A method has been developed for computing electromagnetic fields and eddy-current heating in and around the core ends of large generators. The effect of tooth geometry. Pistoye slots, cooling ducts, anisotropy saturation, distributed eddy currents and variable stacking factor are included. The calculation is formulated as a 2-potential 3-dimensional nonlinear boundary-value problem, and solved by an iterative finite-difference scheme with crosscoupled harmonics. The predicted axial fields have been compared with measurements on a 500 MW machine. List of symbols A = vector potential = matrix of coefficients in difference equations for 0 B = magnetic-flux-density vector = source terms in difference equations for 0 = matrix of coefficients in difference equations for i,H,H) = source terms in difference equations for t// E = electric-field-strength vector H = (H r , H e , H z ) = magnetic-field-strength vector Hmin -constant in empirical relation for hysteresis heating H o = saturation magnetic field in Frohlichpermeability relation r = (J r , Je,0) = eddy-current-density vector n = normal direction to boundary qjj = 1 , 3 = source terms of stream-function equation r = radial co-ordinate t = time X = (r, 9, z) = position vector z = axial co-ordinate z = unit vector in axial direction a,0 = constants in the empirical relation hysteresis heating 7 = stacking factor 6 = circumferential co-ordinate -angle subtended at machine axis for M = 0 0 0 0 0 " 0 = permeability tensor Mt. e tc. = H 2 =Fourier components of fx t zero-field relative permeability of iron limiting relative permeability of iron £/ = $ji + i^j2. where / = 1 or 3 a = electrical conductivity 0 = magnetic-field scalar potential i// = eddy-current stream function CJ = angular velocity of rotor superscript i = value in iron
IntroductionThe increasing size of turbogenerators has led to the power dissipation in the laminated iron core, caused by stray magnetic fields, becoming embarrassingly high. The range of leading powerfactor operation for large generators can in some circumstances be limited by excessive temperature rises in the end region. Any operating restrictions which have to be imposed as the result of excessive temperatures can result in increased operating costs. Since the installation of the first 500 MW generators in the UK much work in the heavy electrical industry and universities has been aimed at understanding the reasons for high losses, and at predicting the effect of changes in design so that the full potential of the designs is realised.Accurate prediction of the magnetic fields and loss has not hitherto been possible. Although the fundamental electromagnetic equations are well known, they have not been solved in regions with geometrically complicated boundaries and nonlinear material properties; rather the literature is confined to solving magnetic fields in the region outside the iron. As a consequence, regions such as conducting screens, casings and the end winding are now relatively well understood electromagnetically so that screen h...
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