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We address the problem of assisting human dispatchers in operating power grids in today's changing context using machine learning, with theaim of increasing security and reducing costs. Power networks are highly regulated systems, which at all times must meet varying demands of electricity with a complex production system, including conventional power plants, less predictable renewable energies (such as wind or solar power), and the possibility of buying/selling electricity on the international market with more and more actors involved at a Europeanscale. This problem is becoming ever more challenging in an aging network infrastructure. One of the primary goals of dispatchers is to protect equipment (e.g. avoid that transmission lines overheat) with few degrees of freedom: we are considering in this paper solely modifications in network topology, i.e. re-configuring the way in which lines, transformers, productions and loads are connected in sub-stations. Using years of historical data collected by the French Transmission Service Operator (TSO) "Réseau de Transport d'Electricité" (RTE), we develop novel machine learning techniques (drawing on "deep learning") to mimic human decisions to devise "remedial actions" to prevent any line to violate power flow limits (so-called "thermal limits"). The proposed technique is hybrid. It does not rely purely on machine learning: every action will be tested with actual simulators before being proposed to the dispatchers or implemented on the grid.