The modern power system is undergoing a profound transformation characterized by the large-scale integration of renewable energy sources (RES) such as wind and photovoltaics. This transition, while essential for decarbonization, introduces significant technical challenges to system stability. A primary concern is the declining system inertia and the associated deterioration of frequency stability. Conventional grid-connected inverters, which serve as the interface for these RES to the grid, predominantly utilize grid-following (GFL) control strategies. These GFL inverters act as controlled current sources, synchronizing to the grid voltage via a phase-locked loop (PLL) and injecting prescribed active and reactive power. Crucially, they lack intrinsic mechanisms to actively support grid frequency during disturbances. As their penetration increases, displacing traditional synchronous generators (SGs), the power system’s innate ability to resist frequency deviations diminishes, elevating the risk of frequency collapse during contingencies.
To mitigate this critical issue, extensive research has been directed towards enhancing the frequency support capabilities of inverter-based resources (IBRs). Solutions range from modified GFL controls with frequency feedback to the more fundamental paradigm shift towards grid-forming (GFM) control strategies. This article provides a comprehensive analysis of frequency support mechanisms in power systems and examines the evolution of inverter control from a frequency stability perspective. Following this analysis, an improved GFM control strategy is proposed, designed to deliver superior transient frequency support without relying on the emulation of synchronous machine dynamics, thereby achieving a more effective and rapid active power response.
Fundamentals of Power System Frequency Stability and GFL Inverter Response
Traditional Frequency Dynamics
The frequency stability of a traditional power system, dominated by SGs, relies on a well-defined sequence of responses following a power imbalance (e.g., a sudden loss of generation or a large load increase). The dynamic process can be segmented into distinct stages:
- Instantaneous Power Redistribution: Immediately after a disturbance, the power imbalance is initially compensated by the inherent synchronizing torque between generators, causing a nearly instantaneous change in their power angles according to their synchronizing power coefficients. This is governed by the power-angle relationship:
$$P_e = \frac{V_s V_r}{X} \sin \delta$$
where \(P_e\) is the electrical power, \(V_s\) and \(V_r\) are voltages, \(X\) is the reactance, and \(\delta\) is the power angle. - Inertial Response: This is the most critical stage for limiting the initial Rate of Change of Frequency (RoCoF) and the frequency nadir. The kinetic energy stored in the rotating masses of SGs is released or absorbed. The governing equation is the swing equation:
$$J \frac{d \Delta \omega}{dt} = P_m – P_e – D \Delta \omega$$
where \(J\) is the moment of inertia, \(\Delta \omega\) is the speed deviation, \(P_m\) is the mechanical power, and \(D\) is the damping coefficient. The term \(J \frac{d \Delta \omega}{dt}\) represents the inertial power response, which acts within hundreds of milliseconds. - Primary and Secondary Frequency Regulation: Subsequently, governor action (primary frequency control) adjusts the mechanical power input over seconds to arrest the frequency deviation. Finally, automatic generation control (secondary frequency control) acts over minutes to restore frequency to its nominal value and re-dispatch generation economically.
The essence of effective frequency containment lies in the speed of the active power response. The inertial response, being the fastest, plays a pivotal role in determining the maximum frequency deviation before slower primary control acts.
Frequency Disturbance Characteristics of GFL Inverters
A standard GFL inverter control structure is depicted in the block diagram below. Its core feature is the PLL, which extracts the grid voltage phase angle \(\theta_{PLL}\) for Park transformations, enabling decoupled control of active (\(P\)) and reactive (\(Q\)) current components.
During a grid frequency disturbance, the PLL continuously tracks the changing grid phase. Consequently, the phase angle of the inverter’s output voltage vector remains locked to the grid voltage vector. The power angle between the inverter’s internal voltage and the grid voltage, therefore, remains largely constant. As per the power-angle equation, this results in no inherent change in the active power flow from the inverter in response to the frequency change. The GFL inverter continues to inject its pre-disturbance power setpoint.
This behavior is detrimental to system frequency stability. When a portion of SGs is replaced by GFL-controlled RES, the system not only loses their inertial and primary frequency response but also finds that these new resources do not participate in the instantaneous redistribution of the disturbance power. The entire power imbalance must be compensated by the remaining SGs, increasing their stress and worsening the overall frequency response characteristic (higher RoCoF and deeper frequency nadir).
GFL Inverters with Frequency Feedback Support
A common enhancement to basic GFL control is the incorporation of frequency support loops. The grid frequency \(f\) is measured, and its deviation from nominal \(\Delta f\) and its derivative \(df/dt\) (RoCoF) are used to modify the active power reference \(P^*\).
$$P^*_{new} = P^*_{set} + \Delta P_f + \Delta P_{rocof}$$
$$\Delta P_f = -k_f \cdot (f – f_N)$$
$$\Delta P_{rocof} = -k_J \cdot \frac{d f}{d t}$$
where \(k_f\) is the droop (primary frequency response) coefficient and \(k_J\) is the virtual inertia coefficient.
While this approach provides some level of support, it has inherent limitations. The RoCoF signal is typically noisy and requires heavy low-pass filtering, which introduces a significant time delay (often 200-300 ms). This delay severely compromises the speed of the “virtual inertial” response, making it far less effective than the natural inertial response of SGs in arresting the initial frequency drop.
Grid-Forming Inverter Strategies for Frequency Support
Grid-forming control represents a fundamental shift in philosophy. A GFM inverter controls its output voltage magnitude and frequency, behaving as a voltage source behind an impedance. It does not rely on a PLL for synchronization; instead, it establishes the grid voltage waveform itself or synchronizes stably with other sources. This intrinsic characteristic allows it to actively participate in frequency stabilization.
Droop-Based GFM Control
The foundational GFM strategy is the power-frequency (\(P-f\)) droop control. The inverter’s output frequency is set according to:
$$\omega = \omega_0 – k_p (P_{ref} – P_e)$$
where \(\omega_0\) is the nominal frequency, \(k_p\) is the droop coefficient, \(P_{ref}\) is the power setpoint, and \(P_e\) is the measured output power. The angle \(\theta\) for the voltage synthesis is obtained by integrating the frequency: \(\theta = \int \omega \, dt\).
During a grid frequency disturbance, the integrator state (angle) cannot change instantaneously. If the grid frequency drops, a transient phase difference appears between the GFM inverter’s voltage and the grid voltage. This difference increases the power angle \(\delta\), causing the inverter to inject more active power according to the power-angle relationship, thereby opposing the frequency drop. This provides a form of frequency-deviation-based support, analogous to the primary frequency response of SGs. However, classic droop control lacks an explicit mechanism to respond to the RoCoF, i.e., it lacks inherent inertia.
Virtual Synchronous Generator (VSG) Control
To explicitly emulate the inertial behavior of SGs, the Virtual Synchronous Generator (VSG) algorithm is employed. It directly implements a digital version of the swing equation:
$$P_{ref} – P_e = J \omega_0 \frac{d \Delta \omega}{dt} + D \Delta \omega$$
The output frequency \(\omega\) is derived from this equation. Similar to droop control, the angle is obtained via integration.
The VSG strategy provides both inertial response (through the \(J \frac{d \omega}{dt}\) term) and damping/primary response (through the \(D \Delta \omega\) term). When a frequency event occurs, the inertia term provides an immediate power surge proportional to RoCoF, while the droop term provides sustained power support proportional to the frequency deviation. The inertial response arises because the algorithm’s internal frequency and angle states have inertia and cannot jump, creating a beneficial transient power angle shift.
However, a key design challenge in VSG control is the trade-off between frequency support strength and power reference tracking speed. A large virtual inertia \(J\) enhances frequency support but slows down the response to changes in the power setpoint \(P_{ref}\). Furthermore, for renewable sources without integrated energy storage, the sustained primary frequency response (from the \(D \Delta \omega\) term) may not be sustainable as it requires a reserve of active power.
An Improved Grid-Forming Control Strategy for Enhanced Frequency Support
The core objective during a frequency disturbance is not inertia per se, but a fast and appropriate active power response to counteract the imbalance. Emulating synchronous machine dynamics is one means to this end, but not necessarily the only or most optimal one for power electronic interfaces. Furthermore, it is desirable to decouple the fast transient support function from the sustained primary frequency response, especially for resource-constrained renewable systems.
Based on this rationale, an improved GFM control strategy is proposed. Its block diagram and operational principles are centered on three key functional parts, designed to achieve rapid power tracking and superior transient frequency support.
Control Structure and Principle
1. Power Loop Regulator: A fast PI controller processes the error between the active power reference \(P_{ref}\) and the measured power \(P_e\). Its output is a frequency deviation signal \(\Delta \omega_0\), which drives the power error to zero.
$$\Delta \omega_0 = \left( K_{p} + \frac{K_{i}}{s} \right) (P_{ref} – P_e)$$
This ensures precise and rapid tracking of the active power setpoint.
2. Steady-State Frequency Support: The signal \(\Delta \omega_0\) is scaled by a coefficient \(k_{\omega}\) to generate a power compensation signal \(\Delta P_{f}\) that is fed forward to the power reference. This loop can be configured to provide traditional droop-based primary frequency response if needed and if power reserves exist.
$$\Delta P_{f} = k_{\omega} \cdot \Delta \omega_0$$
3. Transient Frequency Accelerator: This is the novel element for enhanced dynamic support. A standard PLL (used here only for fast, accurate frequency measurement, not for synchronization) measures the instantaneous grid frequency \(\omega_{grid}\). The deviation from the nominal frequency \(\omega_0\) is calculated and multiplied by a transient acceleration gain \(k_{acc}\).
$$\Delta \omega_{acc} = k_{acc} \cdot (\omega_0 – \omega_{grid})$$
The total frequency command for the voltage angle generation is then:
$$\omega_{cmd} = \omega_0 + \Delta \omega_0 + \Delta \omega_{acc}$$
Finally, the voltage phase angle is obtained by integration: \(\theta = \int \omega_{cmd} \, dt\).
Mechanism of Enhanced Support
The key innovation lies in the transient accelerator term \(\Delta \omega_{acc}\). During a sudden grid frequency drop (\(\omega_{grid} < \omega_0\)), this term immediately becomes positive, adding a positive frequency component to \(\omega_{cmd}\). Upon integration, this causes the inverter’s internal voltage angle \(\theta\) to actively advance relative to the case where this term is absent.
In contrast, conventional GFM strategies (droop or VSG) rely solely on the fact that their internal angle lags behind the changing grid angle because it cannot jump. The proposed strategy goes further: it not only maintains its angle (due to the integrator) but also proactively shifts it in the direction that increases the power angle \(\delta\). This results in a larger transient power surge from the grid-connected inverter, providing stronger opposition to the frequency change. The effect is analogous to, and can be tuned to exceed, the inertial response of a VSG, but with a more direct and faster actuation path. Crucially, this transient support is inherently temporary; as the grid frequency stabilizes, the \(\Delta \omega_{acc}\) term vanishes, allowing the power loop to seamlessly return to tracking its setpoint.
| Control Strategy | Core Synchronization | Primary Frequency Response | Inertial (RoCoF) Response | Response Speed | Power Tracking | Key Limitation |
|---|---|---|---|---|---|---|
| Basic GFL | PLL (Grid-Following) | No | No | N/A | Excellent | Worsens system frequency stability |
| GFL with Freq. Feedback | PLL (Grid-Following) | Yes (via \(k_f\)) | Delayed/Filtered (via \(k_J\)) | Slow (200-300 ms delay) | Good | Slow transient response due to filtering |
| Droop-Based GFM | Angle Integration (Grid-Forming) | Yes (inherent via \(k_p\)) | No | Fast (ms) | Good | Lacks inherent inertia |
| VSG GFM | Virtual Swing Eq. (Grid-Forming) | Yes (via \(D\)) | Yes (via \(J\)) | Fast (ms) | Limited by inertia \(J\) | Trade-off between support & tracking |
| Proposed Improved GFM | Angle Integration (Grid-Forming) | Configurable (via \(k_{\omega}\)) | Enhanced Transient (via \(k_{acc}\)) | Very Fast (ms) | Excellent (fast PI power loop) | Requires PLL for measurement |
Simulation Verification and Performance Analysis
To validate the theoretical analysis and demonstrate the efficacy of the proposed control strategy, a simulation model of a 100 kW grid-connected inverter was established using the parameters listed below.
| Parameter | Value |
|---|---|
| Rated Power | 100 kW |
| Grid Voltage (L-L, RMS) | 800 V |
| DC-Link Voltage | 1200 V |
| Nominal Frequency | 50 Hz |
| Filter Inductance | 135 μH |
| Switching Frequency | 5 kHz |
The control strategies were subjected to severe grid frequency step disturbances: a -1 Hz step at t=2s and a +1 Hz step at t=3s. The active power response was monitored for comparison.
Comparison 1: GFL vs. Enhanced GFL. The simulation confirmed the basic GFL inverter’s power output remained constant during the frequency steps, offering no support. The enhanced GFL with frequency feedback did provide a power response, but with a noticeable delay of approximately 250 ms before reaching its target support level, highlighting the limitation of its filtered RoCoF path.
Comparison 2: Enhanced GFL vs. Droop-GFM. The droop-based grid-forming inverter demonstrated a significantly faster active power response, reacting within milliseconds to the frequency step. This validates the fundamental advantage of the GFM paradigm in providing rapid frequency-deviation-based support.
Comparison 3: Droop-GFM vs. VSG. As expected, the VSG control provided a larger initial power surge compared to the basic droop controller, thanks to its virtual inertia term. This demonstrates the benefit of RoCoF-based response in reducing the initial RoCoF and improving the frequency nadir.
Comparison 4: VSG vs. Proposed Improved GFM. The proposed strategy was tuned to provide a comparable steady-state droop effect. Critically, its transient response to the frequency step was both faster and larger in magnitude than that of the VSG. The transient accelerator term \(k_{acc}\) acted immediately upon detecting the frequency deviation, commanding a larger phase shift and thus a greater power injection. This result confirms the strategy’s ability to deliver superior transient frequency support. Furthermore, the power loop’s response to a change in \(P_{ref}\) was tested and found to be faster than the VSG (even with a low virtual inertia), demonstrating the decoupling of fast tracking from strong support.
Verification without Sustained Droop. A final simulation was run with the steady-state frequency support coefficient \(k_{\omega}\) set to zero. The results showed that the improved grid-connected inverter still provided a substantial transient power pulse during the frequency event (due to \(k_{acc}\)), which then decayed as the frequency stabilized, allowing the inverter to return exactly to its original power setpoint. This mode is particularly suitable for RES without active power reserves, allowing them to provide critical transient support without engaging in sustained primary frequency response.
Conclusion
The transition to a power system with high penetration of inverter-based resources necessitates a fundamental evolution in control strategies to maintain frequency stability. Traditional grid-following inverters are inherently passive from the grid’s perspective and can exacerbate frequency instability. While modified GFL controls with frequency feedback offer a partial solution, their transient response is often too slow due to necessary filtering.
Grid-forming control strategies present a more robust solution by establishing voltage source behavior. Classical approaches like droop control and Virtual Synchronous Generator emulation provide frequency support, but they involve trade-offs between support strength, response speed, and power tracking performance. The analysis underscores that the ultimate goal is a rapid and decisive active power response from the grid-connected inverter during disturbances.
The improved grid-forming control strategy proposed in this work addresses these trade-offs directly. By employing a fast power control loop augmented with a transient frequency accelerator, it achieves several key advantages: 1) Excellent command tracking performance, 2) Configurable steady-state frequency support, and 3) Superior transient frequency support that can exceed the performance of virtual inertia-based methods. The strategy operates on the principle of proactively adjusting the inverter’s voltage phase to create a beneficial power angle shift, rather than solely relying on the emulation of physical machine dynamics.
Simulation studies validate the analysis, showing that the proposed control enables the grid-connected inverter to respond with more active power in a shorter time during frequency events, leading to better frequency containment. Future work will focus on the practical implementation challenges, including parameter tuning considering the limited energy buffer in renewable energy DC links, stability analysis under weak grid conditions, and the coordination of multiple such inverters in a complex power system. The development and deployment of advanced grid-forming strategies are essential for ensuring the reliable and stable operation of the future decarbonized power grid.