Magnetization current inrush in transformers

ANALYTICAL solutions to nonlinear transients such as the phenomena of inrush currents in transformers are notoriously difficult to obtain unless a simple, convenient relationship exists between the dependent variables. Generally the transient may be determined by a graphical or step-by-step process. This procedure is lengthy and tedious and results only in a particular numerical solution which does not yield insight into the influence of changes of design or operating conditions. In light of these difficulties, it is desirable in this problem to make assumptions and approximations which will produce a simple convenient relationship between the variables, resulting in an analytical expression for the first crest and successive crests of the inrush magnetizing current.