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Joint Optimization of Maintenance and Production in Offshore Wind Farms: Balancing the Short- and Long-Term Needs of Wind Energy Operation. (arXiv:2303.06174v1 [eess.SY]) arxiv.org/abs/2303.06174

Joint Optimization of Maintenance and Production in Offshore Wind Farms: Balancing the Short- and Long-Term Needs of Wind Energy Operation

The rapid increase in scale and sophistication of offshore wind (OSW) farms poses a critical challenge related to the cost-effective operation and management of wind energy assets. A defining characteristic of this challenge is the economic trade-off between two concomitant processes: power production (the primary driver of short-term revenues), and asset degradation (the main determinant of long-term expenses). Traditionally, approaches to optimize production and maintenance in wind farms have been conducted in isolation. In this paper, we conjecture that a joint optimization of those two processes, achieved by rigorously modeling their short- and long-term dependencies, can unlock significant economic benefits for wind farm operators. In specific, we propose a decision-theoretic framework, rooted in stochastic optimization, which seeks a sensible balance of how wind loads are leveraged to harness short-term electricity generation revenues, versus alleviated to hedge against longer-term maintenance expenses. Extensive numerical experiments using real-world data confirm the superior performance of our approach, in terms of several operational performance metrics, relative to methods that tackle the two problems in isolation.

arxiv.org

Deflated HeteroPCA: Overcoming the curse of ill-conditioning in heteroskedastic PCA. (arXiv:2303.06198v1 [math.ST]) arxiv.org/abs/2303.06198

Deflated HeteroPCA: Overcoming the curse of ill-conditioning in heteroskedastic PCA

This paper is concerned with estimating the column subspace of a low-rank matrix $\boldsymbol{X}^\star \in \mathbb{R}^{n_1\times n_2}$ from contaminated data. How to obtain optimal statistical accuracy while accommodating the widest range of signal-to-noise ratios (SNRs) becomes particularly challenging in the presence of heteroskedastic noise and unbalanced dimensionality (i.e., $n_2\gg n_1$). While the state-of-the-art algorithm $\textsf{HeteroPCA}$ emerges as a powerful solution for solving this problem, it suffers from "the curse of ill-conditioning," namely, its performance degrades as the condition number of $\boldsymbol{X}^\star$ grows. In order to overcome this critical issue without compromising the range of allowable SNRs, we propose a novel algorithm, called $\textsf{Deflated-HeteroPCA}$, that achieves near-optimal and condition-number-free theoretical guarantees in terms of both $\ell_2$ and $\ell_{2,\infty}$ statistical accuracy. The proposed algorithm divides the spectrum of $\boldsymbol{X}^\star$ into well-conditioned and mutually well-separated subblocks, and applies $\textsf{HeteroPCA}$ to conquer each subblock successively. Further, an application of our algorithm and theory to two canonical examples -- the factor model and tensor PCA -- leads to remarkable improvement for each application.

arxiv.org
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