Analytical Approach to the Variable Turns-Ratio Autotransformers [includes discussion]
Eli A. Mishkin · Transactions of the American Institute of Electrical Engineers Part III Power Apparatus and Systems · 1953
Autotransformers with variable turns-ratio are at present in widespread use in testing and research laboratories, as they produce an a-c supply whose voltage may be varied easily with but negligible losses. The autotransformer's theory is developed by deriving analytically its characteristic triangle, that is, its numerical ohmic and reactive inherent voltage drops. The ohmic component is found directly from the connection's diagram. The reactive component is derived by calculating the autotransformer's stray field energy. The iron of the magnetic core is assumed to be perfectly permeable. It allows the actual core, made in the form of a hollow cylinder, to be contracted to an infinitesimal width. The winding, too, is replaced by a currents-carrying cylindrical surface. The end effects are neglected and the whole problem is converted into a 2-dimensional one. A solution of the Laplace equation of the vector potential with due regard to the boundary conditions yields the stray field's energy. The inherent numerical voltage regulation, short-circuit currents, and power factor are given as functions of the turns-ratio. The current, in a single short-circuited turn, proves to be very high (about 15 times the rated current). This makes it necessary to provide the sliding brush with a fairly high resistance.