a b s t r a c tThe ongoing evolution of the power system towards a "SmartGrid" implies a dominant role of power electronic converters, but poses strict requirements on their control strategies to preserve stability and controllability. In this perspective, the definition of decentralized control schemes for power converters that can provide grid support and allow for seamless transition between grid-connected or islanded operation is critical. Since these features can already be provided by synchronous generators, the concept of Virtual Synchronous Machines (VSMs) can be a suitable approach for controlling power electronics converters. This paper starts with a discussion of the general features offered by the VSM concept in the context of SmartGrids. A specific VSM implementation is then presented in detail together with its mathematical model. The intended emulation of the synchronous machine characteristics is illustrated by numerical simulations. Finally, stability is assessed by analysing the eigenvalues of a small-signal model and their parametric sensitivities.

Abstract-This paper presents a comparison of the small-signal stability properties for Virtual Synchronous Machines (VSMs) with dynamic and quasi-stationary representation of the internal Synchronous Machine (SM) model. It is shown that the dynamic electrical equations may introduce poorly damped oscillations when realistic stator impedance values for high power SMs are used. The quasi-stationary implementation is less sensitive to the impedance of the virtual machine model, but depends on filtering of the measured d-and q-axis components of the ac-side voltage to avoid instability or poorly damped oscillations. It is demonstrated how both implementations can be made stable and robust for a wide range of grid impedances. However, the dynamic electrical model depends on a high virtual resistance for effectively damping internal oscillations associated with dccomponents in the ac currents during transients. Thus, when using SM parameters with low virtual stator resistance for decoupling the active and reactive power control, the quasi-stationary VSM implementation is preferable.

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Control structures containing cascaded loops are used in several applications for the stand-alone and parallel operation of three-phase power electronic converters. Potential interactions between these cascaded loops and the complex functional dependence between the controller parameters and the system dynamics prevent the effective application of classical tuning methods in the case of converters operating with a low switching frequency. A tuning approach guided by the eigenvalue parametric sensitivities calculated from a linearized model of the converter and its control system is proposed in this paper. The method is implemented in the form of an iterative procedure enforcing the stability of the system and ensuring that the system eigenvalues are moved away from critical locations. Numerical simulations in the time domain are presented to verify the improvement in the dynamic performance of the system when tuned with the presented algorithm compared with a conventional rule-based tuning method.Index Terms-Control design, dc-ac power converters, eigenvalues and eigenfunctions, power conversion. I. INTRODUCTIONA C VOLTAGE controllers are required in several power converter applications for stand-alone and parallel operation, such as uninterruptible power supplies (UPSs) and microgrids [1]- [5]. Such ac voltage control loops can be implemented to directly control the output voltage, as discussed in [3] and [4], but control schemes with inner loop current controllers are often preferred since they allow for explicit limitations and protections against overcurrents. In most applications, the references for these ac voltage controllers are provided by outer Manuscript