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In recent years, several applications have been proposed in the context of distribution networks. Many of these can be formulated as an optimal power flow problem, a mathematical optimization program which includes a model of the…
Forecasting over graph-structured sensor networks demands models that capture both deterministic spatial trends and stochastic variability, while remaining efficient enough for repeated inference as new observations arrive. We propose…
As power systems transition toward renewable-rich and inverter-dominated operations, accurate time-domain dynamic analysis becomes increasingly critical. Such analysis supports key operational tasks, including transient stability…
This paper addresses the problem of voltage regulation in power distribution networks with deep-penetration of distributed energy resources, e.g., renewable-based generation, and storage-capable loads such as plug-in hybrid electric…
In this paper, we address the well-posedness of an evaporation model for a spherical liquid droplet taking into account the convective impact of an air flow in the ambient gas phase. From a mathematical perspective, we are dealing with a…
As power systems become more complex and uncertain, low-voltage distribution networks face numerous challenges, including three-phase imbalances caused by asymmetrical loads and distributed energy resources. We propose a robust stochastic…
We present a method for the approximate propagation of mean and covariance of a probability distribution through ordinary differential equations (ODE) with discontinous right-hand side. For piecewise affine systems, a normalization of the…
Deep Learning models possess two key traits that, in combination, make their use in the real world a risky prospect. One, they do not typically generalize well outside of the distribution for which they were trained, and two, they tend to…
Compartmental ordinary differential equation (ODE) models are used extensively in mathematical biology. When transit between compartments occurs at a constant rate, the well-known linear chain trick can be used to show that the ODE model is…
The way in which electric power depends on the topology of circuits with mixed voltage and current sources is examined. The power flowing in any steady-state DC circuit is shown to depend on a minimal set of key variables called fundamental…
Conventional optimal power flow (OPF) solvers assume full observability of the involved system states. However, in practice, there is a lack of reliable system monitoring devices in the distribution networks. To close the gap between the…
Out-of-distribution (OOD) detection is a crucial part of deploying machine learning models safely. It has been extensively studied with a plethora of methods developed in the literature. This problem is tackled with an OOD score…
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…
The concept of passivity is central to analyze circuits as interconnections of passive components. We illustrate that when used differentially, the same concept leads to an interconnection theory for electrical circuits that switch and…
We develop a system-theoretic framework for the structured analysis of distributed optimization algorithms with decomposable cost functions. We model such algorithms as a network of interacting dynamical systems and derive tests for…
Distributed vertical power delivery has emerged as a promising approach to meet aggressive current-density, efficiency, and transient response requirements in high-performance computing systems. Tight integration of voltage regulators…
The non-linearity and non-convexity of power flow models and the phase coupling challenge the analysis and optimization of unbalanced distribution networks. To tackle the challenges, this paper proposes an online feedback-based linearized…
The growing integration of distributed energy resources (DERs) in distribution grids raises various reliability issues due to DER's uncertain and complex behaviors. With a large-scale DER penetration in distribution grids, traditional…
We propose a hierarchical distributed algorithm to solve optimal power flow (OPF) problems that aim at dispatching controllable distributed energy resources (DERs) for voltage regulation at minimum cost. The proposed algorithm features…
We analyze a system of nonlinear stochastic partial differential equations (SPDEs) of mixed elliptic-parabolic type that models the propagation of electric signals and their effect on the deformation of cardiac tissue. The system governs…