A multi-scale transients model of a doubly fed induction generator (DFIG)-based wind energy conversion system (WECS) is developed, implemented, and validated. All ac circuit and control quantities of the electrical part are modeled by analytic signals rather than just real signals. In addition to the real parts, the analytic signals also comprise orthogonal imaginary parts. While measured Fourier spectra of real ac quantities involve positive and negative frequency components, they only involve positive frequency components when extended and represented as analytic signals. With the introduced shift frequency operator, the analytic signal can now be shifted in the frequency domain to reduce its maximum frequency contents and thus allow for a larger timestep size in accordance with the Nyquist criterion. If the shift frequency is set equal to the ac fundamental frequency, then the affiliated ac voltages and currents become dynamic phasors. At a zero shift, however, instantaneous signals can be tracked as in an electromagnetic transients program (EMTP). This is illustrated here for the voltage sourced converters (VSC) of the WECS. By appropriate selection of the shift frequency, both electromagnetic and electromechanical transients are simulated efficiently. Studies involving wind power fluctuations, three-phase-to-ground fault and single-phase-to-ground fault confirm these claims. Index Terms-Doubly fed induction generator (DFIG), electromagnetic transients, electromechanical transients, multi-scale, interface, voltage-sourced converter (VSC), wind energy conversion system (WECS).

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In multi-infeed hybrid AC-DC (MIDC) systems, the asynchronous interconnection between regional grids, the complicated system dynamics and possible cascading failures have an enormous effect on the frequency stability. In order to deal with the frequency instability problems in emergency situations, this paper proposes a decentralized emergency frequency control strategy based on coordinated droop for the MIDC system. First, a P-f droop control for LCC-HVDC systems is introduced and the coordinated droop mechanism among LCC-HVDC systems and generators is designed. Then, to reasonably allocate the power imbalance among LCC-HVDC systems and generators, an optimal emergency frequency control (OEFC) problem is formulated, and the optimal droop coefficients are selected in a decentralized approach, which can deal with various control objectives. A Lyapunov stability analysis shows that the closedloop equilibrium is locally asymptotically stable considering the LCC-HVDC dynamics. The effectiveness of the proposed emergency control strategy is verified through simulations.

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