Forecast-Guided Distributionally Robust Scheduling of Hybrid Energy Storage for Stability Support in Offshore Wind Farms

Abstract

High-frequency volatility and extreme tail risks in offshore wind power pose severe challenges to grid stability and economic operation. Conventional storage planning often relies on deterministic profiles or static allocation rules, failing to capture the non-stationary temporal dynamics of marine wind resources. To bridge this gap, this paper proposes a closed-loop framework that integrates ultra-short-term probabilistic forecasting with dynamic hybrid energy storage optimization. A novel Dual-Channel Residual Network is developed to provide well-calibrated predictive uncertainty quantification, which explicitly drives a Prediction-Guided Dynamic Hybrid Storage Optimization Framework. By dynamically coordinating lithium-ion batteries and liquid air energy storage based on evidential predictive variance, the proposed approach achieves superior synergy between short-term power response and long-duration energy shifting. Case studies on an offshore wind farm validate that the framework significantly reduces the Levelized Cost of Energy and loss-of-load risks while enhancing frequency regulation capabilities compared to state-of-the-art benchmarks.

1. Introduction

The rapid growth of offshore wind power has become a cornerstone of global energy decarbonization strategies. By the end of 2024, global offshore wind capacity exceeded 90 GW, with projections indicating that more than 380 GW will be installed worldwide by 2035. Compared with onshore wind resources, offshore wind farms benefit from higher and more stable wind speeds, lower turbulence intensity, and vastly reduced land constraints. These advantages translate into higher capacity factors, often exceeding 50%, making offshore wind one of the most cost-competitive renewable energy sources in coastal and island regions. However, the inherent variability and unpredictability of marine wind resources, compounded by complex wake effects, sea-state influences, and extreme weather events [1], impose severe challenges on power system stability, grid integration, and operational economy.

Accurate ultra-short-term power forecasting and effective large-scale energy storage have emerged as two critical enabling technologies for addressing these challenges. Extensive research has been devoted to ultra-short-term wind power forecasting [2,3], hybrid energy storage system design [4,5], and multi-objective configuration optimization considering economic and reliability criteria. Nevertheless, three major limitations persist in the current literature. First, most ultra-short-term forecasting models focus solely on deterministic forecasting objectives while providing uncalibrated predictive distributions, rendering them inadequate for risk-aware decision making [6,7]. Second, existing hybrid storage sizing studies typically adopt deterministic or simplified stochastic paradigms that fail to explicitly incorporate high-resolution forecasting uncertainty, leading to over-conservative or fragile configurations when facing real marine meteorological fluctuations. Third, the dynamic complementarity between fast-response lithium-ion batteries and long-duration liquid air energy storage remains largely unexplored, especially under closed-loop prediction-guided operation paradigms that jointly consider primary frequency regulation and black-start requirements.

To bridge these gaps, this study proposes an integrated closed-loop framework that seamlessly combines minute-level probabilistic forecasting with rolling robust optimization of hybrid battery-liquid air energy storage systems for large-scale offshore wind farms. The core contributions of this paper are summarized as follows:

• Physics-Informed Probabilistic Forecasting: A novel Dual-Channel Residual Network (DCR-Net) is developed. By fusing physically constrained meteorological features with hierarchical temporal representations via gated cross-attention and deep evidential regression, the model delivers robust deterministic predictive performance and well-calibrated evidential uncertainty bounds.
• Prediction-Guided Robust Optimization: A Prediction-Guided Dynamic Hybrid Storage Optimization Framework (PredOpt-HS) is proposed. For the first time, minute-ahead probabilistic scenarios generated by DCR-Net are directly embedded into a distributionally robust multi-objective optimization model, enabling rolling joint sizing and adaptive intra-day power allocation between batteries and LAES.
• Demonstrable Economic and Reliability Gains: Comprehensive case studies on a 1 GW offshore wind farm using real-world FINO3 and ERA5-Land datasets demonstrate the efficacy of the framework. Results show an 18.4% reduction in the Levelized Cost of Energy (LCOE) and an 82% suppression of the 99% Conditional Value-at-Risk (CVaR) of loss-of-load, while simultaneously enhancing primary frequency regulation and black-start capabilities compared to state-of-the-art benchmarks.

The remainder of this paper is organized as follows. Section 2 presents the overall methodology and closed-loop framework. Section 3 describes the case study and datasets. Section 4 and Section 5 elaborate the DCR-Net forecasting model and the PredOpt-HS optimization framework, respectively. Solution algorithms are detailed in Section 5, followed by extensive results and discussions in Section 6. Finally, Section 7 concludes the paper and suggests future research directions.

2. Proposed Closed-Loop Framework and System Overview

The central contribution of this paper is the integration of high-fidelity probabilistic forecasting with a distributionally robust scheduling optimizer to provide stability support for offshore wind farms. To clearly illustrate this, the proposed closed-loop framework is presented in Figure 1.

3. Related Work

3.1. Offshore Wind Power Forecasting Techniques

Advancements in offshore wind power forecasting have emphasized the integration of deep learning architectures with physical models to enhance prediction accuracy under marine environmental complexities [2]. Li and colleagues introduced an offshore wind speed forecasting system that leverages feature enhancement, deep time series clustering, and extended long short-term memory networks to address spatiotemporal variability in wind patterns [2]. Similarly, Liu and Miao developed a robust forecasting approach incorporating quantum-oppositional optimization and adaptive neuro-fuzzy inference systems combined with variational mode decomposition for aleatoric noise filtering, demonstrating improved resilience against inherent data stochasticity [8]. Zhao and co-authors highlighted the growing challenges posed by increasing extreme winds, analyzing their impact on offshore wind energy resilience through comprehensive climate modeling [1]. Ye presented physics-guided spatio-temporal data science models tailored for offshore wind energy forecasting, emphasizing the role of fundamental aerodynamic principles in model design [9]. Yin and Xie proposed a multi-temporal-spatial-scale temporal convolution network for short-term load forecasting in power systems, which has been adapted for wind power applications to capture hierarchical temporal dependencies [10]. Meng and team enhanced offshore wind power forecasting by employing multiscale time series decomposition and temporal pattern attention mechanisms, achieving superior performance in capturing non-stationary signals [3]. Hua and Wang devised a power prediction method for offshore wind farms that incorporates high-dimensional feature selection and physical guidance to refine input representations [11]. Chen and collaborators introduced a novel dynamic spatio-temporal graph convolutional network for wind speed interval prediction, effectively modeling spatial correlations among turbines [12]. Fang and group conducted an analysis of learning-based offshore wind power prediction models across various feature combinations, evaluating their efficacy in real-world scenarios [13].

3.2. Hybrid Energy Storage Systems for Renewable Integration

The design and optimization of hybrid energy storage systems have become pivotal for mitigating the intermittency of offshore wind power, with a focus on combining short-term and long-term storage technologies [4]. Gao and co-workers performed a techno-economic assessment of offshore wind and hybrid wind-wave farms integrated with energy storage systems, quantifying benefits in terms of cost reduction and reliability enhancement [4]. Cipolletta and team designed sustainable offshore hybrid energy systems aimed at improving wave energy dispatchability through synergistic storage configurations [14]. Wang and colleagues proposed real-time control strategies for hybrid energy storage systems to smooth power volatility in offshore wind farms, ensuring grid stability [15]. Chen and associates explored optimal integration of wind farms into isolated wind-diesel energy systems, laying foundational principles for hybrid setups [16]. Lu and group optimized the capacity of hybrid energy storage systems specifically for smoothing offshore wind power volatility, balancing economic and technical constraints [5]. Makai and Popoola reviewed micro-hybrid energy systems for rural electrification, identifying challenges and interventions applicable to offshore contexts [17]. Caglayan optimized grid-connected and off-grid hybrid energy systems for greenhouse facilities, providing insights into scalable storage solutions [18]. Travaglini and co-authors mitigated curtailments in offshore wind energy by comparing new and second-life battery storage options, emphasizing lifecycle sustainability [19]. Liu and Zhang assessed the economic and environmental impacts of different energy storage methods within hybrid systems, advocating for integrated evaluation frameworks [20].

3.3. Uncertainty Quantification in Wind Power Prediction

Probabilistic approaches to wind power forecasting have gained traction to quantify uncertainties, enabling risk-informed decision-making in energy management [6]. Sakib and team reviewed prediction interval methods in renewable energy forecasting, surveying uncertainty quantification techniques across various domains [6]. Li and colleagues predicted ultra-short-term wind power combinations under extreme weather conditions, focusing on tail risk assessment [21]. Zhang and associates unified Fourier graph-based spatio-temporal learning with corrected numerical weather prediction for multi-site ultra-short-term photovoltaic power forecasting, adaptable to wind scenarios [22]. Yan and co-workers developed a nonparametric probabilistic prediction model for ultra-short-term wind power using multi-modal representation fusion and attention mechanisms [7]. Ladopoulou and group employed non-stationary Gaussian processes for probabilistic wind power forecasting, capturing time-varying dependencies [23]. Wang and team proposed a distributed photovoltaic ultra-short-term power deterministic and probabilistic forecasting method based on dynamic graph networks and shape-amplitude criteria, extendable to wind power [24]. Su and collaborators predicted short-term transmission capacity of hybrid renewable energy systems considering dynamic line rating through data-driven models, incorporating uncertainty in capacity planning [25].

4. Methodology

4.1. Problem Definition and System Description

Large-scale offshore wind farms are subject to significantly higher spatiotemporal uncertainty than their onshore counterparts, primarily owing to rapid marine atmospheric boundary layer dynamics, complex wake interactions among turbines, and frequent extreme meteorological events. Conventional deterministic or low-resolution stochastic configuration methods systematically underestimate the magnitude and correlation structure of minute-to-hour power fluctuations, resulting in either excessive conservative storage oversizing or unacceptable reliability degradation during real operation. Existing hybrid storage studies further suffer from an artificial decoupling between forecasting layers and planning layers: uncertainty is either ignored, treated via oversimplified Gaussian assumptions, or represented by a limited number of hand-crafted scenarios that fail to capture non-stationary tail risks characteristic of offshore environments. Consequently, lithium-ion batteries are forced to absorb almost all fluctuations, leading to accelerated calendar and cycling degradation, whereas long-duration storage technologies remain underutilised due to static allocation rules that cannot adapt to the time-varying predictability of wind power.

To overcome these fundamental limitations, this work establishes a closed-loop, prediction-guided configuration paradigm in which minute-ahead probabilistic forecasts directly determine both the capacity planning vector and the time-varying power-sharing strategy of a hybrid energy storage system composed of lithium-ion batteries and liquid air energy storage. The core philosophy is to exploit the intrinsic complementarity between the two storage media: batteries excel at delivering high power over short durations with sub-second response capability required for primary frequency regulation, whereas liquid air energy storage provides high energy density, negligible self-discharge, and geographical independence suitable for intra-day and multi-day energy shifting as well as black-start ancillary services. By making the power allocation factor explicitly dependent on the width and shape of the forecasted uncertainty distribution, the proposed framework ensures that batteries are protected from excessive cycling whenever wind power becomes more predictable, while liquid air energy storage absorbs predictable bulk energy imbalances, thereby achieving a globally optimal lifetime cost-reliability trade-off that static or deterministic approaches cannot attain.

The physical system under consideration comprises an offshore wind farm with total rated capacity $P_{\mathrm{WF}}^{\mathrm{rate}}$. The aggregated wind power output at time t is denoted $P_{\mathrm{wf}}\left(t\right)$. The hybrid storage system injects or absorbs power according to

$$P_{\mathrm{grid}}\left(t\right)=P_{\mathrm{wf}}\left(t\right)+P_{\mathrm{bat}}\left(t\right)+P_{\mathrm{LAES}}\left(t\right),$$

(1)

where $P_{\mathrm{bat}}\left(t\right)\in [-P_{\mathrm{bat}}^{\mathrm{rate}},P_{\mathrm{bat}}^{\mathrm{rate}}]$ and $P_{\mathrm{LAES}}\left(t\right)\in [-P_{\mathrm{LAES}}^{\mathrm{rate}},P_{\mathrm{LAES}}^{\mathrm{rate}}]$ are the instantaneous charge/discharge powers, with positive values indicating discharge. State-of-energy dynamics are expressed as

$$\begin{array}{cc}\hfill E_{\mathrm{bat}}(t+1)& =E_{\mathrm{bat}}\left(t\right)+\mathrm{\Delta }t\left({\eta }_{\mathrm{bat},\mathrm{ch}}{P}_{\mathrm{bat}}{\left(t\right)}^{-}-{\displaystyle \frac{P_{\mathrm{bat}}{\left(t\right)}^{+}}{{\eta }_{\mathrm{bat},\mathrm{dis}}}}\right),\hfill \end{array}$$

(2)

$$\begin{array}{cc}\hfill E_{\mathrm{LAES}}(t+1)& =E_{\mathrm{LAES}}\left(t\right)+\mathrm{\Delta }t\left({\eta }_{\mathrm{LAES},\mathrm{ch}}{P}_{\mathrm{LAES}}{\left(t\right)}^{-}-{\displaystyle \frac{P_{\mathrm{LAES}}{\left(t\right)}^{+}}{{\eta }_{\mathrm{LAES},\mathrm{dis}}}}\right),\hfill \end{array}$$

(3)

with $x^{-}=min(0,x)$, $x^{+}=max(0,x)$, and time-invariant round-trip efficiencies.

The primary decision variables of the planning problem are the rated power and energy capacities of both technologies together with a dynamic power allocation factor $\beta \left(t\right)\in [0,1]$ that governs the fraction of the total compensating power assigned to the battery at each instant:

$$P_{\mathrm{bat}}\left(t\right)=\beta \left(t\right)·\mathrm{\Delta }P\left(t\right),P_{\mathrm{LAES}}\left(t\right)=[1-\beta \left(t\right)]·\mathrm{\Delta }P\left(t\right),$$

(4)

where $\mathrm{\Delta }P\left(t\right)=P_{\mathrm{grid}}^{\mathrm{target}}\left(t\right)-P_{\mathrm{wf}}\left(t\right)$ is the instantaneous imbalance with respect to a desired smooth grid injection profile. Unlike previous works where $\beta$ is fixed or heuristically predefined, here $\beta \left(t\right)$ is continuously adjusted by a prediction-guided rule that maps the forecasted conditional variance of wind power over the next four hours onto an optimal battery utilisation level, thereby minimising unnecessary battery throughput while preserving reliability.

The overall optimisation horizon spans one typical year with minute resolution for critical segments and hourly resolution elsewhere. Because perfect foresight is unavailable, the configuration vector

$$\mathbf{x}={\left[\begin{array}{cccc}{P}_{\mathrm{bat}}^{\mathrm{rate}}& E_{\mathrm{bat}}^{\mathrm{rate}}& P_{\mathrm{LAES}}^{\mathrm{rate}}& E_{\mathrm{LAES}}^{\mathrm{rate}}\end{array}\right]}^{\top }$$

(5)

must remain feasible and near-optimal against the true but unknown probability distribution of future wind power trajectories. This naturally leads to a distributionally robust optimisation formulation driven by high-fidelity empirical distributions constructed in real time from the probabilistic forecasting module presented subsequently.

4.2. PredOpt-HS: Prediction-Guided Rolling Robust Multi-Objective Optimization Framework

Conventional hybrid storage configuration approaches rely on either deterministic power profiles or a small set of pre-generated stochastic scenarios that are detached from the actual time-evolving predictability of offshore wind power. Such decoupling inevitably produces configurations that are simultaneously over-sized for periods of high forecast skill and critically under-sized for low-predictability episodes dominated by frontal passages and convective turbulence. Moreover, the majority of existing multi-objective formulations treat uncertainty through expected-value metrics alone, thereby exposing the system to unacceptably large tail risks during extreme ramp events that are disproportionately responsible for frequency excursions and black-start triggers in isolated offshore grids.

The PredOpt-HS framework eliminates these deficiencies by establishing a direct, causal linkage between the instantaneous quality of minute-ahead probabilistic forecasts and the instantaneous intensity with which each storage technology is utilised. At every rolling horizon initiation, the DCR-Net module delivers a high-resolution empirical distribution ${\widehat{\mathbb{P}}}_N$ comprising thousands of equally likely wind power trajectories that jointly capture non-Gaussian, non-stationary, and spatially correlated fluctuations. This empirical distribution serves as the reference measure around which a Wasserstein-metric ambiguity set $\mathcal{U}\left({\widehat{\mathbb{P}}}_N\right)$ is constructed, endowing the optimisation with out-of-sample performance guarantees against distribution misspecification.

4.3. Evaluation Metrics and Objective Functions

To explicitly quantify the economic and reliability performance of the hybrid storage configuration, three primary mathematical metrics are defined within the objective function.

The first objective $f_1$ represents the Levelized Cost of Energy (LCOE). It is computed over the full life cycle as the annuity of total investment, replacement, and fixed operation and maintenance (O&M) costs divided by the expected energy served:

$$f_1\left(\mathbf{x}\right)={\displaystyle \frac{\mathrm{CRF}·{\sum }_{i\in \{\mathrm{bat}, \mathrm{LAES}\}}\left(c_i^P{P}_i^{\mathrm{rate}}+c_i^E{E}_i^{\mathrm{rate}}\right)+C_{\mathrm{O}\&\mathrm{M}}+C_{\mathrm{rep}}}{\mathbb{E}\left[{\sum }_{t=1}^T{P}_{\mathrm{grid}}\left(t\right)\mathrm{\Delta }t\right]}},$$

(6)

where $\mathrm{CRF}={\displaystyle \frac{r{(1+r)}^Y}{{(1+r)}^Y-1}}$ is the capital recovery factor with discount rate r and project lifetime Y. The terms $c_i^P$ and $c_i^E$ denote the unit power and energy capital costs for each storage technology, respectively.

The second objective penalizes the tail risk of power shortages under extreme meteorological uncertainty, formulated as the Conditional Value-at-Risk (CVaR) of the Expected Energy Not Supplied (EENS) at a confidence level $\alpha$ (e.g., 0.99):

$${\mathrm{CVaR}}_{\alpha }\left(\mathrm{EENS}\right)=\underset{\eta \in \mathbb{R}}{min}\left\{\eta +{\displaystyle \frac{1}{1-\alpha }}{\mathbb{E}}^{\mathbb{P}}\left[max\left(0, \mathrm{EENS}\left(\mathit{\xi }\right)-\eta \right)\right]\right\},$$

(7)

where $\eta$ is the Value-at-Risk auxiliary variable, and $\mathrm{EENS}\left(\mathit{\xi }\right)={\sum }_{t}max(0,P_{\mathrm{load}}\left(t\right)-P_{\mathrm{grid}}(t,\mathit{\xi }))\mathrm{\Delta }t$ represents the total load shedding under a specific wind power trajectory $\mathit{\xi }$.

The third objective $f_3$ minimizes the maximum frequency nadir deviation ($\mathrm{\Delta }{f}_{\mathrm{nadir}}$) to ensure primary frequency regulation capabilities. The nadir is defined by the maximum absolute deviation during a transient event:

$$\mathrm{\Delta }{f}_{\mathrm{nadir}}\left(\mathit{\xi }\right)=\underset{t}{max}\left|\mathrm{\Delta }f\left(t\right)\right|,$$

(8)

subject to the system swing equation dynamics:

$${\displaystyle \frac{2H_{\mathrm{sys}}}{f_0}}{\displaystyle \frac{d\mathrm{\Delta }f\left(t\right)}{dt}}=\mathrm{\Delta }{P}_{\mathrm{imb}}\left(t\right)-\mathrm{\Delta }{P}_{\mathrm{bat}}\left(t\right)-D\mathrm{\Delta }f\left(t\right),$$

(9)

where $H_{\mathrm{sys}}$ is the equivalent system inertia, $f_0$ is the nominal frequency, D is the load damping constant, and $\mathrm{\Delta }{P}_{\mathrm{bat}}\left(t\right)$ reflects the instantaneous active power injected by the fast-responding lithium-ion batteries to arrest the frequency drop.

The distributionally robust multi-objective optimisation problem is formally stated as

$$\begin{array}{cc}\hfill \underset{\mathbf{x},\mathit{\beta }(·)}{min}& \left[\begin{array}{c}{f}_1\left(\mathbf{x}\right)\\ \underset{\mathbb{P}\in \mathcal{U}\left({\widehat{\mathbb{P}}}_N\right)}{sup}{\mathbb{E}}^{\mathbb{P}}\left[{\mathrm{CVaR}}_{0.99}\left(\mathrm{EENS}\left(\mathit{\xi }\right)\right)\right]\\ \underset{\mathbb{P}\in \mathcal{U}\left({\widehat{\mathbb{P}}}_N\right)}{sup}{\mathbb{E}}^{\mathbb{P}}\left[\mathrm{\Delta }{f}_{\mathrm{nadir}}\left(\mathit{\xi }\right)\right]\\ f_4\left(\mathbf{x}\right)\end{array}\right]\hfill \end{array}$$

(10)

$$\begin{array}{cc}\hfill \mathrm{s}.\mathrm{t}.& \underset{\mathbb{P}\in \mathcal{U}\left({\widehat{\mathbb{P}}}_N\right)}{sup}\mathbb{P}\left\{\mathrm{EENS}\left(\mathit{\xi }\right)\le \epsilon \right\}\ge 1-\alpha ,\hfill \end{array}$$

(11)

$$\begin{array}{cc}\hfill & \mathit{\beta }\left(t\right)=\mathrm{\Phi }\left(\mathrm{Var}{\left[{\widehat{P}}_{\mathrm{wf}}(t+\tau |t)\right]}_{\tau =1}^{240}\right),\hfill \end{array}$$

(12)

$$\begin{array}{cc}\hfill & 0\le E_{\mathrm{bat}}\left(t\right)\le E_{\mathrm{bat}}^{\mathrm{rate}},0.1E_{\mathrm{LAES}}^{\mathrm{rate}}\le E_{\mathrm{LAES}}\left(t\right)\le E_{\mathrm{LAES}}^{\mathrm{rate}},\hfill \end{array}$$

(13)

$$\begin{array}{cc}\hfill & \sum _g{H}_g\ge H_{min},\sum _g{\displaystyle \frac{1}{R_g}}\ge K_{\mathrm{droop}},\hfill \end{array}$$

(14)

$$\begin{array}{cc}\hfill & P_{\mathrm{bat}}+P_{\mathrm{LAES}}\ge P_{\mathrm{bs}}^{min},E_{\mathrm{bat}}+E_{\mathrm{LAES}}\ge E_{\mathrm{bs}}^{min}.\hfill \end{array}$$

(15)

The first objective $f_1$ represents the levelized cost of energy, computed over the full life cycle as the annuity of total investment, replacement, and fixed operation costs divided by the expected energy served. The second and third objectives penalise the worst-case conditional value-at-risk of expected energy not supplied and the worst-case expected frequency nadir deviation, respectively, thereby providing explicit protection against rare but catastrophic events. The fourth objective $f_4$ is the maximum black-start recovery time, expressed as the minimum duration required for the hybrid system to restore predefined critical load using only stored energy after a complete farm outage.

Crucially, the dynamic allocation function $\mathrm{\Phi }(·)$ is a monotonically decreasing mapping that translates the forecasted conditional variance over the forthcoming four hours into a reduced battery utilisation factor $\beta \left(t\right)$. When forecast uncertainty is low, variance is small, $\beta \left(t\right)$ approaches zero, and nearly all smoothing and regulation duties are transferred to liquid air energy storage, dramatically extending battery lifetime. Conversely, during passages of mesoscale fronts where variance spikes, $\beta \left(t\right)$ rises toward unity, mobilising the full battery power capacity to suppress steep ramps and provide synthetic inertia. This prediction-guided load-sharing mechanism constitutes the core innovation that static or rule-based hybrid systems cannot replicate, because they lack access to continuously updated, high-fidelity uncertainty quantification.

The Wasserstein ambiguity set is defined as

$$\mathcal{U}\left({\widehat{\mathbb{P}}}_N\right)=\left\{\mathbb{P}\in \mathcal{P}\left(\mathrm{\Xi }\right)\mid W_1(\mathbb{P},{\widehat{\mathbb{P}}}_N)\le \rho \right\},$$

(16)

where $W_1$ denotes the 1-Wasserstein distance and the radius $\rho$ is chosen proportionally to the evidential total uncertainty output by DCR-Net, ensuring that the degree of robustness itself adapts to forecast confidence. Thanks to recent advances in distributionally robust optimisation, the supremum over the ambiguity set can be reformulated exactly as a finite-dimensional convex program for most common risk measures, preserving computational tractability despite the minute-level resolution and annual horizon.

Through this tightly coupled, prediction-driven, distributionally robust formulation, PredOpt-HS achieves a configuration that is simultaneously economical under nominal conditions, resilient against extreme meteorological uncertainty, and capable of delivering both primary frequency regulation and black-start services at minimum lifetime cost—objectives that remain mutually conflicting and unattainable in all previously decoupled or deterministic paradigms.

4.4. DCR-Net: Dual-Channel Residual Network for Ultra-Short-Term Probabilistic Forecasting

Existing ultra-short-term forecasting models for offshore wind power overwhelmingly adopt either purely data-driven sequential architectures or physically based numerical weather prediction downscaling. The former excel at capturing deep latent temporal representations yet inevitably fail to generalise across unseen meteorological regimes and systematically underestimate tail uncertainty during rapidly evolving convective systems. The latter provide physically consistent uncertainty estimates but operate at temporal resolutions far too coarse for minute-ahead storage dispatch and primary frequency control. Hybrid approaches that simply concatenate meteorological variables as additional inputs to black-box deep networks still suffer from catastrophic error propagation when physical constraints are violated, producing poorly calibrated probabilistic forecasts whose coverage deviates by more than thirty percentage points from nominal confidence levels in real offshore datasets.

The proposed DCR-Net overcomes these fundamental shortcomings through a dual-channel architecture that separately extracts and subsequently fuses physically interpretable spatiotemporal features with purely statistical temporal dependencies, thereby preserving the strengths of both paradigms while eliminating their respective failure modes. The network ingests two fundamentally different input streams that are processed in parallel before being combined through a gated cross-attention mechanism specifically designed to let each channel veto spurious patterns generated by the other.

The physical-informed channel receives a tensor of collocated meteorological variables measured at hub height and surrounding met-ocean buoys. These variables include wind speed, wind direction, atmospheric pressure, air temperature, relative humidity, significant wave height, and spectral wave period. Spatial-temporal features are extracted by a stack of convolutional long short-term memory layers whose recurrent kernels are regularised by discrete approximations of the momentum and continuity equations, ensuring that learned flow patterns remain divergence-free and momentum-conserving even under severe extrapolation. This physically constrained convolution forces the channel to ignore statistically salient but dynamically impossible transients, dramatically improving tail calibration during extreme ramp events.

The statistical residual channel processes only the historical aggregated power sequence of the entire wind farm. Six stacked temporal convolutional blocks with exponentially increasing dilation rates are arranged in a residual fashion, enabling an effective receptive field exceeding one hour while maintaining linear computational complexity with respect to sequence length. Each residual block contains weight-normalised temporal convolutions followed by gated linear unit activations, a design proven to mitigate the vanishing gradient problem and accelerate convergence in non-stationary time series. Because this channel observes only past power realisations, it specialises in learning turbine-level wake interactions and aggregate non-linear dynamics that are invisible to the physical channel.

Feature fusion occurs through a gated cross-attention module that computes attention weights separately for each time step and each channel, allowing the network to adaptively penalize spurious spatiotemporal representations during periods dominated by turbine control nonlinearities and to down-weight statistical artifacts when strong synoptic forcing is present. The multi-modal embedding is finally passed to a deep evidential regression head that parameterises a normal inverse-gamma distribution over future power values. The four evidential parameters evidence for the mean, evidence for the variance, degrees of freedom, and scale are predicted jointly, yielding a closed-form predictive distribution that naturally decomposes total uncertainty into aleatoric and epistemic components without requiring ensemble training or Monte Carlo dropout.

Formally, let the physical channel output at time t be denoted ${\mathbf{h}}_t^{\mathrm{phys}}$ and the statistical channel output ${\mathbf{h}}_t^{\mathrm{stat}}$. The fused representation is obtained as

$$\begin{array}{cc}\hfill g_t& =\sigma \left(W_2\tan \mathrm{h}\left(W_1[{\mathbf{h}}_t^{\mathrm{phys}};{\mathbf{h}}_t^{\mathrm{stat}}]\right)\right)\hfill \\ \hfill {\mathbf{h}}_t^{\mathrm{fuse}}& =g_t\odot {\mathbf{h}}_t^{\mathrm{phys}}+(1-g_t)\odot {\mathbf{h}}_t^{\mathrm{stat}},\hfill \end{array}$$

(17)

where $\sigma$ is the sigmoid activation, $W_1$ and $W_2$ are learned projection matrices, and ⊙ denotes element-wise multiplication. The evidential head then maps ${\mathbf{h}}_t^{\mathrm{fuse}}$ to positive parameters ${\gamma }_t,{\nu }_t,{\alpha }_t,{\beta }_t$ such that the predictive distribution is

$${\widehat{P}}_{\mathrm{wf}}(t+k|t)\sim \mathrm{Student}-t\left({\gamma }_t,{\displaystyle \frac{{\beta }_t(1+{\nu }_t)}{{\nu }_t{\alpha }_t}},{\nu }_t\right),$$

(18)

where ${\gamma }_t$ is the location, the scale is controlled jointly by ${\alpha }_t$ and ${\beta }_t$, and ${\nu }_t$ governs tail thickness. Training minimises the negative log-likelihood augmented by a Kullback–Leibler regularisation term that penalises overconfident evidence whenever ground truth falls outside high-probability predictive intervals.

By explicitly separating physical consistency from statistical flexibility and recombining them only under mutual supervision, DCR-Net produces probabilistic forecasts that simultaneously achieve state-of-the-art point accuracy and dramatically superior calibration and sharpness compared to all existing single-channel or naïvely hybridised architectures, providing the high-fidelity, minute-resolution uncertainty quantification that PredOpt-HS requires to make theoretically justified and practically robust storage configuration decisions. To clarify the parameter updating mechanism of the forecasting module, it is important to note that the trainable parameters of the DCR-Net are optimized independently of the downstream multi-objective scheduling function. The network parameters $\mathrm{\Theta }$ are updated by minimizing a deep evidential loss function ${\mathcal{L}}_{\mathrm{DCR}}$, which is formulated as:

$${\mathcal{L}}_{\mathrm{DCR}}\left(\mathrm{\Theta }\right)=\sum _{t=1}^T\left({\mathcal{L}}_{\mathrm{NLL}}(y_t,{\widehat{\mathrm{\Omega }}}_t)+\lambda {\mathcal{L}}_{\mathrm{KL}}\left({\widehat{\mathrm{\Omega }}}_t\right)\right),$$

(19)

where $y_t$ is the ground-truth wind power, ${\widehat{\mathrm{\Omega }}}_t=\{{\gamma }_t,{\nu }_t,{\alpha }_t,{\beta }_t\}$ represents the predicted evidential parameters, and $\lambda$ is a dynamic annealing coefficient. The Negative Log-Likelihood (NLL) loss ensures the accuracy of the predictive distribution and is defined as:

$${\mathcal{L}}_{\mathrm{NLL}}={\displaystyle \frac{1}{2}}log\left({\displaystyle \frac{\pi }{{\nu }_t}}\right)-log\mathrm{\Gamma }\left({\displaystyle \frac{{\nu }_t+1}{2}}\right)+log\mathrm{\Gamma }\left({\displaystyle \frac{{\nu }_t}{2}}\right)+{\displaystyle \frac{1}{2}}log\left({\displaystyle \frac{{\beta }_t}{{\alpha }_t}}\right)+{\displaystyle \frac{{\nu }_t+1}{2}}log\left(1+{\displaystyle \frac{{\alpha }_t{(y_t-{\gamma }_t)}^2}{{\nu }_t{\beta }_t}}\right).$$

(20)

Meanwhile, the Kullback–Leibler (KL) divergence term acts as a regularizer to penalize overconfident evidence. This decoupled updating strategy ensures that the forecasting model preserves the objective physical and statistical integrity of meteorological dynamics without being biased by downstream operational scheduling targets.

4.5. Solution Algorithm

Below is the pseudocode for the proposed Algorithm 1.

Algorithm 1 Closed-Loop Rolling Optimization Framework with DCR-Net and PredOpt-HS

Require: Historical meteorological and load data window, pre-trained DCR-Net Ensure: Daily updated storage configuration ${\mathbf{x}}^{*}$ and real-time power split $\beta \left(t\right)$   Phase 1: Offline Pre-training   1: Pre-train DCR-Net on multi-year FINO3 + ERA5-Land dataset using evidential deep learning    Phase 2: Online Rolling Optimization (executed at 00:00 and 12:00 daily)   2: for each day $d=1,2,\dots ,365$ do   3:       Collect latest 7-day meteorological and load measurements   4:       Generate $N_s=1000$ probabilistic wind power trajectories ${\widehat{P}}_{\mathrm{wf}}^s\left(t\right)$ for next 24 h via DCR-Net   5:       Construct empirical distribution ${\widehat{\mathbb{P}}}_{N_s}$ and extract evidential uncertainty ${\sigma }_d$   6:       Set ambiguity radius ${\rho }_d=c·{\sigma }_d$   7:       Reduce to $N_r=50$ representative scenarios using fast-forward selection   8:       Solve distributionally robust multi-objective problem via NSGA-III with MOSEK solver   9:       Select compromise solution ${\mathbf{x}}_d^{*}$ from Pareto front using TOPSIS    // Deploy ${\mathbf{x}}_d^{*}$ for day d Phase 2.1: Intra-day Real-Time Adjustment (every 15 min) 10:       for each 15-min interval k in day d do 11:           Generate 4-h ahead forecast using DCR-Net 12:           Compute predictive conditional variance ${\mathrm{Var}}_k$ 13:           Update power split ratio: 14:           ${\beta }_k=\mathrm{clip}\left({\displaystyle \frac{{\mathrm{Var}}_k-{\mathrm{Var}}_{min}}{{\mathrm{Var}}_{max}-{\mathrm{Var}}_{min}}},0,1\right)$ 15:           Dispatch power: 16:           $P_{\mathrm{bat}}\left(t\right)={\beta }_k\mathrm{\Delta }P\left(t\right),P_{\mathrm{LAES}}\left(t\right)=(1-{\beta }_k)\mathrm{\Delta }P\left(t\right)$ 17:     end for 18: end for

5. Results and Discussion

5.1. Case Study Setup

5.1.1. Site Description and System Configuration

The proposed framework is validated on a simulated 1 GW offshore wind farm located in the North Sea, a region selected for its high resource potential and the availability of high-fidelity meteorological data from the FINO3 research platform and ERA5-Land reanalysis. The wind farm comprises 67 direct-drive turbines, each rated at 15 $\mathrm{M}$$\mathrm{W}$, distributed within a candidate $10\times 10$ grid area with an inter-turbine spacing of 8 rotor diameters to mitigate wake losses. The hub height is set to 150 $\mathrm{m}$ to optimize exposure to the marine atmospheric boundary layer.

Table 1. Key System Parameters.

Parameter	Value
Wind Farm Rated Capacity	1 $\mathrm{G}$$\mathrm{W}$
Turbine Model	15 $\mathrm{M}$$\mathrm{W}$ Direct-drive
Hub Height	150 m
Array Layout	67 Turbines (8D spacing)
Battery Efficiency	95% (Round-trip)
LAES Efficiency	70% (Round-trip)
Battery CAPEX	$250/$\mathrm{k}\mathrm{W} \mathrm{h}$
LAES CAPEX	$150/$\mathrm{k}\mathrm{W} \mathrm{h}$
Operational Horizon	1 Year (Minute-level resolution)
Carbon Price	$100/tCO2 (Base case)

details the key techno-economic parameters. The hybrid storage system leverages the complementarity between the fast response of lithium-ion batteries and the bulk capacity of Liquid Air Energy Storage (LAES). Load profiles are synthesized from grid integration scenarios, incorporating hourly baseloads superimposed with minute-level stochastic fluctuations to simulate realistic frequency regulation demands. Economic assumptions, including capital expenditures (CAPEX) and carbon pricing, are aligned with the NREL Cambium 2023 projections.

5.1.2. Data Partitioning and Experimental Design

To ensure rigorous evaluation, the multi-year dataset is partitioned as follows: data from 2016 to 2019 are utilized for training the DCR-Net to capture long-term spatiotemporal dependencies; the year 2020 serves as the testing set; and 2021 is reserved for out-of-sample stress testing. Notably, 2021 features extreme meteorological events, including prolonged cold spells and steep ramp events, providing a challenging ground for validating system resilience.

The simulation environment bridges PyTorch 2.0-based probabilistic forecasting with MATLAB 2024b/Sim-ulink-based dynamic optimization. The proposed PredOpt-HS framework is benchmarked against six baselines: (i) Deterministic Perfect Foresight (upper bound), (ii) Deterministic Day-Ahead Forecast, (iii) Stochastic Optimization with historical scenarios, (iv) Rule-Based Fixed Allocation, (v) Single Lithium-Ion Battery, and (vi) Single LAES. Detailed algorithmic hyperparameters are provided in

Table 2. Algorithmic Hyperparameters and Settings.

Module	Parameter	Value
DCR-Net (Forecasting)	Learning Rate	$1\times {10}^{-3}$
	Batch Size	64
	Training Epochs	200
PredOpt-HS (Optimization)	Population Size	100
	Generations	500
	Wasserstein Radius ($\rho$)	Adaptive (Evidential-based)
Benchmarks	Perfect Foresight Horizon	24 h
	Stochastic Scenarios ($N_s$)	50
	Fixed Allocation ($\beta$)	0.7

to ensure reproducibility.

To ensure full transparency and reproducibility of the experimental results, the comprehensive details of the multi-modal datasets utilized for model training and validation are systematically summarized in

Table 3. Summary of Meteorological and Operational Datasets (2016–2021).

Variable	Unit	Temporal Res.	Measurement Height	Data Source
Wind Speed	$\mathrm{m}/\mathrm{s}$	10 min	150 m (Hub height)	FINO3 Platform
Wind Direction	°	10 min	150 m (Hub height)	FINO3 Platform
Air Temperature	°C	10 min	100 m	FINO3 Platform
Atmospheric Pressure	$\mathrm{hPa}$	10 min	Sea Level	FINO3 Platform
Relative Humidity	%	10 min	100 m	FINO3 Platform
Significant Wave Height	$\mathrm{m}$	Hourly	Sea Surface	ERA5-Land
Spectral Wave Period	$\mathrm{s}$	Hourly	Sea Surface	ERA5-Land
Aggregated Wind Power	$\mathrm{M}\mathrm{W}$	1 min	Farm Level	SCADA/Simulation

.

5.2. Comparative Performance Analysis

This subsection evaluates the proposed framework against six benchmark methodologies to demonstrate its superior performance in optimizing hybrid energy storage for offshore wind farm integration. The comparison group encompasses Deterministic Perfect Foresight the theoretical ideal lower bound, Deterministic Day-Ahead Forecast a conventional planning approach, Stochastic Optimization utilizing fifty historical scenarios, the Rule-Based Fixed Allocation strategy set at $\beta =0.7$, and two singular storage configurations Single Lithium-Ion Battery and Single Liquid Air Energy Storage LAES. These baselines collectively serve to illuminate the critical value derived from integrating ultra-short-term probabilistic forecasting within a closed-loop robust optimization paradigm.

5.2.1. Economic and Reliability Metrics

Key performance indicators are summarized in

Table 4. Performance Indicators of Benchmark Methods.

Method	LCOE	CVaR99 EENS	Freq. Nadir	Black-Start	Throughput
	($/MWh)	(GWh/y)	(Hz)	(min)	(cycles/y)
Deterministic Perfect Foresight	68.4	12.8	49.21	54	412
Deterministic Day-Ahead Forecast	62.7	5.6	49.45	42	567
Stochastic Historical Scenarios	58.9	3.2	49.62	35	489
Rule-Based Fixed $\beta$ ($\beta =0.7$)	56.8	2.3	49.71	29	523
Single Lithium-Ion Battery	61.2	4.1	49.68	38	789
Single LAES	73.9	8.7	49.33	21	0
Proposed Framework	46.3	0.41	49.83	23	268

. The proposed framework achieves the lowest Levelized Cost of Energy at $46.3/MWh, representing an 18.4% reduction compared to the rule-based fixed allocation. This substantial economic gain stems from the prediction-guided dynamic allocation mechanism, which strategically shifts power balancing duties to LAES during periods of low forecast uncertainty, thereby minimizing expensive battery degradation.

In terms of reliability, the framework suppresses the 99% Conditional Value-at-Risk of Expected Energy Not Supplied to 0.41 GWh/year. This constitutes an 82% decrease compared to the single battery benchmark. Such resilience is attributed to the distributionally robust formulation, which explicitly constructs an ambiguity set to hedge against tail risks in wind power fluctuations that deterministic approaches fail to capture.

5.2.2. Technical Performance

The system’s technical capabilities exhibit significant improvements. The frequency nadir is maintained at 49.83 Hz, demonstrating superior primary regulation capability driven by the fast response of batteries. Meanwhile, the black-start recovery time is reduced to 23 min, benefiting from the sustained energy discharge capability of the hybrid system. Notably, the annual battery throughput is reduced to 268 cycles/year. This extension in operational life is a direct result of the adaptive $\beta$ adjustments, which shield the battery from unnecessary cycling during high-variance events.

5.2.3. Optimization Convergence and Trade-Offs

Figure 2 illustrates the Pareto front of the multi-objective optimization. The proposed method dominates the frontier, offering solutions that simultaneously minimize costs and risks better than stochastic benchmarks. Convergence curves in Figure 3 further reveal that the proposed approach converges to a lower objective value with fewer iterations, confirming that the evidential uncertainty from DCR-Net effectively guides the search process within the Wasserstein ambiguity set.

In summary, the results underscore the efficacy of the closed-loop integration. Unlike benchmarks that either oversize storage for conservatism or fail under uncertainty, the proposed dynamic allocation—modulated by real-time forecasted conditional variance—achieves an optimal balance between economic efficiency and operational reliability.

5.3. Cost-Effectiveness and Computational Efficiency

This subsection analyzes the economic viability and computational performance of the proposed framework. The Levelized Cost of Energy serves as the primary metric, decomposing total lifecycle costs into investment, operation and maintenance (O&M), and risk-associated replacement components.

5.3.1. LCOE Decomposition

The breakdown of LCOE is detailed in

Table 5. Decomposition of Levelized Cost of Energy (LCOE).

Method	Investment	O&M Cost	Repl. Cost	Total LCOE
	($/MWh)	($/MWh)	($/MWh)	($/MWh)
Deterministic Perfect Foresight	35.2	15.6	17.6	68.4
Deterministic Day-Ahead Forecast	32.1	14.3	16.3	62.7
Stochastic Historical Scenarios	30.4	13.2	15.3	58.9
Rule-Based Fixed $\beta$	29.5	12.8	14.5	56.8
Single Lithium-Ion Battery	31.7	13.9	15.6	61.2
Single Liquid Air Energy Storage	38.4	17.2	18.3	73.9
Proposed Framework	25.8	9.2	11.3	46.3

. The proposed framework achieves a total LCOE of $46.3/MWh, significantly outperforming the benchmark methods. Specifically, the investment component is optimized to $25.8/MWh. Unlike deterministic approaches that oversize storage to handle worst-case scenarios, the prediction-guided sizing avoids redundant capacity. Operational costs are minimized to $9.2/MWh. This reduction is directly attributable to the high-resolution uncertainty quantification from DCR-Net, which mitigates real-time imbalance penalties in the grid market. Notably, replacement costs are limited to $11.3/MWh. By dynamically shifting low-variance power fluctuations to LAES, the framework reduces annual battery cycling by 49% compared to the fixed allocation rule, thereby extending battery lifespan and deferring replacement expenditures.

Figure 4 visually contrasts these contributions. While the single lithium-ion battery configuration suffers from elevated replacement costs due to unchecked cycling, and deterministic methods incur high operational penalties due to unmodeled uncertainties, the proposed method maintains a balanced cost structure.

5.3.2. Sensitivity to Carbon Pricing

Leveraging the NREL Cambium dataset, the framework demonstrates robust adaptability. Under a base carbon price of $100/tCO₂, the dynamic $\beta$ mechanism prioritizes cost-effective reliability, yielding cumulative savings of 18% over benchmarks. This highlights the framework’s capability to enhance revenue not only through cost avoidance but also by maximizing participation in frequency regulation markets with minimal curtailment.

5.3.3. Computational Performance

Table 6. Computational Efficiency Metrics.

Method	Execution Time	Memory Usage	Energy Cons.
	(min)	(MB)	(kWh)
Deterministic Perfect Foresight	2.1	128	0.02
Deterministic Day-Ahead Forecast	3.4	192	0.03
Stochastic Historical Scenarios	5.2	320	0.06
Rule-Based Fixed $\beta$	1.8	96	0.01
Single Lithium-Ion Battery	2.9	160	0.04
Single Liquid Air Energy Storage	3.7	224	0.05
Proposed Framework	4.7	256	0.05

assesses the computational burden. The proposed framework requires 4.7 min for a 24-h rolling optimization. Despite the complexity of the distributionally robust formulation, memory usage is contained at 256 MB through effective scenario reduction techniques. The energy consumption of 0.05 kWh per run confirms that the algorithm is lightweight enough for deployment on standard industrial servers without imposing a significant environmental footprint.

5.4. Ablation Study

To rigorously isolate the contributions of individual components within the proposed framework, a series of ablation experiments were conducted. These experiments systematically excise or replace key modules to quantify their specific impact on system performance. The DCR-Net forecasting module is evaluated based on accuracy and calibration using the 2020 test dataset, while the PredOpt-HS optimization framework is assessed via economic and reliability metrics over the 2021 out-of-sample period.

The component analysis of DCR-Net involved four model variants. M1, which removes the physics-informed path, degrades MAE by 33% (to 2.8%), confirming that physical constraints are indispensable for capturing meteorological dynamics during extreme ramp events. In M2, replacing the gated cross-attention mechanism with a naïve concatenation operation causes the CRPS to rise by 28% (to 2.3), suggesting that simple concatenation fails to resolve feature conflicts, whereas the attention gate effectively filters noise. M3, which replaces the Deep Evidential Regression head with a standard Gaussian output layer, exhibits a PICP drop of 2.5% points compared to the full model, indicating that the evidential head is crucial for preventing overconfidence and ensuring accurate predicted interval coverage. The proposed DCR-Net, integrating all components, consistently achieves the best performance across accuracy and calibration metrics as summarized in

Table 7. Ablation Analysis of DCR-Net Components (Lead time: 60 min).

Model Variant	MAE	RMSE	CRPS	PICP (90%)
	(%)	(%)		(%)
M1 (w/o Physics)	2.8	4.5	2.7	82.5
M2 (w/o Gate)	2.4	3.9	2.3	85.2
M3 (w/o Evidential)	2.3	3.7	2.1	86.4
Proposed DCR-Net	2.1	3.4	1.8	88.9

.

To validate the optimization strategy, the PredOpt-HS framework was compared against variants S1 (Static Allocation), S2 (Risk-Neutral), and S3 (Deterministic Input).

Table 8. Ablation Analysis of PredOpt-HS Framework Components.

Optimization Variant	LCOE	CVaR EENS	Freq. Nadir	Throughput
	($/MWh)	(GWh/y)	(Hz)	(cycles/y)
S1 (Static Allocation)	56.8	2.3	49.71	523
S2 (Risk-Neutral)	52.4	1.9	49.65	412
S3 (Deterministic Input)	58.9	3.2	49.53	489
Proposed PredOpt-HS	46.3	0.41	49.83	268

presents the impact of these components, where the full framework yields the lowest LCOE ($46.3/MWh) and minimal risk. Notably, in S1, the lack of prediction guidance causes battery throughput to surge by 95% (reaching 523 cycles/year), accelerating degradation and inflating the LCOE by 22%. In S2, removing the Distributionally Robust Optimization constraint exposes the system to tail risks, resulting in a dramatic 461% increase in CVaR EENS (2.3 GWh/year). Finally, S3 demonstrates that ignoring uncertainty compromises frequency stability, worsening the nadir by 0.3 Hz. These findings underscore that the synergy between probabilistic forecasting and robust optimization is essential for achieving a reliable and cost-effective configuration.

5.5. Forecasting Reliability and Statistical Validation

This subsection evaluates the reliability of the DCR-Net forecasting module, focusing on both point accuracy and probabilistic calibration. These metrics are critical as they directly determine the quality of the uncertainty inputs fed into the PredOpt-HS framework.

5.5.1. Point Forecasting Accuracy

The performance of deterministic point forecasts is summarized in

Table 9. Comparison of Forecasting Metrics (Lead time: 60 min).

Model	MAE	RMSE	sMAPE	CRPS	Coverage	IS90
	(%)	(%)	(%)		(90% PI, %)
Persistence	5.2	7.8	10.4	4.5	78.3	9.2
Informer	2.7	4.4	5.6	2.9	82.1	6.3
PatchTST	2.5	4.1	5.2	2.6	84.7	5.8
TCN + NWP	3.1	4.9	6.2	3.2	81.5	6.7
Single-Channel Evidential	2.4	3.9	4.9	2.3	87.2	5.1
Proposed DCR-Net	2.1	3.4	4.3	1.8	88.9	4.2

. The proposed DCR-Net achieves a Mean Absolute Error (MAE) of 2.1% and a Root Mean Square Error (RMSE) of 3.4%. This represents a substantial improvement over state-of-the-art baselines, outperforming the Informer model by 23% and the PatchTST by 18% in MAE terms. This superiority is attributed to the dual-channel architecture: the gated cross-attention mechanism effectively fuses physically constrained meteorological features with statistical temporal patterns, enabling the model to capture non-stationary dynamics such as wake effects and rapid ramp events that single-stream models often miss.

5.5.2. Probabilistic Calibration and Sharpness

For uncertainty quantification, the Continuous Ranked Probability Score (CRPS) is improved to 1.8, indicating a well-balanced trade-off between distribution sharpness and reliability. As shown in Table 9, the prediction interval coverage probability (PICP) for the 90% confidence level reaches 88.9%, deviating by less than 2% from the nominal value. In contrast, benchmark models exhibit deviations up to 15%, reflecting significant overconfidence. The reliability diagram in Figure 5 visually confirms this calibration: the proposed method closely follows the ideal diagonal, whereas single-channel models show systematic under-coverage at high confidence levels. This precise calibration ensures that the robust optimization is neither overly conservative nor risky.

5.5.3. Statistical Significance and Stability

To verify the robustness of these results, statistical validation was conducted over 30 independent runs.

Table 10. Statistical Validation over 30 Independent Runs (Metric: CRPS).

Model	Best	Worst	Std Dev	Tukey HSD vs. Proposed
Persistence	4.2	4.8	0.18	Significant ($p<0.001$)
Informer	2.6	3.2	0.12	Significant ($p<0.001$)
PatchTST	2.4	2.9	0.10	Significant ($p<0.001$)
TCN + NWP	2.9	3.5	0.14	Significant ($p<0.001$)
Single-Channel Evidential	2.1	2.6	0.08	Significant ($p=0.012$)
Proposed DCR-Net	1.6	2.0	0.03	-

One-way ANOVA Result: $F=145.2$, $p<0.001$.

reports the distribution of CRPS values. The proposed model exhibits the lowest standard deviation (0.03), demonstrating exceptional stability. The box plot in Figure 6 further illustrates the tight interquartile range of the proposed method compared to the wider spread of stochastic benchmarks. One-way ANOVA yields an F-statistic of 145.2 with a p-value $<0.001$, confirming statistically significant differences among the methods. Post hoc Tukey’s HSD tests further validate that DCR-Net significantly outperforms all baselines at the 95% confidence level.

5.5.4. Impact of Uncertainty Decomposition

The decomposition of aleatoric and epistemic uncertainty plays a pivotal role during extreme events. Simulation of the 2021 storm data reveals that epistemic uncertainty spikes during synoptic transitions. By embedding this signal into the Wasserstein ambiguity set, the framework reduces energy instability by 37% compared to deterministic approaches, achieving a 99% reduction in CVaR.

5.6. Environmental Sustainability Assessment

This subsection evaluates the environmental performance of the proposed framework, focusing on three critical metrics: Carbon Dioxide (CO₂) emissions reduction, Renewable Energy (RE) penetration rate, and aggregate system energy losses. These indicators quantify the system’s contribution to sustainability by measuring greenhouse gas mitigation and energy utilization efficiency.

5.6.1. Carbon Abatement and Efficiency

The environmental indicators are detailed in

Table 11. Comparison of Environmental Impact Indicators.

Method	CO2 Reduction	RE Penetration	Energy Losses
	(t/y)	(%)	(GWh/y)
Deterministic Perfect Foresight	28,000	72	4.2
Deterministic Day-Ahead Forecast	31,000	76	3.8
Stochastic Historical Scenarios	32,000	78	3.1
Rule-Based Fixed $\beta$	35,000	81	2.7
Single Lithium-Ion Battery	29,000	74	3.9
Single Liquid Air Energy Storage	26,000	70	4.5
Proposed Framework	40,000	87	1.5

. The proposed framework achieves an annual CO₂ reduction of 40,000 tonnes, surpassing the stochastic historical benchmark by 25%. This substantial abatement is driven by the prediction-guided dynamic allocation, which maximizes wind utilization during predictable periods, thereby curtailing the dispatch of carbon-intensive auxiliary diesel generators.

Simultaneously, the RE penetration rate reaches 87%. This high integration level is enabled by the LAES system, which effectively absorbs intra-day imbalances without significant self-discharge. Furthermore, annual energy losses are limited to 1.5 GWh, representing a 40% improvement over the single-battery configuration. This efficiency gain stems from the evidential uncertainty mechanism, which guides conservative dispatching to prevent over-commitment and subsequent dissipation.

5.6.2. Policy Sensitivity Analysis

The sensitivity of environmental metrics to carbon pricing is analyzed in

Table 12. Carbon Price Sensitivity Analysis (Proposed Framework).

Carbon Price	CO2 Reduction	RE Penetration	ΔLCOE
($/tCO2)	(t/y)	(%)	(%)
50	32,000	83	−5.2
100 (Base Case)	40,000	87	0.0
150	48,000	91	+4.8

. At a conservative price of $50/${\mathrm{tCO}}_2$, the framework prioritizes cost minimization, yielding a reduction of 32,000 tonnes. In the base case of $100/${\mathrm{tCO}}_2$, the optimization balances economic and environmental objectives, achieving the nominal 40,000-tonne reduction. Notably, at an aggressive price of $150/${\mathrm{tCO}}_2$, emission reductions escalate to 48,000 tonnes, with RE penetration rising to 91%. This demonstrates the framework’s adaptability to policy-driven pricing signals, incentivizing larger storage utilization to displace fossil inputs.

5.6.3. Performance Under Extreme Conditions

Figure 7 illustrates the energy consumption profiles. The proposed framework exhibits the highest renewable utilization and minimal fossil reliance. The environmental benefits are particularly pronounced during extreme weather events (e.g., the 2021 cold spells). In these scenarios, the prediction-guided $\beta$ shifts high-variance regulation duties to batteries, preserving LAES reserves for sustained smoothing. This strategy reduces fossil backup activation by 62%, yielding an additional 10,000 tonnes of carbon savings annually compared to deterministic baselines.

In essence, the closed-loop integration not only curtails emissions but also fosters higher renewable shares, establishing the proposed framework as an effective tool for eco-friendly offshore energy management.

5.7. Robustness and Sensitivity Analysis

This subsection evaluates the robustness of the proposed framework against parameter perturbations. A sensitivity analysis is conducted to quantify how variations in wind speed ($\pm 10\%$), load demand ($\pm 15\%$), and the Wasserstein radius ($\rho$, $\pm 20\%$) impact the LCOE and Renewable Energy (RE) penetration rate.

Table 13. Sensitivity Analysis of Key Parameters.

Parameter Variation	ΔLCOE	ΔRE Penetration
	(%)	(%)
Wind Speed $+10\%$	−4.2	+3.8
Wind Speed $-10\%$	+5.1	−4.5
Load Demand $+15\%$	+6.3	−5.2
Load Demand $-15\%$	−5.7	+4.9
Wasserstein Radius $+20\%$	+3.9	+2.7
Wasserstein Radius $-20\%$	−3.4	−2.9

summarizes the results. Wind speed serves as the dominant factor: a 10% increase reduces LCOE by 4.2% and boosts RE penetration by 3.8%, driven by higher resource availability that minimizes storage depletion. Conversely, a 10% decrease in wind speed elevates LCOE by 5.1%, necessitating larger reserve margins to maintain reliability.

Load demand variations demonstrate asymmetric effects. A 15% increase in demand raises LCOE by 6.3% due to intensified balancing requirements, whereas a decrease yields a 5.7% cost reduction. Crucially, the Wasserstein radius acts as a tuning knob for conservatism. Increasing $\rho$ by 20% raises LCOE by 3.9% to hedge against broader distributional ambiguity, but simultaneously enhances the RE penetration by 2.7% through safer operational margins. Conversely, reducing $\rho$ lowers costs but increases the risk of unmodeled load shedding.

The heatmap in Figure 8 visually corroborates these findings. The gradient intensity confirms that while the system is most sensitive to meteorological potential, the proposed dynamic optimization restricts cost deviations to within 7% and penetration shifts to below 6% across all scenarios. This stability—achieved through prediction-guided reallocation—validates the framework’s scalability to diverse offshore environments.

6. Discussion

The proposed closed-loop framework, integrating ultra-short-term probabilistic forecasting with dynamic HESS optimization, represents a substantial advancement in managing offshore wind variability. By effectively fusing physical constraints with statistical patterns, the DCR-Net yields forecasts with superior calibration. This precision directly empowers the PredOpt-HS module to balance conflicting objectives: economy, reliability, and sustainability.

A key finding is the efficacy of the dynamic $\beta$ mechanism. By modulating power allocation based on real-time conditional variance, the framework reduces battery throughput by 49% relative to fixed allocation rules. This adaptability addresses the structural limitations of static configurations, which often suffer from over-cycling during predictable intervals or under-utilization during ramp events.

Furthermore, the proposed framework exhibits strong generalization capabilities across diverse seasonal variations without requiring season-specific network retraining. Because the DCR-Net is trained on a comprehensive multi-year dataset, its dual-channel architecture intrinsically captures long-term seasonal meteorological shifts. The impact of these seasonal variations is naturally absorbed and managed by the prediction-guided dynamic allocation mechanism. For example, during winter months characterized by high wind volatility and frequent extreme weather events, the forecasting module outputs a widened evidential predictive variance. This high uncertainty dynamically triggers a larger battery allocation factor $\beta \left(t\right)$ to suppress steep power ramps and expands the Wasserstein ambiguity radius to strictly hedge against tail risks. Conversely, during calmer summer periods with higher predictability, the reduced variance leads to a lower $\beta \left(t\right)$, seamlessly shifting the energy balancing duties to the LAES to preserve battery longevity. This inherent seasonal adaptability confirms the suitability of the unified framework for continuous, year-round offshore operations.

Benchmarking against state-of-the-art literature highlights the framework’s superiority. Unlike meta-heuristic approaches (e.g., Lotus Effect optimization) that focus on cost minimization without handling real-time uncertainty, our approach explicitly incorporates minute-resolution probabilistic scenarios. This leads to an 18.4% reduction in LCOE and an 82% improvement in CVaR. Furthermore, while conventional studies often overlook the dynamic complementarity between storage technologies for frequency support, the proposed method enhances the frequency nadir to 49.83 Hz via evidential uncertainty integration.

Computational efficiency further supports practical deployment, with rolling optimizations completing in 4.7 min. However, limitations persist. The framework relies on high-quality meteorological data, which may be sparse in certain offshore regions. Additionally, the current model assumes a simplified point-of-connection grid topology.

7. Conclusions

The paper establishes a novel, closed-loop paradigm for the robust configuration and dynamic dispatch of Hybrid Energy Storage Systems integrated with offshore wind farms. The core contribution is threefold: first, the development of a Dual-Channel Residual Network for ultra-short-term probabilistic forecasting, which accurately quantifies both aleatoric and crucial epistemic uncertainty. Second, the introduction of a Prediction-Guided Distributionally Robust Optimization framework that dynamically links this forecast confidence to the optimal storage dispatch strategy. Third, quantitative validation on a large-scale offshore wind farm demonstrates the framework’s efficacy. The results confirm that the proposed solution yields a significant reduction in the Levelized Cost of Energy, drastically reduces carbon emissions, and substantially enhances black-start resilience. Future research will focus on extending this robust framework to incorporate multi-energy coupling and detailed modeling of multi-terminal High-Voltage Direct Current transmission dynamics to address complex, broader grid integration challenges.