Abstract-When the total current going through a transformer window is equal to zero, only a negligible part of the magnetic energy reaches its core. This is shown by finite-element-method simulations carried out on several two-winding transformers having different shapes. Moreover, induction and energy-density values obtained by 3-D simulations and by 2-D approximations are very close to each other. These two key observations justify the use of formulas that give the induction created by straight rectangular cross-sectional wires, as used in the partial-elementequivalent-circuit method, to compute the window field and, thus, to value the leakage inductances. To refine this approach, weak magnetic-core effects are accounted for by introducing the magnetic images of currents that flow in the windings. A comparison between the calculated values and measured ones is provided.
Abstract-This paper begins with the definition of ideal coupler, the justification of negative inductance concept and the establishment of various equivalences between circuits. Then, an energy-based recursive method for designing for the equivalent circuit of an n-input magnetic system is presented and the leakage transformer concept is introduced. The obtained circuits allow easy checking of inequalities that inductance matrix elements must satisfy. Advantage is then taken from winding identity and dominant coupling to simplify circuit design. This new knowledge is applied to design equivalent circuits for a three-phase inductor and a three-column six-winding transformer. Finally, key points of a strategy intended to experimental identification of all circuit elements are given.
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