# Power System Oscillations with Different Prevalence of Grid-Following and Grid-Forming Converters

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## Abstract

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## 1. Introduction

- The different impact of grid-following and grid-forming controls on the oscillatory characteristics of the system is examined from a theoretical point of view, looking at the underlying reasons for the expected differences and recognizing the relationship between synchronisation mechanism and inertial capability as the main drive of the oscillatory behaviour of the power converter;
- The electromechanical oscillations and the inter-area modes in converter-dominated power systems are investigated considering an overall systemic point of view, with closed-loop dynamics and the representation of the equivalent swinging dynamics of the system, verifying the theoretical considerations and offering more specific insights into the phenomena with a comprehensive modal analysis;
- The theoretical considerations derived and presented in the work are then applied to the existing Colombian interconnected national grid with the expected integration of renewable energy sources, remarking the different impact of grid-following and grid-forming control strategies on the electromechanical power-frequency oscillations of the system.

## 2. Synchronisation Mechanism and Inertial Capabilities of Power Converters

## 3. Electromechanical Oscillations in Converter-Dominated Power Systems

## 4. Case Study: The Colombian Interconnected National System

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Fundamental representation of grid-following synchronisation mechanism and controls with inertia functionality.

**Figure 2.**Fundamental representation of grid-forming synchronisation mechanism and controls with inertia functionality.

**Figure 5.**Comparison and validation of phasor RMS and full EMT models for a step change in the active power reference: (

**a**) grid-following; (

**b**) grid-forming.

**Figure 6.**Generic two-area network for the study of the electromechanical oscillations in converter-dominated power systems.

**Figure 8.**Participation factors for the identified modes in the electromechanical oscillations region: (

**a**) grid-following in both areas; (

**b**) grid-forming in both areas; (

**c**) grid-following in Area 1 and grid-forming in Area 2; (

**d**) grid-forming in Area 1 and grid-following in Area 2.

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

Grid-following | |

Proportional gain P control ${K}_{pP}$ (pu) | 1 |

Integral gain P control ${K}_{pI}$ (pu) | 10 |

Proportional gain Q control ${K}_{qP}$ (pu) | 1 |

Integral gain Q control ${K}_{qI}$ (pu) | 10 |

Proportional gain PLL ${K}_{pllP}$ (pu) | 60 |

Integral gain PLL ${K}_{pllI}$ (pu) | 900 |

Synthetic inertia gain H (s) | 3 |

Filtered derivative time constant ${T}_{der}$ (s) | 0.01 |

Grid-forming | |

Proportional gain Q/V control ${K}_{qP}$ (pu) | 1 |

Integral gain Q/V control ${K}_{qI}$ (pu) | 10 |

Virtual inertia constant H (s) | 3 |

Virtual friction factor D (pu) | 0.1 |

Synchronous machine | |

Inertia constant H (s) | 3 |

Synchronous reactance d-axis ${X}_{d}$ (pu) | 1.3 |

Transient reactance d-axis ${X}_{d}^{{}^{\prime}}$ (pu) | 0.18 |

Subtransient reactance d-axis ${X}_{d}^{{}^{\u2033}}$ (pu) | 0.1 |

Synchronous reactance q-axis ${X}_{q}$ (pu) | 1.2 |

Transient reactance q-axis ${X}_{q}^{{}^{\prime}}$ (pu) | 0.25 |

Subtransient reactance q-axis ${X}_{q}^{{}^{\u2033}}$ (pu) | 0.1 |

Transient time constant d-axis ${T}_{do}^{{}^{\prime}}$ (s) | 5.89 |

Subtransient time constant d-axis ${T}_{do}^{{}^{\u2033}}$ (s) | 0.03 |

Transient time constant q-axis ${T}_{qo}^{{}^{\prime}}$ (s) | 0.6 |

Subtransient time constant q-axis ${T}_{qo}^{{}^{\u2033}}$ (s) | 0.07 |

Exciter controller gain K (pu) | 200 |

Exciter filter derivative time constant ${T}_{A}$ (s) | 3 |

Exciter filter delay time constant ${T}_{B}$ (s) | 10 |

Exciter time constant ${T}_{E}$ (s) | 0.05 |

Governor controller droop R (pu) | 0.05 |

Governor time constant ${T}_{1}$ (s) | 0.5 |

Turbine derivative time constant ${T}_{2}$ (s) | 3 |

Turbine delay time constant ${T}_{3}$ (s) | 10 |

Eigenvalue | Damping Ratio $\mathsf{\zeta}$ (%) | Frequency f (Hz) |
---|---|---|

${\lambda}_{2}=-1.47\phantom{\rule{3.33333pt}{0ex}}-$ j6.57 | 21.91 | 1.05 |

${\lambda}_{3}=-$0.06 − j5.94 | 1.06 | 0.95 |

${\lambda}_{4}=-$0.75 − j6.21 | 12.00 | 0.99 |

${\lambda}_{5}=-$0.75 − j6.22 | 12.06 | 0.98 |

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

Synchronous machine | |

Inertia constant H (s) | 2–8 |

Synchronous reactance d-axis ${X}_{d}$ (pu) | 1.3 |

Transient reactance d-axis ${X}_{d}^{{}^{\prime}}$ (pu) | 0.18 |

Subtransient reactance d-axis ${X}_{d}^{{}^{\u2033}}$ (pu) | 0.1 |

Synchronous reactance q-axis ${X}_{q}$ (pu) | 1.2 |

Transient reactance q-axis ${X}_{q}^{{}^{\prime}}$ (pu) | 0.25 |

Subtransient reactance q-axis ${X}_{q}^{{}^{\u2033}}$ (pu) | 0.1 |

Transient time constant d-axis ${T}_{do}^{{}^{\prime}}$ (s) | 5.89 |

Subtransient time constant d-axis ${T}_{do}^{{}^{\u2033}}$ (s) | 0.03 |

Transient time constant q-axis ${T}_{qo}^{{}^{\prime}}$ (s) | 0.6 |

Subtransient time constant q-axis ${T}_{qo}^{{}^{\u2033}}$ (s) | 0.07 |

Excitation system | |

Exciter controller gain K (pu) | 100 |

Exciter filter derivative time constant ${T}_{A}$ (s) | 3 |

Exciter filter delay time constant ${T}_{B}$ (s) | 10 |

Exciter time constant ${T}_{E}$ (s) | 0.5 |

Governor/turbine (thermal) | |

Governor controller droop R (pu) | 0.05 |

Governor time constant ${T}_{1}$ (s) | 0.5 |

Turbine derivative time constant ${T}_{2}$ (s) | 3 |

Turbine delay time constant ${T}_{3}$ (s) | 10 |

Governor/turbine (hydro) | |

Turbine reduction of gate stroke ${A}_{T}$ (pu) | 1.2 |

Turbine damping factor ${D}_{turb}$ (pu) | 0.5 |

Turbine nominal head ${H}_{dam}$ (pu) | 1 |

No-load flow at nominal head ${Q}_{nl}$ (pu) | 0.08 |

Permanent droop ${R}_{perm}$ (pu) | 0.05 |

Temporary droop ${R}_{temp}$ (pu) | 0.3 |

Filter time constant ${T}_{F}$ (s) | 0.05 |

Gate servo time constant ${T}_{G}$ (s) | 0.5 |

Washout time constant ${T}_{R}$ (s) | 5 |

Water inertia time constant ${T}_{W}$ (s) | 1 |

Maximum gate velocity $VE{L}_{M}$ (pu) | 0.2 |

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**MDPI and ACS Style**

Musca, R.; Gonzalez-Longatt, F.; Gallego Sánchez, C.A.
Power System Oscillations with Different Prevalence of Grid-Following and Grid-Forming Converters. *Energies* **2022**, *15*, 4273.
https://doi.org/10.3390/en15124273

**AMA Style**

Musca R, Gonzalez-Longatt F, Gallego Sánchez CA.
Power System Oscillations with Different Prevalence of Grid-Following and Grid-Forming Converters. *Energies*. 2022; 15(12):4273.
https://doi.org/10.3390/en15124273

**Chicago/Turabian Style**

Musca, Rossano, Francisco Gonzalez-Longatt, and Cesar A. Gallego Sánchez.
2022. "Power System Oscillations with Different Prevalence of Grid-Following and Grid-Forming Converters" *Energies* 15, no. 12: 4273.
https://doi.org/10.3390/en15124273