" Derivations of critical boundaries for system stability in terms of injection impedance. " Derivations of characteristic curves of constant P, Q, V and delta in injection impedance plane. " Example of how one of the derived mappings provides an analytical load flow solution.
JEPE 1805No. of Pages 1, Model 5G
Abstract-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.
Abstract-This paper presents the details of a new real-time stability assessment method. The method assesses a particular mechanism of stability: each generator's capability to generate sufficient steady state electromechanical torque. The lack of sufficient steady state torque causes aperiodic increase in rotor angle and a loss of synchronism, referred to as aperiodic small signal instability. The paper provides the theoretical background of the method and an analytical assessment criterion. Furthermore, a mathematical mapping of the generators' operating points that enables informative visualization of multiple operating points is derived in the paper. Finally, results from time-domain simulation of instability scenarios in the Nordic32 test system are presented and results used for testing the assessment method. The results illustrate the method's capability to efficiently identify the location of the emerging problem and to quantify margins to stability boundary.Index Terms-Power system measurements, power system monitoring, power system stability.
In this paper, it is investigated how detailed the model of a synchronous machine needs to be in order to assess transient stability using a Single Machine Equivalent (SIME). The results will show how the stability mechanism and the stability assessment are affected by the model detail. In order to identify the transient stability mechanism, a simulation with a high-order model was used as reference. The Western System Coordinating Council System (WSCC) and the New England & New York system are considered and simulations of an unstable and a stable scenario are carried out, where the detail of the machine models is varied. Analyses of the results suggest that a 4 th -order model may be sufficient to represent synchronous machines in transient stability studies.
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