Search arXivSearch

arXiv · 2503.09028

Degradation-based Energy Management for Microgrids in the Presence of Energy Storage Elements

Abstract

Integration of Inverter-based Resources (IBRs) such as solar-powered plants which lack the intrinsic characteristics such as the inertial response of the traditional synchronous-generator (SG) based sources presents a new challenge in the form of analyzing the grid stability under their presence. For example, solar power is available for approximately from 9 AM-5 PM. However, the result of the rise in power consumption after 6 PM and the reverting back to the non-renewable source of power generation during that period puts immense stress on the grid, testing the ramp limitations of the SGs. Failure to meet the required power demand due to SG ramp limitations leads to failure of the power grid and other catastrophes. Numerous mitigation techniques exist in order to address the ramping issues with adding the energy storage elements (ESE) to the grid being one. ESEs have higher ramping capabilities compared to the traditional SGs. Also, the ESEs can store the energy and supply it to the grid when required making them extremely responsive to high ramp situations. However, the rate of degradation of the ESEs is faster than the SGs. This raises an important issue of addressing the degradation of the ESEs while meeting the required power demand objectives and constraints. This work proposes a battery degradation-aware model predictive energy management strategy and it is tested via a numerical simulation on multiple physical systems such as Shipboard Power Systems (SPS). Moreover, the risk arising due to the fault in the IBR is also studied by means of a numerical simulation. Overall, the goal of this study is to make the existing power grid more robust, resilient, and risk-free from component degradation and eventual failures.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Satish Vedula. 2025-03-25. Degradation-based Energy Management for Microgrids in the Presence of Energy Storage Elements. https://arxiv.org/abs/2503.09028

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

KEEP EXPLORING

Related papers

Dynamic Programming-Compatible Uncertainty Sets in Robust Markov Decision Processes

In this paper, we investigate the compatibility of robust Markov Decision Processes (RMDPs) with dynamic programming under various assumptions on the uncertainty set, i.e., we investigate when one can solve an RMDP by solving a fixed point equation. We show that in all generality, s-rectangular and sa-rectangular uncertainty sets are the only models of uncertainty that are compatible with dynamic programming. Our analysis shows that existing non-rectangular models, including r-rectangularity, are only weakly compatible with dynamic programming, as they require the assumption that rewards do not depend on the next state. In this case, our results imply that one can always construct a rectangular uncertainty set that is equivalent, for both policy evaluation and optimization, to the dynamic programming-compatible non-rectangular model. This highlights a key limitation: dynamic-programming-compatible non-rectangular uncertainty sets, although practically relevant for uncertainty quantification, do not provide a genuinely distinct assessment of policy performance. Interestingly, our proof techniques rely on identifying a novel simultaneous solvability property, which we show is central to several important properties of RMDPs, including the existence of stationary optimal policies and dynamic programming-based formulations. The simultaneous solvability property enables a unified approach to studying all existing models of uncertainty, rectangular and non-rectangular alike.

math.OC

A simple and practical adaptive trust-region method

We present an adaptive trust-region method for unconstrained optimization that allows inexact solutions to the trust-region subproblems. Our method is a simple variant of the classical trust-region method of Ssorensen. The method achieves the best possible convergence bound up to an additive logarithmic term for finding an $ε$-approximate stationary point, i.e., $O( Δ_f L^{1/2} ε^{-3/2}) + \tilde{O}(1)$ iterations, where $L$ is the Lipschitz constant of the Hessian, $Δ_f$ is the optimality gap, and $ε$ is the termination tolerance for the gradient norm. This improves over existing trust-region methods whose worst-case bound is at least a factor of $L$ worse. We compare our performance with state-of-the-art trust-region (TRU) and cubic regularization (ARC) methods from the GALAHAD library on the CUTEst benchmark problems with at least 100 variables. We also compare with the recently developed Universal trust-region (UTR) method, using the same subproblem solver. In terms of shifted geometric mean of wall-clock times our method's is between $1.2\times$ and $2\times$ faster. We report similar improvements for number of function evaluations, factorizations, gradient evaluations and Hessian evaluations. Compared to the conference version of this paper, our revised method includes several practical enhancements. These modifications dramatically improved performance, including almost an order of magnitude reduction in the shifted geometric mean of wall-clock times. We also show that it suffices for the function to be continuously twice-differentiable to guarantee that either the minimum gradient norm converges to zero or the objective value tends towards negative infinity, even when the iterates diverge.

math.OC

Rough Stochastic Pontryagin Maximum Principle and an Indirect Shooting Method

We derive first-order Pontryagin optimality conditions for stochastic optimal control with deterministic controls for systems modeled by rough differential equations (RDE) driven by Gaussian rough paths. This Pontryagin Maximum Principle (PMP) applies to systems following stochastic differential equations (SDE) driven by Brownian motion, yet it does not rely on forward-backward SDEs and involves the same Hamiltonian as the deterministic PMP. The proof consists of first deriving various integrable error bounds for solutions to nonlinear and linear RDEs by leveraging recent results on Gaussian rough paths. The PMP then follows using standard techniques based on needle-like variations. As an application, we propose the first indirect shooting method for nonlinear stochastic optimal control and show that it converges 10x faster than a direct method on a stabilization task.

math.OC