# Online Energy Price Matrix Factorization for Power Grid Topology Tracking

arXiv: https://arxiv.org/abs/1410.6095 · HTML: https://mlsanity.com/paper/1410.6095/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2014.

## Built on by (most cited first, 2 of 2)

- [Learning Distribution Grid Topologies: A Tutorial](https://mlsanity.com/paper/2206.10837/) (2022)
- [Unsupervised Congestion Status Identification Using LMP Data](https://mlsanity.com/paper/2411.10058/) (2024)

## Abstract (arXiv)

Grid security and open markets are two major smart grid goals. Transparency of market data facilitates a competitive and efficient energy environment, yet it may also reveal critical physical system information. Recovering the grid topology based solely on publicly available market data is explored here. Real-time energy prices are calculated as the Lagrange multipliers of network-constrained economic dispatch; that is, via a linear program (LP) typically solved every 5 minutes. Granted the grid Laplacian is a parameter of this LP, one could infer such a topology-revealing matrix upon observing successive LP dual outcomes. The matrix of spatio-temporal prices is first shown to factor as the product of the inverse Laplacian times a sparse matrix. Leveraging results from sparse matrix decompositions, topology recovery schemes with complementary strengths are subsequently formulated. Solvers scalable to high-dimensional and streaming market data are devised. Numerical validation using real load data on the IEEE 30-bus grid provide useful input for current and future market designs.