Decomposition of drift vector field: An application to multi-machine transient stability enhancement

Knowledge of a potential function is of prime importance in stability analysis of systems. In mechanical systems, energy is considered as potential function. Passivity based methods in literature aim in finding potential function, which may prove unsuccessful for certain class of systems e.g. biological systems. Unfortunately, no general rules exist for the construction of a Lyapunov function, so expertise and intuition of the designer on the specific system is required to define a candidate function. Present paper proposes a systematic method to generate a potential function after decomposing a drift vector field representing a general dynamical system. The method finds application in lossy multi-machine systems for deriving a control law using gradient formulation without solving partial differential equations. The results validated on examples in the area of power system are used in transient stability analysis and enhancement.