Related papers: Voltage Stability Studies for Distribution Network…
The paper considers some class of dynamical systems that called density systems. For such systems the derivative of quadratic function depends on so-called density function. The density function is used to set the properties of phase space,…
Many critical infrastructure systems have network structure and are under stress. Despite their national importance, the complexity of large-scale transport networks means we do not fully understand their vulnerabilities to cascade…
We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multi-dimensional focusing nonlinear media with a potential (lattice), which can be periodic,…
Inverter-based distributed energy resources facilitate the advanced voltage control algorithms in the online setting with the flexibility in both active and reactive power injections. A key challenge is to continuously track the…
This paper considers the problem of voltage regulation in distribution networks. The primary motivation is to keep voltages within preassigned operating limits by commanding the reactive power output of distributed energy resources (DERs)…
With the sharp increase of power demand, large-scale blackouts in power grids occur frequently around the world. Cascading failures are the main causes of network outages. Therefore, revealing the complicated cascade mechanism in grids is…
We review selected results related to robustness of networked systems in finite and asymptotically large size regimes, under static and dynamical settings. In the static setting, within the framework of flow over finite networks, we discuss…
In this paper, the impact of stochastic load and renewable generation uncertainty on the dynamic voltage stability margin is studied. Stochastic trajectories describing the uncertainty of load, wind and solar generation have been…
This work considers stochastic operators in general inner-product spaces, and in particular, systems with stochastically time-varying input delays of a known probability distribution. Stochastic dissipativity and stability are defined from…
The energy mix of future power systems will include high shares of wind power and solar PV. These generation facilities are generally connected via power-electronic inverters. While conventional generation responds dynamically to the state…
Signaling molecules play an important role for many cellular functions. We investigate here a general system of two membrane reaction-diffusion equations coupled to a diffusion equation inside the cell by a Robin-type boundary condition and…
Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction--diffusion theory, which connects cellular signalling and transport…
The concept of Turing instability, namely that diffusion can destabilize the uniform steady state, is well known either in the context of partial differential equations (PDEs) or in networks of dynamical systems. Recently reaction-diffusion…
This paper proposes a nonlinear, adaptive controller to increase the stability margin of a direct-current (DC) small-scale electrical network containing a constant power load, whose value is unknown. Due to their negative incremental…
A dynamic mitigation mechanism for instability growth was proposed and discussed in the paper [Phys. Plasmas 19, 024503 (2012)]. In the present paper the robustness of the dynamic instability mitigation mechanism is discussed further. The…
We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random directed graphs with a prescribed distribution of indegrees and outdegrees. We obtain two remarkable results for such…
This paper develops a dynamic monetary model to study the (in)stability of the fractional reserve banking system. The model shows that the fractional reserve banking system can endanger stability in that equilibrium is more prone to exhibit…
We consider the dynamics of a smart grid system characterized by widespread distributed generation and storage devices. We assume that agents are free to trade electric energy over the network and we focus on the emerging market dynamics.…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
In distribution systems, power injection variability due to growing penetrations of distributed energy resources (DERs) and dispatchable loads can lead to power quality issues such as severe voltage unbalance. To ensure the safe operation…