Research on the Coordinated Optimisation of Green Asset-Backed Note Financing and Hydrogen Energy Storage Market Transactions Based on Stackelberg Games

Abstract

Hydrogen energy storage serves as a pivotal technology for integrating high proportions of renewable energy, yet its development faces constraints due to substantial investment requirements and imperfect market mechanisms. Green Asset-Backed Notes (ABNs) offer potential to alleviate financing constraints; however, their synergistic effects with hydrogen storage market strategies remain unexplored. This paper constructs a two-layer Stackelberg game model integrating ABN financing with day-ahead trading. Multi-scenario analysis reveals that ABN financing costs significantly influence the operational economics of energy storage: low-cost financing enhances hydrogen storage’s price responsiveness and arbitrage capabilities, whereas high costs suppress its market participation. The research provides quantitative evidence for leveraging financial instruments to enhance hydrogen storage competitiveness.

1. Introduction

1.1. Challenges Facing Intraday Electricity Market Mechanisms and Hydrogen Energy Storage Participation

Against the macro backdrop of global energy transition and the development of new power systems, electricity markets have increasingly emerged as pivotal mechanisms for optimising resource allocation and signalling prices. As the starting point for the sequential operation of electricity spot markets, intraday markets bear the critical functions of balancing next-day electricity supply and demand whilst establishing time-of-use price signals. Practices in mature electricity markets (such as PJM and the Nordic market) indicate that day-ahead markets predominantly adopt a centralised auction clearing model based on Security Constrained Economic Dispatch (SCED) [1]. Market participants submit supply or demand curves, and the system operator conducts clearing with the objective of maximising social welfare, subject to network and security constraints. This process establishes node prices (LMP) or regional prices reflecting spatiotemporal marginal costs [1]. This mechanism aims to guide the optimal temporal and spatial allocation of resources through price signals, while providing a value realisation channel for flexible resources such as energy storage. However, the integration of high proportions of renewable energy introduces significant uncertainty, posing new challenges to market clearing algorithms, price formation, and risk management [2].

China’s electricity spot markets are accelerating their development, with clearing rules designed to guide the optimal allocation of flexible resources, including energy storage. Domestic day-ahead markets typically employ either a ‘generation-side quantity-only bidding, consumer-side quantity-and-price bidding’ model or a two-way bidding approach. The clearing process adheres to economic dispatch principles while progressively incorporating mechanisms reflecting location signals [3]. A core challenge in current market design lies in creating a fair and effective participation environment for flexible resources like energy storage. Hydrogen storage, with its advantages of large-scale capacity and long-duration operation, emerges as a key option for integrating fluctuating renewable energy. However, its substantial initial investment, extended payback period, and inadequacies in existing market rules for pricing emerging technologies severely constrain its commercialisation and market competitiveness. Consequently, exploring economically viable participation pathways for hydrogen storage has become an urgent research priority. International experiences, such as the European green bond market [4] and U.S. renewable energy financing mechanisms [5], demonstrate that well-designed green securitization can lower capital costs and attract institutional investors.

1.2. The Enabling Mechanism of Green Asset-Backed Notes (ABN)

Breaking through hydrogen storage investment bottlenecks requires innovative financing models. Green Asset-Backed Notes (ABN), as a financial instrument that securitises future revenue rights in advance, offer a viable financing solution for hydrogen storage projects [4]. Its core logic involves using the anticipated, stable electricity market revenues (such as electricity energy and ancillary service income) following project grid connection as underlying assets. Through risk isolation and credit enhancement measures, notes are issued to secure low-cost funding during the construction phase or early operational period. This not only optimises the project’s cash flow structure and reduces financial costs but, more significantly, transforms financing decisions from exogenous variables into endogenous decision variables—where financing scale and cost directly influence the operator’s risk tolerance and bidding strategy within the market. Consequently, researching the synergistic optimisation of ABN financing and market trading strategies is key to enhancing the economic viability and market competitiveness of hydrogen storage projects.

1.3. Research Status on Electricity Market Trading Strategies Based on Stackelberg Games

Within multi-tiered, multi-stakeholder electricity market environments, game theory serves as a natural analytical tool for strategic interactions. Among these, Stackelberg games (leader–follower games) are particularly favoured for their ability to clearly depict market forces with hierarchical decision structures (e.g., market-powerful operators versus price-takers) [3,5]. While numerous studies have employed Stackelberg models to analyse electricity market trading strategies, research focusing on the coupled decision-making of ‘green ABN financing’ and ‘hydrogen storage operations’ remains largely unexplored.

(1)

Distributed Energy Resource Aggregators and Market Transactions. Extensive literature has examined games where distributed energy resource (DER) aggregators act as leaders, with users or distribution system operators as followers. For instance, one study constructed a data-driven Stackelberg game model to analyse DER aggregators’ strategic bidding behaviour in day-ahead markets [3]; another proposed a Nash–Stackelberg hybrid game approach to examine bidding strategies among multiple DER aggregators in electricity markets [6].

(2)

Virtual Power Plants (VPPs) and Electric Vehicle (EV) Management. Addressing how VPP operators can guide orderly EV charging through pricing strategies, a Stackelberg game model was established with VPP as the leader and EV users as followers, incorporating wind power output uncertainty [7].

(3)

Integrated Energy Systems and Hydrogen Trading. With growing attention on electricity-hydrogen coupling, research has begun applying Stackelberg games to systems integrating hydrogen energy. For instance, one study developed Stackelberg game-based optimised bidding and management strategies for regional electricity–hydrogen integrated systems, where electricity–hydrogen operators serve as leaders [8]. Another research proposed a multi-objective robust dynamic pricing and operational strategy optimisation method based on Stackelberg games for integrated energy systems incorporating hydrogen energy storage (HES) [9].

(4)

Market design and investment decisions. Game models have also been employed to analyse higher-level market design issues. For instance, one study utilised a financial Stackelberg game approach to analyse optimal capacity expansion and differentiated capacity payment mechanisms under risk aversion and market power [1]. Another research constructed a distribution system expansion planning model based on a two-layer Stackelberg game, incorporating long-term renewable energy contracts [10].

(5)

Bidding Strategies for Hydrogen Systems. Some research directly addresses hydrogen systems’ market participation. For instance, one study explored optimal bidding strategies for hydrogen storage systems synergising with renewables in electricity markets [11]; another analysed risk-constrained bidding strategies for electro–hydrogen coupling systems in day-ahead and reserve markets [12]. Furthermore, the literature has evaluated the value of power-to-gas (P2G) as a flexibility option in integrated electricity and hydrogen markets, analysing how flexible electricity demand from hydrogen electrolysers can stabilise the market value of wind and solar power [2].

Despite these substantial achievements, two common shortcomings persist: firstly, most studies treat the investment and financing costs of energy storage (including hydrogen storage) as exogenous parameters, failing to consider the direct impact of financing decisions on market behaviour in an endogenous manner; secondly, there is a lack of frameworks integrating green financial instruments (such as ABNs) with market trading strategies for energy storage.

This paper pioneers the synergistic optimisation of ‘Green Asset-Backed Notes (ABN) financing decisions’ and ‘hydrogen storage day-ahead market trading strategies’ within a unified two-layer Stackelberg game framework. The model’s primary architecture is as follows: Participants: Hydrogen storage operators (HESO) are designated as market leaders (upper layer), while power generators, electricity consumers, grid companies, and other market entities serve as followers (lower layer). Upper-layer model (leader): The HESO makes decisions to maximise net daily operating profits. Its decision variables are dual: (1) ABN financing scale (i.e., the volume of notes issued against future revenue rights), which directly determines available working capital and financing costs; (2) Day-ahead market bidding strategy (including price and volume curves for electricity sales/purchases). Lower-layer model (followers): Other market participants respond under given market price signals and hydrogen storage output plans, aiming to minimise their respective costs or maximise their revenues. Their collective behaviour forms new market prices through the market clearing model. Coupling variables: The upper and lower models are tightly coupled through three key variables: ABN financing costs (influencing the upper-layer objective function), hydrogen storage day-ahead output plans (serving as input from the upper layer to the lower-layer market), and market price feedback (where lower-layer clearing outcomes feed back to the upper layer to influence returns). By solving the equilibrium of this game, this paper reveals how ABN financing costs, hydrogen storage techno-economic parameters, and market conditions jointly influence optimal financing scale and market bidding strategies. This provides novel, quantifiable decision support for hydrogen storage projects seeking to enhance market competitiveness through financial innovation.

2. Analysis of Intraday Electricity Market Clearing Mechanisms with Hydrogen Energy Storage Participation

2.1. Hydrogen Energy Storage Participation in Electricity Market Transactions

Against the backdrop of global energy transition, Hydrogen Energy Storage Systems (HESS) are emerging as indispensable key enablers within new power systems, owing to their unique advantages of large-scale, long-duration, and cross-seasonal storage capabilities. Their operational principle follows the conversion pathway of ‘electricity–hydrogen–electricity’ or ‘electricity–hydrogen–use’: during periods of electricity surplus or low electricity prices, electrical energy is converted into hydrogen via water electrolysis and stored; during periods of electricity shortage or peak electricity prices, the stored hydrogen energy is reconverted into electrical energy via fuel cells and fed back into the grid, or supplied directly as a clean fuel to sectors such as industry and transport. This dual flexibility as both “producer” and “consumer” establishes the foundation for its deep engagement in electricity market transactions.

2.1.1. Functions of Hydrogen Energy Storage in the Intraday Market

Within the intraday electricity and ancillary services markets, the multifunctional value of hydrogen energy storage is particularly prominent [13].

(1)

As a controllable load, it actively absorbs electricity during renewable energy surpluses, performing peak shaving and valley filling to smooth net load curves.

(2)

As a generation unit, it sells electricity during peak pricing periods, participating in energy market auctions to capture arbitrage profits.

(3)

Hydrogen storage systems offer rapid response times and high regulation precision, reliably providing ancillary services such as frequency regulation and reserve capacity, significantly enhancing the reliability and flexibility of power systems.

Therefore, by optimising its operational strategy within the day-ahead market, hydrogen storage not only realises its own economic value but also provides critical services for the safe, economical, and low-carbon operation of power systems, serving as a model for integrating market mechanisms with emerging technologies.

2.1.2. Mathematical Model of Hydrogen Energy Storage Systems

Hydrogen Energy Storage Systems typically comprise three core components: an electrolyser, hydrogen storage apparatus, and either a fuel cell or hydrogen gas turbine [14].

(1)

Electrolyser

As the central component of hydrogen production systems, the electrolyser is modelled as

$$M_H(t)={\displaystyle \frac{{\eta }_{1\_t}{P}_e(t)\sigma }{K}}$$

(1)

$$P_e(t)=P_{p-e}(t)+P_{g-e}(t)$$

(2)

M_H(t) denotes the hydrogen production rate of the electrolyser at time t; η_{1_t} represents the conversion efficiency of the electrolyser; P_e(t) indicates the input power to the electrolyser; P_p-e(t) and P_g-e(t) denote the power outputs from the photovoltaic system and the grid to the electrolyser respectively; and σ signifies the energy conversion coefficient. As the conversion equipment does not recover the steam energy during combustion when converting energy, K here represents the hydrogen’s calorific value.

(2)

Hydrogen Storage Tank

Hydrogen storage tanks, as vital equipment for hydrogen energy transport, play a decisive role in hydrogen filling and release. A general model can be expressed as:

$$E_H(t)=E_H(t-1)+{\eta }_s{M}_H(t)-{\displaystyle \frac{M_f(t)+M_u(t)}{{\eta }_r}}$$

(3)

In the equation, E_H(t) denotes the hydrogen content in the storage tank at time t; η_s and ${\eta }_r$ represent the storage efficiency and release efficiency of the hydrogen storage tank; and M_f(t) and M_u(t) denote the hydrogen output from the storage tank to the fuel cell and the user respectively.

(3)

Fuel Cell Systems

As equipment for generating electricity, the conversion efficiency of fuel cells is central to energy transformation. Their mathematical model is described as follows:

$$P_{f-u}(t)={\displaystyle \frac{{\eta }_{2\_t}{M}_f(t)K}{\sigma }}$$

(4)

In the equation: P_f−u(t) denotes the power output from the fuel cell to the user; η_{2_t} represents the conversion efficiency of the fuel cell.

In this study, the fuel cell is assumed to be a proton exchange membrane fuel cell (PEMFC), which converts hydrogen back to electricity with high efficiency and fast response, making it suitable for grid-scale applications. The model uses a constant efficiency η₂, representing the average performance under rated operating conditions.

2.2. Green Asset-Backed Notes

As a capital- and technology-intensive sector, the power industry faces extended investment recovery cycles for large-scale infrastructure projects, rendering traditional bank loans insufficient to fully meet funding requirements. Against the backdrop of deepening power sector reforms, enterprises confront intensifying market competition, with financing constraints becoming increasingly pronounced. Green Asset-Backed Notes (ABNs) leverage the stable future cash flows of ‘green’ projects. Through genuine asset sales, risk isolation, and structured layering, they effectively mobilise existing assets and reduce financing costs. This provides a vital financing channel for new energy enterprises, helping to alleviate the financing difficulties within the power sector.

The transaction process for asset-backed notes is illustrated in Figure 1. Similar to other asset securitisation projects, the originator first sells the underlying assets to a special purpose vehicle (SPV), effecting a substantive transfer of ownership. Subsequently, the SPV publicly issues ABNs backed by the cash flows generated from these underlying assets. The key steps in asset-backed note transactions involve the sale of underlying assets, the SPV acting as trustee to issue commercial paper, and investors purchasing the notes, thereby enabling corporate financing. The specific transaction process is as follows:

• The issuer enters into an agreement with investors to issue asset-backed notes, committing to repay principal and interest using cash flows generated from the underlying assets.
• The issuer continues to operate the underlying assets, ensuring they generate stable and reliable cash flows.
• The issuer enters into an agreement with a bank, designating it as the escrow bank responsible for safeguarding and recording cash inflows from the underlying assets.
• Within stipulated timeframes, the escrow bank transfers corresponding receivables to the bond registration and settlement institution per the agreement, ensuring principal and interest payments on the ABN.
• The bond registration and settlement institution transfers funds to investor accounts during settlement periods to repay principal and interest.

Figure 1. ASN transaction process.

Figure 1. ASN transaction process.

Green asset securitisation constitutes a financing mechanism whereby standardised securities are issued through structured design, underpinned by the future predictable cash flows of green projects such as renewable energy generation and high-efficiency transmission and distribution facilities [15]. Its core lies in transforming environmentally beneficial assets into tradable products within capital markets through risk isolation and cash flow restructuring, thereby channelling capital towards critical domains of the power system’s low-carbon transition. Precisely because green asset securitisation possesses the core characteristics and advantages outlined in

Table 1. Core characteristics and advantages of green asset securitisation.

Features/Advantages	Instruction
Risk structure	Through asset pooling and bankruptcy isolation via special purpose vehicles (SPVs), we diversify technical and operational risks associated with individual projects, attract diverse capital sources, and reduce the overall financing costs and risk exposure of renewable energy projects.
Transparency and certification	Relying on independent third parties to verify and continuously disclose the project’s ‘green attributes’ (such as carbon reduction quantities and energy efficiency improvement metrics), in compliance with technical standards within the power industry, enhances credibility and compliance.
Policy coordination	Benefiting from policy incentives such as green bond certification, fiscal interest subsidies, and priority grid connection, these measures align with the objectives of new power system development, thereby establishing a coordinated mechanism linking policy, technology, and finance.
Liquidity design	Supports structured securities design (such as senior/subordinated structures) to cater to investors with varying risk appetites, enhancing the liquidity of long-term power infrastructure investments in the secondary market and accelerating capital recycling.
System function	Provide scalable financing channels for key sectors including clean energy, energy storage, and smart grids to drive technological upgrades and low-carbon transformation of power assets, thereby enhancing grid resilience and energy security.

, it has become a vital financing instrument for supporting the development of new power systems.

2.3. Microgrids

Typical microgrid electricity loads can be categorised into three types: industrial loads, morning and evening residential loads, and commercial loads. Electricity loads exhibit pronounced fluctuations, with typical load characteristics manifesting in two primary aspects: firstly, daily load patterns follow discernible rhythms. For instance, residential users exhibit lower daytime demand and higher night-time consumption. Secondly, load switching issues arise. Sudden increases or decreases in high-capacity loads during specific periods can cause their inherent volatility to impact the entire power system’s operation.

(1)

Industrial load

Industrial loads typically exhibit stable characteristics with continuous production patterns, showing minimal fluctuations throughout the day. They maintain relatively high levels between 08:00 and 18:00, with a slight decline during night-time hours. Their 24 h load curve can be represented by the following composite function:

$$P_{industrial}(t)=P_{base}\times \left[0.7+0.2\times \sin \left({\displaystyle \frac{\pi (t-6)}{12}}\right)+0.1\times \sin \left({\displaystyle \frac{\pi (t-12)}{6}}\right)\right]\times \left[1+\epsilon (t)\right]$$

(5)

In the equation, P_base denotes the base load power (kW), t represents time t ϵ [0, 24] (hours), and ε(t) is the random fluctuation term, ε(t) ~ N(0, 0.05²).

(2)

Morning and Evening Residential Load

Residential load exhibits distinct morning and evening peaks, namely the morning peak (7:00 to 9:00) and evening peak (18:00 to 22:00), with relatively low load during late night hours. This pattern may be represented by a double Gaussian superposition function:

$$P_{residential}(t)=P_{base}\times \left[0.5+0.3\times e^{-{\displaystyle \frac{{(t-8)}^2}{2{\sigma }_1^2}}}+0.4\times e^{-{\displaystyle \frac{{(t-19)}^2}{2{\sigma }_2^2}}}+0.1\times \sin \left({\displaystyle \frac{\pi (t-12)}{12}}\right)\right]\times \left[1+\eta (t)\right]$$

(6)

In the equation, σ₁ denotes the early peak width parameter, with σ₁ = 1.5; σ₂ denotes the late peak width parameter, with σ₂ = 1.5; and η(t) ~ N(0, 0.08²) represents the random fluctuation term. The weighting coefficients (0.3, 0.4, and 0.1) in Equation (6) are derived from typical residential load patterns reported in [16] and calibrated using empirical data from the China Southern Power Grid region. These coefficients reflect the relative contributions of morning peak, evening peak, and baseline load components in the residential sector.

(3)

Commercial Load

Commercial load exhibits a single peak characteristic during daytime hours with extremely low night-time demand [17]. This is primarily manifested by a rapid rise commencing at 09:00, maintaining high levels between 12:00 and 16:00, followed by a sharp decline after 18:00. This pattern can be approximated using a segmented trigonometric function:

$$P_{commercial}(t)=\left\{\begin{array}{c}{P}_{base}\times \left[0.3+0.1\times \sin \left({\displaystyle \frac{\pi (t-5)}{4}}\right)\right]\times \left[1+\varsigma (t)\right],6\le t\le 9\\ P_{base}\times \left[0.8+0.2\times \sin \left({\displaystyle \frac{\pi (t-12)}{10}}\right)\right]\times \left[1+\varsigma (t)\right],10\le t\le 20\\ P_{base}\times 0.25\times \left[1+\varsigma (t)\right],Other times\end{array}\right.$$

(7)

Here, ζ(t) ~ N(0, 0.1²) represents the random fluctuation term.

2.4. Multi-Microgrid Energy Trading Platform

The microgrid energy trading system architecture proposed herein is illustrated in Figure 2, comprising three principal components: the grid, hydrogen storage operators, and microgrids. Hydrogen storage operators establish an internal electricity market within the microgrid cluster by receiving and processing microgrid interaction data, alongside implementing a financing mechanism through the issuance of standardised securities. They are responsible for setting internal electricity purchase and sale prices within the market, deriving operational benefits from the resulting price differentials. Microgrids are equipped with independent energy management systems capable of optimising power outputs across individual units within a single microgrid to respond to grid time-of-use pricing signals. Consequently, the energy trading platform coordinates optimised matching transactions between hydrogen storage and microgrid clusters through a game-theoretic model.

3. Collaborative Optimisation Strategy for Electricity Market Transactions Based on Stackelberg Game Theory

To coordinate the investment returns of hydrogen storage operators with the diverse energy demands of microgrid clusters, a collaborative optimisation model for hydrogen storage-microgrid clusters is constructed based on Stackelberg game theory. Within this model, hydrogen storage operators serve as upper-level leaders, while microgrid clusters function as lower-level followers, forming a principal-agent game structure. Concurrently, the model quantifies the logical relationships between ABN financing costs, market transaction electricity prices, and differentiated loads, calculating the system’s optimal capacity allocation and operational strategy under financing constraints.

3.1. Upper-Level Model: Hydrogen Storage Operator

(1)

Objective Function

The objective function of the hydrogen storage operator’s upper-level model is to maximise the operator’s daily revenue (F(x)), as shown below [18]:

$$F(x)=\max C_{ess}={\displaystyle \sum _{\omega =1}^W{T}_{\omega }(C_{ess,b,\omega }+C_{serve,\omega }+C_{p,\omega }+C_{ABN}-C_{ess,s,\omega }-C_{th,\omega }-C_{inv,\omega })}$$

(8)

In the formula, C_ess,b,w and C_ess,s,w represent the electricity sales revenue and electricity purchase costs of the hydrogen energy storage power station respectively; C_serve,w denotes the service fee revenue of the hydrogen energy storage power station; C_p,w signifies the hydrogen production revenue of the hydrogen energy storage power station; C_ABN indicates the financial support obtained through the ABN financing mechanism; C_th,w denotes the operational costs of the hydrogen energy storage power station; and C_inv,w represents the investment and maintenance costs of the hydrogen energy storage power station.

The revenue from electricity sales and the cost of electricity purchases for hydrogen energy storage power stations are

$$C_{ess,b,\omega }={\displaystyle \sum _{i=1}^N{\displaystyle \sum _{t=1}^{N_T}\lambda (t)P_{ess,b,\omega ,i}(t)\Delta t}}$$

(9)

$$C_{ess,s,\omega }={\displaystyle \sum _{i=1}^N{\displaystyle \sum _{t=1}^{N_T}\sigma (t)P_{ess,s,\omega ,i}(t)\Delta t}}$$

(10)

The service fee revenue from hydrogen energy storage power stations is

$$C_{ess,serve,\omega }={\displaystyle \sum _{i=1}^N{\displaystyle \sum _{t=1}^{N_T}\theta (t)\left[P_{ess,b,\omega ,i}(t)+P_{ess,s,\omega ,i}(t)\right]\Delta t}}$$

(11)

The operational and maintenance costs for hydrogen energy storage power stations are

$$C_{th,\omega }={\displaystyle \sum _{i=1}^N{\displaystyle \sum _{t=1}^{N_T}\epsilon (t)\left[P_{\omega ,t,+}^{th}-P_{\omega ,t,-}^{th}\right]\Delta t}}$$

(12)

The investment and maintenance costs for hydrogen energy storage power stations are

$$C_{inv,\omega }={\displaystyle \frac{{\eta }_p{P}_{ess}^{\max }+{\eta }_s{E}_{ess}^{\max }}{T_s}}+M_{ess}$$

(13)

In the formula: P_ess,b,w,i(t) and P_ess,s,w,i(t) denote the power sold and purchased by the energy storage power station at time t respectively; λ(t) and σ(t) denote the selling and purchasing prices at time t respectively; θ(t) denotes the service fee unit price; ε(t) represents the hydrogen transaction price, which fluctuates with market conditions; $P_{{w,t}^{,+}}^{th}$ and $P_{{w,t}^{,-}}^{th}$ denote the typical daily hydrogen charging and discharging power, respectively; η_p and η_s denote the power and capacity costs of the energy storage power station, respectively; $P_{ess}^{max}$ and $E_{ess}^{max}$ denote the maximum charging/discharging power and maximum capacity of the energy storage power station, respectively; T_s denotes the operational days of the energy storage power station; and M_ess denotes the daily operational and maintenance costs.

(2)

Constraints

The constraints for hydrogen production in electrolytic cells are:

$$\left\{\begin{array}{c}0\le X_{EC}\le X_{EC}^{\max }\\ m_{EC,t}=k_{EC}{P}_{EC,t}\\ 0\le P_{EC,t}\le X_{EC}\end{array}\right.$$

(14)

Hydrogen fuel cell capacity constraints are approximately

$$\left\{\begin{array}{c}0\le X_{HFC}\le X_{HFC}^{\max }\\ P_{HFC,t}^e={\eta }_{HFC}^e{m}_{HFC,t}\\ \begin{array}{c}{P}_{HFC,t}^h={\eta }_{HFC}^h{m}_{HFC,t}\\ k_{HFC}^{down}{X}_{HFC}\le P_{HFC,t}^h-P_{HFC,t-1}^h\le k_{HFC}^{up}{X}_{HFC}\\ 0\le P_{HFC,t}^e\le X_{HFC}\\ \begin{array}{c}{P}_{ch}^{\min }\le P_{ch,t}\le P_{ch}^{\max }\\ P_{dis}^{\min }\le P_{dis,t}\le P_{dis}^{\max }\end{array}\end{array}\end{array}\right.$$

(15)

PV generation and transmission constraints are approximately

$$\left\{\begin{array}{c}{P}_{PV}^{\min }\le P_{PV,t}\le P_{PV}^{\max }\\ G_{PV}^{\min }\le P_{PV,t}-P_{PV,t-1}\le G_{PV}^{\max }\\ 0\le P_{PV,t}^{cut}\le P_{PV,t}\end{array}\right.$$

(16)

The return on investment constraint is approximately

$${\displaystyle \frac{C_d}{I_{total}}}\ge R_{\min }$$

(17)

In the formula: $X_{EC}^{max}$ denotes the upper limit of the electrolyser’s rated capacity, m_EC,t and P_EC,t represent the hydrogen production rate and power consumption of the electrolyser at time t, respectively, k_EC denotes the electrical hydrogen production conversion coefficient. $X_{HFC}^{max}$ denotes the upper limit of the hydrogen fuel cell’s rated capacity, m_HFC,t, $P_{HFC,t}^e$ and $P_{HFC,t}^h$ represent the hydrogen consumption, power generation, and heat output of the fuel cell at time t respectively, ${\eta }_{HFC}^e$ and ${\eta }_{HFC}^h$ denote the power conversion and heat conversion coefficients respectively, $k_{HFC}^{down}$ and $k_{HFC}^{up}$ denote the downward and upward ramp coefficients of the fuel cell respectively, $P_{ch}^{min}$ and $P_{ch}^{max}$ denote the minimum and maximum charging power of the fuel cell respectively, $P_{dis}^{min}$ and $P_{dis}^{max}$ denote the minimum and maximum discharging power respectively, $P_{PV}^{min}$ and $P_{PV}^{max}$ denote the minimum and maximum output power of the photovoltaic power generation system respectively, P_PV,t represents the photovoltaic power generation output at time t, $G_{PV}^{min}$ denotes the limit value of the photovoltaic downward ramp rate; $G_{PV}^{max}$ denotes the limit value of the photovoltaic upward ramp rate, C_d denotes daily income, and I_total denotes total investment.

(3)

Decision Variables and Coupling Variables

Decision variables: ABN financing scale and hydrogen storage capacity.

Coupling variables: ABN financing cost, hydrogen storage daily output schedule, market price feedback.

3.2. Lower-Level Model: Microgrid Cluster

(1)

Objective Function

The sub-model focuses on optimising the minimisation of daily operating costs for a microgrid cluster serving diverse loads via hydrogen storage. Its objective is to minimise the aggregate cost incurred by the microgrid cluster in purchasing electricity from the grid.

$$C(x)=\min C_g={\displaystyle \sum _{\omega =1}^W{T}_{\omega }(C_{g,b,\omega }+C_{\omega }+C_{serve,\omega }+C_{ess,b,\omega }-C_{ess,s,\omega })}$$

(18)

In the formula, C_g,b,w represents the cost of purchasing electricity from the grid for the microgrid, while C_w denotes the cost of acquiring other energy sources.

$$C_{g,b,\omega }={\displaystyle \sum _{i=1}^N{\displaystyle \sum _{i=1}^{N_T}\tau (t)P_{g,\omega ,i}(t)\Delta t}}$$

(19)

In the equation, P_g,w,i(t) denotes the power purchased by the microgrid from the grid at time t, and τ(t) represents the purchase price of electricity by the microgrid at time t.

(2)

Constraints

Power balance for microgrid clusters: the sum of power inputs to the microgrid equals the sum of power consumed by the microgrid.

$$P_{GT,\omega ,i}(t)+P_{Wind,\omega ,i}(t)+P_{PV,\omega ,i}(t)+P_{g,\omega ,i}(t)+P_{ess,\omega ,i}(t)=P_{ess,s,\omega ,i}(t)+P_{load,\omega ,i}(t)+P_{loss,\omega ,i}(t)$$

(20)

Electrical load balancing in microgrid clusters: the sum of the power purchased and sold by microgrid clusters equals the sum of the charging and discharging power of the energy storage systems.

$${\displaystyle \sum _{i=1}^N\left[P_{ess,b,\omega ,i}(t)-P_{ess,s,\omega ,i}(t)\right]}=P_{ess,+}(t)-P_{ess,-}(t)$$

(21)

Electricity purchase constraints:

$$0\le P_{g,\omega ,i}(t)\le P_{g,mg}^{\max }$$

(22)

Furthermore, the maximum power exchange between the microgrid and the energy storage power station should also be constrained.

In the equation, P_GT,w,i(t), P_Wind,w,i(t), and P_PV,w,i(t) denote the output power of the gas turbine, fan, and photovoltaic system respectively at time t; P_load,w,i(t) represents the load power generated by the microgrid; P_loss,w,i(t) signifies the total power loss within the microgrid; and $P_{g,mg}^{max}$ indicates the maximum power purchased by the microgrid from the grid.

3.3. Stackelberg Game

As illustrated in Figure 3, this depicts the constructed two-layer Stackelberg game-based architecture for hydrogen energy storage and multi-type microgrid systems. Within this framework, the Hydrogen Energy Storage System serves as the upper-layer leader, securing financial backing through the ABN financing mechanism while determining energy storage capacity allocation and hydrogen electricity purchase/sale pricing. The lower-layer followers comprise three differentiated microgrid clusters: industrial, commercial, and residential. Each responds to price signals according to its distinct load characteristics (steady continuous industrial load, daytime single peak for commercial load, morning and evening dual peaks for residential load), optimising strategies for grid electricity procurement, hydrogen energy trading, and renewable energy consumption. The system integrates distributed energy sources such as wind and solar power, establishing a synergistic ‘generation–storage–load’ interaction mechanism. This architecture achieves dynamic equilibrium between hydrogen storage investment operations and microgrid energy costs through iterative game theory, providing an innovative solution for optimising low-carbon building microgrid clusters.

This paper employs a two-layer Stackelberg game model based on master–slave game theory, as depicted in Equation (23) [19]:

$$\begin{array}{ll}\Gamma & =\left\{N,S,P,C\right\}\\ & =\left\{W_S\cup W_M,S,P,{\left\{C_i\right\}}_{i\in N}\right\}\end{array}$$

(23)

In the formula: N, S, P, and C denote the set of participants, the set of strategies, and the utility function respectively; W_S represents the shared hydrogen storage power station, and W_M represents the microgrid cluster users. W_S U W_M denotes the two parties in the game theory: the hydrogen storage power station and the microgrid cluster; strategy spaces S and P respectively represent the economic allocation strategies for electricity purchase and sale by the hydrogen storage power station and the microgrid cluster, and the power allocation strategy agreed between the microgrid cluster and the hydrogen storage power station; utility functions C_S and C_M respectively represent the economic benefits of hydrogen storage. The utility functions must satisfy the following: (a) the lower-level follower model is constrained by the upper-level leader’s decisions, meaning the microgrid cluster’s constraints in the lower-level model incorporate the upper-level hydrogen storage station’s constrained strategy condition F(x); (b) the upper-level leader predicts the lower-level follower’s power demand to inform decision-making, meaning the upper-level leader model’s utility function incorporates consideration of the lower-level model’s utility C(x).

The bi-level Stackelberg game model is solved using an iterative algorithm based on the diagonalization method. At each iteration, the upper-level leader (hydrogen storage operator) solves its profit maximisation problem given the lower-level followers’ (microgrid clusters) reaction functions, which are obtained by solving their cost minimization problems. The lower-level problems are convex and solved using the CPLEX solver (version 12.10) with the dual simplex method and an optimality gap of 0.01%. The iterative process continues until the relative change in the upper-level objective function between consecutive iterations is less than 1 × 10⁻⁶, which is defined as the convergence criterion. The algorithm typically converges within 20–30 iterations for all scenarios tested.

4. Case Study Analysis

4.1. Simulation Environment

To characterise the impact of varying ABN financing costs on hydrogen energy storage operational systems, five distinct scenarios were designed to simulate conditions ranging from baseline operation to multiple extreme cases. The normal scenario serves as the baseline, employing a moderate ABN financing cost rate (5.0%) reflecting typical market financing conditions. The high-demand scenario and low-financing-cost scenario present stark contrasts: the former maintains a 4.0% financing cost rate despite a 40% increase in demand, while the latter reduces the ABN financing cost rate to 2.0% under normal demand levels, aiming to examine the critical impact of low-cost financing on energy storage investment. The high renewable energy scenario similarly employs a low 3.0% financing cost rate to accommodate investment demands arising from large-scale renewable energy integration. Particularly noteworthy is the high volatility scenario: despite a 20% demand increase, its ABN financing cost rate reaches 6.0%, fully illustrating the characteristic rise in financing costs within high-risk market environments. The parameter configurations for the five distinct scenes are presented in

Table 2. Five different scene parameter configuration tables.

Number	Scene Name	Demand Factor	Renewable Energy Factor	Market Volatility	ABN Financing Cost Ratio	Scene Description
1	Normal	1.0	1.0	0.10	5.0%	Benchmark scenario, with all parameters at average levels
2	High demand	1.4	0.8	0.15	4.0%	Electricity demand has increased significantly, while the proportion of renewable energy has decreased.
3	Highly renewable energy	0.8	1.6	0.12	3.0%	Renewable energy generation has increased substantially, while electricity demand has decreased.
4	low financing costs	1.0	1.0	0.08	2.0%	ABN financing costs have been significantly reduced, with all other parameters remaining normal.
5	High volatility	1.2	1.1	0.3	6.0%	Market prices fluctuate sharply, presenting a high degree of risk.

:

4.2. Simulation Analysis

As illustrated in Figure 4, the horizontal axis represents the 24 h scheduling cycle, with the left vertical axis indicating charging and discharging power (kW) and the right vertical axis showing electricity purchase and sale prices (RMB/kWh). The figure illustrates that under the low ABN financing cost scenario (2.0%), charging and discharging behaviour exhibits high synergy with the price curve: concentrated charging occurs during low-price periods (e.g., 0.3–0.5 yuan/kWh), while arbitrage discharging takes place during peak-price periods (e.g., 1.2–1.4 yuan/kWh). with the charging/discharging power curve exhibiting a distinct mirror relationship to the price differential curve. Conversely, under the high ABN financing cost scenario (6.0%), although price differentials persist, charging/discharging behaviour becomes markedly conservative. The amplitude of charging/discharging is constrained and response is delayed, reflecting how financing cost constraints diminish the incentive for arbitrage operations. Notably, while the high-volatility scenario exhibits the greatest price differential (reaching up to 0.8 yuan/kWh), its actual charge–discharge utilisation rate falls below that of scenarios with smaller price differentials but lower financing costs due to the constraints imposed by high financing costs. This indicates that the purchase-sale price differential presents arbitrage opportunities, yet the ability and extent to capitalise on these opportunities are determined by ABN financing costs. Lower financing costs enhance the system’s responsiveness to price signals, enabling energy storage to fully exploit arbitrage windows. Conversely, higher financing costs compel the system to prioritise cost recovery over profit maximisation, adopting a cautious strategy even under favourable price conditions.

As illustrated in Figure 5, the convergence characteristics of Stackelberg game solutions under varying scenarios are revealed. The figure demonstrates that the low financing cost scenario (ABN cost rate of 2.0%) exhibits optimal convergence performance, with iteration error decreasing rapidly and stably, reaching the convergence threshold within a limited number of iterations, whereas the high volatility scenario (ABN cost rate of 6.0%) exhibits pronounced convergence difficulties, with iterative error fluctuating significantly and decreasing slowly, requiring more iterations to approach convergence. This contrast directly reflects the significant impact of ABN financing costs on iterative error: lower financing costs reduce the rigidity of constraints on upper-level investment decisions, fostering greater coordination in the strategic space of both parties and thereby accelerating the search for equilibrium solutions. Conversely, higher financing costs increase decision complexity and constraint rigidity, limiting the scope for strategic adjustments by both parties, thus prolonging the convergence process and amplifying the final error. Notably, convergence curves for both standard scenarios (ABN cost rate 5.0%) and high-demand scenarios (4.0%) validate this pattern—despite increased demand introducing complexity, relatively lower financing costs maintain favourable convergence in the latter. This phenomenon indicates that within the Stackelberg game framework, the financing cost parameter not only influences economic decisions but also directly impacts the algorithm’s convergence characteristics by altering the constraints. Optimising the financing cost structure thus holds dual significance for enhancing both the efficiency and stability of the model’s solution process.

As shown in Figure 6, under the low financing cost scenario (ABN cost rate of 2.0%), the hydrogen storage SOC curve exhibits relatively stable fluctuations with regular charging and discharging behaviour. The system can fully charge to a higher hydrogen storage SOC level during off-peak periods and discharge moderately during peak periods. Overall, the hydrogen storage SOC remains within the ideal operating range of 40–85%, demonstrating optimised operational capability under sufficient financing support. Conversely, in the high financing cost scenario (ABN cost rate 6.0%), the hydrogen storage SOC curve exhibits pronounced fluctuations with overall levels remaining low. Insufficient charging is evident, with the hydrogen storage SOC frequently falling below the 30% safety threshold. This reflects a conservative operational strategy driven by financing constraints—operators must limit charging and discharging frequency and depth to control costs, sacrificing some arbitrage opportunities. The hydrogen storage SOC curves under the standard scenario (ABN cost rate 5.0%) and high-demand scenario (4.0%) exhibit intermediate states: the former shows relatively regular but limited fluctuations in hydrogen storage SOC, while the latter, despite more frequent discharging due to demand pressure, also exhibits noticeable undercharging issues. Notably, the hydrogen storage SOC curve in the high renewable energy scenario (ABN cost rate 3.0%) exhibits a distinctive two-stage pattern: rapid charging during periods of high renewable generation, followed by concentrated discharging during evening peak hours. This demonstrates the system’s capacity for flexible renewable energy integration supported by lower financing costs. These differences indicate that ABN financing costs fundamentally alter hydrogen storage SOC management strategies by directly influencing capacity allocation and operational economics. Lower financing costs grant systems greater operational flexibility and risk tolerance, whereas higher costs compel more conservative, short-term operational approaches. This ultimately manifests in the shape, amplitude, and stability of hydrogen storage SOC curves.

As illustrated in Figure 7, the horizontal axis presents five distinct operational scenarios, while the vertical axis denotes the ABN financing scale (in units of 10k CNY). The bar chart clearly reveals the dynamic relationship between financing costs and financing demand. The low financing cost scenario (ABN cost rate of 2.0%) stands out with the tallest financing bar, indicating that the significant cost advantage markedly stimulates investment willingness, with financing scale reaching 1.8 times that of the normal scenario. Conversely, in the high volatility scenario (ABN cost rate of 6.0%), despite a 20% increase in demand, excessively high financing costs lead to a substantial contraction in financing scale, amounting to only 60% of the normal scenario. Notably, the high renewable energy scenario—though featuring a 1.6-fold renewable energy factor—achieved over 30% greater financing scale than the normal scenario under a moderate 3.0% financing cost, demonstrating synergistic effects between clean energy policies and financing mechanisms. This comparative analysis demonstrates that ABN financing costs serve not only as a key lever influencing financing scale but also as a core parameter regulating the balance between investment risk and returns across different scenarios. Lower financing costs effectively amplify positive impacts on both the demand side and the renewable energy sector, whereas higher financing costs suppress system expansion willingness, even in the face of evident market demand growth and arbitrage opportunities.

While Figure 4, Figure 5 and Figure 6 qualitatively illustrate the operational behaviour of hydrogen storage under different scenarios, a comprehensive assessment of economic viability requires quantitative metrics. To this end, we compute four key performance indicators (KPIs) for each scenario: net present value (NPV), internal rate of return (IRR), payback period, and average daily arbitrage gain. These indicators capture both the long-term investment attractiveness and the short-term operational profitability of hydrogen storage projects.

Table 3. Key economic and operational performance indicators across scenarios.

Scenario	NPV (10k CNY)	IRR (%)	Payback Period (Years)	Avg. Arbitrage Gain (CNY/Day)
Normal	1250	8.5	9.2	3450
High demand	1680	10.2	8.1	4120
Highly renewable energy	2100	12.4	7.3	4980
Low financing costs	2350	14.1	6.5	5620
High volatility	820	6.3	11.8	2780

summarises these results, enabling a direct comparison of how ABN financing costs influence the overall economic performance across scenarios.

5. Conclusions

This study examines the impact of Green Asset-Backed Notes (ABNs) on hydrogen energy storage participation in electricity market trading strategies. A two-level Stackelberg game model integrating ABN financing decisions with market transactions was constructed, revealing the critical influence of the interaction between financing costs and market conditions on hydrogen storage operational strategies. Findings indicate that lower ABN financing costs effectively enhance hydrogen storage’s price responsiveness and arbitrage opportunities, improving system economics and operational flexibility. Conversely, high financing costs suppress storage deployment incentives and market participation. This research not only fills a gap in the field of synergistic optimisation between green finance and hydrogen storage but also provides policymakers and storage operators with a decision-making framework that balances financing optimisation and market transactions. It holds practical significance for promoting the large-scale application of hydrogen storage and the sustainable development of electricity markets.

While the proposed model provides valuable insights, several limitations should be acknowledged. First, the hydrogen storage system is modelled with simplified linear efficiencies and does not account for degradation over time or part-load performance variations. Second, the market is assumed to be perfectly competitive, neglecting potential market power or strategic withholding behaviours. Third, regulatory uncertainties and policy changes (e.g., carbon pricing, subsidy phase-outs) are not considered. Future work could extend the model to incorporate non-linear degradation, stochastic market prices, and multi-year investment horizons with rolling horizon optimisation.