# Heterogeneous Inertia Estimation for Power Systems with High Penetration of Converter-Interfaced Generation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Frequency Dynamics

#### 2.1. Synchronous Generators Dynamics

#### 2.2. Frequency Dynamics of Grid-Forming Converter-Interfaced Generation

#### 2.3. Aggregated Frequency Dynamics

## 3. Parameterization and Regression

## 4. Simulation-Based Analysis

#### 4.1. Case Study I: Estimation Performance and Validation

#### 4.2. Case Study II: Effect of Inertia Heterogeneity on the Inertia Estimation

- A.
- Inertia and damping estimation at the machine level: machine parameters identification

- B.
- System inertia estimation with mixed generation

## 5. Discussion and Conclusions

- The proposed estimation method, has very high accuracy. It is demonstrated that, in real-world scenarios with stochastic load variations, the estimation still works with an estimation error of less than 1%.
- The estimation method can be applied during normal operation and hence it can provide continuous online estimations.
- The estimation method can be used for identifying the inertia and damping coefficients of both SGs and converter-interfaced generation with high accuracy. The estimation errors are less than 0.5% and 3% for SGs and converter-interfaced generation, respectively.
- The estimation method successfully estimates the amount of virtual inertia provided by the low-pass filter used in droop controllers. This result confirms the relationship between droop controllers and VSM and shows that the swing equation can be used for modelling the droop control. Furthermore, additional control parameters can be identified, i.e., using Equation (13), the cut-off frequency of the low pass filter of the converter can be calculated.
- The proposed approach eliminates the impact of damping, including PFC and FFR, on the accuracy of inertia estimation. Hence, the knowledge of PFC and FFR models is not required.
- When it comes to systems with heterogeneous inertia, estimating the overall system inertia at the system level results in large estimation errors. Hence, it is crucial to estimate the local inertia at an area level. This approach would be desirable by SOs not only to achieve accurate estimation results but also because the local inertia values per area are needed for protective actions and regional ancillary markets. Moreover, a distributed approach, considerably reduces the amount of data that needs to be centrally processed.
- The time scale difference between FFR and PFC affects the convergence time of the inertia estimation of systems with mixed generation.
- The inertia estimation accuracy can be further improved by performing the estimation at a machine level, in contrast to at an area level, and then calculate the overall system inertia.
- The timescale difference between the FFR and PFC affects the damping coefficient estimation accuracy. Hence, for the damping coefficient estimation it is crucial to either perform the estimation per area with resources of similar control timescales or in case the knowledge of the PFC models is available, include the PFC models into the parameterization and estimate the damping resulting from the faster controls, i.e., converter-interfaced generation.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**IEEE 39-bus New England test system. The base case system presented in (

**a**) constitutes only synchoronous generators. The modified system in (

**b**) includes converter-interfaced generation, placed at buses 5, 8, 9 and 10.

**Figure 3.**The inertia estimation performance under different load profiles in terms of (

**a**) the estimated total inertia constant and (

**b**) the relative estimation error of the actual total inertia constant.

**Figure 4.**The trajectory of the estimated inertia during normal operation for different measurement time resolutions.

**Figure 5.**Comparison of the inertia estimation performance of systems with mixed generation: (

**a**) the estimated total inertia constant in scenarios S1, S2 and S3; (

**b**) the estimated total inertia constant in scenarios S4 and S5; (

**c**) the relative estimation error of the total inertia constant in systems with mixed generation.

**Figure 6.**Comparison of the system unweighted average frequency, COI frequency and the average frequency in different areas of the system following a load step at bus 36.

**Figure 7.**The impact of parameterization on the damping coefficient estimation: (

**a**) comparison of the effect of parameterization on the damping estimation in Area 2 of the 39-bus system; (

**b**) comparison of the overall system damping under different scenarios.

Generator | Inertia Constant H (s) | Generator | Inertia Constant H (s) |
---|---|---|---|

SG1 | 5 | SG6 | 3.48 |

SG2 | 3.03 | SG7 | 2.64 |

SG3 | 3.58 | SG8 | 2.43 |

SG4 | 2.86 | SG9 | 3.45 |

SG5 | 2.6 | SG10 | 4.2 |

Machine | Estimated Inertia Constant H (s) | Relative Estimation Error | Estimated Damping Coefficient D (p.u) | Relative Estimation Error |
---|---|---|---|---|

SG1 | 5.0127 | 0.25% | 19.9579 | −0.21% |

SG2 | 3.0162 | −0.46% | 19.9386 | −0.0031% |

SG3 | 3.5856 | 0.16% | 19.9966 | −0.017% |

SG4 | 2.8659 | 0.21% | 19.9962 | −0.015% |

VSM5 | 2.6187 | 0.72% | 19.5195 | −2.40% |

SG6 | 3.4865 | 0.19% | 19.9987 | −0.007% |

SG7 | 2.6469 | 0.26% | 19.9994 | −0.003% |

Droop8 | 0.3275 | 2.91% | 19.8112 | −0.94% |

Droop9 | 0.3275 | 2.91% | 18.6245 | −6.88% |

Droop10 | 0.3275 | 2.91% | 19.9257 | −0.37% |

**Table 3.**Summary of the different scenarios used for estimating the overall inertia of systems with mixed generation.

Scenario | Inertia Estimation Manner | FFR Parameters Known | PFC Parameters Known |
---|---|---|---|

S1 | at system level | X | X |

S2 | at system level | X | |

S3 | at system level | ||

S4 | at area level | X | X |

S5 | at machine level |

Scenario | Inertia Constant Estimation Error |
---|---|

S1 | 23.96% |

S2 | 23.45% |

S3 | 21.80% |

S4 | 4.69% |

S5 | 0.29% |

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**MDPI and ACS Style**

Nouti, D.; Ponci, F.; Monti, A. Heterogeneous Inertia Estimation for Power Systems with High Penetration of Converter-Interfaced Generation. *Energies* **2021**, *14*, 5047.
https://doi.org/10.3390/en14165047

**AMA Style**

Nouti D, Ponci F, Monti A. Heterogeneous Inertia Estimation for Power Systems with High Penetration of Converter-Interfaced Generation. *Energies*. 2021; 14(16):5047.
https://doi.org/10.3390/en14165047

**Chicago/Turabian Style**

Nouti, Diala, Ferdinanda Ponci, and Antonello Monti. 2021. "Heterogeneous Inertia Estimation for Power Systems with High Penetration of Converter-Interfaced Generation" *Energies* 14, no. 16: 5047.
https://doi.org/10.3390/en14165047