### Abstract

Grid security and open markets are two major smart grid goals. Transparency of market data facilitates a competitive and efficient energy environment. But 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 typically calculated as the Lagrange multipliers of network-constrained economic dispatch; that is, via a linear program (LP) typically solved every 5 min. Since the grid Laplacian matrix is a parameter of this LP, someone apart from the system operator could try inferring this topology-related matrix upon observing successive LP dual outcomes. It is first shown that the matrix of spatio-temporal prices can be factored 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 synthetic and real-load data on the IEEE 30-bus grid provide useful input for current and future market designs.

Original language | English (US) |
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Article number | 7226869 |

Pages (from-to) | 1239-1248 |

Number of pages | 10 |

Journal | IEEE Transactions on Smart Grid |

Volume | 7 |

Issue number | 3 |

DOIs | |

State | Published - May 2016 |

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### Keywords

- Alternating direction method of multipliers (ADMM)
- compressive sensing
- economic dispatch
- graph Laplacian
- locational marginal prices (LMPs)
- online convex optimization

### Cite this

*IEEE Transactions on Smart Grid*,

*7*(3), 1239-1248. [7226869]. https://doi.org/10.1109/TSG.2015.2469098