# Unsupervised Congestion Status Identification Using LMP Data

arXiv: https://arxiv.org/abs/2411.10058 · HTML: https://mlsanity.com/paper/2411.10058/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 41 references that are in the map.
- First posted on arXiv 15 Nov 2024.

## Builds on (most cited first, 10 of 10)

- [A note on the sample complexity of the Er-SpUD algorithm by Spielman, Wang and Wright for exact recovery of sparsely used dictionaries](https://mlsanity.com/paper/1601.02049/) (2016)
- [Dual Principal Component Pursuit](https://mlsanity.com/paper/1510.04390/) (2015)
- [Finding a sparse vector in a subspace: Linear sparsity using alternating directions](https://mlsanity.com/paper/1412.4659/) (2014)
- [Learning from Past Bids to Participate Strategically in Day-Ahead Electricity Markets](https://mlsanity.com/paper/1811.06113/) (2018)
- [Probabilistic Forecast of Real-Time LMP and Network Congestion](https://mlsanity.com/paper/1503.06171/) (2015)
- [Learning the LMP-Load Coupling From Data: A Support Vector Machine Based Approach](https://mlsanity.com/paper/1603.07276/) (2016)
- [Impact of Local Transmission Congestion on Energy Storage Arbitrage Opportunities](https://mlsanity.com/paper/1702.04816/) (2017)
- [Online Energy Price Matrix Factorization for Power Grid Topology Tracking](https://mlsanity.com/paper/1410.6095/) (2014)
- [A Holistic Approach to Forecasting Wholesale Energy Market Prices](https://mlsanity.com/paper/1807.07120/) (2018)
- [Segmentation of Subspaces in Sequential Data](https://mlsanity.com/paper/1504.04090/) (2015)

## Built on by (most cited first, 1 of 1)

- [A Data-Driven Pool Strategy for Price-Makers Under Imperfect Information](https://mlsanity.com/paper/2411.14694/) (2024)

## Abstract (arXiv)

Having a better understanding of how locational marginal prices (LMPs) change helps in price forecasting and market strategy making. This paper investigates the fundamental distribution of the congestion part of LMPs in high-dimensional Euclidean space using an unsupervised approach. LMP models based on the lossless and lossy DC optimal power flow (DC-OPF) are analyzed to show the overlapping subspace property of the LMP data. The congestion part of LMPs is spanned by certain row vectors of the power transfer distribution factor (PTDF) matrix, and the subspace attributes of an LMP vector uniquely are found to reflect the instantaneous congestion status of all the transmission lines. The proposed method searches for the basis vectors that span the subspaces of congestion LMP data in hierarchical ways. In the bottom-up search, the data belonging to 1-dimensional subspaces are detected, and other data are projected on the orthogonal subspaces. This procedure is repeated until all the basis vectors are found or the basis gap appears. Top-down searching is used to address the basis gap by hyperplane detection with outliers. Once all the basis vectors are detected, the congestion status can be identified. Numerical experiments based on the IEEE 30-bus system, IEEE 118-bus system, Illinois 200-bus system, and Southwest Power Pool are conducted to show the performance of the proposed method.