Increased attention towards wind power is driven by the vision of achieving carbon neutrality. Wind power remains the leading non-hydro renewable technology, generating 1870 TWh in 2021. A total of 830 GW of wind power capacity was installed cumulatively in 2021, with 93 % being onshore systems and the remaining 7 % being offshore wind farms [1], as shown in Fig. 1. National policy support continues to serve as the primary catalyst for the proliferation of wind power worldwide. A striking example of this phenomenon is China's unveiling of its 14th Five-Year Planning in June 2022, wherein an ambitious target of 33 % of electricity generation from renewables, including an impressive 18 % derived from wind and solar technologies, is set for achievement by 2025. Further bolstering this global shift towards sustainable energy, the federal government of the United States introduced the Inflation Reduction Act in August 2022. This transformative legislation not only expands the realm of renewable energy support through the implementation of tax credits and other comprehensive measures but also ensures a sustained commitment to fostering the growth of the sector over the next decade.

The intrinsic intermittence of wind power, however, leads to the challenge of electricity supply and demand match in space and time [2]. As an emerging flexible resource, energy storage enables the reduction of mismatched electricity and the reliability improvement of the power grid. Energy storage can be divided into short-duration energy storage technology and long-duration energy storage (LDES) technology according to the duration of continuous discharge [3]. Numerous studies have unequivocally shown that achieving deep decarbonization of the power system necessitates the widespread implementation of LDES technologies to effectively address intermittent electricity supply shortages on a weekly and seasonal basis [4,5]. Typical LDES technologies include pumped storage, compressed air storage, liquid flow battery, as well as hydrogen energy storage (HES). Among them, HES has dominant advantages in terms of storage capacity and discharge duration, as shown in Fig. 2. Hydrogen Council [6] demonstrated that the demand for HES in the power system increases exponentially as renewable energy grows to a 60–70 % share.

The motivation of this study is to develop a bi-level configuration and operation collaborative optimization model of the SHES system within a wind farm cluster. Additionally, the study seeks to establish a sharing mechanism for the SHES system, which will delineate the strategies for cost-sharing and benefit-distribution among the participating entities.

In literature, some scholars have proposed the integration of wind power and hydrogen systems to establish a wind‑hydrogen system. This innovative approach offers several advantages, including the ability to regulate energy fluctuations in renewable energy sources, facilitate increased wind power consumption, and enhance the overall benefits derived from wind power [7,8]. The integration of wind power and the HES system offers a novel solution to address the challenges of wind energy storage. This approach demonstrates excellent economic feasibility, significant research implications, and promising market prospects [9]. Meng et al. [10] proposed that excess wind power could be absorbed through electrolysis cell hydrogen production, which could be sold directly or generated by fuel cells when wind power is insufficient. Loisel et al. [11] used hydrogen storage to absorb excess wind power, and the capacity configuration and economics of the hydrogen system were analyzed based on the capacity limitation of wind power transmission. Kroniger and Madlener [12] consider the participation of wind‑hydrogen systems in the electricity market and configure the optimization of the hydrogen system by leveraging time arbitrage and providing auxiliary services from the standpoint of wind farms to maximize their advantages.

The configuration and operation optimization of energy systems has emerged as a focal point of interest in recent years, drawing significant attention from academia [[13], [14], [15], [16], [17], [18]]. Regarding wind-HES system configuration or operation optimization, many valuable studies can be found. As for the former, Zhang et al. [19] conducted a comparative analysis of capacity configurations in off-grid and grid-connected multi-energy systems incorporating wind turbines, photovoltaic panels, hydrogen storage, and batteries. Zhou et al. [20] formulated an optimization model for configuring gas-wind-PV‑hydrogen integrated energy systems and proposed a novel and practical strategy for satisfying deviations. Xu et al. [21] developed a data-driven framework for optimizing the sizing of gas-wind-PV‑hydrogen systems and introduced a modified version of NSGA-II, utilizing reinforcement learning, to obtain a Pareto set. Phan-Van et al. [22] proposed a unique sizing model for green hydrogen production from dedicated offshore wind and PV plants, utilizing net present value, discounted payback time, and levelized cost of energy and of hydrogen as economic evaluation criteria. Ma et al. [23] presented a nonlinear modeling of the offshore wind‑hydrogen-battery system and applied convex programming to optimize the plant sizes. Ke et al. [24] proposed a sizing model for wind-photovoltaic‑hydrogen storage integrated energy systems considering Energy Trilemma. Wang et al. [25] proposed a multi-objective distributionally robust optimization (DRO) model for hydrogen-involved total renewable energy CCHP planning.

As for the latter, Zheng et al. [26] proposed a data-driven robust chance-constrained-based decision framework and applied it to the optimal day-ahead operation of a real-life wind/hydrogen system. Xiao et al. [27] formulated the operational problem of the proposed wind-electrolysis hydrogen storage system into a mixed-integer linear programming model. Mirzaei et al. [28] proposed a stochastic security-constrained unit commitment (SCUC) with wind energy considering the coordinated operation of price-based demand response and HES system. Wei et al. [29] developed an optimal dispatching model of a power grid integrating wind‑hydrogen systems and utilized linearization techniques to efficiently solve the optimization problem. Abdelghany et al. [30] presented a so-called model predictive controller for the optimal operations of grid-connected wind farms with hydrogen-based ESSs and local loads. Yu et al. [31] modeled a risk-averse stochastic operation of hydrogen storage systems and wind generation using a scenario-based stochastic approach by considering a price-responsive demand response program. Qu et al. [32] concerned the participation of flexible renewable energy hubs equipped with wind farms, bio-waste units, and hydrogen, thermal, and compressed air storage systems in the energy market based on the market clearing price model.

Beyond the aforementioned literature, there exists a body of research that concurrently explores the collaborative configuration and operation of wind-HES systems, which is often referred to as bi-level or two-layer collaborative optimization. [33,34]. Ma et al. [35] proposed a cooperative configuration and operation model for the wind‑hydrogen-heating multi-agent energy system based on the Nash bargaining game theory. Cooper et al. [36] developed a framework to optimize the configuration and operation of a large-scale wind-powered hydrogen electrolyzer hub under the variable power supply. Garcia and Weisser [37] carried out a joint optimization of configuration and operation for wind-diesel system with hydrogen storage and used a linear programming solution as a benchmark to improve heuristic dispatch rules. Wang et al. [38] proposed a combined configuration and operation model of wind power-pumped storage‑hydrogen energy storage based on deep learning and intelligent optimization. Cooper et al. [39] developed a framework for the configuration and operation of a large-scale wind-powered hydrogen electrolyzer hub, the objective is to minimize the levelized cost of hydrogen produced by the system.

The previous works have made respectful contributions to the field. However, some challenges need to be addressed. Firstly, for existing studies on the collaboration configuration and operation optimization of wind-HES systems, most of the models are single-layer optimization models, which fail to take into account the interaction between configuration and operation, making it difficult to achieve global optimization. Secondly, studies on the configuration and operation of wind-HES systems mostly focus on independent energy storage configurations without considering a shared mechanism, resulting in low utilization efficiency of energy storage.

The sharing economy refers to an economic model in which individuals and businesses share access to goods and services via platforms or other intermediaries [40]. Shared energy storage has emerged as an appealing approach to leverage energy storage in renewable energy systems, essentially applying the concept of the sharing economy to energy storage [[41], [42], [43], [44]]. In comparison to individual energy storage methods, shared energy storage offers the potential to reduce cost inefficiencies and maximize the utilization coefficient of energy storage resources by decoupling ownership and usage rights of energy storage equipment [45]. The comparative of pertinent literature with the present study is shown in Table 1.

To this end, this study proposes a novel approach, suggesting a collaborative optimization model for the configuration and operation of a SHES for a wind farm cluster. The potential contributions of this study can be summarized as follows:

• 1)

  Although numerous studies have introduced bi-level configuration and operation collaborative optimization models for energy storage systems, this is the first study to propose a bi-level optimization model for SHES. In terms of configuration and operation collaborative modeling, SHES systems are more complex than traditional energy storage systems, as this complexity is reflected in both the sharing mechanisms and the storage components. In the proposed model, the upper layer is dedicated to capacity configuration optimization, designed to maximize the annual operational profit for the SHES. The lower layer, on the other hand, focuses on hourly operation optimization, aiming to minimize the operational costs over a typical day. These two layers interact iteratively to achieve a globally optimized solution for both the configuration and operation of the SHES.

• 2)

  A novel sharing mechanism is designed for the HES in this study. Existing research has primarily focused on shared energy storage mechanisms on the grid side or demand side, whereas this study explores shared energy storage mechanisms on the power source side. The wind farms within the cluster collectively form a consortium to invest the SHES. Investment costs are distributed according to the installed capacity of each wind farm. Operation and maintenance costs, on the other hand, are divided in line with the power generation of each wind farm. As for the revenue, it is shared between the wind farms and an emerging energy storage operator. The above mechanism can ensure that both wind farms and the energy storage operator have sufficient motivation to participate in SHES.

• 3)

  In a market-oriented environment, this study considers various operational modes, including the ‘E-H-E' mode and the ‘E-H' mode, which are more practical. The former emphasizes the bidirectional conversion of electricity to hydrogen, and then back to electricity while the latter focuses more on the unidirectional conversion of electricity to hydrogen. These two modes have different application scenarios and complement each other. The SHES system can decide which mode to adopt based on real-time electricity prices and a fixed hydrogen price, aiming to maximize profitability.

The study is structured as follows. After the Introduction, we review the structure and mechanism of a SHES in the next Section. In Section 3, the mathematical model of a SHES for wind power plants (WPPs) is elaborated. Section 4 establishes a bi-level collaborative optimization model of a SHES. A case study of Xinjiang province is illustrated in Section 5, while the last section concludes the study.