Power flow in the air gap of linear electrical machines by utilization of the Poynting vector: Part 1 - Analytical expressions

Analytical solutions and estimations for the power flow in the air gap of linear electrical machines of different geometries are derived from Poynting's theorem. The different geometries considered are flat one-sided, multi-sided, and tubular linear electrical machines. The radial power flow for all considered geometries is dependent on the area of the air gap, the electric field, the magnetic field, and the load angle. The tangential power flow for both flat one-sided and tubular linear electrical machines is dependent of the area of the air gap, number of poles, the electric field, the magnetic field, and the load angle. The number of poles could be increased to decrease the tangential power flow in flat linear electrical machines. The expression for the tangential flow in tubular linear electrical machines is so complicated that it is difficult to draw conclusions from it.