Analytic Calculation of External Magnetic Field of High Voltage Toroid-Type Air-Core Reactors

Compared with high voltage column-type air-core reactors (HVCAR), high voltage toroid-type air-core reactors (HVTAR) generate much smaller external magnetic flux density (EMD) during operation, which significantly reduces magnetic clearance (MC), thereby reducing space occupied by air-core reactors. For HVTAR, existing methods such as finite element method (FEM) and numerical integration methods using the Biot-Savart law, cannot reveal the influence of the parameters of reactors on EMD. This paper proposes an analytic formula for EMD, in view of the special winding structure of HVTAR. It can directly reveal the influence of the working current, the number of coil units,
n
, and the size of the reactor on EMD. The analysis shows that the EMD decays with
ρ
^{n + 1}
_P
, which is much faster than the attenuation rate of
ρ
³
_P
of column-type reactors. The analytic formula is verified by comparison with the results of FEM. The analytic formula is simple and practical to calculate the EMD and MC quickly and guide the electromagnetic design of HVTAR directly.