Dynamical Analysis of an Autotransformer

The auto-transformer differs from a two winding transformer, in that the power is transferred from primary to secondary inductively as well as by conduction because there is a direct electrical connection between the primary and secondary windings of an auto-transformer. This is unlike a two winding transformer where the primary and secondary windings are electrically isolated. Therefore, the mathematical model for two winding transformer cannot be simply extended, with little modifications, to use for an auto-transformer. In the literature survey, the mathematical models of an auto-transformer are found to be application specific, which suggests that there is a scope for deriving a general mathematical model for the same. In this paper, a mathematical model of auto-transformer is derived, and it is solved numerically to obtain insights into the dynamics of the auto-transformer system. In an auto-transformer, the wiper position is an additional input to the system along with the input applied voltage. Simulations are carried out to see the autotransformer operation when it is supplying lagging and leading power factor loads, and when the wiper position is changing gradually after the initial turn-on transients are over. Also, the operation is shown when the input voltage is a step function. It is found that the model gives satisfactory results which are verified from the steady-state relations derived from the phasor diagram obtained for the steady-state operation.