Two-Degree-of-Freedom Proportional Integral Controllers for Stability Enhancement of Power Electronic Converters in Weak Grids: Inverter and Rectifier Operating Modes
Abstract
:1. Introduction
2. System Description
3. Small-Signal Model
3.1. State-Space Representation
3.2. Model Validation
4. System Stability
4.1. PLL Bandwidth
4.1.1. Inverter Mode
4.1.2. Rectifier Mode
4.2. Current Controllers
4.3. Weighting Factor b of Current Controllers
5. Robustness and Performance Analysis
6. Conclusions
- During inverter operation, a low PLL bandwidth improves the system stability, enabling the connection of VSCs to weaker grids. Conversely, during rectifier operation, a high PLL bandwidth enhances the system stability.
- The settling time of the inner current control loops has a minor impact on the stability during inverter operation, with faster current controls only marginally increasing the stability. Conversely, faster current control loops significantly reduce the stability margins during rectifier operation, potentially leading to system instability.
- The reference weighting factor b of the 2DOF-PI used in the current loops has a minor impact on the stability during inverter operation, with smaller values of b worsening the stability. On the contrary, lower values of b improve the system stability during rectifier operation, with b having a significant impact.
- During rectifier operation, although a lower value of the parameter b reduces the stability limits, it enhances system performance for typical PLL and current controller design parameters by increasing the damping, consequently reducing oscillations.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
2DOF-PI | Two-Degree-of-Freedom Proportional Integral |
GFL | Grid Following |
GFM | Grid Forming |
PI | Proportional Integral |
PCC | Point of common coupling |
PLL | Phase-Locked Loop |
SCR | Short circuit ratio |
VCC | Vector current control |
VSC | Voltage Source Converter |
Appendix A
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Description | Parameter | Value |
---|---|---|
Transformer leakage inductance | 112.7 mH | |
Transformer copper resistance | 1.416 | |
Filter capacitance | 0.623 F | |
Damping resistance of the filter | 104.1 | |
Filter inductance | 150.7 mH | |
Filter copper resistance | 1.890 | |
Line-to-ground grid voltage | 38.11 kV | |
Converter rated active power | P | 8 MW |
Grid angular frequency | rad/s |
Description | Parameter | Value |
---|---|---|
Grid SCR | 4 | |
Grid ratio | 10 | |
Proportional gain of the current PI controllers | 57 V/A | |
Integral gain of the current PI controllers | 7100 V/As | |
Reference weighting factor for the current PI controllers | b | |
Proportional gain of the PLL PI controller | 125 rad/s | |
Integral gain of the PLL PI controller | 4000 rad/s2 |
Variable | (A) | (A) | (A) | (A) | (kV) | (rad) |
Value | 47.467 | −15.457 | 47.299 | −24.066 | 42.117 | 0.204 |
Settling Time (ms) | b | ||
---|---|---|---|
5 | 239.2 | 1.12 × | 0.75 |
10 | 118.7 | 2.78 × | 0.75 |
15 | 78.5 | 1.24 × | 0.75 |
20 | 58.4 | 6.97 × | 0.75 |
20 | 46.3 | 4.46 × | 0.75 |
30 | 38.3 | 3.10 × | 0.75 |
Controller | (Hz) | (Hz) | b |
---|---|---|---|
C1 | 10 | 25.5 | 0.25 |
C2 | 40 | 25.5 | 0.25 |
C3 | 10 | 25.5 | 1 |
C4 | 40 | 25.5 | 1 |
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Vidal-Albalate, R.; Tejedor Bomboi, J.J.; Díaz-Sanahuja, C.; Peñarrocha-Alós, I. Two-Degree-of-Freedom Proportional Integral Controllers for Stability Enhancement of Power Electronic Converters in Weak Grids: Inverter and Rectifier Operating Modes. Electronics 2025, 14, 1565. https://doi.org/10.3390/electronics14081565
Vidal-Albalate R, Tejedor Bomboi JJ, Díaz-Sanahuja C, Peñarrocha-Alós I. Two-Degree-of-Freedom Proportional Integral Controllers for Stability Enhancement of Power Electronic Converters in Weak Grids: Inverter and Rectifier Operating Modes. Electronics. 2025; 14(8):1565. https://doi.org/10.3390/electronics14081565
Chicago/Turabian StyleVidal-Albalate, Ricardo, José Jesús Tejedor Bomboi, Carlos Díaz-Sanahuja, and Ignacio Peñarrocha-Alós. 2025. "Two-Degree-of-Freedom Proportional Integral Controllers for Stability Enhancement of Power Electronic Converters in Weak Grids: Inverter and Rectifier Operating Modes" Electronics 14, no. 8: 1565. https://doi.org/10.3390/electronics14081565
APA StyleVidal-Albalate, R., Tejedor Bomboi, J. J., Díaz-Sanahuja, C., & Peñarrocha-Alós, I. (2025). Two-Degree-of-Freedom Proportional Integral Controllers for Stability Enhancement of Power Electronic Converters in Weak Grids: Inverter and Rectifier Operating Modes. Electronics, 14(8), 1565. https://doi.org/10.3390/electronics14081565