A Framework for Robust Assessment of Power Grid Stability and Resiliency

Abstract

Abstract-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.

Exponential convergence under distributed averaging integral frequency control

“…The contribution of this paper is primarily theoretical: existing approaches to the problem of optimal frequency control have mostly relied on non-strictly decreasing energy -or Lyapunov functions, using LaSalle's invariance principle and related results to guarantee convergence to an invariant manifold on which the Lyapunov function's derivative vanishes (see Schiffer et al, 2017;Vu and Turitsyn, 2017 for exceptions). Since this does not lead to strong results on convergence, we design a strictly decreasing Lyapunov function that does prove exponential convergence to the optimal synchronous solution.…”

Inverse Stability Problem and Applications to Renewables Integration

“…Indeed, the convergence from δ 0 to an EP is guaranteed when the system's energy function is bounded under some threshold [2], [3]. In [5], we observed that if the EP is in the interior of the set P characterized by phasor angular differences smaller than π/2, then the nonlinear power flows can be strictly bounded by linear functions of angular differences. Exploiting this observation, we show that the energy function of power system can be approximated by quadratic functions of the EP and the system state, and from which we obtain an estimate of the inverse stability region.…”

“…Though Φ is not closed, the decrease of E(δ, δ * ) inside Φ assures the limit set to be inside Φ. As such, we can apply the LaSalle's Invariance Principle and use a proof similar to that of Theorem 1 in [5] to show that, if δ 0 is inside Φ then the system state will only evolve inside this set and eventually converge to δ * . So, to check if the system state converges from δ 0 ∈ P to δ * , we only need to check if E(δ 0 , δ * ) < E min (δ * ).…”

Identifying Parameter Space for Robust Stability in Nonlinear Networks: A Microgrid Application

“…More recent works have used advanced computational techniques, such as sum-of-squares (SOS) algorithms, for parametric stability analysis using Lyapunov functions [17]- [21]. Lyapunov-based methods have been applied to robust stability analysis and control problems in power grids [22], [23]. Chebyshev minimax formulation has been used for identifying the parametric stability region for linear systems (with Lur'e-type nonlinearity) [24].…”