الفهرس 
DERIVATION OF THE ELECTROMAGNETIC EQUATIONSOnly 14 pages are availabe for public view
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Abstract
Electromagnetic equations are formulated for the ma-
chine behaviour during steady state operation and under
transient conditions. Two dimensional analyses of the
magnetic field are made over a half pole pitch of the
cross-section of the machine. Complete consideration is
taken for the nonlinearities of the iron material and the
induced eddy currents in the solid rotor and damper wedges.
The finite element and nodal methods are used to find the
discrete form of the partial differential equations. The
validity of the discrete equations under transient condi-
tions are ensured using Ampere’s circuital law. The closed
windings of the stator and rotor are considered through
conductivity matrices. The problem is nonlinear because
of the dependence of the iron reluctivities on the resultant
field, and an iterative procedure is used for its
solution. The Newton-Raphson method together with the
sparsity techniques of Jennings are found to be the best
for the problem solution during steady state. The predictor-corrector
method is added for progressing forward in
time under transient conditions.
The numerical method is applied to a turbine-generator
to obtain the steady state balanced 3 phase short circuit
currents at different values of field current A transient problem resulting of closing the field
winding through a discharge resistance for a short circuit-
ed machine is studied. Flux plots and eddy current density
distributions are obtained at successive instants in time.
The resulting field and stator current decrement curves are
compared with the experimental results, good agreement is
found.
The slip frequency test used for assessment of the
machine reactances on d andoq axes is simulated numerically.
The periodic variation of the magnetic vector potential is
obtained using the theory of complex variables. It is
found that the solution is convergent and is obtainable
after a small number of iterations. Solutions are obtained
for different values of slip. Iri each of which the flux
and eddy current density plots are obtained at certain
instants in time. It is found that the measurement of
one value of the d-axis reactance in the slip test is not
correct, it depends on the value of the slip. A numerical computation is made to estimate such variation because of
the effect of the induced eddy currents in the rotor
circuits.