The global transition towards sustainable energy, coupled with ambitious carbon neutrality goals, has propelled new energy technologies to the forefront of power system development. Modern grids are increasingly characterized by high shares of renewables and power electronics, forming a “double-high” new-type power system. Unlike traditional synchronous generators, new energy sources and energy storage systems connect to the grid or loads primarily through highly controllable and efficient power electronic converters, specifically on-grid inverters.
In this context, grid-forming control strategies, which mimic the behavior of synchronous generators to provide voltage support and synthetic inertia, have become essential for maintaining power system stability. The mainstream grid-forming controls are droop control and Virtual Synchronous Generator (VSG) control. However, each faces significant challenges when an on-grid inverter must operate reliably in multiple modes.
In islanded (stand-alone) mode, the primary task of the on-grid inverter control is to establish and regulate the microgrid’s voltage and frequency. While VSG control provides excellent inertia and damping for frequency stability, traditional droop control offers virtually no inertia, leading to a very high initial Rate-of-Change-of-Frequency (RoCoF) during load transients, which can jeopardize system stability.
Conversely, in grid-connected mode, the primary objective shifts to accurately and quickly injecting the reference active power into the main grid. Here, droop control exhibits good power tracking with minimal overshoot, but VSG control often suffers from significant power overshoot, oscillation, and a slow response due to its inherent inertia. Therefore, neither conventional strategy can simultaneously meet the distinct performance demands of both operational modes for a versatile on-grid inverter.
To address these limitations, this work proposes a novel improved control strategy. The core innovation lies in the design of dual adaptive coefficients that seamlessly blend the advantages of droop and VSG control. This strategy enables a single on-grid inverter to provide superior dynamic performance: fast, non-oscillatory power tracking in grid-connected mode and sufficient synthetic inertia with fast recovery in islanded mode.
Analysis of Conventional Control Strategies for On-Grid Inverters
To understand the proposed improvement, a brief analysis of the conventional strategies is necessary. The typical system consists of a DC source (e.g., battery), a three-phase inverter, an LC filter, and a connection to the grid or local load. The control structure includes power calculation, the core grid-forming strategy (droop or VSG), and inner voltage and current loops.
The fundamental difference lies in the active power-frequency ($P-\omega$) control loop. Droop control implements a simple proportional relationship:
$$ \omega = \omega_{ref} – k_p (P – P_{ref}) $$
where $\omega$ is the output frequency, $\omega_{ref}$ is the reference frequency, $P$ is the measured power, $P_{ref}$ is the reference power, and $k_p$ is the droop coefficient.
VSG control, aiming to emulate the swing equation of a synchronous generator, is described by:
$$ J \frac{d \omega}{dt} = P_{ref} – P – D (\omega – \omega_{ref}) $$
where $J$ is the virtual inertia and $D$ is the damping coefficient.
Small-signal analysis around an operating point reveals the distinct transfer functions. For an on-grid inverter in grid-connected mode, assuming a stiff grid ($\Delta\omega_g \approx 0$), the transfer function from reference power change ($\Delta P_{ref}$) to output power change ($\Delta P$) is crucial.
- Droop Control:
$$ H_{droop}^{P}(s) = \frac{\Delta P(s)}{\Delta P_{ref}(s)} = \frac{K_{droop}}{s + K_{droop}} $$
where $K_{droop} = \frac{k_p V_0 V_g}{X \omega_0}$. It is a first-order system, typically with no overshoot. - VSG Control:
$$ H_{vsg}^{P}(s) = \frac{\Delta P(s)}{\Delta P_{ref}(s)} = \frac{\omega_n^2}{s^2 + 2\xi\omega_n s + \omega_n^2} $$
where $\omega_n = \sqrt{\frac{V_0 V_g}{J X \omega_0}}$ and $\xi = \frac{D}{2} \sqrt{\frac{X \omega_0}{J V_0 V_g}}$. It is a second-order system prone to overshoot and oscillation if $\xi$ is small.
For islanded mode, the response to a load change ($\Delta P_L$) is key. The transfer function to frequency deviation ($\Delta \omega$) is:
- Droop Control: $H_{droop}^{\omega}(s) = -k_p$. This implies an instantaneous frequency change, i.e., infinite initial RoCoF, indicating no inertia.
- VSG Control: $H_{vsg}^{\omega}(s) = -\frac{1}{J s + D}$. This provides a finite initial RoCoF of $\Delta P_L / J$.
The contrasting behaviors are summarized in the table below, highlighting the core problem for a multi-mode on-grid inverter.
| Operational Mode | Key Performance Metric | Droop Control Performance | VSG Control Performance |
|---|---|---|---|
| Grid-Connected | Power Tracking (Step Response) | No overshoot, moderate settling time. | Large overshoot & oscillation, long settling time. |
| Islanded | Frequency Stability (Initial RoCoF) | Very high (poor, no inertia). | Low, tunable via $J$ (good inertia support). |
Proposed Improved Control Strategy with Dual Adaptive Coefficients
The proposed strategy intelligently combines the structures of droop and VSG control through a novel controller block $H_{control}(s)$, which is dynamically tuned by two adaptive coefficients. The block diagram of the improved active power control loop is shown below.
The controller is formulated as:
$$ H_{control}(s) = k_p \cdot \frac{1 – G_c(s) \cdot \left( \frac{s}{\omega_0 J k_p} + 1 \right)}{(T s + 1) \cdot \left( \frac{s}{\omega_0 J k_p} + 1 \right)} $$
where $G_c(s)$ is the adaptive coordination coefficient and $J$ is made adaptive via the adaptive inertia coefficient. $T$ is a time constant for high-frequency attenuation.
1. Design of the Adaptive Coordination Coefficient ($G_c$)
The purpose of $G_c$ is to dynamically weight the influence of the VSG-like path versus the droop path in the controller. During a transient:
- When the absolute RoCoF ($|d\omega/dt|$) is large (e.g., right after a load step), the on-grid inverter needs strong inertia support. $G_c$ should be large to emphasize the VSG characteristic.
- As the RoCoF decreases and the system enters the recovery phase, $G_c$ should decrease to emphasize the faster droop characteristic, speeding up the settling time.
To achieve this smooth and bounded transition, $G_c$ is designed using a hyperbolic tangent function of the RoCoF:
$$ G_c = n \cdot \tanh\left( \left| \frac{d\omega}{dt} \right| \right) $$
where $n$ is a coordination factor that scales the coefficient. This ensures $0 \leq G_c < n$, providing a continuous and automatic transition between control behaviors based on the system’s instantaneous need.
2. Design of the Adaptive Inertia Coefficient ($J$)
To further refine dynamics, especially to eliminate the power overshoot inherent in VSG, the virtual inertia $J$ is made adaptive. Recall the VSG’s damping ratio $\xi$ and natural frequency $\omega_n$:
$$ \omega_n = \sqrt{\frac{V_0 V_g}{J X \omega_0}}, \quad \xi = \frac{D}{2} \sqrt{\frac{X \omega_0}{J V_0 V_g}} $$
For a given, fixed damping coefficient $D$ (set equal to $1/k_p$ for steady-state consistency), $J$ is inversely proportional to $\xi^2$. A smaller $\xi$ gives larger $J$ (more inertia) but causes overshoot. A $\xi$ close to 1 gives minimal overshoot but smaller inertia.
The strategy is to start with a low damping ratio $\xi_0$ to provide sufficient inertia at the transient’s onset, then increase $\xi$ to damp oscillations and accelerate settling. Therefore, $\xi$ is designed as:
$$
\xi = \begin{cases}
\xi_0 + 0.8 \cdot \tanh(0.9 \cdot \Delta t), & \text{if } \left|\frac{d\omega}{dt}\right| \geq M_{th} \text{ and } \frac{d\omega}{dt} \cdot \Delta \omega > 0 \\
\xi_0, & \text{otherwise}
\end{cases}
$$
where $M_{th}$ is a RoCoF threshold, and $\Delta t$ is the duration since the RoCoF exceeded the threshold. This increases $\xi$ during the frequency recovery phase. The corresponding adaptive inertia is then calculated as:
$$ J = \frac{X D^2}{4 \omega_0 V_0 V_g \xi^2} $$
This dual-adaptive mechanism allows the on-grid inverter to possess high virtual inertia when needed for stability and to rapidly switch to a damped, fast-responding mode for quick recovery and precise power tracking.
3. Parameter Design Summary
A systematic parameter design ensures stability and desired performance. Key steps include setting $D=1/k_p$ for steady-state alignment, choosing $k_p$ based on allowable steady-state frequency deviation, selecting $\xi_0$ and $T$ for dynamic response, and tuning $n$ and $M_{th}$ for the adaptive laws. A representative parameter set is shown below.
| Parameter | Symbol | Value |
|---|---|---|
| Droop Coefficient | $k_p$ | 5.0e-5 |
| Initial Damping Ratio | $\xi_0$ | 0.2 |
| Adaptive Time Constant | $T$ | 0.2 s |
| Coordination Factor | $n$ | 4 |
| RoCoF Threshold | $M_{th}$ | 0.01 rad/s² |
Experimental Validation via Hardware-in-the-Loop (HIL)
The proposed improved control strategy was validated using a Control Hardware-in-the-Loop (CHIL) platform. The power circuit (inverter, grid, load) was simulated in a real-time simulator (OPAL-RT 4510), while the proposed control algorithm was implemented on a physical DSP controller (TMS320F28335). The performance was compared against traditional Droop Control, VSG Control, and a referenced Generalized Droop Control (GDC).
1. Grid-Connected Mode: Power Tracking Performance
The on-grid inverter reference active power $P_{ref}$ was stepped from 20 kW to 30 kW. The active power output responses are compared below.
The proposed strategy demonstrates a clear advantage for the on-grid inverter in this mode. The quantitative comparison is summarized in the following table.
| Control Strategy | Overshoot | Oscillation | Settling Time |
|---|---|---|---|
| Droop Control | None | No | ~5.0 s |
| VSG Control | 21.3% | Yes | >13 s |
| GDC | 20.5% | Yes | >17 s |
| Proposed Improved Control | None | No | ~2.5 s |
2. Islanded Mode: Frequency Response Performance
The load power $P_L$ was stepped from 20 kW to 40 kW in islanded mode. The system frequency deviation was measured.
The proposed strategy successfully provides the essential inertia support that droop control lacks, while recovering much faster than VSG. The key metrics are compared below.
| Control Strategy | Initial RoCoF (abs) | Inertia Support | Settling Time |
|---|---|---|---|
| Droop Control | 5.40 rad/s² | Very Poor | ~0.5 s |
| VSG Control | 0.30 rad/s² | Excellent | ~7.0 s |
| GDC | 0.30 rad/s² | Excellent | >16 s |
| Proposed Improved Control | 0.31 rad/s² | Excellent | ~4.0 s |
Conclusion
This work has presented a novel improved control strategy for on-grid inverters that must operate reliably in both grid-connected and islanded modes. By introducing dual adaptive coefficients—an adaptive coordination coefficient ($G_c$) and an adaptive inertia coefficient ($J$)—the strategy seamlessly merges the strengths of traditional droop and VSG control.
The adaptive coordination coefficient enables the controller to automatically emphasize inertia provision during high-RoCoF transients and emphasize fast response during the recovery phase. The adaptive inertia coefficient further refines this by adjusting the damping ratio online, which is key to completely eliminating power overshoot and oscillation.
Experimental results from a hardware-in-the-loop platform confirm the strategy’s superior performance. For the on-grid inverter in grid-connected mode, it achieves fast, non-oscillatory power tracking without any overshoot, outperforming both VSG and droop control in settling time. In islanded mode, it provides synthetic inertia and damping equivalent to VSG control (with a low, stable initial RoCoF) but with a significantly faster frequency recovery time.
In summary, this improved control strategy significantly enhances the applicability and dynamic performance of on-grid inverters in modern power systems with multiple operational scenarios, contributing to the stability and flexibility of grids with high penetrations of renewable energy.