Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2401.16703

Plane Wave Dynamic Model of Electric Power Networks with High Shares of Inverter-Based Resources

Amirhossein Sajadi·Bri-Mathias Hodge
View original source ↗Read source document ↗Export metadata ↓

Abstract

Contemporary theories and models for electric power system stability are predicated on a widely held assumption that the mechanical inertia of the rotating mass of synchronous generators provides the sole contribution to stable and synchronized operation of this class of complex networks on subsecond timescales. Here we formulate the electromagnetic momentum of the field around the transmission lines that transports energy and present evidence from a real-world bulk power network that demonstrates its physical significance. We show the classical stability model for power networks that overlooks this property, known as the "swing equation", may become inadequate to analyze systems with high shares of inverter-based resources, commonly known as "low-inertia power systems". Subsequently, we introduce a plane wave dynamic model, consistent with the structural properties of emerging power systems with up to 100% inverter-based resources, which identifies the concept of inertia in power grids as a time-varying component. We leverage our theory to discuss a number of open questions in the electric power industry. Most notably, we postulate that the changing nature of power networks with a preponderance of variable renewable energy power plants could strengthen power network stability in the future; a vision which is irreconcilable with the conventional theories.

Explore related subjects

eess.SYcs.SY

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Amirhossein Sajadi, Bri-Mathias Hodge. 2024-01-30. Plane Wave Dynamic Model of Electric Power Networks with High Shares of Inverter-Based Resources. https://arxiv.org/abs/2401.16703

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

KEEP EXPLORING

Related papers

arXiv2026

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↗
arXiv2026

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↗
arXiv2026

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↗