Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Unit Commitment Predictor With a Performance Guarantee: A Support Vector Machine Classifier

Farzaneh Pourahmadi, Jalal Kazempour

TL;DR

The paper tackles the computational burden of UC by learning binary on/off decisions for conventional units to provide warm-starts for MISOCP solvers. It advances a three-step UC predictor based on data collection, binary SVM classification (including linear, kernelized, and distributionally robust variants), and prediction/decision making with feasibility and out-of-sample guarantees. The kernelized SVM with regularization consistently offers the best out-of-sample performance and practical speedups, achieving notable reductions in computation time (up to a factor of about 1.7) and enabling near-optimal solutions within tight time limits, as demonstrated on IEEE 6-bus and 118-bus systems. This approach yields actionable savings for system operators under time-constrained UC tasks and sets a foundation for more advanced, correlation-aware and transfer-learning extensions.

Abstract

The system operators usually need to solve large-scale unit commitment problems within limited time frame for computation. This paper provides a pragmatic solution, showing how by learning and predicting the on/off commitment decisions of conventional units, there is a potential for system operators to warm start their solver and speed up their computation significantly. For the prediction, we train linear and kernelized support vector machine classifiers, providing an out-of-sample performance guarantee if properly regularized, converting to distributionally robust classifiers. For the unit commitment problem, we solve a mixed-integer second-order cone problem. Our results based on the IEEE 6- and 118-bus test systems show that the kernelized SVM with proper regularization outperforms other classifiers, reducing the computational time by a factor of 1.7. In addition, if there is a tight computational limit, while the unit commitment problem without warm start is far away from the optimal solution, its warmly-started version can be solved to (near) optimality within the time limit.

Unit Commitment Predictor With a Performance Guarantee: A Support Vector Machine Classifier

TL;DR

The paper tackles the computational burden of UC by learning binary on/off decisions for conventional units to provide warm-starts for MISOCP solvers. It advances a three-step UC predictor based on data collection, binary SVM classification (including linear, kernelized, and distributionally robust variants), and prediction/decision making with feasibility and out-of-sample guarantees. The kernelized SVM with regularization consistently offers the best out-of-sample performance and practical speedups, achieving notable reductions in computation time (up to a factor of about 1.7) and enabling near-optimal solutions within tight time limits, as demonstrated on IEEE 6-bus and 118-bus systems. This approach yields actionable savings for system operators under time-constrained UC tasks and sets a foundation for more advanced, correlation-aware and transfer-learning extensions.

Abstract

The system operators usually need to solve large-scale unit commitment problems within limited time frame for computation. This paper provides a pragmatic solution, showing how by learning and predicting the on/off commitment decisions of conventional units, there is a potential for system operators to warm start their solver and speed up their computation significantly. For the prediction, we train linear and kernelized support vector machine classifiers, providing an out-of-sample performance guarantee if properly regularized, converting to distributionally robust classifiers. For the unit commitment problem, we solve a mixed-integer second-order cone problem. Our results based on the IEEE 6- and 118-bus test systems show that the kernelized SVM with proper regularization outperforms other classifiers, reducing the computational time by a factor of 1.7. In addition, if there is a tight computational limit, while the unit commitment problem without warm start is far away from the optimal solution, its warmly-started version can be solved to (near) optimality within the time limit.
Paper Structure (16 sections, 1 theorem, 22 equations, 9 figures, 1 table, 1 algorithm)

This paper contains 16 sections, 1 theorem, 22 equations, 9 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature review
  3. Our research questions, contributions, and outline
  4. Overview of the Proposed UC predictor
  5. Step 1: Data Collection
  6. Step 2: Learning by Binary Classification
  7. Linear SVM
  8. Reformulating Linear SVM
  9. Distributionally robust SVM
  10. Kernelized SVM
  11. Distributionally Robust Kernelized SVM
  12. Step 3: Prediction and Decision Making
  13. Experimental results
  14. IEEE 6-bus test system
  15. IEEE 118-bus test system
  16. ...and 1 more sections

Key Result

Theorem 1

Given the set of feature vectors $\mathbf{X}$ drawn from an unknown discrete distribution and its corresponding set of strategy vectors $\mathbf{Y}$, the probability of coming across a feature vector $\mathbf{x}_{H+1}$ that corresponds to an unobserved strategy vector $\mathbf{y}_{H+1}$ is where $H_1$ is the number of unique strategies that have been observed only once, $\tau=2\sqrt{2}+\sqrt{3}$,

Figures (9)

  • Figure 1: The overall structure of the proposed UC predictor.
  • Figure 2: The IEEE $6$-bus test system with three conventional units $\rm{G}1$-$\rm{G}3$, two wind farms $\rm{W}1$-$\rm{W}2$, and three loads $\rm{L}1$-$\rm{L}3$.
  • Figure 3: The number of missclassified samples and CPU time for SVM classifiers using $50$, $500$, and $5,000$ training samples and $1,000$ test samples.
  • Figure 4: A matrix of plots for the training dataset and biased and unbiased testing datasets. The diagonal plots (x-axis: in per-unit; y-axis: frequency of occurrence) display the wind production level frequency. The off-diagonal plots (both axes in per-unit) display the correlation of two wind farms $\rm{W}1$-$\rm{W}2$.
  • Figure 5: The expected hinge loss of the kernelized SVM classifier, for every unit and hour, in the training and testing stages (with biased and unbiased test data).
  • ...and 4 more figures

Theorems & Definitions (1)

  • Theorem 1