Real-Time Thevenin Impedance Computation

Stable and secure operation of power systems becomes increasingly difficult when a large share of the power production is based on distributed and non-controllable renewable energy sources. Real-time stability assessment is dependent on very fast computation of different properties of the grid operating state, and strict time constraints are difficult to adhere to as the complexity of the grid increases. Several suggested approaches for real-time stability assessment require Thevenin impedances to be determined for the observed system conditions. By combining matrix factorization, graph reduction, and parallelization, we develop an algorithm for computing Thevenin impedances an order of magnitude faster than previous approaches. We test the factor-and-solve algorithm with data from several power grids of varying complexity, and we show how the algorithm allows realtime stability assessment of complex power grids at millisecond time scale.