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When subject to transient voltage excitation, local concentration of voltage takes place in an ordinary transformer in which the capacitance charging current of the coils to ground is supplied through the winding, or the ratio of inductance and capacitance of the various parts throughout the winding is not constant. Calculations and tests of voltage distribution in the winding, caused by the impact of (a) damped high-frequency oscillations, and (b) unidirectional traveling waves, are given. In order to make the analysis clearer, the transformer winding is considered as a network of inductances and capacitances, and this term ``network'' is used throughout the paper. Certain simplified and typical networks are considered. Transformers having one terminal grounded, such as are used in three-phase star connection, particularly in high voltage systems, are frequently built with the insulation graded to other windings and ground, in the order of the normal frequency voltage stress. The danger of such a practise is shown in power transformers which are subject to transient overvoltage, since voltage oscillation in the winding may raise the voltage to ground at intermediate points above the terminal voltage, unless the design of the winding eliminates oscillation. The theoretical and experimental data given show that the distribution and magnitude of voltage stresses existing during recognized standard insulation tests are essentially different from stresses created by transient voltages. This permits the construction of transformers that would satisfactorily pass standard insulation tests but at the same time would not be suitable for average service.