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The presented book is a collection of selected papers that the author's team has been developing for more than 20 years in the field of AC step voltage regulators. The number of publications on the proposed topic comprises more than 50 works, only 14 of which are included in the book. The research done has been published in numerous books, journals, annuals and international conferences all over the world. The book discusses the parameters, the basic equations for the electrical equilibrium and the action of autotransformer discrete alternating voltage regulators (ADAVR). The ADAVR in question are non-linear devices and their transient analysis especially in the time domain raises major difficulties. They are caused by the fact that the matrices of the differential equations that describe the electrical equilibrium of ADAVR in the time domain are singular, i.e. their determinants are equal to zero. This makes impossible the direct usage of the known numerical methods to solve these systems of equations.