0278-0046 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2016.2638810, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS Evaluation of Virtual Synchronous Machines with Dynamic or Quasi-Stationary Machine Models Olve Mo, Salvatore D'Arco and Jon Are Suul, Member, IEEE 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 dc- components 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. Index Terms— Small-Signal Stability, Synchronous Machine Swing Equation, Virtual Synchronous Machine I. INTRODUCTION ONTROL strategies based on the concept of Virtual Synchronous Machines (VSMs) have the potential to become a flexible framework for providing converter-based grid services in future power systems. Indeed, VSM based control strategies for Voltage Source Converters (VSCs) have especially been developed to serve two main purposes [1]-[5]: i) Providing virtual inertia and thereby contributing to the total equivalent inertia of the grid. Manuscript received, April 30, 2016, revised September 10, 2016, accepted September 24, 2016. The work of SINTEF Energy Research in this paper was supported by the project "Releasing the Potential of Virtual Synchronous Machines – ReViSM" through the Blue Sky instrument of SINTEF Energy Research as a Strategic Institute Programme (SIP) financed by the national Basic Funding Scheme of Norway O. Mo and S. D'Arco are with SINTEF Energy Research, 7465 Trondheim, Norway, (e-mail: Olve.Mo@sintef.no, Salvatore.D'Arco@sintef.no) J. A. Suul is with SINTEF Energy Research, 7465 Trondheim, Norway, and with the Department of Electric Power Engineering, Norwegian University of Science and Technology, 7495 Trondheim, Norway, e-mail: Jon.A.Suul@sintef.no ii) Enabling operation in both grid-connected and islanded system configurations without any change of control structure and parameters. To obtain both these functionalities, VSMs must rely on a similar power-balance-based synchronization mechanism as Synchronous Machines (SMs). Thus, VSMs will not depend on conventional Phase Locked Loops (PLLs) for grid synchronization [5], [6]. All VSM implementations include a representation of a SM, executed in real time to generate internal control references. The internal model can represent the SM behavior with different degrees of fidelity, while it must be formulated according to the interfaces with the other control loops of the power converter. In general, there are two dominating architectures, depending on whether the machine model provides a current reference or a voltage reference for controlling the converter operation [6]. Examples of VSM implementations where the internal SM model generates references for a current controller have for instance been presented in [1] [4], [5], [7]-[11]. Alternatively, the internal SM model can provide voltage references, as discussed for different implementations of the voltage control in [12]-[16], [17] and [18]-[21], respectively. Among the current-based VSM implementations, the electrical part of the internal SM model can be represented with two different approaches. Indeed, the first proposals of VSM-based control included modelling of the dynamic electrical equations of the SM [1], [3]-[5], [7]-[14]. However, implementations based on a quasi-stationary representation of the SM stator windings have recently been proposed in [22], [23]. The quasi-stationary approach introduces a further simplification of the modelling, since all transient electrical dynamics of the emulated SM are neglected. Both these two types of implementations have been individually demonstrated by numerical simulations and/or laboratory experiments. In general, it is also clear that the steady-state behavior will be identical for these two types of implementations while differences will appear in the transient performances. However, from previous publications it is not clear which implementation will have the most preferable dynamic properties. This paper is presenting a comparison and assessment of dynamic properties and small-signal stability of VSM implementations based on a Dynamic Electrical Model (DEM) or a Quasi-Stationary Electrical Model (QSEM). For this purpose, implementations of DEM- and QSEM-based VSMs C