Virtual Flux Control Methods for Grid-Forming Converters: A Four-Method Comparison
Abstract
:1. Introduction
GFM Approach | Class | Definition | Advantages/Disadvantages |
---|---|---|---|
Methodology | Droop control [14,15,16,17,18] | Mimics the behavior of a SG governor | ✓ Simple implementation
✗ Does not provide inertial response |
Synchronous machine-based controllers [19,20,21,22,23,24] | Mimics the behavior of a SG | ✓ Emulates inertial response and provides damping capabilities
✗ Output power can be more oscillating | |
Nonlinear control algorithms [25,26,27,28,29] | Emulates the dynamics of a weakly nonlinear oscillator using a single dead-zone oscillator | ✓ No need to determine any control angle
✓ Allows the synchronization of several converters running in parallel ✗ Does not provide inertial emulation or fault-ride through capability | |
Voltage Vector Control | Field-Oriented Control [30,31,32,33] | Decouples control of both the converter’s voltage and frequency using two PI controllers | ✓ Good dynamics and waveforms
✓ Fixed switching frequency (PWM) |
Flatness theory [34,35,36] | Ensures full control over all system variables by imposing a desired trajectory on flat outputs | ✓ Easy implementation
✓ Fixed switching frequency (PWM) | |
Direct control [38,39,40] | Regulates a key variable of the converter without relying on conventional internal control loops | ✓ Fast dynamic response and high robustness
✗ Variable switching frequency | |
Model predictive control [41,42,43,44,45] | Uses a mathematical model to predict the converter’s future behavior and determine the optimal control action | ✓ Fast transient performance, inclusion of nonlinearities and constraints
✗ Variable switching frequency (can be addresed through the cost function) | |
Current Limitation | Switch to GFL control [49,50] | Uses a backup PLL | ✗ May cause instabilities |
Saturate regulators [51,52,53] | Saturates the reference currents of the internal current control | ✗ Can adversely affect the control angle, potentially compromising the converter’s stability | |
Virtual impedances [54,55,56] | Increase the converter’s output impedance | ✓ Balances current limitation and stability
✗ Requires complex design | |
Virtual-flux-based control [57,58] | Does not use current control loops | ✓ Easy design and implementation, limiting current in a robust way |
2. System Description and Virtual Flux Measurement
3. Control Schemes
3.1. Virtual Flux-Oriented Control
3.2. Flatness-Based Control
3.3. Direct Control
3.4. Model Predictive Control
4. HIL Results and Comparison
- Reactive Power Capability: GFM units must be capable of both generating and absorbing reactive power.
- Voltage Regulation: GFM converters are expected to maintain control over their internal voltage vector, both in magnitude and angle, regardless of grid or load conditions.
- Active Power Control: These converters must emulate the behavior of synchronous machines, supplying active power in response to control setpoints.
- Frequency Support: GFM units should respond to frequency deviations by adjusting their active power output, thereby contributing to system frequency stability.
- Damping of Oscillations: PSS or equivalent mechanisms are encouraged to mitigate low-frequency oscillations. In this case, prior validation has been conducted by the authors using Hardware-in-the-Loop simulations [62].
- Fault Ride Through and Dynamic Current Injection: GFM converters must remain connected during grid faults and must be able to inject reactive current rapidly to support voltage recovery.
- ROCOF Response: These units must be able to provide inertial response by injecting active power during periods of high rate of change of frequency (ROCOF), in addition to regular frequency support.
- Phase Jump Response: In events involving sudden phase angle changes between the converter and the grid, the system must manage transient power exchanges to maintain stability.
4.1. Frequency Variation
4.2. Phase Jump
4.3. Low Voltage Ride-Through
4.4. Islanded Mode Operation
4.5. Switching Frequency Comparison
5. Discusion and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
ACL | Active Current Limiter; |
APS | Active Power Synchronization; |
DC | Direct Control; |
ENTSO-E | European Network of Transmission System Operators for Electricity; |
FBC | Flatness-Based Control; |
FOC | Field-Oriented Controller; |
GFL | Grid-following; |
GFM | Grid-forming; |
HIL | Hardware-in-the-Loop; |
IBR | Inverter-Based Resources; |
IRENA | International Renewable Energy Agency; |
MPC | Model Predictive Control; |
NESO | National Energy System Operator; |
PSS | Power System Stabilizer; |
PLL | Phase-Locked Loop; |
PWM | Pulse Width Modulation; |
RES | Renewable Energy Source; |
RCL | Reactive Current Limiter; |
ROCOF | Rate of Change of Frequency; |
RPC | Reactive Power Controller; |
SG | Synchronous Generator; |
VFOC | Virtual-Flux Orientation Control; |
VSC | Voltage Source Controller; |
VOC | Virtual Oscillation-based Controller. |
Appendix A
Appendix A.1. System Parameters
Parameter | Value | Units |
DC voltage, | 1200 | V |
Converter rated power, | 2 | MVA |
Converter rated voltage (line to line), | 690 | V |
Filter resistance, | 0.7104 | mΩ |
Filter inductance, | 200 | μH |
Filter capacitance, | 200 | μF |
Nominal frequency, | 50 | Hz |
Switching frequency, | 3000 | Hz |
Appendix A.2. Control System Parameters
Parameter | Value | Units |
Damping constant, D | 50 | p.u. |
Inertia constant, H | 3.5 | s |
PSS time constant, | 1.2 | s |
PSS constant, | 0.01 | p.u. |
RCL gain, | 0.15 | p.u. |
RCL gain, | 0.15 | p.u. |
Damping factor, | 0.7 | p.u. |
Natural frequency, | 2000 | rad/s |
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Output | Sector | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||
1 | 1 | |||||||||||||
1 | 0 | |||||||||||||
1 | −1 | |||||||||||||
−1 | 1 | |||||||||||||
−1 | 0 | |||||||||||||
0 | 0 | 0 | |
1 | 0 | 0 | |
1 | 1 | 0 | |
0 | 1 | 0 | |
0 | 1 | 1 | |
0 | 0 | 1 | |
1 | 0 | 1 | |
1 | 1 | 1 |
Method | Block Diagram | Inertial Respone & ACL | Phase Jump | Sag Entry & RCL | Sag Exit | Islanded Mode | |
---|---|---|---|---|---|---|---|
Virtual Flux-Oriented Control | ✓✓ | ✗✗ | ✓ | ✗ | ✓✓ | ✓✓ | |
Flatness-Based Control | ✓✓ | ✓✓ | ✗✗ | ✓✓ | ✓✓ | ✓✓ | |
Direct Control | ✓✓ | ✗ | ✓✓ | ✗✗ | ✓✓ | ✗ | |
Model Predictive Control | ✓✓ | ✓ | ✗✗ | ✓ | ✓✓ | ✗✗ |
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Dolado Fernández, J.; Eloy-García, J.; Arnaltes Gómez, S.; Kouro, S.; Renaudineau, H.; Rodríguez Amenedo, J.L. Virtual Flux Control Methods for Grid-Forming Converters: A Four-Method Comparison. Appl. Sci. 2025, 15, 5157. https://doi.org/10.3390/app15095157
Dolado Fernández J, Eloy-García J, Arnaltes Gómez S, Kouro S, Renaudineau H, Rodríguez Amenedo JL. Virtual Flux Control Methods for Grid-Forming Converters: A Four-Method Comparison. Applied Sciences. 2025; 15(9):5157. https://doi.org/10.3390/app15095157
Chicago/Turabian StyleDolado Fernández, Juan, Joaquín Eloy-García, Santiago Arnaltes Gómez, Samir Kouro, Hugues Renaudineau, and José Luis Rodríguez Amenedo. 2025. "Virtual Flux Control Methods for Grid-Forming Converters: A Four-Method Comparison" Applied Sciences 15, no. 9: 5157. https://doi.org/10.3390/app15095157
APA StyleDolado Fernández, J., Eloy-García, J., Arnaltes Gómez, S., Kouro, S., Renaudineau, H., & Rodríguez Amenedo, J. L. (2025). Virtual Flux Control Methods for Grid-Forming Converters: A Four-Method Comparison. Applied Sciences, 15(9), 5157. https://doi.org/10.3390/app15095157