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Data-driven Estimation of Under Frequency Load Shedding after Outages in Small Power Systems

Mohammad Rajabdorri, Lukas Sigrist, Enrique Lobato, Matthias C. M. Troffaes, Behzad Kazemtabrizi

TL;DR

The paper tackles UFLS estimation after outages in small island power systems by proposing a data-driven workflow that uses a dynamic SFR model to label UFLS amounts and learn their relation to a compact feature set. It develops two MILP-encodable learners: a novel regression-tree with convex-region partitions and a standard Tobit model for censored outcomes, applied to the La Palma island system. The regression-tree achieves a high-accuracy out-of-sample MAE of $0.213$ MW, while the Tobit model reaches $0.4967$ MW, with the former offering a more favorable MILP representation (e.g., 18 constraints) for integration into security-constrained planning. This approach enables more accurate UFLS estimation within scheduling problems, improving frequency response and reserve allocation while reducing operation costs in small island grids.

Abstract

This paper presents a data-driven methodology for estimating Under Frequency Load Shedding (UFLS) in small power systems. UFLS plays a vital role in maintaining system stability by shedding load when the frequency drops below a specified threshold following loss of generation. Using a dynamic System Frequency Response (SFR) model we generate different values of UFLS (i.e., labels) predicated on a set of carefully selected operating conditions (i.e., features). Machine Learning (ML) algorithms are then applied to learn the relationship between chosen features and the UFLS labels. A novel regression tree and the Tobit model are suggested for this purpose and we show how the resulting non-linear model can be directly incorporated into a Mixed Integer Linear Programming (MILP) problem. The trained model can be used to estimate UFLS in security-constrained operational planning problems, improving frequency response, optimizing reserve allocation, and reducing costs. The methodology is applied to the La Palma island power system, demonstrating its accuracy and effectiveness. The results confirm that the amount of UFLS can be estimated with the Mean Absolute Error (MAE) as small as 0.213 MW for the whole process, with a model that is representable as a MILP for use in scheduling problems such as unit commitment among others.

Data-driven Estimation of Under Frequency Load Shedding after Outages in Small Power Systems

TL;DR

The paper tackles UFLS estimation after outages in small island power systems by proposing a data-driven workflow that uses a dynamic SFR model to label UFLS amounts and learn their relation to a compact feature set. It develops two MILP-encodable learners: a novel regression-tree with convex-region partitions and a standard Tobit model for censored outcomes, applied to the La Palma island system. The regression-tree achieves a high-accuracy out-of-sample MAE of MW, while the Tobit model reaches MW, with the former offering a more favorable MILP representation (e.g., 18 constraints) for integration into security-constrained planning. This approach enables more accurate UFLS estimation within scheduling problems, improving frequency response and reserve allocation while reducing operation costs in small island grids.

Abstract

This paper presents a data-driven methodology for estimating Under Frequency Load Shedding (UFLS) in small power systems. UFLS plays a vital role in maintaining system stability by shedding load when the frequency drops below a specified threshold following loss of generation. Using a dynamic System Frequency Response (SFR) model we generate different values of UFLS (i.e., labels) predicated on a set of carefully selected operating conditions (i.e., features). Machine Learning (ML) algorithms are then applied to learn the relationship between chosen features and the UFLS labels. A novel regression tree and the Tobit model are suggested for this purpose and we show how the resulting non-linear model can be directly incorporated into a Mixed Integer Linear Programming (MILP) problem. The trained model can be used to estimate UFLS in security-constrained operational planning problems, improving frequency response, optimizing reserve allocation, and reducing costs. The methodology is applied to the La Palma island power system, demonstrating its accuracy and effectiveness. The results confirm that the amount of UFLS can be estimated with the Mean Absolute Error (MAE) as small as 0.213 MW for the whole process, with a model that is representable as a MILP for use in scheduling problems such as unit commitment among others.
Paper Structure (13 sections, 13 equations, 10 figures, 1 table, 1 algorithm)

This paper contains 13 sections, 13 equations, 10 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methodology
  3. Data Generation
  4. Labeling the Data
  5. Learning Process
  6. Proposed Regression Tree
  7. Tobit Model
  8. Results
  9. Data Generation and Analysis
  10. Learning Process
  11. With Regression Tree
  12. With Tobit Model
  13. Conclusion

Figures (10)

  • Figure 1: model.
  • Figure 2: Proposed regression tree.
  • Figure 3: Pearson correlation between inertia, weighted $K$, lost power, power reserve, and the amount of .
  • Figure 4: and scatter plot of the features and the labels.
  • Figure 5: Histogram of amount.
  • ...and 5 more figures