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Autoreclosing circuit breakers have long been used in e.h.v.-transrnission-system engineering to improve the security of supply, principally by combating transient instability, but the continual reduction in stability margins that is being encountered in the design of primary power supplies, due mainly to the changing characteristics of generators, emphasises the contribution of reclosure to the transient-stability problem. The paper accordingly provides a comprehensive analysis, by digital computer, of the effect of 3phase and single-phase autoreclosing arrangements on the stability boundaries of single- and duplicate-line supplies and records investigations of spontaneous resynchronisation after reclosure. The mathematical model, on which the stability assessments given in the paper are based, takes into account the contribution to stability of synchronous-machine excitation and prime-mover power-control systems, following synmietrical- and unsymmetrical-disturbance conditions. Stability boundaries are presented, corresponding to cases where, as has hitherto been the widespread practice in stability studies, the possibility of successful pole slipping is precluded; the orthodox boundaries are then extended to allow for generators regaining synchronism after one or two pole slips. The principal machine variables are examined under pole-slipping operation, and the case of reapplication of full system voltage on to a short circuit that has been sustained through the first circuit-breaker opening is considered in detail. The equations of the model, subject to the constraints imposed on them by transmission-line faults and subsequent line switchingÂ¿though amenable to solution by either analogue or digital methodsÂ¿have been solved in the present series of analytical studies by the Atlas computer at Manchester University, and the development of the solution by digital techniques is described.