Stability analysis of a PMSG based Virtual Synchronous Machine

Transient stability of photovoltaic-hydro microgrid systems is poor due to lack of inertia and the intermittent nature of photovoltaic systems. The stability of such systems can be improved by using virtual synchronous machines which add inertia into the system to allow for higher PV penetration without losing stability. A PV-hydro system was simulated in MATLAB/Simulink to analyze the transient stability problems due to PV fluctuations and/or load or generation changes. Virtual synchronous machine was added which reduced the frequency deviations and the high rate of change of frequency. The results indicate that the transient stability of photovoltaic-hydro microgrid systems can be improved by using virtual synchronous machines using a minimum amount of energy storage. However, the power requirements of the virtual synchronous machine's converter was found to be high compared to the overall system size. Furthermore, high PV penetration levels were achieved by adding virtual synchronous machine to the system.

Grid-connected power converters can be operated as virtual synchronous machines (VSMs) to mimic the dynamics of conventional synchronous machines. VSMs can provide inertial responses to the power grid, and present desired dynamics when connected to weak grids that featured by high grid impedances. However, when the VSM is connected to a strong grid with low grid impedance, its stability margin will be reduced, which is particularly analyzed in this paper. Moreover, we demonstrate that the VSM's stability can be improved by properly reducing the virtual inertia. Based on the stability analysis, an adaptive inertia control (AIC) is proposed, which can regulate the virtual inertia according to the identified grid impedance to ensure that the VSM has a desired stability margin under various grid strength. The grid impedance is identified in real time along the system trajectory, using the recursive least square algorithm to enable the implementation in the controller. Simulations verify the validity of the analysis and the effectiveness of the AIC on improving the VSM's stability when considering various power grid strength.

The increasing penetration of converter-interfaced generation raises critical concerns for power system stability, especially during rapid transients and system split events that are not yet adequately addressed in current grid code compliance tests. This paper assesses the resilience of a Virtual Synchronous Machine (VSM) in comparison with a grid-following photovoltaic (PV) inverter through a combined framework of standardized benchmark tests and realistic system split scenarios. In benchmark testing, the VSM provided synthetic inertia by delivering a transient-power burst from a 0.30 p.u. setpoint to 0.545 p.u. (on a 20 MVA base, representing 54.5% of rated capacity) under a −0.4 Hz/s frequency ramp, corresponding to an equivalent inertia constant of approximately 15 s. With the limited frequency-sensitive mode–underfrequency (LFSM-U) function enabled, it sustained additional active power up to 0.61 p.u. once the frequency fell below 49.8 Hz. The PV inverter, by contrast, demonstrated compliance with conventional grid requirements: it curtailed power through LFSM-O during overfrequency conditions and injected 0.25 p.u. of reactive current during a fault ride-through (FRT) event at 1.129 p.u. voltage. In system split tests, the VSM absorbed surplus PV generation, stabilizing frequency after a transient rise to 52.8 Hz and containing voltage excursions beyond 1.2 p.u. During imbalance stress, it absorbed 1.266 MW against its 1.0 MW rating for approximately 2–3 s, corresponding to a 26.6% overload that falls within typical IGBT transient thermal capability but would require supervisory intervention (e.g., PV curtailment or load management) if sustained. These results demonstrate that while the PV inverter contributes valuable voltage support, only the grid-forming VSM maintains frequency stability and ensures secure islanded operation. The novelty of this study lies in integrating standardized compliance tests with system split scenarios, providing a comprehensive framework for evaluating grid-forming controls under both regulatory and resilience-oriented perspectives and informing the evolution of future grid codes.

A modelling and stability analysis method of a virtual synchronous machine (VSM) is proposed in this study. VSM technology is used to solve the problems caused by the high permeability of distributed energy. Though VSM has inertia and damping characteristics, it is more prone to oscillate than a synchronous generator because of the characteristic and unexpected harmonics generated by power electronic elements. The traditional linear time invariant based model is difficult to analyse a time‐variant system and cannot analyse harmonic coupling mechanism accurately. This study proposes a new model of a grid‐connected VSM by using the harmonic state‐space modelling approach, which is a typical linear time‐varying periodic model and considers different harmonics of the system. The stability of the system is analysed by eigenvalues of system matrix, which is based on the harmonic state‐space model. The theoretical modelling method and stability analysis are verified by direct time‐domain simulation results.

The low‐frequency dynamics of virtual synchronous machine (VSM) depends on multiple factors. In this study, the oscillation mode of a single VSM is first identified by exploring the evolution of oscillation from synchronous mode to sub‐synchronous mode with the variation of structure and parameters. The inter‐oscillation modes among multiple VSMs modelled in quasi‐state phasor domain are then studied by decomposing into mean motion and relative motion. Inspired by and weak‐coupling‐based coherency identification, the associated VSM group can be fast identified and used for effective stabilizer location. The approximate eigenvalues can be fast obtained by system decomposition in uniform‐damping scenarios or by extended‐equal‐area‐criterion approach in non‐uniform‐damping scenario. An improved design for lead–lag compensation is proposed to damp both synchronous and sub‐synchronous oscillation of VSMs. Effectiveness of the proposed control strategy in grid‐connected/islanded mode is verified with real‐time simulation.

Transmission system operators (TSOs) are increasingly requesting frequency support, reactive power compensation, and grid-forming capability to power plants interfaced by power converters. In these plants, a large number of converters is operated in parallel and all of them should be adequately coordinated to provide these services. For that purpose, the virtual synchronous machine (VSM) control technique is commonly adopted. However, the dynamic characteristics of the whole plant depend on the number of converters connected, their size, control parameters, and electrical interconnections. This makes it difficult to know the aggregated dynamic characteristic of the plant and how each VSM contributes to the plant response. In this article, the operation of VSMs in parallel configuration for island and grid-connected applications is studied. The developments make it possible to adapt the VSMs parameters so that the grid sees the power plant as an equivalent generator whose low-frequency characteristics do not vary with the number of converters in operation. The developments were validated in a laboratory consisting of four 15 kVA converters operating as VSMs, and a grid emulator.

In this article, the slip mechanism in the rotor-dynamics of the induction machine is emulated to improve the transient stability of grid-forming converter (or virtual synchronous machine). Different from the synchronous machine, the speeds of the rotor and of the rotating magnetic field in the stator are different in the induction machine. This slip frequency in the induction machine offers another degree-of-freedom to regulate the frequency, playing a similar role of the damper winding in the synchronous machine. It can inject transient damping to the system, and virtually increase the feedback power to smooth the power angle variations when severe fault occurs. The effectiveness of the proposed controller on improving both small-signal and transient stability (large-signal) is presented. The proposed algorithm is verified by experiments.

Traditional power systems based on synchronous generators often feature low frequency electromechanical oscillations. However, the integration of renewable energy sources through power converters can help tackling this issue. In fact, thanks to the concept of Virtual Synchronous Machine (VSM), it is possible to make the inverters behave as real synchronous machines (SMs). This way, the inverters can be integrated into the grid as traditional SMs and can even outperform them when it comes to damping low frequency oscillations in the power system. In order to do that, proper damping algorithms must be adopted in the VSM model. Therefore, this paper presents a simple and straighforward damping method for VSMs based on a single lead-lag filter acting on the VSM active power feedback. The proposed method and its integration in the VSM model are described. Then, the proposed solution has been experimentally compared to conventional methods, along with comparison metrics, to highlight its benefits.

This paper identifies the importance of considering the full-order virtual synchronous machine (VSM) dynamics while tuning parameters in its cascaded voltage and current control loops. Via a numerical example, we highlight that the conventional tuning method of the voltage and current loops may not ensure system stability. This is because the tuning method does not consider full-order system dynamics. Thus, we improve the tuning method for the VSM voltage and current loops using small-signal analysis of the full-order VSM model. The proposed tuning method ensures system stability in the small-signal sense, and it is computationally inexpensive. We verify the effectiveness of the proposed tuning method via numerical simulations.

Due to the lack of system inertia driven by the increasing integration of renewable energy, a virtual synchronous machine (VISMA) concept has been developed to provide backup inertia, maintaining microgrid stability and resiliency. To enhance an inertia support in regards to frequency stability, this paper proposes a novel control approach using multiple VISMAs with different P-f droop characteristics. This approach can effectively enhance frequency stability of the microgrid under the situation of low system inertia. The stability difference and efficacy between single VISMA and multiple VISMAs are investigated over microgrid performance with contrastive scenarios. Transient and steady-state responses are also compared. The analysis results reveal that the multiple-VISMA configuration suppresses frequency oscillation better than the single VISMA configuration, maintaining stable microgrid operation. This work also provides a recent overview of a practical multiple-VISMA system in regards to frequency stability improvement.

Electronic power interfaces are commonly used in microgrids for renewable energy integration and a control method based on a virtual synchronous machine (VSM) represents an attractive alternative to conventional approaches. This control method has several advantages, however, a number of issues still need to be properly addressed, including those of power quality and harmonic current sharing. In this paper, a finite-gain repetitive controller (FGRC) is proposed to improve the current harmonic distribution in microgrids based on VSMs. Stability, transient performance, and performance under frequency variations are studied analytically. When compared to other control options, the method proposed here is capable of dealing with all harmonics simultaneously. A comparative analysis is provided to emphasize the contributions of this paper. The control system improvements were tested on a prototype microgrid consisting of two 15 kVA VSMs, distribution line impedances, and a non-linear load.

This paper presents a single-phase virtual synchronous machine (VSM) and its possible application for providing vehicle-to-grid (V2G) services from domestic battery chargers of electric vehicles (EVs). In a VSM, the power converter is controlled to emulate the inertia and damping effect of a synchronous machine. Thus, a VSM-based EV charger can contribute to the spinning reserve and the frequency regulation of the power system. In case of grid outages, the VSM can seamlessly establish an islanded grid and supply local loads from the battery onboard the EV. In order to avoid the influence on the virtual inertia from power oscillations associated with a single-phase circuit, the proposed control scheme relies on a virtual two-phase system for calculating active and reactive powers. The proposed VSM implementation is described in detail, and its dynamic performances in grid-connected as well as stand-alone operation are demonstrated by numerical simulations and by laboratory experiments.

Stability of power grids with synchronous generators (SGs) and renewable\ngeneration interfaced with grid-forming converters (GFCs) under dc-side current\nlimitation is studied. To that end, we first consider a simple 2-bus test\nsystem and reduced-order models to highlight the fundamental difference between\ntwo classes of GFC controls -- (A) droop, dispatchable virtual oscillator\ncontrol (dVOC) and virtual synchronous machine (VSM), and (B) matching control.\nNext, we study Lyapunov stability and input-output stability of the dc voltage\ndynamics of class-A GFCs for the simple system and extend it to a generic\nsystem. Next, we provide a sufficiency condition for input-to-state stability\nof the 2-bus system with a class-B GFC and extend it for a generic system.\nFinally, time-domain simulations from a reduced-order averaged model of the\nsimple test system and a detailed switched model of the GFC validate the\nproposed conditions.\n

With the increase of distributed power generation integrated into the power grid through power electronic converters, the problem of inertia reduction in power system has been caused, a new control technology is needed to enable distributed power sources to actively participate in the voltage and frequency regulation of the grid. In this paper, a model predictive control (MPC) strategy based on virtual synchronous machine (VSM) for the grid-connected converter is proposed. The method does not require traditional pulse width modulation and current inner loop control. When the voltage and frequency of power grid change, the active power and reactive power can respond in time and simulate characteristics of traditional synchronous machine. The simulation results are given to verify the effectiveness of the control strategy presented above.

During the last decade virtual synchronous machines (VSMs) have been intensively investigated and plenty of control strategies have been proposed as possible implementations. Some of the proposed control strategies aim to reproduce the inertia of a synchronous machine (SM), but rely on a dedicated unit for the synchronization to the main grid. However, one of the most appealing features of a SM is its ability to self-synchronize itself to the grid thanks to the intrinsic power synchronization mechanism. The Synchronous Power Control (SPC) is among the control strategies proposed in the literature based on the power synchronization mechanism. In this paper, the aforementioned control is deeply investigated. Its concept is first introduced and a small-signal model of an SPC-based grid connected converter is developed. Subsequently, a comprehensive parameter sensitivity analysis is performed in order to identify the effects of control parameters variations on the eigenvalues of the system under different grid conditions. Time-domain simulations in MATLAB/Simulink/PLECS confirm the validity of the developed frequency-domain model.