This paper studies real-time estimation of stability margin of a power system under disturbances by continuous measurement data. The paper presents a Ball-On-Concave-Surface (BOCS) mechanics system as a power system's adaptive equivalent representing its real-time status and the stability region about a monitored variable. The parameters of the equivalent are adaptive to the operating condition and can online be identified from the phase-plane trajectories of the monitored variable. Accordingly, the stability margin and risk of instability can be estimated. Case studies on a two-generator system and a 179-bus system show that the BOCS system can be applied either locally or for wide-area stability monitoring in real-time calculation of stability margin. This paper proposes a new idea for using real-time measurements to develop and identify a power system's adaptive equivalent as a basis for online prediction of instability.