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Integrating power electronics to the grid has introduced new small signal–signal stability challenges, which are commonly studied with average time-invariant models and, more recently, with harmonic state–space models. In both approaches, it is common to obtain the models by following an analytical formulation, which can be tedious and impractical in systems with different controllers and topologies, just to mention a few examples. This paper proposes a numerical approach based on shooting methods and the recursive evaluation of the time-variant Jacobian along the steady-state orbits to construct automatically a periodic linear time-variant model and its respective linear time-invariant model using the extended harmonic domain; these models include explicitly the harmonic components. The proposed modeling approach can be applied to systems with different converter topologies, controllers, and modulation techniques. A nonlinear periodic switched system (grid-connected parallel inverter-based microgrid) is used to validate the proposed linearization approach. • Applicable to periodic switched nonlinear systems. • Shooting methods compute the steady state directly. • Convergence to stable and unstable periodic steady-state solution. • Jacobian is computed numerically as a by-product of the shooting method. • The small-signal model considers the effects of any modulation pattern. [ABSTRACT FROM AUTHOR]

• An optimal design method in the Extended Harmonic Domain of the LCL filters. • Quantitative and qualitative assessment of different LCL filter design methods. • A Review of Passive Power Filters. • A Matlab graphic user interface (GUI) for the design of LCL filters. This paper presents a design method based on the extended harmonic domain modeling for L and LCL passive filters of active-front-end PWM two-level voltage source converters for grid-connected renewable energy sources. The proposed design method is tested under several operating scenarios, such as high and low power levels and switching frequencies. Also, a dedicated graphical user interface (GUI) with five other design methods is provided to ease the evaluation of the proposed design method. The GUI also computes the power quality indexes and the steady-state waveforms for each design methodology. In addition to this, an in-depth overview of filtering technologies and applications is presented to identify the primary practical use of passive filtering and to justify the use of LCL filter in grid-connected systems. The obtained results show that the proposed design method leads to the smallest passive filter parameters, and it is the only method that fulfills all the imposed power quality requirements as well as power specifications. [ABSTRACT FROM AUTHOR]