Adaptive Virtual Synchronous Machine (AVSM)

• AVSM is a control strategy where inverter parameters such as virtual inertia, damping, and droop are dynamically adjusted online to emulate synchronous generators.
• Adaptive mechanisms in AVSM employ optimization, fuzzy-neural networks, and feedback control to reduce frequency deviations and improve response times in low-inertia systems.
• Practical implementations demonstrate AVSM’s effectiveness in grid-tied inverters and islanded microgrids by minimizing overshoot and enhancing power quality under changing grid conditions.

Adaptive Virtual Synchronous Machine (AVSM) denotes a virtual synchronous machine or virtual synchronous generator whose machine-like control parameters are not fixed, but adjusted online according to operating conditions, disturbances, or performance objectives. In the underlying VSM/VSG concept, grid-tied or grid-forming power electronic converters are controlled to behave, at least on the electromechanical time scale, like synchronous generators by providing virtual inertia, damping, droop, and voltage-support behavior. The motivation is the same across the literature considered here: increased penetration of inverter-interfaced renewable energy sources reduces available rotational inertia and weakens conventional frequency and voltage support, so converter controls are endowed with synthetic swing-equation dynamics and then made adaptive when fixed parameters are no longer sufficient across changing scenarios (Ademola-Idowu et al., 2018, Li et al., 2021, Breesam et al., 23 Jun 2025).

1. Conceptual scope and relation to VSM, VSG, VISMA, and ViSC

Virtual Synchronous Machines are control strategies for grid-tied inverters that make them behave, at least in the electromechanical time scale, like synchronous generators. In low-inertia power systems with high renewable penetration, physical rotating masses are replaced by power-electronic interfaces, so the natural inertial response to power imbalances is lost. VSMs restore this functionality by measuring frequency and rate of change of frequency, computing a virtual swing equation, and modulating inverter active power output accordingly. In islanded systems, the same concept appears as a grid-forming Virtual Synchronous Generator, regulating voltage and frequency at the point of common coupling while supporting power quality under changing loads (Ademola-Idowu et al., 2018, Besati et al., 2023).

Across the cited work, “adaptive” means that the synthetic machine parameters are treated as dynamic control variables rather than fixed design constants. The most common adaptive quantities are virtual inertia, virtual damping, and droop, but the literature also includes adaptive reactive-power droop, adaptive voltage/reactive-power behavior, state-dependent converter models, and software-defined supervisory layers that alter operating modes or controller parameters. A concise definition stated explicitly in one of the microgrid studies is that an AVSM is “a VSM whose key parameters (virtual inertia, damping, droop, etc.) are continuously adjusted online according to operating conditions, rather than being fixed or only scheduled offline” (Breesam et al., 23 Jun 2025).

Terminology varies by application. “VISMA” is used for a Virtual Synchronous Machine with storage in an islanded microgrid; “ViSC” denotes a virtual synchronous condenser for full-converter wind turbines; “SDViSC” extends that idea into software-defined control and networking; and some papers describe architectures that are “essentially an adaptive VSM/VSG scheme” without naming them AVSM explicitly. This terminological variation indicates that AVSM is better understood as a control principle than as a single canonical block diagram (Dewenter et al., 2016, Jiang et al., 2023, Besati et al., 2023).

2. Dynamic models and adaptive control variables

The basic electromechanical template is the swing equation. In one widely used form,

$$J \frac{d\omega}{dt} = P_m - P_e - D(\omega - \omega_0),$$

where $J$ is virtual inertia, $D$ is virtual damping, $\omega$ is the virtual rotor speed, $P_m$ is the commanded or “mechanical” input power, and $P_e$ is measured electrical output power. Closely related formulations appear in torque form, power form, and small-signal frequency form across the VSG and VSM literature (Breesam et al., 23 Jun 2025, Li et al., 2021, Ren et al., 2020).

For power-system-level VSM design, the inverter’s active-power modulation is often written directly as an inertia-and-damping law. One formulation gives the active power change as

$$\Delta P = \tilde{\mathbf{m}} \frac{d \Delta \omega}{dt} + \tilde{\mathbf{d}} \Delta \omega,$$

where $\tilde{\mathbf{m}}$ and $\tilde{\mathbf{d}}$ are the virtual inertia and damping gain vectors. In this setting, the VSM gains augment the physical inertia and damping of the grid and directly shape RoCoF, frequency nadir, and settling time (Ademola-Idowu et al., 2018).

In ESS-based microgrids, the same idea appears in transfer-function form: $$\Delta P_{vi}(s) = \frac{(k_v s + D_v)\,\Delta f(s)}{(1 + s T_{ESS})\,R_v},$$ where $J$0 is the virtual inertia characteristic constant, $J$1 is virtual damping, $J$2 is virtual droop, and $J$3 is the ESS inverter time constant. Here the AVSM interpretation is explicit: $J$4, $J$5, and $J$6 are virtual machine parameters implemented purely in converter control yet entering the microgrid frequency dynamics in the same structural positions as physical inertia, damping, and governor droop (Breesam et al., 23 Jun 2025).

The variables chosen for adaptation depend on the application. In weak-grid decoupling, the adaptive quantities are $J$7, $J$8, and reactive-power droop $J$9. In fuzzy-neural microgrid control they are $D$0, $D$1, and $D$2. In inertia-and-feedback adaptive VSG control they are $D$3 and the output-speed feedback gain $D$4, with $D$5 introduced to increase damping ratio without large transient changes in droop. In some converter-specific architectures, adaptivity also enters through state-dependent internal models such as shoot-through and non-shoot-through Thevenin impedances or duty-ratio-dependent boost gain (Breesam et al., 23 Jun 2025, Breesam et al., 23 Jun 2025, Ren et al., 2020, Besati et al., 2023).

3. Adaptive mechanisms and design methodologies

A substantial part of AVSM research begins from optimization rather than from direct online learning. One line of work formulates virtual inertia and damping selection as a constrained and regularized $D$6 minimization problem. In that formulation, the objective

$D$7

is minimized subject to box constraints on virtual inertia and damping and Lyapunov equations for the controllability and observability Gramians. The regularization parameter $D$8 explicitly trades off more inertia, favoring low RoCoF and better nadir, against less inertia, favoring faster settling. The same paper states that it does not itself implement an AVSM, but it identifies online optimization, gain scheduling, local adaptive laws, and supervisory MPC as direct extensions (Ademola-Idowu et al., 2018).

An earlier microgrid study optimized VISMA parameters $D$9, $\omega$0, $\omega$1, and $\omega$2 by minimizing the cost

$\omega$3

with Parallel Tempering. Different perturbation scenarios and different weightings $\omega$4 produced different optima, and the resulting optimal parameters agreed with analytical predictions. This suggests that AVSM behavior can be interpreted as scenario-dependent motion among multiple locally optimal parameter sets rather than as a single globally best tuning (Dewenter et al., 2016).

Other approaches make the adaptation law explicit. The representative mechanisms are summarized below.

Reference	Adaptive quantities	Mechanism
(Ademola-Idowu et al., 2018)	$\omega$5	constrained and regularized $\omega$6 minimization with projected gradient descent
(Dewenter et al., 2016)	$\omega$7	Parallel Tempering over scenario-dependent cost functional
(Breesam et al., 23 Jun 2025)	$\omega$8	fuzzy neural network controller with online back-propagation
(Ren et al., 2020)	$\omega$9	inertia adaptation plus output-speed feedback for damping augmentation
(Breesam et al., 23 Jun 2025)	$P_m$0	fuzzy logic based on $P_m$1 and $P_m$2
(Saadatmand et al., 2019)	$P_m$3 with learned effective behavior	heuristic dynamic programming with critic and action networks
(Saadatmand et al., 2019)	$P_m$4 in predictive control	neural network predictive controller using a learned plant model

Learning-based AVSM methods differ mainly in how they map measurements to parameter updates. In the fuzzy-neural microgrid design, the inputs are $P_m$5 and RoCoF, the outputs are $P_m$6, $P_m$7, and $P_m$8, Gaussian membership functions are updated online, and the learning rates are $P_m$9, $P_e$0, and $P_e$1. The intended behavior is explicit: large $P_e$2 or high RoCoF increases virtual inertia and damping and reduces droop $P_e$3; mild deviations relax the parameters to reduce unnecessary ESS stress (Breesam et al., 23 Jun 2025).

In the inertia-and-feedback adaptive VSG, the central modification is the introduction of an output-speed feedback gain $P_e$4, yielding a damping ratio

$P_e$5

The paper’s adaptive law varies $P_e$6 according to the signs of $P_e$7 and $P_e$8, while $P_e$9 is chosen to keep the response overdamped, suppress power overshoot, and constrain frequency deviation within the allowable range (Ren et al., 2020).

The neural optimal-control papers move further away from direct parameter tuning. One uses heuristic dynamic programming with critic and action networks to generate the inverter voltage magnitude $$\Delta P = \tilde{\mathbf{m}} \frac{d \Delta \omega}{dt} + \tilde{\mathbf{d}} \Delta \omega,$$0 from measured powers, errors, and phase angle; the other replaces the traditional PI-based VSG voltage channel with a neural network predictive controller that learns the inverter–grid mapping and chooses $$\Delta P = \tilde{\mathbf{m}} \frac{d \Delta \omega}{dt} + \tilde{\mathbf{d}} \Delta \omega,$$1 by receding-horizon optimization. In both cases, the adaptive behavior is expressed through network weights and control actions rather than through explicit time-varying $$\Delta P = \tilde{\mathbf{m}} \frac{d \Delta \omega}{dt} + \tilde{\mathbf{d}} \Delta \omega,$$2 or $$\Delta P = \tilde{\mathbf{m}} \frac{d \Delta \omega}{dt} + \tilde{\mathbf{d}} \Delta \omega,$$3, but the papers present them as adaptive virtual-inertia or adaptive VSG schemes for non-inductive grids (Saadatmand et al., 2019, Saadatmand et al., 2019).

4. Converter topologies and operating contexts

AVSM is not tied to one converter topology or one grid condition. In weak grids with high $$\Delta P = \tilde{\mathbf{m}} \frac{d \Delta \omega}{dt} + \tilde{\mathbf{d}} \Delta \omega,$$4, one central problem is active–reactive power coupling. For a grid-forming inverter connected through $$\Delta P = \tilde{\mathbf{m}} \frac{d \Delta \omega}{dt} + \tilde{\mathbf{d}} \Delta \omega,$$5, the power equations

$$\Delta P = \tilde{\mathbf{m}} \frac{d \Delta \omega}{dt} + \tilde{\mathbf{d}} \Delta \omega,$$6

show that both active and reactive power depend on both internal voltage magnitude $$\Delta P = \tilde{\mathbf{m}} \frac{d \Delta \omega}{dt} + \tilde{\mathbf{d}} \Delta \omega,$$7 and power angle $$\Delta P = \tilde{\mathbf{m}} \frac{d \Delta \omega}{dt} + \tilde{\mathbf{d}} \Delta \omega,$$8. The AVSM response proposed for that setting is to adapt $$\Delta P = \tilde{\mathbf{m}} \frac{d \Delta \omega}{dt} + \tilde{\mathbf{d}} \Delta \omega,$$9 to remove static coupling and $\tilde{\mathbf{m}}$0 to suppress dynamic coupling, using fuzzy logic driven by measured reactive power $\tilde{\mathbf{m}}$1 and grid impedance ratio $\tilde{\mathbf{m}}$2 (Breesam et al., 23 Jun 2025).

In islanded and non-ideal grids, the Y-Source Inverter paper embeds VSG behavior into a single-stage boost-and-invert topology with continuous input current and mitigated dead-time issues. Its upgraded VSG control based on YZSI combines outer power–frequency and reactive–voltage loops, dq0-based current and voltage control, adaptive boost through duty ratio $\tilde{\mathbf{m}}$3, and explicit Thevenin impedance modeling for shoot-through and non-shoot-through states. The paper states that the term AVSM is not used explicitly, but that the upgraded VSG control is “essentially an adaptive VSM/VSG scheme tailored for islanded and weak grids” (Besati et al., 2023).

A different extension appears in PV generation without storage. There, a VSG is implemented through the DC–DC converter by reserving active power using a predefined power-versus-voltage curve and exploiting the analogy between the synchronous-generator power-angle characteristic and the PV array $\tilde{\mathbf{m}}$4–$\tilde{\mathbf{m}}$5 curve. The key conceptual mapping is

$\tilde{\mathbf{m}}$6

so PV voltage deviation plays the role of power-angle deviation, enabling emulated governor and swing-equation action without an energy storage device (Zhong et al., 2021).

Wind-farm implementations broaden the concept further. The software-defined virtual synchronous condenser paper represents a virtual-machine architecture for full-converter wind turbines with mechanical rotor emulation, AVR, virtual friction, quasi-stationary electrical stator model, and Tustin-discretized software services deployed over software-defined networking. The DFIG wind-farm paper, although it does not explicitly propose an AVSM, provides a five-layer VSM hierarchy—virtual shaft controller, virtual flux controller, rotor current loops, DC-link voltage loop, and grid-side current loops—together with a full small-signal linearization that preserves loop-to-loop and machine-to-machine couplings. This suggests that AVSM can be realized either as a supervisory software layer or as coordinated tuning across all converter control layers (Jiang et al., 2023, Garcia-Aguilar et al., 6 Oct 2025).

5. Experimental evidence and reported performance

The strongest direct AVSM evidence in the supplied literature comes from the adaptive fuzzy-neural microgrid study. In simulation and real-time hardware-in-the-loop on an embedded ARM SAM3X8E (Cortex-M3), the controller trains itself online to choose $\tilde{\mathbf{m}}$7, $\tilde{\mathbf{m}}$8, and $\tilde{\mathbf{m}}$9, keeps frequency deviation within “less than 0.03 Hz,” maintains RoCoF within $\tilde{\mathbf{d}}$0 Hz/s, and yields the smallest overshoot and shortest stabilizing/recovery time relative to no VSG, fixed VSG, adaptive inertia only, and fuzzy adaptive three-parameter control. The same study reports online training times of about 2 s after RES connection and about 7 s after RES disconnection (Breesam et al., 23 Jun 2025).

The weak-grid decoupling AVSM paper validates its fuzzy adaptation on an OPAL-RT OP4610 real-time simulator with a physical ARM-based SAM3X8E controller and a $\tilde{\mathbf{d}}$1 simulation time step. Under high $\tilde{\mathbf{d}}$2 and weak-grid conditions, the method is reported to eliminate static and dynamic power coupling, reduce power angle, and improve active power delivery capability. Reported examples include power-angle reduction from about $\tilde{\mathbf{d}}$3 rad to about $\tilde{\mathbf{d}}$4 rad and active-power delivery increases of $\tilde{\mathbf{d}}$5, $\tilde{\mathbf{d}}$6, $\tilde{\mathbf{d}}$7, and $\tilde{\mathbf{d}}$8 for specific $\tilde{\mathbf{d}}$9 combinations (Breesam et al., 23 Jun 2025).

The YZSI-based islanded-grid implementation reports power-quality and efficiency metrics rather than explicit online self-tuning metrics. MATLAB/Simulink results show PCC voltage of $$\Delta P_{vi}(s) = \frac{(k_v s + D_v)\,\Delta f(s)}{(1 + s T_{ESS})\,R_v},$$0, frequency regulated around $$\Delta P_{vi}(s) = \frac{(k_v s + D_v)\,\Delta f(s)}{(1 + s T_{ESS})\,R_v},$$1, THD of PCC voltage of about $$\Delta P_{vi}(s) = \frac{(k_v s + D_v)\,\Delta f(s)}{(1 + s T_{ESS})\,R_v},$$2, continuous input current, and efficiency of about $$\Delta P_{vi}(s) = \frac{(k_v s + D_v)\,\Delta f(s)}{(1 + s T_{ESS})\,R_v},$$3 before inductive load connection and $$\Delta P_{vi}(s) = \frac{(k_v s + D_v)\,\Delta f(s)}{(1 + s T_{ESS})\,R_v},$$4 after load connection. These results are presented as evidence that the topology-plus-control combination maintains voltage and frequency under non-ideal load conditions and supports AVSM-like behavior in islanded operation (Besati et al., 2023).

The software-defined virtual synchronous condenser prototype demonstrates that software-defined realization can retain fast dynamics while adding cyber-physical flexibility. In an RTDS-based digital twin of a $$\Delta P_{vi}(s) = \frac{(k_v s + D_v)\,\Delta f(s)}{(1 + s T_{ESS})\,R_v},$$5 offshore wind farm, Tustin-based SDViSC at $$\Delta P_{vi}(s) = \frac{(k_v s + D_v)\,\Delta f(s)}{(1 + s T_{ESS})\,R_v},$$6 ms reproduces hardware ViSC behavior; under a voltage reference step from $$\Delta P_{vi}(s) = \frac{(k_v s + D_v)\,\Delta f(s)}{(1 + s T_{ESS})\,R_v},$$7 to $$\Delta P_{vi}(s) = \frac{(k_v s + D_v)\,\Delta f(s)}{(1 + s T_{ESS})\,R_v},$$8 p.u., SDViSC reaches about $$\Delta P_{vi}(s) = \frac{(k_v s + D_v)\,\Delta f(s)}{(1 + s T_{ESS})\,R_v},$$9 p.u. faster than a synchronous condenser; and under fault conditions its current is limited to about $J$00 p.u. versus about $J$01 p.u. for the synchronous condenser. The same paper reports that SDViSC remains stable at lower SCR than the synchronous condenser in the tested weak-grid scenarios (Jiang et al., 2023).

A complementary form of evidence appears in the adaptive feedback-parameter VSG paper. Compared with existing adaptive strategies, the proposed $J$02 and $J$03 adaptation keeps the system overdamped, suppresses power overshoot, and reduces the required maximum virtual inertia from about $J$04 or $J$05 in other adaptive schemes to about $J$06, thereby reducing the storage margin requirement while keeping frequency deviation within the allowable range (Ren et al., 2020).

6. Limitations, misconceptions, and open problems

The literature does not present AVSM as a solved or uniform design problem. Several papers explicitly describe only foundations. The $J$07-based optimal-design paper provides a mathematically rigorous backbone for adaptive tuning but does not itself implement an AVSM; the DFIG wind-farm paper develops a multi-loop VSM framework almost tailor-made for adding adaptation, but its tuning remains offline and centered on a single operating point; and the YZSI-VSG paper provides an adaptive architectural foundation rather than a full self-tuning parameter law (Ademola-Idowu et al., 2018, Garcia-Aguilar et al., 6 Oct 2025, Besati et al., 2023).

Modeling assumptions are a recurring limitation. The $J$08 design relies on linearization around an operating point, DC power-flow assumptions, and omission of detailed inverter dynamics, converter control delays, and voltage/reactive-power dynamics. The fuzzy-neural controller is model-free at the adaptation layer, but its performance still depends on frequency and RoCoF measurements, learning-rate selection, and initialization of membership centers, widths, and weights. The predictive neural controller uses offline training and may require retraining if operating conditions depart substantially from the training set (Ademola-Idowu et al., 2018, Breesam et al., 23 Jun 2025, Saadatmand et al., 2019).

Energy and converter limits remain fundamental. The VSG review emphasizes that virtual inertia design must account for ESS state of charge, ramping rate, and renewable-energy limits; the SDViSC work shows that converter short-circuit current is limited to about $J$09 p.u.; the PV-without-storage VSG can only provide headroom-based support by de-loading from maximum power; and the adaptive feedback-parameter VSG paper frames large inertia or droop excursions as a storage-margin problem. This suggests that AVSM adaptation is always bounded by available energy and converter ratings, even when the control law itself appears unconstrained (Li et al., 2021, Jiang et al., 2023, Zhong et al., 2021, Ren et al., 2020).

A common misconception is that AVSM necessarily implies one particular algorithmic family. The cited work shows otherwise: AVSM behavior can arise from projected-gradient optimization, Parallel Tempering, fuzzy logic, fuzzy-neural online learning, heuristic dynamic programming, neural predictive control, converter-state-aware multi-loop control, or software-defined supervisory scheduling. What unifies these approaches is not a shared optimizer but the replacement of fixed virtual-machine parameters by operating-point-dependent ones (Dewenter et al., 2016, Saadatmand et al., 2019, Breesam et al., 23 Jun 2025).

Open problems are identified directly in the reviewed material. The virtual-inertia review calls for multi-parameter adaptivity rather than adaptation of only one parameter, coherent treatment of hybrid energy sources, and coordination among multiple VSGs. The fuzzy-neural microgrid paper points to multi-VSG and distributed AI extensions. The software-defined wind-farm work raises formal stability analysis under communication impairments, cyber-security, and scalability. The DFIG multi-loop study calls for multi-operating-point design and optimization of crossover frequencies and phase margins. Taken together, these points indicate that the next stage of AVSM research lies in coordinated, constraint-aware, multi-device adaptation under uncertain physical and cyber conditions (Li et al., 2021, Breesam et al., 23 Jun 2025, Jiang et al., 2023, Garcia-Aguilar et al., 6 Oct 2025).