The analysis of the small-signal stability of conventional power systems is well established, but for inverter based microgrids there is a need to establish how circuit and control features give rise to particular oscillatory modes and which of these have poor damping. This paper develops the modeling and analysis of autonomous operation of inverter-based microgrids. Each sub-module is modeled in state-space form and all are combined together on a common reference frame. The model captures the detail of the control loops of the inverter but not the switching action. Some inverter modes are found at relatively high frequency and so a full dynamic model of the network (rather than an algebraic impedance model) is used. The complete model is linearized around an operating point and the resulting system matrix is used to derive the eigenvalues. The eigenvalues (termed "modes") indicate the frequency and damping of oscillatory components in the transient response. A sensitivity analysis is also presented which helps identifying the origin of each of the modes and identify possible feedback signals for design of controllers to improve the system stability. With experience it is possible to simplify the model (reduce the order) if particular modes are not of interest as is the case with synchronous machine models. Experimental results from a microgrid of three 10-kW inverters are used to verify the results obtained from the model. Index Terms-Inverter, inverter model, microgrid, power control, small-signal stability.

This paper presents an Energy Management System (EMS

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Rectifiers and voltage regulators acting as constant power loads form an important part of a microgrid's total load. In simplified form, they present a negative incremental resistance and beyond that, they have control loop dynamics in a similar frequency range to the inverters that may supply a microgrid. Either of these features may lead to a degradation of small-signal damping. It is known that droop control constants need to be chosen with regard to damping, even with simple impedance loads.Actively controlled rectifiers have been modelled in non-linear state-space form, linearised around an operating point, and joined to network and inverter models. Participation analysis of the eigenvalues of the combined system identified that the low-frequency modes are associated with the voltage controller of the active rectifier and the droop-controllers of the inverters. The analysis also reveals that when the active load DC-voltage controller is designed with large gains, the voltage controller of the inverter becomes unstable. This dependency has been verified by observing the response of an experimental microgrid to step changes in power demand. Achieving a well-damped response with a conservative stability margin does not compromise normal active rectifier design, but notice should be taken of the inverter-rectifier interaction identified.

Abstract-The trend toward using inverters in distributed generation systems and micro-grids has raised the importance of achieving low-distortion, high-quality power export from inverters. Both switching frequency effects and pre-existing grid voltage distortion can contribute to poor power quality. A well designed filter can attenuate switching frequency components but has an impact on the control bandwidth and the impedance presented to grid distortion. This paper describes a filter designed to incorporate an isolating transformer and the design of a complementary controller that rejects grid disturbance, maintains good waveform quality and achieves real and reactive power control. A realistic discrete time implementation is discussed and validated with experimental results.