Virtual Synchronous Generator (VSG)

• Virtual Synchronous Generator (VSG) is a grid-forming control paradigm that emulates synchronous machine dynamics with synthetic inertia and damping.
• It implements advanced control schemes, including complex-coefficient design and compensators, to optimize voltage regulation and minimize power overshoots.
• Experimental and simulation validations demonstrate that VSG achieves faster rise times, reduced overshoot, and robust stability under varying grid conditions.

A Virtual Synchronous Generator (VSG) is a grid-forming control paradigm for power-electronic inverters that emulates the electromechanical swing dynamics, inertia, and damping of synchronous machines. VSGs have become a critical enabler for the reliable integration of inverter-based resources (IBRs) in decarbonizing power systems by providing synthetic inertia, frequency, and voltage regulation services, as well as supporting grid stability across a spectrum of network conditions (Xu et al., 2024).

1. Modeling, Control, and Dynamic Analysis of VSGs

The classical VSG emulates the swing equation:

$$2H \frac{d\Delta\omega}{dt} = P_{\rm ref} - P_e - D\,\Delta\omega,$$

where $H$ is the virtual inertia, $D$ is the damping, $P_{\rm ref}$ the power setpoint, and $P_e$ the measured electrical power. Frequency- and voltage-regulation are accomplished through emulation of synchronous-machine active-frequency and reactive-voltage coupling. The DQ-frame inner control implements cascaded voltage and current PI controllers. Under standard assumptions (neglecting high-frequency $LC$ resonance, $R_g \approx 0$), the open-loop transfer function for the inner voltage loop is (Xu et al., 2024):

$G_{OL}(s) = \frac{C_i(s)C_v(s)}{1 + L_P(s)},$

with $L_P(s) = \frac{sL_s + k_c C_i(s)}{sL_g + j X_g}$, where $L_s, L_g$ are filter and grid inductances, $H$0 are the PI controllers, and $H$1 is a current-feeding gain.

The closed-loop system is a complex second-order SISO transfer function:

$H$2

with non-real-conjugate poles $H$3, determining both voltage-magnitude regulation and $H$4-axis oscillatory dynamics.

2. Optimized Voltage Control via Complex-Coefficient Design

Classical VSGs exhibit deficiencies in strong-grid scenarios, including slow voltage regulation, underdamped resonances, and detrimental coupling between voltage and real-power transients—such as voltage-coupled power spikes induced by swift $H$5 transformation (Xu et al., 2024).

A new control methodology introduces:

• A complex current-feeding gain $H$6 (with both real and imaginary parts) enabling direct placement of closed-loop poles for targeted speed and damping (e.g., rise time ≈20 ms, overshoot ≤5%). The controller sets both poles at $H$7 and $H$8, producing a well-damped response with closed-loop bandwidth $H$9 Hz.
• A transient power-overshoot compensator $D$0, designed as a first-order lag matched to the inner PI time constant, which virtually eliminates the spurious active-power spike resulting from fast voltage reference steps.

The sequential design guarantees closed-loop left-half-plane pole placement, phase margin ≥$D$1, and robustness to variations in $D$2 and $D$3.

3. Vectorized Geometric Pole Analysis and Stability Criterion

Vectorized geometric pole analysis reparameterizes pole locations as:

$D$4

where $D$5 are functions of the control parameters and grid reactance. The crucial analytical outcome is a scalar stability criterion:

$D$6

which efficiently guides controller selection to guarantee robust voltage regulation even in strong grids.

The geometric perspective enables direct intuition for loop tuning and visualizes the effect of gain changes on damping and stability margins.

4. Mitigating Power-Voltage Decoupling and Resonance Interactions

Conventional VSGs are susceptible to voltage-coupled subsynchronous resonance (vSSCI) phenomena in networks with high reactance or very strong grids. The enhanced control scheme (Xu et al., 2024):

• Achieves power-voltage decoupling: Simulation and experimental results show the active-power response to a voltage step is reduced from +7.5 dB (factor × 2.4) for conventional (real-gain) controllers to +0.9 dB (factor × 1.1) with the new complex-gain + compensator design.
• Suppresses underdamped vSSCI oscillations: The complex-coefficient controller consistently delivers rise times of 15–20 ms with <5% overshoot (versus 100 ms, 30–50% overshoot for baseline) and maintains stability across severe grid parameter changes.

The design also simplifies tuning, as explicit closed-form solutions exist for selecting optimal gains and compensator parameters.

5. Experimental and Simulation Validation

The proposed complex-gain and two-fold compensator design have been validated on both simulated and hardware testbeds (Xu et al., 2024).

Empirical Results (as reported):

Metric	Baseline VSG (real gain)	Complex-gain VSG (proposed)
Rise time (10–95%)	up to 100 ms	15–20 ms
Overshoot	30–50%	<5%
vSSCI oscillation	present, 2–30 Hz	none
Bandwidth (−3 dB)	≈18 Hz	≈21.6 Hz (with $D$7)
Power response to $D$8	+7.5 dB (×2.4)	+0.9 dB (×1.1)
Robustness (grid $D$9)	may go unstable	always well-damped

Under 60° phase jump or substantial grid impedance change, the complex-coefficient VC loop maintains stability and recovers in <20 ms. Hardware results confirm: (1) loss of stability when $P_{\rm ref}$0 violates the $P_{\rm ref}$1 bound, (2) >80% reductions in current/power peaks with $P_{\rm ref}$2, (3) rapid damping for severe grid disturbances.

6. Broader Context: Grid-Level Dynamics, Integration, and Planning

Robust VSG voltage control is a linchpin for the decarbonized grid, but broader system-level stability requires harmonized design across layers (Raman et al., 2022). Notably:

• VSG platforms must provide both “virtual inertia” and active stability buffering via emulated impedance ("stability storage"), as high system inertia alone does not guarantee stability in networks with many VSGs.
• Practical frameworks now recommend tracking distributed stability metrics, such as the DSM (Distributed Stability Metric), and establishing ancillary-market incentives for “stability storage” services alongside inertial support.
• VSG voltage-control robustness as per (Xu et al., 2024) is a critical local enabler, but global small-signal stability mandates real-time impedance adaptation and coordination (Raman et al., 2022).

7. Practical Implementation Guidelines

For deploying advanced VSG voltage control in real-world IBRs:

• Utilize complex-coefficient voltage control for all grid-forming inverters in networks where grid strength varies or grid reactance is substantial.
• Ensure that the stability criterion $P_{\rm ref}$3 is always met by tracking $P_{\rm ref}$4 and $P_{\rm ref}$5 in the parameter scheduling logic.
• Adopt direct pole placement or 1-parameter optimization (e.g., ISE minimization) for tuning $P_{\rm ref}$6 on the commissioning setpoint; adapt online as grid impedance varies.
• Always combine fast voltage regulation with compensating lags for power-overshoot minimization, especially in networks prone to $P_{\rm ref}$7–$P_{\rm ref}$8 cross-coupling.
• Validate on both simulation and hardware-in-the-loop platforms for worst-case grid scenarios, and define standard operating envelopes for $P_{\rm ref}$9, $P_e$0, and grid phase jumps as shown in the hardware case studies.

The approach is now considered a robust, theory-grounded advancement over prior art, delivering faster, more stable grid integration, and dramatically simplifying tuning and commissioning of VSG-based IBRs in a variety of power-system contexts (Xu et al., 2024).