  This paper proposes a novel approach to estimate the steady-state angle
stability limit (SSASL) by using the nonlinear power system dynamic model in
the modal space. Through two linear changes of coordinates and a simplification
introduced by the steady-state condition, the nonlinear power system dynamic
model is transformed into a number of single-machine-like power systems whose
power-angle curves can be derived and used for estimating the SSASL. The
proposed approach estimates the SSASL of angles at all machines and all buses
without the need for manually specifying the scenario, i.e. setting sink and
source areas, and also without the need for solving multiple nonlinear power
flows. Case studies on 9-bus and 39-bus power systems demonstrate that the
proposed approach is always able to capture the aperiodic instability in an
online environment, showing promising performance in the online monitoring of
the steady-state angle stability over the traditional power flow-based
analysis.
