4 research outputs found
Stability and Control of Power Systems using Vector Lyapunov Functions and Sum-of-Squares Methods
Recently sum-of-squares (SOS) based methods have been used for the stability
analysis and control synthesis of polynomial dynamical systems. This analysis
framework was also extended to non-polynomial dynamical systems, including
power systems, using an algebraic reformulation technique that recasts the
system's dynamics into a set of polynomial differential algebraic equations.
Nevertheless, for large scale dynamical systems this method becomes
inapplicable due to its computational complexity. For this reason we develop a
subsystem based stability analysis approach using vector Lyapunov functions and
introduce a parallel and scalable algorithm to infer the stability of the
interconnected system with the help of the subsystem Lyapunov functions.
Furthermore, we design adaptive and distributed control laws that guarantee
asymptotic stability under a given external disturbance. Finally, we apply this
algorithm for the stability analysis and control synthesis of a network
preserving power system.Comment: to appear at the 14th annual European Control Conferenc
Estimating Relevant Portion of Stability Region using Lyapunov Approach and Sum of Squares
Traditional Lyapunov based transient stability assessment approaches focus on
identifying the stability region (SR) of the equilibrium point under study.
When trying to estimate this region using Lyapunov functions, the shape of the
final estimate is often limited by the degree of the function chosen, a
limitation that results in conservativeness in the estimate of the SR. More
conservative the estimate is in a particular region of state space, smaller is
the estimate of the critical clearing time for disturbances that drive the
system towards that region. In order to reduce this conservativeness, we
propose a methodology that uses the disturbance trajectory data to skew the
shape of the final Lyapunov based SR estimate. We exploit the advances made in
the theory of sum of squares decomposition to algorithmically estimate this
region. The effectiveness of this technique is demonstrated on a power systems
classical model.Comment: Under review as a conference paper at IEEE PESGM 201