An energy-efficient description of electromagnetism based on a reversible interpretation of Faraday’s Law is described. Space aggregation and time reconciliation of all scales involved in power system management are derived from two constants of motion, respectively Gibbs free energy and kinetic energy embedded in the whole system. At the upper space scale, a simplified description of the grid based on the Kuramoto model is proved to be suitable for assessing the stability of the synchronous state of a power system. In addition, the Gibbs free energy embedded in the power grid takes the form of a X − Y lattice-gas Hamiltonian, showing the critical role of reactive power in maintaining synchronism. Finally, the transient stability of the power system is considered from these two constants of motion, before any operation from the dispatch.
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