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In this paper, a three-phase transformer model is developed to be suitable for slow transient and power-quality studies. The proposed model takes into account the eddy currents, the magnetic core topology, and the nonlinear characteristics of the core material. In order to model the eddy currents effects in the magnetic core, Bertotti's work for the eddy currents is used and nonlinear resistors dependent on the magnetic core topology are proposed. A systematic procedure is developed for the determination of the incremental self and mutual inductances of the windings. The nonlinear characteristics of the core material are represented either by a magnetization curve or by a hysteresis loop. The hysteresis loop is introduced either by the mathematical model proposed by Tellinen or by the macroscopic model presented by Jiles--Atherton. Simulations results are compared to published measurements in order to verify the proposed model. Index Terms--Eddy currents, lumped parameters, magnetic circuits, magnetic hysteresis, time-domain analysis, transformers.

In this paper, a linearized equivalent electrical circuit of a photovoltaic generator is developed. The proposed model is based on nonlinear and well-tested current-voltage equations which are however used in an alternative mathematical manner. The application of a linearization process, which differs from the well-known piecewise linear scheme and is based on Taylor's series approximation, leads to uncoupling of the current and voltage quantities in each time step of a digital simulation. Using the proposed equivalent photovoltaic generator circuit, the application of nodal analysis on equivalent resistive circuits derives a photovoltaic system model of linear algebraic equations. This remarkably simplifies photovoltaic systems modeling because one can develop a photovoltaic generator element in electromagnetic transient programs for power systems analysis, of great value to power engineers who are involved in photovoltaic systems modeling. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]