A system and method for monitoring and managing three-phase power flows in electrical transmission and distribution networks through the use of a deterministic, non-iterative method using an holomorphic embedding and algebraic approximants for determining the power flows in the three phases of a power generating system having an electrical grid. Such method is capable of determining whether or not a physical solution to the load flow problem exists, or if the system is in a state of voltage collapse. It may be employed in either real-time or off-line analytic applications for balanced or unbalanced electric power systems, in particular for monitoring and analyzing unbalanced conditions in three-phase electrical networks and for the accurate calculation of short-circuit conditions.
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