New stability approach applied to large-scale power systems with generator flux decay

In this work, the Lyapunov's direct method is used to carry out transient stability analysis of an N-machine power system considering a more sophisticated generator model. Each generator is represented by the so-called 2-axis model [1], in which the two voltage components E'q and E'd of the generator internal voltage E' are considered to be changing with time. The system loads are represented by constant shunt impedances, then the system nodes (except the generator internal nodes) are eliminated, and finally the system reduced admittance matrix of the order N, is computed. Applying the decomposition-aggregation method, the system is decomposed such that each subsystem includes three machines, instead of only one machine as considered so far [2], in addition to the comparison machine. Describing each generator by a fourth-order dynamic model, and considering non-uniform mechanical damping, the system mathematical model (the transfer conductances are included) is determined and decomposed into (N-1/3 15th -order interconnected subsystems. Each of them is decomposed into free subsystem, containing six nonlinear functions, and interconnections. A vector Lyapunov function is constructed and used for the system aggregation. A square aggregation matrix of the order (N-1)/3 is obtained, whose stability implies asymptotic stability of the system equilibrium. As an illustrative example, the developed approach is applied to a 10-machine, 11-bus power system, and an estimate for the system asymptotic stability domain is determined. The system transient stability computations are carried out considering a 3-phase short circuit fault, and the approach is used to determine directly the critical time for clearing the fault. It is found that the developed approach is suitable and can be easily used for practical and on-line stability studies of power systems (number of machines may be more than 10). The developed approach can also reduce the conservativeness of the decomposition-aggregation method.