—A large-scale integration of renewable generation, usually interfaced to the network through power electronics, has led to an overall decrease in power system inertia. This paper presents novel insights on the fundamental stability prop- erties of such systems. For that purpose, a uniform set of Differential-Algebraic Equations (DAEs) describing a generic, low-inertia power system has been developed. A full-order, state- of-the-art control scheme of both synchronous and converter- based generators are included, with the latter differentiating between the grid-forming and grid-following mode of operation. Furthermore, the dynamics of transmission lines and loads are captured in the model. Using modal analysis techniques such as participation factors and parameter sensitivity, we determine the most vulnerable segments of the system and investigate the adverse effects of the underlying control interference. Finally, the appropriate directions for improving the system stability margin under different generation portfolios have been proposed. Index Terms —differential-algebraic equations, voltage source converter, synchronous generator, small-signal stability, low- inertia systems I. I NTRODUCTION In an effort to render the electric power system more sustainable, increasing shares of renewable generation, e.g., wind turbines and solar panels, are being deployed all around the world. Due to physical properties of such units and the fact that they are typically interfaced via V oltage Source Converters (VSCs) to the system, their interaction with the grid is substantially different compared to traditional plants and thus poses many challenges for power system modeling, analysis and control [1]. On the one hand, with the reduction of total system inertia and the associated faster frequency dynamics, the existing protection and under-frequency load shedding schemes are becoming obsolete. On the other, a high penetration of fast-acting VSCs introduces a timescale separation between the corresponding controls of synchronous and converter-based generators, which can adversely affect frequency and voltage stability. With the aim of providing solutions to the underlying problems, detailed and accurate models of low-inertia systems, usually in the form of Differen- tial Algebraic Equations (DAEs), are needed for the purposes of small-signal analysis. The ﬁeld of small-signal analysis is well established for conventional power systems [2], [3]. With the increasing integration of renewables, a number of publications addressing modeling and stability of 100 % inverter-based microgrids has emerged. The focus of these studies differentiates drastically, varying from individual converter operation modes in a single- machine inﬁnite-bus equivalent [4]–[6] to operation of real- This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 691800. This paper reﬂects only the authors’ views and the European Commission is not responsible for any use that may be made of the information it contains.size distribution grids [7]–[9]. In contrast, the currently on- going transition phase towards inertia-less power systems has been somewhat neglected in the literature. Having in mind that operators in Ireland [10], Texas [11] and South Australia [12] are already facing obstacles regarding excessively high wind penetration during certain periods of the day, the funda- mental understanding of low-inertia systems and their stability properties is of crucial importance. The existing literature on power systems with low rotational inertia conﬁnes itself to very basic network models and often oversimpliﬁed generator control schemes, mostly due to the lack of a uniform state-space formulation for stability analyses. Moreover, the focus is primarily set on distribution networks and microgrids, thus neglecting the potential impact of line dynamics. In [13], the interactions between a VSM-controlled generator and a converter-interfaced load are investigated by considering small-signal stability under different operating conditions. While the authors include a dynamical model of the load and the interconnecting line, they analyze stability only via a basic parameter sweep of the VSM inertia constant and load impedance. Alternatively, a two-bus microgrid comprised of VSC and Synchronous Generator (SG) was studied in [14] and [15]. The work in [14] considers line dynamics and relatively detailed control structures of both units, but only aims at model validation and the impact of operating points on DAE linearization. On the other hand, the authors in [15] provide insightful remarks regarding the permissible penetration levels ofgrid-following inverters, as well as the relevance of different controllers on small-signal stability. However, they employ an impractical inverter scaling method, which obstructs such DAE implementation on a larger system, and disregard dynamics of the lines. Another limitation of this work lies in oversimpliﬁed control schemes, e.g., omittance of Power System Stabilizer (PSS) and important ﬂux dynamics from the SG model. Furthermore, neither of the aforementioned studies employs participation factors for identifying the adverse interactions and determining the true root of instability, nor considers the impact of different converter operation modes. This study combines the work from [14] and [16], and improves on it in several ways. First, we introduce a uniform, high-ﬁdelity DAE formulation of a generic, low-inertia system that captures all relevant physical properties and associated dynamics, including synchronous and converter-based gen- erators, as well as the dynamics of loads and transmission lines. Second, we highlight the issues related to timescale separation in such systems, and subsequently derive analytic expressions for necessary control criteria pertaining to the impact of transmission line dynamics. Finally, we determine the most vulnerable segments of the system and investigate the adverse effects of the underlying control interference. As a result, some new insights on the overall stability of low- and no-inertia systems are presented, together with the appropriate directions for improving the system stability margin under different generation portfolios. The remainder of the paper is structured as follows. In Section II, the state-of-the-art converter control scheme is speciﬁed. Section III presents the dynamics of a synchronous generator equipped with a prime mover, governor and voltage excitation system. Subsequently, in Section IV the uniform mathematical formulation of the sys- tem, as well as the appropriate synchronization and reference frame alignment are elaborated. Furthermore, the associated timescale separation characteristic of low-inertia systems is described. The simulation results from different case studies and the respective stability margins are illustrated in Section V, whereas Section VI draws the main conclusions and discusses the outlook of the study. II. VSC C ONTROL DESIGN The proposed converter model is based on a state-of-the-art VSC control scheme presented in Fig. 1, where the converter is connected to the system through an RLC ﬁlter and a trans- former. The outer control loop consists of active and reactive power controllers, which provide the output voltage angle and magnitude reference by adjusting the predeﬁned setpoints according to a measured power imbalance. The reference voltage vector signal is sent to the inner control loop consisting of cascaded voltage and current controllers operating in a Synchronously-rotating Reference Frame (SRF). In order to detect the system frequency at the Point of Common Coupling (PCC), a Phase-Locked Loop (PLL) synchronization unit is included in the model. However, in case of a grid-forming converter this unit is bypassed via ! c=!0, with!0being the nominal system frequency. Complete control is implemented in the internal SRF, with the(abc=dq )-block denoting a sequence of power-invariant Clarke (Tc)and Park (Tp)transformations from a stationary (abc)-frame to the SRF: xdq=r 2 32 4coscos (2 3) cos (+2 3) sinsin (2 3) sin (+2 3)3 5 | {z } TpTcxabc(1) It should be noted that the mathematical model is deﬁned in per unit (denoted by lower-case symbols), and the quantities in the (dq)-frame are described in complex space vector form: xxdq=xd+jxq(2) with thedqsuperscript omitted in the remainder of the paper. Furthermore, the external control setpoints, e.g., the active power reference, are marked with x, whereas the internally computed