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The energy transition is causing many stability-related challenges for power systems. Transient stability refers to the ability of a power grid's bus angles to retain synchronism after the occurrence of a major fault. In this paper a…
Transient stability assessment of power systems needs to account for increased risk from uncertainties due to the integration of renewables and distributed generators. The uncertain operating condition of the power grid hinders reliable…
The transition to a new low emission energy future results in a changing mix of generation and load types due to significant growth in renewable energy penetration and reduction in system inertia due to the exit of ageing fossil fuel power…
Small signal analysis is a special case of analytical approaches using Taylor expansions of power system differential equations with the truncation performed at order one. The truncated Taylor expansions (TTEs) at higher orders can lead to…
Transient growth analysis has been extensively studied in asymptotically stable flows to identify their short-term amplification of perturbations. Generally, in global transient growth analyses, matrix-free methods are adopted, requiring…
In this work, it is demonstrated that the usual power system dynamic model exhibits a feedforward-feedback control structure. The distinct properties of the feedforward and feedback subsystems are identified and studied using respective…
Systems far from equilibrium approach stability slowly due to "anti-mixing" characterized by regions of the phase-space that remain disconnected after prolonged action of the flow. We introduce the Optimal Growth Mode (OGM) to capture this…
Traditional centralized stability analysis struggles with scalability in large complex modern power grids. This two-part paper proposes a compositional and equilibrium-free approach to analyzing power system stability. In Part I, we prove…
Recent works have established the utility of sparsity-promoting norms for extracting spatially-localized instability mechanisms in fluid flows, with possible implications for flow control. However, these prior works have focused on linear…
This paper assesses the transient stability of a synchronous machine connected to an infinite bus through the notion of invariant sets. The problem of computing a conservative approximation of the maximal positive invariant set is…
Power systems are getting more complex than ever and are consequently operating close to their limit of stability. Moreover, with the increasing demand of renewable wind generation, and the requirement to maintain a secure power system, the…
The theory of transient growth describes how linear mechanisms can cause temporary amplification of disturbances even when the linearized system is asymptotically stable as defined by its eigenvalues. This growth is traditionally quantified…
This paper proposes a new approach to perform small-signal stability analysis based on linearization of implicit multilinear models. Multilinear models describe the system dynamics by multilinear functions of state, input, and algebraic…
Dynamic simulation plays a crucial role in power system transient stability analysis, but traditional numerical integration-based methods are time-consuming due to the small time step sizes. Other semi-analytical solution methods, such as…
Nonlinear modal decoupling (NMD) was recently proposed to nonlinearly transform a multi-oscillator system into a number of decoupled oscillators which together behave the same as the original system in an extended neighborhood of the…
This two-part paper proposes a compositional and equilibrium-free approach to analyzing power system stability. In Part I, we have established the stability theory and proposed stability conditions based on the delta dissipativity. In Part…
Power systems are globally experiencing an unprecedented growth in size and complexity due to the advent of nonconventional generation and consumption technologies. To navigate computational complexity, power system dynamic models are often…
Power distribution systems are becoming much more active with increased penetration of distributed energy resources. Because of the intermittent nature of these resources, the stability of distribution systems under large disturbances and…
This work analyzes accelerating and decelerating wall-driven flows by quantifying the upper bound of transient energy growth using a Lyapunov-type approach. By formulating the linearized Navier-Stokes equations as a linear time-varying…
Transient stability is crucial to the reliable operation of power systems. Existing theories rely on the simplified electromechanical models, substituting the detailed electromagnetic dynamics of inductor and capacitor with their impedance…