# The Impact of Phase-Locked Loop (PLL) Architecture on Sub-Synchronous Control Interactions (SSCI) for Direct-Driven Permanent Magnet Synchronous Generator (PMSG)-Based Type 4 Wind Farms

^{*}

## Abstract

**:**

_{2}) emissions, but this reduction depends on the fraction of renewable sources used to generate electricity. Wind energy is thus a vital candidate and has experienced a remarkable surge recently, establishing itself as a leading renewable power source worldwide. The research on Direct-Driven Permanent Magnet Synchronous Generator (PMSG)-based type 4 wind farms has indicated that the Phase-locked Loop (PLL) bandwidth significantly impacts Sub-Synchronous Resonance (SSR). However, the influence of PLL architecture on SSR remains unexplored and warrants investigation. Therefore, this paper investigates PLL architectural variations in PLL Loop Filter (LF) to understand their impact on SSR in type 4 wind farms. Specifically, an in-depth analysis of the Notch Filter (NF)-based enhanced PLL is conducted using eigenvalue analysis of the admittance model of a PMSG-based type 4 wind farm. The findings demonstrate that the NF-based enhanced PLL exhibits superior performance and improved passivity in the sub-synchronous frequency range, limiting the risk of SSR below 20 Hz. Additionally, Nyquist plots are employed to assess the impact on system stability resulting in increased stability margins. In the future, it is recommended to further investigate and optimize the PLL to mitigate SSR in wind farms.

## 1. Introduction

_{2}) emissions have resulted in a focus on road transportation, which accounts for nearly 17% of global emissions [1,2]. Electric vehicles (EVs) are a promising solution, but their net zero emissions depend on the energy mix used to generate electricity [1]. Using renewable energy sources for powering the batteries of EVs can significantly reduce net CO

_{2}emissions [1]. It is necessary to increase the proportion of renewable electricity used to power EVs as the propulsion systems improve [1,2].

- Phase Detector (PD);
- Loop Filter (LF);
- Voltage Controlled Oscillator (VCO).

## 2. System Modelling and Description

#### 2.1. Inner Current Controller

#### 2.2. Outer Controllers

#### 2.2.1. DC Voltage Controller

#### 2.2.2. Reactive Power Controller

#### 2.3. Small Signal Modelling

#### 2.4. Phase-Locked Loop

## 3. System Passivity Analysis

#### 3.1. Analyzing the Behavior of Eigenvalue ${\lambda}_{1}$ for Different Bandwidth Variations

#### 3.2. Analyzing the Behavior of Eigenvalue ${\lambda}_{2}$ for Different Bandwidth Variations

## 4. PLL Enhancement by Sub-/Super-Synchronous Damping Controller

#### Impact of SSRDC Based PLL Parametric Variations on the System Eigenvalues

## 5. PLL with Enhanced Filtering

#### 5.1. Impact of NF Bandwidth ${\omega}_{NF}$

#### 5.2. Impact of NF Damping Coefficient $\xi $

#### 5.3. Impact of NF on PLL Bandwidth

## 6. Equivalent System for Admittance-Based Analysis

## 7. Nyquist Stability Analysis to Explore the Risk of SSCI

#### 7.1. Impact of A Typical PLL on Stability

#### 7.2. Impact of An SSRDC-Based PLL

#### 7.3. Impact of PLL with Notch Filter on Stability

## 8. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature and Abbreviations

EV | Electric vehicles | PLL | Phase-locked Loop |

PMSG | Permanent Motor Synchronous Generator | SSR | Sub-Synchronous Resonance |

LF | Loop Filter | NF | Notch Filter |

VSWT | Variable Speed Wind Turbine | SSCI | Sub-Synchronous Control Interactions |

PCC | Point of Common Coupling | SSRDC | Sub-Synchronous Resonance Damping Controller |

SRF | Synchronous Reference Frame | SSC | Stator Side Converter |

GSC | Grid Side Converter | PWM | Pulse Width Modulation |

${L}_{f}$ | GSC filter internal inductance | ${C}_{dc}$ | DC-link Capacitance |

${R}_{f}$ | GSC filter internal resistance | ${\alpha}_{dc}$ | Bandwidth of DC voltage controller |

${\omega}_{1}$ | Grid frequency | ${\alpha}_{Q}$ | Bandwidth of reactive power controller |

${\alpha}_{cc}$ | Bandwidth of current controller | ${\alpha}_{PLL}$ | Bandwidth of PLL |

${T}_{dM}$ | Discretization computation delay | ${\underset{\_}{v}}_{gsc}$ | GSC output voltage vector |

${\underset{\_}{v}}_{pcc}$ | Grid voltage vector measured at the PCC | ${\underset{\_}{i}}_{f}$ | GSC filter current vector |

${\underset{\_}{v}}_{gsc}^{*}$ | GSC reference voltage vector | ${\theta}_{g}$ | Grid voltage angle |

${H}_{dM}$ | Modulator transfer function | ${F}_{cc}$ | Current controller PI regulator |

${H}_{ff}$ | Low-pass feed-forward filter of grid voltage in current controller | ${K}_{pc}$, ${K}_{ic}$ | Current controller proportional and integral gains |

${P}_{w}$ | Power from SSC | ${P}_{conv}$ | Power output of GSC |

${Q}_{g}$ | Reactive power injected into the grid | ${F}_{Q}$ | Reactive power PI regulator |

${H}_{f\_Q}$ | Transfer function of low-pass filter for grid voltage in reactive power controller | ${K}_{iQ}$ | Reactive power controller integral gain |

${F}_{dc}$ | DC voltage PI regulator | ${H}_{f\_dc}$ | Transfer function of low-pass filter for grid voltage in DC voltage controller |

${K}_{p\_dc}$ | DC voltage regulator proportional gain | ${F}_{PLL}$ | Open-loop transfer function of PLL |

${K}_{p\_PLL}$, ${K}_{I\_PLL}$ | PLL proportional and integral gains | ${Y}_{W\_true}$ | Input Admittance Matrix |

${\mathsf{\lambda}}_{1}$, ${\mathsf{\lambda}}_{2}$ | Eigenvalues of ${Y}_{W\_true}$ | ${\underset{\_}{i}}_{f}^{dq*}$ | GSC reference current |

## References

- Ghotge, R.; Yitzhak, S.; Samira, F.; Zofia, L.; Ad van, W. Optimized Scheduling of EV Charging in Solar Parking Lots for Local Peak Reduction under EV Demand Uncertainty. Energies
**2020**, 13, 1275. [Google Scholar] [CrossRef] [Green Version] - Rastgoo, S.; Zahra, M.; Morteza Azimi, N.; Mohammad, Z.; Sanjeevikumar, P. Using an Intelligent Control Method for Electric Vehicle Charging in Microgrids. World Electr. Veh. J.
**2022**, 13, 222. [Google Scholar] [CrossRef] - El Mourabit, Y.; Derouich, A.; Allouhi, A.; El Ghzizal, A.; El Ouanjli, N.; Zamzoumyes, O. Sustainable production of wind energy in the main Morocco’s sites using permanent magnet synchronous generators. Int. Trans. Electr. Energy Syst.
**2020**, 30, e12390. [Google Scholar] [CrossRef] - El Mourabit, Y.; Derouich, A.; El Ghzizal, A.; El Ouanjli, N.; Zamzoum, O. Nonlinear backstepping control for PMSG wind turbine used on the real wind profile of the Dakhla-Morocco city. Int. Trans. Electr. Energy Syst.
**2020**, 30, e12297. [Google Scholar] [CrossRef] - Global Wind Energy Council. Global Wind Report. 2023. Available online: https://gwec.net/globalwindreport2023/ (accessed on 19 June 2023).
- REN21. Renewables Global Status Report. Available online: https://www.ren21.net/reports/global-status-report/ (accessed on 19 June 2023).
- Ackermann, T. Wind Power in Power Systems, 2nd ed.; John Wiley & Sons: Chichester, UK, 2012. [Google Scholar]
- Ghasemi, H.; Gharehpetian, G.B.; Nabavi-Niaki, S.A.; Aghaei, J. Overview of subsynchronous resonance analysis and control in wind turbines. Renew. Sustain. Energy Rev.
**2013**, 27, 234–243. [Google Scholar] [CrossRef] - Ahmed, S.D.; Al-Ismail, F.S.; Shafiullah, M.; Al-Sulaiman, F.A.; El-Amin, I.M. Grid integration challenges of wind energy: A review. IEEE Access
**2020**, 8, 10857–10878. [Google Scholar] [CrossRef] - Ali, S.W.; Sadiq, M.; Terriche, Y.; Naqvi, S.A.R.; Mutarraf, M.U.; Hassan, M.A.; Yang, G.; Su, C.-L.; Guerrero, J.M. Offshore wind farm-grid integration: A review on infrastructure, challenges, and grid solutions. IEEE Access
**2021**, 9, 102811–102827. [Google Scholar] [CrossRef] - Damas, R.N.; Son, Y.; Yoon, M.; Kim, S.Y.; Choi, S. Subsynchronous oscillation and advanced analysis: A review. IEEE Access
**2020**, 8, 224020–224032. [Google Scholar] [CrossRef] - IEEE Subsynchronous Resonance Working Group. Terms, definitions and symbols for subsynchronous oscillations. IEEE Trans. Power Appar. Syst.
**1985**, 104, 1326–1334. [Google Scholar] - Gu, K.; Feng, W.; Xiao-Ping, Z. Sub-synchronous interactions in power systems with wind turbines: A review. IET Renew. Power Gener.
**2019**, 13, 4–15. [Google Scholar] [CrossRef] - Adam, J.; Pappu, V.A.; Dixit, A. ERCOT experience screening for Sub-Synchronous Control Interaction in the vicinity of series capacitor banks. In Proceedings of the Power and Energy Society General Meeting, San Diego, CA, USA, 22–26 July 2012. [Google Scholar]
- Sebia, M.; Bentarzi, H. Sub-Synchronous Torsional Interaction Study and Mitigation Using a Synchro-Phasors Measurement Unit. Eng. Proc.
**2022**, 14, 8. [Google Scholar] - Shair, J.; Xie, X.; Yan, G. Mitigating subsynchronous control interaction in wind power systems: Existing techniques and open challenges. Renew. Sustain. Energy Rev.
**2019**, 108, 330–346. [Google Scholar] [CrossRef] - Adams, J.; Carter, C.; Huang, S.-H. ERCOT experience with sub-synchronous control interaction and proposed remediation. In Proceedings of the Transmission and Distribution Conference and Exposition (T&D), Orlando, FL, USA, 7–10 May 2012. [Google Scholar]
- Sahni, M.; Badrzadeh, B.; Muthumuni, D.; Cheng, Y.; Yin, H.; Huang, S.-H.; Zhou, Y. Sub-synchronous interaction in wind power plants-part II: An ERCOT case study. In Proceedings of the Power and Energy Society General Meeting, San Diego, CA, USA, 22–26 July 2012. [Google Scholar]
- Nath, R.; Grande-Moran, C. Study of Sub-Synchronous Control Interaction due to the Interconnection of Wind Farms to a Series Compensated Transmission System. In Proceedings of the Transmission and Distribution Conference and Exposition, Orlando, FL, USA, 7–10 May 2012. [Google Scholar]
- Liu, H.; Xie, X.; He, J.; Xu, T.; Yu, Z.; Wang, C.; Zhang, C. Subsynchronous Interaction Between Direct-Drive PMSG Based Wind Farms and Weak AC Networks. IEEE Trans. Power Syst.
**2017**, 32, 4708–4720. [Google Scholar] [CrossRef] - Yunhong, L.; Hui, L.; Wenyuan, N.; Xiaorong, X. Impact on SSR of wind farms connected to series-compensated lines from the different structures of power grid. J. Eng.
**2017**, 2017, 2158–2163. [Google Scholar] [CrossRef] - Beza, M.; Bongiorno, M. On the Risk for Subsynchronous Control Interaction in Type 4 Based Wind Farms. IEEE Trans. Sustain. Energy
**2019**, 10, 1410–1418. [Google Scholar] [CrossRef] - Xu, Y.; Zhang, M.; Fan, L.; Miao, Z. Small-Signal Stability Analysis of Type-4 Wind in Series-Compensated Networks. IEEE Trans. Energy Convers.
**2020**, 35, 529–538. [Google Scholar] [CrossRef] - Yang, S.; Shen, R.; Shu, J.; Zhang, T.; Li, Y.; Zhang, B.; Hao, Z. PLL Based Sub-/Super-Synchronous Resonance Damping Controller for D-PMSG Wind Farm Integrated Power Systems. IEEE Trans. Energy Convers.
**2022**, 37, 2370–2384. [Google Scholar] [CrossRef] - Yan, G.; Wang, D.; Jia, Q.; Hu, W. Equivalent Modeling of Dfig-Based Wind Farms for Sub-Synchronous Resonance Analysis. Energies
**2020**, 13, 5426. [Google Scholar] [CrossRef] - Perera, U.; Oo, A.M.T.; Zamora, R. Sub Synchronous Oscillations under High Penetration of Renewables—A Review of Existing Monitoring and Damping Methods, Challenges, and Research Prospects. Energies
**2022**, 15, 8477. [Google Scholar] [CrossRef] - Xie, X.; Zhang, X.; Liu, H.; Liu, H.; Li, Y.; Zhang, C. Characteristic analysis of subsynchronous resonance in practical wind farms connected to series-compensated transmissions. IEEE Trans. Energy Convers.
**2017**, 32, 1117–1126. [Google Scholar] [CrossRef] - Golestan, S.; Guerrero, J.M.; Vasquez, J.C. Three-phase PLLs: A review of recent advances. IEEE Trans. Power Electron.
**2016**, 32, 1894–1907. [Google Scholar] [CrossRef] [Green Version] - Pan, H.; Li, Z.; Wei, T. A novel phase-locked loop with improved-dual adaptive notch filter and multi-variable filter. IEEE Access
**2019**, 7, 176578–176586. [Google Scholar] [CrossRef] - Sun, X.; Hu, C.; Lei, G.; Yang, Z.; Guo, Y.; Zhu, J. Speed sensorless control of SPMSM drives for EVs with a binary search algorithm-based phase-locked loop. IEEE Trans. Veh. Technol.
**2020**, 69, 4968–4978. [Google Scholar] [CrossRef] - Eial Awwad, A. Dynamic Performance Enhancement of a Direct-Driven PMSG-Based Wind Turbine Using a 12-Sectors DTC. World Electr. Veh. J.
**2022**, 13, 123. [Google Scholar] [CrossRef] - Harnefors, L.; Bongiorno, M.; Lundberg, S. Input-admittance calculation and shaping for controlled voltage-source converters. IEEE Trans. Ind. Electron.
**2007**, 54, 3323–3334. [Google Scholar] [CrossRef]

**Figure 3.**A Typical PLL for grid angle tracking [23].

**Figure 4.**Trend of eigenvalue ${\lambda}_{1}$ for different variations of inner controller, outer controllers and PLL bandwidths.

**Figure 5.**Trend of eigenvalue ${\lambda}_{2}$ for different variations of inner controller, outer controllers and PLL bandwidths.

**Figure 6.**A PLL with Sub—Synchronous Damping Controller (SSRDC) [24].

**Figure 7.**Trend of eigenvalue ${\lambda}_{2}$ for different parametric variations of SSRDC—based PLL.

**Figure 9.**Trend of eigenvalue ${\lambda}_{2}$ for different parametric variations of a NF—based PLL.

**Figure 10.**Trend of eigenvalue ${\lambda}_{2}$ for different parametric variations of NF—based PLL—with y axis limited to [−4, 2].

**Figure 15.**Comparison of PLL variants at the pivot value of the PLL Bandwidth ${\alpha}_{PLL}=0.2\mathrm{p}.\mathrm{u}.$

Parameter | Value | Parameter | Value |
---|---|---|---|

${L}_{f}$ | 0.15 p.u. | ${C}_{dc}$ | 1 p.u. |

${R}_{f}$ | 0.015 p.u. | ${\alpha}_{dc}$ | 0.2 p.u. |

${\omega}_{1}$ | 1 p.u. | ${\alpha}_{Q}$ | 0.2 p.u. |

${\alpha}_{cc}$ | 4 p.u. | ${\alpha}_{PLL}$ | 0.2 p.u. |

${T}_{dM}$ | 3 ms (This is equivalent to 1.5 samples at a 5 kHz sampling rate.) |

Loop | Controller | Bandwidth | Case 1 | Case 2 (Pivot Values) | Case 3 |
---|---|---|---|---|---|

Inner | Current Controller | ${\alpha}_{cc}$ | 2 p.u. | 4 p.u. | 6 p.u. |

Outer | DC Voltage Controller | ${\alpha}_{dc}$ | 0.1 p.u. | 0.2 p.u. | 0.4 p.u. |

Reactive Power Controller | ${\alpha}_{Q}$ | 0.1 p.u. | 0.2 p.u. | 0.4 p.u. | |

PLL | PLL | ${\alpha}_{PLL}$ | 0.1 p.u. | 0.2 p.u. | 0.4 p.u. |

Parameter | Value | Parameter | Value |
---|---|---|---|

${K}_{SSO}$ | 0.042 | $\xi $ | 0.3 |

${H}_{0}$ | 1 | ${\omega}_{SSO}$ | 1.5 p.u. |

Parameter | Value |
---|---|

${R}_{g}$ | 0.02 p.u. |

${L}_{g}$ | 0.25 p.u. |

${C}_{g}$ | 0.075 p.u. |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ashraf, A.; Saadi, M.
The Impact of Phase-Locked Loop (PLL) Architecture on Sub-Synchronous Control Interactions (SSCI) for Direct-Driven Permanent Magnet Synchronous Generator (PMSG)-Based Type 4 Wind Farms. *World Electr. Veh. J.* **2023**, *14*, 206.
https://doi.org/10.3390/wevj14080206

**AMA Style**

Ashraf A, Saadi M.
The Impact of Phase-Locked Loop (PLL) Architecture on Sub-Synchronous Control Interactions (SSCI) for Direct-Driven Permanent Magnet Synchronous Generator (PMSG)-Based Type 4 Wind Farms. *World Electric Vehicle Journal*. 2023; 14(8):206.
https://doi.org/10.3390/wevj14080206

**Chicago/Turabian Style**

Ashraf, Arslan, and Muhammad Saadi.
2023. "The Impact of Phase-Locked Loop (PLL) Architecture on Sub-Synchronous Control Interactions (SSCI) for Direct-Driven Permanent Magnet Synchronous Generator (PMSG)-Based Type 4 Wind Farms" *World Electric Vehicle Journal* 14, no. 8: 206.
https://doi.org/10.3390/wevj14080206