Transient Theory of Synchronous Generators under Unbalanced Conditions

The paper contains a mathematical theory of the operation of a synchronous generator after the closing of a switch at its terminals, under the assumption that the speed remains constant after the change. The theory is first formulated for the general case where the external circuit consists of any unbalanced impedances and source voltages. It is then applied to the three well-known conditions of unbalanced short-circuit. The method of solution is fully explained for the line-to-line short-circuit, while only the equations and the results are quoted for the line-to-neutral and the double-line-to-neutral short-circuits. The solution is obtained by the method of the Laplace transformation, but its application is more difficult than in ordinary circuit theory or in the case of a generator under balanced conditions, because the differential equations, although linear, have variable coefficients. The solutions are obtained as infinite series, which can be summed, however, for the cases given. For each of the three short-circuit conditions, comparative experimental and theoretical results are given for a small synchronous machine. The theoretical curves were calculated from the mathematical expressions, using the measured constants of the machine.