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The main aim of this paper is to present a new modelling of transformers in Simulink/Matlab enabling to simulate slow transients more accurate than the existing models used in the software. In this paper, first several types of transformer cores and their magnetic behaviors are described. Next, for accurate simulation of slow transients, extended transformer models based on duality principle of magnetic circuits is introduced. Then, two conventional three-and five-legged core transformers are simulated in Simulink/Matlab and in order to verify accuracy of models, simulation results are compared with those obtained from measurements. Finally, ferroresonance simulations are examined by both the proposed models and existing transformer models in Matlab/Simulink. The comparison clearly shows inability of existing transformer models to study slow transients for transformers.

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Considering the advantages of DC microgrids, the extension of the conventional AC distribution grid can be implemented using a DC microgrid. This justifies the realization of a hybrid AC/DC microgrid. In the present study, a new global solution is presented to improve the power quality and to fully compensate the reactive power of an AC microgrid using DC bus capacity while introducing a new design for a hybrid AC/DC microgrid. In the new design, backto-back connections of two series and parallel converters, as well as the presentation of new controllers and simultaneous utilization of an earthing switch, are proposed. The proposed method guarantees the quality of the delivered voltage to consumers and the drawn current from the network according to the IEEE-519 and IEEE-1159 standards under different power quality problems (e.g., interruptions, sags, harmonics, and any variation in voltage/current signals from pure sinusoidal). Through the proposed design of the new hybrid AC/DC microgrid, as a new feature, the operation of the network in islanded mode can be achieved in accordance with power quality standards even in the worst load quality conditions. It should be noted that in common hybrid microgrids in islanded mode, the delivered voltage quality is proportional to the quality of the consumer's load current. Another possibility of the proposed design is the instantaneous VAR compensation of nonlinear and induction loads of consumers to keep the power factor of the distribution transformer close to unit value. Simulation results indicate that there are acceptable levels of compensation for different types of power quality problems. Total harmonic distortions and total demand distortions are below 3% in both the grid-connected and isolated modes of the hybrid AC/DC microgrid.

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