Abstract--A global multiscale method based on a dynamic mode decomposition (DMD) algorithm to characterize the global behavior of transient processes recorded using wide-area sensors is proposed. The method interprets global dynamic behavior in terms of both, spatial patterns or shapes and temporal patterns associated with dynamic modes containing essentially singlefrequency components, from which the mode shapes, frequencies and growth and decay rates of the modes can be extracted simultaneously. These modes are then used to detect the coherent and dominant structures within the data.The technique is well suited for fast wide-area monitoring and assessment of global instability in the context of modern data fusion-based estimation techniques. Results of the application of the proposed method to large, high-dimensional data sets are encouraging.

Abstract-It is not uncommon for oscillatory electric power system modes to move close to a resonance in which eigenvalues coincide. In a weak resonance, the modes are decoupled and the eigenvalues do not interact. We analyze general perturbations of a weak resonance and find two distinct behaviors, including interactions near strong resonances in which the eigenvalues quickly change direction. The possible perturbations are illustrated with interactions between electromechanical modes in a 4-generator power system. Some of the interactions are similar to subsynchronous resonance and can lead to oscillatory instability.

This paper presents the power flow modeling of droop-controlled distributed generation units with secondary frequency and voltage restoration control for hierarchically controlled islanded microgrids. These models are incorporated in the conventional Newton-Raphson power flow method as a new bus, without the necessity of a slack bus, and include the gains of the control systems that influence the steady-state solution. Two case studies are addressed. In the first case study, comparisons of the proposed models against the steady-state solutions obtained with PSCAD and Simscape Power System of Simulink, where the closed-loop controls are explicitly modeled, are presented. In the second case study, the proposed method is contrasted against the droop-based approach. The results obtained exhibit low computing effort, reliability, and effectiveness of the proposed models since quadratic convergence behavior is maintained independently of the size and topology of the microgrid. Besides, it is demonstrated that hierarchical and droop controllers lead to different solutions, which confirms the necessity of including the hierarchical control in the power flow model.

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