8 research outputs found
Synchronization stability of lossy and uncertain power grids
Direct energy methods have been extensively developed for the transient stability analysis and contingency screening of power grids. However, there is no analytical energy functions proposed for power grids with losses, which are normal in practice. This paper applies the recently introduced Lyapunov Functions Family approach to the certification of synchronization stability for lossy power grids. This technique does not rely on the global decreasing of the Lyapunov function as in the direct energy methods, and thus is possible to deal with the lossy power grids. We show that this approach is also applicable to uncertain power grids where the stable equilibrium is unknown due to possible uncertainties in system parameters. We formulate this new control problem and introduce techniques to certify the robust stability of a given initial state with respect to a set of equilibria
Geometry-based Estimation of Stability Region for A Class of Structure Preserving Power Grids
The increasing development of the electric power grid, the largest engineered
system ever, to an even more complicated and larger system requires a new
generation of stability assessment methods that are computationally tractable
and feasible in real-time. In this paper we first extend the recently
introduced Lyapunov Functions Family (LFF) transient stability assessment
approach, that has potential to reduce the computational cost on large scale
power grids, to structure-preserving power grids. Then, we introduce a new
geometry-based method to construct the stability region estimate of power
systems. Our conceptual demonstration shows that this new method can certify
stability of a broader set of initial conditions compared to the
minimization-based LFF method and the energy methods (closest UEP and
controlling UEP methods)
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
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
Analytic solution to swing equations in power grids with ZIP Load Models
Objective: This research pioneers a novel approach to obtain a closed-form
analytic solution to the nonlinear second order differential swing equation
that models power system dynamics. The distinctive element of this study is the
integration of a generalized load model known as a ZIP load model (constant
impedance Z, constant current I, and constant power P loads)