A Framework for Robust Assessment of Power Grid Stability and Resiliency

Security assessment of large-scale, strongly nonlinear power grids containing thousands to millions of interacting components is a computationally expensive task. Targeting at reducing the computational cost, this paper introduces a framework for constructing a robust assessment toolbox that can provide mathematically rigorous certificates for the grids' stability in the presence of variations in power injections, and for the grids' ability to withstand a bunch sources of faults. By this toolbox we can "off-line" screen a wide range of contingencies or power injection profiles, without reassessing the system stability on a regular basis. In particular, we formulate and solve two novel robust stability and resiliency assessment problems of power grids subject to the uncertainty in equilibrium points and uncertainty in fault-on dynamics. Furthermore, we bring in the quadratic Lyapunov functions approach to transient stability assessment, offering real-time construction of stability/resiliency certificates and real-time stability assessment. The effectiveness of the proposed techniques is numerically illustrated on a number of IEEE test cases

Lyapunov Functions Family Approach to Transient Stability Assessment

Analysis of transient stability of strongly nonlinear post-fault dynamics is one of the most computationally challenging parts of Dynamic Security Assessment. This paper proposes a novel approach for assessment of transient stability of the system. The approach generalizes the idea of energy methods, and extends the concept of energy function to a more general Lyapunov Functions Family (LFF) constructed via Semi-Definite-Programming techniques. Unlike the traditional energy function and its variations, the constructed Lyapunov functions are proven to be decreasing only in a finite neighborhood of the equilibrium point. However, we show that they can still certify stability of a broader set of initial conditions in comparison to the traditional energy function in the closest-UEP method. Moreover, the certificates of stability can be constructed via a sequence of convex optimization problems that are tractable even for large scale systems. We also propose specific algorithms for adaptation of the Lyapunov functions to specific initial conditions and demonstrate the effectiveness of the approach on a number of IEEE test cases