors for Current Measurement: Analysis for Error Caused by Position of Conductor

This paper analyzes the measurement error, caused by the position of the current-carrying conductor, of circular array of magnetic sensors for current measurement. The circular array of magnetic sensors is an effective approach for AC or DC non-contact measurement, as its low cost, large linear range, wide bandwidth, light weight and low noise. Especially it has claimed that such structure has the excellent reduction ability for the errors caused by the position of the current-carrying conductor, crosstalk current interference, shape of the conduction cross section and the earth magnetic field. However, the positions of the current-carrying conductor, including un-center and un-perpendicularity, has not analyzed in detail until now. In this paper, the theoretical analysis has been proposed based on vector inner and exterior product. In the presented mathematical model of relative error, the un-center offset distance, the un-perpendicular angle, the radius of the circle and the number of the magnetic sensor are expressed in one equation. The comparison of the relative error caused by the position of the current-carrying conductor between four and eight sensors is conducted. The Tunnel Magnetoresistance (TMR) sensors are used in the experimental prototype to verify the mathematical model. The analysis results can be the reference to design the detail of circular array of magnetic sensors for current measurement in practical situation.