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Inclusion of Frequency Nadir constraint in the Unit Commitment Problem of Small Power Systems Using Machine Learning

Mohammad Rajabdorri, Behzad Kazemtabrizi, Matthias Troffaes, Lukas Sigrist, Enrique Lobato

TL;DR

The paper tackles frequency stability in FCUC for small island power systems with inertia scarcity due to renewables. It proposes ML-based nadir modelling using LR and SVM, built from a synthetic training dataset, and integrates the resulting linear classifier as a constraint within MILP UC. It compares the ML approach to an analytical nadir formulation and a base case, demonstrating that ML methods substantially accelerate UC solving while maintaining acceptable frequency response. The study, applied to the La Palma island system, suggests that data-driven nadir constraints are a viable and scalable alternative for FCUC in low-inertia settings and can enable more flexible stochastic/robust UC formulations.

Abstract

As the intention is to reduce the amount of thermal generation and to increase the share of clean energy, power systems are increasingly becoming susceptible to frequency instability after outages due to reduced levels of inertia. To address this issue frequency constraints are being included in the scheduling process, which ensure a tolerable frequency deviation in case of any contingencies. In this paper, a method is proposed to integrate the non-linear frequency nadir constraint into the unit commitment problem, using machine learning. First a synthetic training dataset is generated. Then two of the available classic machine learning methods, namely logistic regression and support vector machine, are proposed to predict the frequency nadir. To be able to compare the machine learning methods to traditional frequency constrained unit commitment approaches, simulations on the power system of La Palma island are carried out for both proposed methods as well as an analytical linearized formulation of the frequency nadir. Our results show that the unit commitment problem with a machine learning based frequency nadir constraint is solved considerably faster than with the analytical formulation, while still achieving an acceptable frequency response quality after outages.

Inclusion of Frequency Nadir constraint in the Unit Commitment Problem of Small Power Systems Using Machine Learning

TL;DR

The paper tackles frequency stability in FCUC for small island power systems with inertia scarcity due to renewables. It proposes ML-based nadir modelling using LR and SVM, built from a synthetic training dataset, and integrates the resulting linear classifier as a constraint within MILP UC. It compares the ML approach to an analytical nadir formulation and a base case, demonstrating that ML methods substantially accelerate UC solving while maintaining acceptable frequency response. The study, applied to the La Palma island system, suggests that data-driven nadir constraints are a viable and scalable alternative for FCUC in low-inertia settings and can enable more flexible stochastic/robust UC formulations.

Abstract

As the intention is to reduce the amount of thermal generation and to increase the share of clean energy, power systems are increasingly becoming susceptible to frequency instability after outages due to reduced levels of inertia. To address this issue frequency constraints are being included in the scheduling process, which ensure a tolerable frequency deviation in case of any contingencies. In this paper, a method is proposed to integrate the non-linear frequency nadir constraint into the unit commitment problem, using machine learning. First a synthetic training dataset is generated. Then two of the available classic machine learning methods, namely logistic regression and support vector machine, are proposed to predict the frequency nadir. To be able to compare the machine learning methods to traditional frequency constrained unit commitment approaches, simulations on the power system of La Palma island are carried out for both proposed methods as well as an analytical linearized formulation of the frequency nadir. Our results show that the unit commitment problem with a machine learning based frequency nadir constraint is solved considerably faster than with the analytical formulation, while still achieving an acceptable frequency response quality after outages.
Paper Structure (21 sections, 19 equations, 9 figures, 5 tables, 1 algorithm)

This paper contains 21 sections, 19 equations, 9 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methodology
  3. UC Formulation
  4. Frequency Dynamics
  5. Rate of Change of Frequency Modelling
  6. Steady State Frequency Modelling
  7. Frequency Nadir Modelling
  8. Frequency nadir: analytical modelling
  9. Frequency Nadir: ML based modelling
  10. Data Generation:
  11. Labelling the Data:
  12. Learning the Model:
  13. Loss Function:
  14. Validation:
  15. Evaluating the Methods
  16. ...and 6 more sections

Figures (9)

  • Figure 1: Summary of the reviewed literature
  • Figure 2: SFR model.
  • Figure 3: Flowchart of the ML based methods
  • Figure 4: Weekly demand for each season
  • Figure 5: Weekly available RES for each season
  • ...and 4 more figures