Data-Driven Modeling of the Temporal Evolution of Breakers' States in the French Electrical Transmission Grid
Résumé
The electrical transmission grid is a complex network whose configuration can be adapted using a set of circuit breakers. As the grid is becoming ever more complex and prone to failures or attacks, being able to monitor the evolution of the breakers' states to detect abnormal behaviors is of the highest importance in order to ensure a safe and secure operation of the grid. In this paper, we propose a data-driven approach to the modeling of the temporal evolution of the breakers' states in an electrical transmission grid. The available data consists of a historical record of the breakers' states over a period during which the electrical transmission grid operated normally. A stochastic modeling framework is introduced where we make the assumption that the state of the grid (given by the states of all breakers, which are known at all time) is a stochastic process which varies around a reference configuration, chosen among a finite set of reference configurations. The current reference configuration of the grid is unknown and constitutes a hidden stochastic process. Then, the evolution of the breakers' states is driven by a continuous-time finitestate hidden Markov model. Based on this framework, we provide a filter-based expectation-maximization approach using a change of probability measure method to estimate the model parameters and the hidden reference configuration. Further, we present a strong scheme with no discretization error on the filter dynamics for numerical purposes. We also present a clustering approach to identify the set of reference configurations of the network.
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