Analytical Approach to the Variable Turns-Ratio Autotransformers [includes discussion]

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.