Accurate evaluation of the magnetic field strength of large substation air-core reactor coils

A circular cylindrical conductor segment is a basic modeling element of substation air-core reactor coils. The analytical expressions for evaluating the stationary and quasi-stationary magnetic field strength of a segment are derived. In the derivation, a surface source model is developed to substitute the given volume current distribution by equivalent surface sources. The magnetic flux density of some sample coils is calculated by using the derived equations. The results are compared with those obtained by the finite element method. Good agreement is observed. The derived equations are very useful for solving problems that involve the accurate calculation of the magnetic field distribution around a coil, the magnitude of forces on a coil, the current distribution in the conductors of a coil and the inductive properties of a coil.