Calculation of the magnetic field of rotating machines. Part 5: Field in the end region of turbogenerators and the eddy-current loss in the end plates of stator cores

Abstract

SynopsisA method of calculating the magnetic field in the end region of a turbogenerator is described. Allowance is made for nonmagnetic stator-core clamping plates and for the magnetic shaft and casing of the machine. The effect of a magnetic rotor-retaining ring is studied, the ring being regarded as a tube of finite permeability separating the stator and rotor end windings. Calculations are compared with experimental results. The field calculated at the surface of the stator-core end plates is used to estimate the eddy-current loss in these plates, and the effect upon this loss of the retain ing-ring permeability and the stator-winding cone angle is considered. List of symbolsA = magnetic vector potential B = magnetic flux density g = halfwavelength of current distribution along axis H = magnetic field strength Io(*) = modified Bessel function of first kind and zero order Ii(x) = modified Bessel function of first kind and first order Ij'OO = derivative of function I\(x) K 0 C*) = modified Bessel function of second kind and zero order K|(x) = modified Bessel function of second kind and first order K{(x) = derivative of function K,(;t) K = surface density of current sheet p = number of pairs of poles a = ^Ig r, 6, z -circular cylindrical co-ordinates s = number of cylindrical current sheets forming stator winding a = constant associated with image current 8 = -^(iplojfjLQfj,,) = skin depth of eddy currents d = phase angle /u 0 = primary magnetic constant (or permeability of free space) \x.,. = relative permeability (suffixes 1, 3 and 5 are used to denote particular regions) p = resistivity <f> = scalar potential o» = angular frequency R = radius of circular current filament KQ = circumferential surface current density Paper 5116 P, first received 13th April and in revised form 1st July 1966 Dr. Stoll is with C. A. Parsons

Calculation of magnetic field and eddy current loss in end clamping ring of 300MVA synchronous condenser based on a novel semi‐analytical method

“…[20], and the eddy current loss of the clamping ring in the turbine generator was approximately estimated in refs. [21,22]. There are many assumptions and empirical coefficients in these calculation methods, which have great limitations.…”

Improved Analytical Algorithm for Magnetic Field of End Windings in 300Mvar Synchronous Condenser

“…Although 3-D FEM is with high calculation precision, there are still many shortcomings in the construction of 3-D model, calculation time and meshing. A complete set of analytical method for calculating the magnetic field and eddy current losses in the end structures of turbine generator was first proposed by P. Hammond in [11][12][13][14][15]. The formula for end-winding current distribution replaced by equivalent current sheets of the sinusoidal type was derived in [16][17].…”

New analytical algorithm for calculating the end leakage magnetic field of a 300Mvar synchronous condenser under no‐load condition

“…The ironless brushless direct current motor with the external rotor is calculated by a 2-D analytical algorithm in [16,17]. In [18], a subdomain model considering the rotor end shaft, but not stator iron, is established, and the leakage magnetic field in the end region and eddy current losses in the clamping ring of the turbogenerator are calculated. In the end region of large machines, the boundary surfaces are plane and cylindrical, and the mirror method can greatly simplify the end model.…”