Search arXivSearch

arXiv · 2312.03576

Operational Resilience Assessment: A Frequency-Domain Approach for DC Microgrids

Abstract

DC shipboard microgrids (SMGs) are highly dynamic systems susceptible to failure due to various cyber-physical disturbances, such as extreme weather and mission operations during wartime. In this paper, the real-time operational resilience (OR) evaluation of DC SMGs against dynamic disturbances is proposed using frequency-domain metrics. To this end, first the drawbacks of time-domain OR evaluation using an energy imbalance index is discussed. As the time-domain energy imbalance index is shown to be incapable of real-time OR assessment, particularly in the context of droop-controlled DC SMGs without secondary voltage restoration control, the $\mathcal{H}_2$ and $\mathcal{H_\infty}$ norms of candidate transfer functions (TFs) of the system are proposed as measures of resilience. It is shown that the proposed norms calculated for the bus impedance TF of the system provides intuitive results in terms of energy imbalance and can be computed in real time. The case studies conducted for the study DC SMG under pulsed power load (PPL) disturbances demonstrate the shortcoming of the time-domain OR evaluation and the capability of the proposed frequency-domain metrics in intuitive OR evaluation of DC SMGs.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ali Hosseinipour, Maral Shadaei, Javad Khazaei. 2023-12-06. Operational Resilience Assessment: A Frequency-Domain Approach for DC Microgrids. https://arxiv.org/abs/2312.03576

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Constrained Feedback Control of Nonlinear Systems via Approximate HJB and Control Barrier Functions

This paper presents a two-stage framework for constrained feedback control of input-affine nonlinear systems. Offline, an approximate value function for the unconstrained problem is computed, for example using Hamilton--Jacobi--Bellman (HJB)-based policy iteration. Online, the proposed quadratic program (QP) minimizes the pre-Hamiltonian evaluated using the approximate value-function gradient subject to safety constraints enforced by control barrier functions (CBFs). This architecture decouples performance optimization from constraint enforcement, allowing constraints to be modified without recomputing the value function. As in CBF-QP architectures based on control Lyapunov functions (CLFs), safety is enforced as a hard constraint; however, the performance objective targets approximate optimality rather than a prescribed Lyapunov decay. Numerical results on a linear 2-state hovercraft and a nonlinear 9-state spacecraft attitude-control problem show agreement with the constrained open-loop optimal control problem (OCP) benchmark in the linear case, and performance close to the OCP benchmark, improving on CLF-based controllers, in the nonlinear case.

eess.SY

Rao-Blackwellized Stein Gradient Descent for Joint State-Parameter Estimation

We present a filtering framework for online joint state estimation and parameter identification in nonlinear, time-varying systems. The algorithm uses a Rao-Blackwellization technique to infer joint state-parameter posteriors efficiently. In particular, conditional state distributions are computed analytically via Kalman filtering, while model parameters, including the measurement-noise covariance, are approximated using particle-based Stein Variational Gradient Descent (SVGD), enabling stable real-time inference. To handle parameters subject to physical constraints, we further introduce constrained variants that enforce them through an alternating direction method of multipliers (ADMM) splitting of the SVGD update, including nonlinear equality constraints that standard particle filters cannot readily handle. We derive a stability bound that relates the approximation error in the parameter posterior to the resulting error in the marginal state distribution. Performance of the proposed filters is validated on three case studies: a fed-batch bioreactor with Haldane kinetics and a damped pendulum, both under physical constraints, and a neural-network-augmented dynamic system. The examples cover parameter estimation under inequality and equality constraints and online neural-network training within a dynamical model.

eess.SY

Firing Rate Neural Network Implementations of Model Predictive Control

Human and animal brains perform planning to enable complex movements and behaviors, a process that can be effectively described using model predictive control (MPC). How could the brain physically implement MPC? In this work, we translate model predictive controllers into firing rate neural networks, offering insights into the nonlinear neural dynamics that underpin planning. We propose a constructive method; no training is required. This is done first applying the projected gradient method to the dual problem to derive a baseline neural network implementation. We then use factorization and contraction analysis to systematically generate alternative network architectures; in other words, we systematically generate hypotheses for how planning is done in the brain via neural dynamics. Finally, we present numerical simulations to study different neural networks performing MPC to balance an inverted pendulum on a cart (i.e., balancing a stick on a hand), including one example in which imposing sparse connectivity (a property observed in brain networks) does not degrade control performance.

eess.SY