Optimal Dispatch Model for Hybrid Energy Storage in Low-Carbon Integrated Energy Systems

Abstract

Integrated Energy Systems (IESs), which leverage the synergistic coordination of electricity, heat, and gas networks, serve as crucial enablers for a low-carbon transition. Current research predominantly treats energy storage as a subordinate resource in dispatch schemes, failing to simultaneously optimise IES economic efficiency and storage operators’ profit maximisation, thereby overlooking their potential value as independent market entities. To address these limitations, this study establishes an operator-autonomous management framework incorporating electrical, thermal, and hydrogen storage in IESs. We propose a joint optimal dispatch model for hybrid energy storage systems in low-carbon IES operation. The upper-level model minimises total system operation costs for IES operators, while the lower-level model maximises net profits for independent storage operators managing various storage assets. These two levels are interconnected through power, price, and carbon signals. The effectiveness of the proposed model is verified by setting up multiple scenarios, for example analysis.

1. Introduction

Integrated Energy Systems (IESs) deployed at the park level, through the coupling of multiple energy carriers such as electricity, heat, gas, and hydrogen, can significantly improve both the penetration of renewable energy and the overall energy utilisation efficiency. As such, IESs serve as a key enabler in the transition toward clean and low-carbon energy systems [1].

In recent years, extensive research has been conducted on various technologies aimed at promoting low-carbon IES operation, including Demand Response (DR), tiered carbon trading mechanisms, Carbon Capture and Storage (CCS), and Power-to-Gas (P2G) strategies [2,3,4]. These approaches have all contributed—albeit to varying extents—to enhancing renewable energy integration and reducing carbon emissions within IESs. However, a critical challenge remains: how to achieve low-carbon objectives while simultaneously ensuring economic viability and operational flexibility of the system. This trade-off remains a central focus of current research efforts. To facilitate comparison, we summarise recent research on storage within IESs in Table 1.

As a crucial component of IES, energy storage plays a central role in ensuring stable system operation and enhancing both economic performance and operational flexibility, primarily through peak shaving and energy shifting mechanisms [5]. Among various storage technologies, electrical energy storage (EES) is the most widely adopted in IES, and most existing studies have focused on the optimal dispatch of EES systems. For instance, ref. [6] proposed a multi-objective bi-level optimal model incorporating energy storage to improve system economics, stability, and environmental sustainability. In [7], storage planning was extended beyond electricity to include multiple energy forms within IES, namely, electricity, heat, and gas. The authors designed the capacity configuration of both electrical and thermal storage systems from the perspective of achieving system-wide economic optimality.

However, conventional electrochemical storage technologies are often limited by their energy density and discharge duration, making them less suitable for high-capacity and long-duration applications. In contrast, hydrogen energy storage (HES) offers advantages such as large capacity, long storage duration, and clean energy characteristics [8]. Furthermore, the synergistic coupling of hydrogen with electricity and heat enables efficient coordination across energy carriers, thereby delivering cost-effective, large-scale, long-duration regulation. This not only facilitates the integration of renewable energy but also effectively mitigates fluctuations in electricity and thermal systems [9]. Consequently, growing attention has been paid to the role of hydrogen storage in IES. For example, ref. [10] developed an IES model comprising wind turbines, gas turbines, hydrogen power units, and hydrogen storage systems, and demonstrated that the incorporation of hydrogen storage significantly reduced wind curtailment and enhanced renewable energy utilization. In [11], an optimal method was proposed for the configuration of an integrated electricity-heat-gas-hydrogen energy system, considering tiered carbon trading and seasonal hydrogen storage. The model effectively addressed the seasonal mismatch between renewable energy output and load demand, while also considering economic and low-carbon performance objectives.

Most of the aforementioned studies primarily focus on the optimal scheduling of either EES or HES. However, given that IESs inherently operate as multi-energy coupled systems, involving electricity, heat, and gas, relying solely on a single type of storage is insufficient to fully exploit the system’s flexibility and low-carbon potential. As a result, the coordinated optimisation of multiple storage types has emerged as a new research focus. For instance, ref. [12] proposed a hybrid renewable energy system combining hydrogen storage and battery systems and utilised advanced algorithms to optimise overall system performance. In [13], a multi-energy storage capacity allocation model was developed to provide various load-shifting strategies, thereby reducing system load fluctuations and enhancing the reliability of the storage system. Furthermore, ref. [14] constructed a bi-level economic optimal model that considers natural gas-hydrogen blending alongside the coordinated operation of multiple types of energy storage. This approach promotes flexible interaction among electrical, thermal, and hydrogen storage systems, thus enhancing multi-energy complementarity within the IES framework.

Although the aforementioned studies have expanded the application of multi-type energy storage systems within IES, most still treat storage as a subordinate component within the overall IES optimal framework, making it difficult to realise its potential value as an independent market participant. In practice, the integrated planning and dispatch of storage with IESs can impose significant investment pressure on the system. Moreover, under a multi-objective environment that includes both carbon trading and demand response (DR), the profit margin of storage systems may be compressed, making it challenging to simultaneously achieve both economic and low-carbon benefits. Against this backdrop, a number of recent studies have begun to explore models in which energy storage participates in IES optimisation as an independent operator. For example, ref. [15] introduced a distributed robust optimal approach to conduct a comprehensive quantitative evaluation of hydrogen storage systems, and proposed a framework to assess their multi-dimensional value, thereby providing methodological support for independent storage operation.

In summary, this paper proposes a bi-level optimal model for the independent scheduling of HES, under the overarching goal of enabling low-carbon operation in IES. The model decouples electrical, thermal, and hydrogen energy storage from the internal structure of the IES and treats them as independent market entities with autonomous decision-making capabilities. The proposed hybrid storage configuration model consists of two hierarchical levels: The upper-level model, governed by the IES operator, aims to minimise the total system operating cost, considering factors such as energy procurement, carbon trading, renewable curtailment penalties, CCS costs, and DR compensation. The lower-level model, led by independent storage operators, aims to maximise net profit by evaluating investment returns and market price signals (electricity, heat, etc.), thereby enabling profit-driven decision-making by storage service providers. The interaction between the two layers is mediated through price and energy signals, forming a bi-level optimal framework with Stackelberg game characteristics. This structure facilitates efficient coordination between system-wide low-carbon objectives and localised profitability targets.

The key advantages of the proposed model include:

(1)

Integrated market-based regulation: By incorporating electricity prices, carbon prices, and emission quotas into a unified market mechanism, the model synergistically embeds DR, CCS, carbon trading, and energy storage optimisation. This enables coordinated decarbonization, cost reduction, and flexibility enhancement through market-driven incentives.

(2)

Independent market roles for multi-energy storage: By assigning autonomous market roles to electrical, thermal, and hydrogen storage units, the model leverages temporal arbitrage and load reshaping to enhance local renewable energy consumption. This supports the system-level coordination of low-carbon operation, economic efficiency, and operational flexibility.

Table 1. Comparison of recent works vs. this paper.

Study	Storage Role	Coupling Scope	Carbon Mechanism	DR Modeling	Solution Approach	Scenarios/KPIs
[2]	Attached to IES	E–H (trading)	price-driven	Integrated DR	Single-level OPF/LP	Cost, trading benefit
[3]	Attached to IES	E–H–Gas with CCS–P2G–CHP	Low-carbon dispatch (implicit)	-	Single-level economic dispatch	Cost, emissions
[4]	Attached to IES	E–H–Gas	Tiered carbon trading	-	Multi-time-scale scheduling	Cost, emissions
[6]	Attached to IES	E–H (planning)	Low-carbon park (implicit)	-	Single-level planning	Cost, capacity planning
[10]	Attached to IES	Gas–Electric with H2 storage	-	-	Single-level dispatch	Curtailment, RES utilization
[11]	Attached to IES	E–H–Gas–H2	-	-	Two-stage sizing (economic–safety)	Seasonal H2 sizing
[14]	Attached to IES	Hydrogen-blended gas + multi-type storage	Low-carbon operation	-	Bi-level (units–storage)	Cost, emissions
[15]	Shared H2 storage (quasi-independent)	Park clusters (H2-centric)	-	-	Coordination/valuation	Multi-value assessment
[16]	Attached to IES	CHP–P2G–CCS	Robust low-carbon dispatch	-	Robust optimization	Cost, emissions
[17]	Attached to IES	E–Gas + P2G	-	Integrated DR	Two-stage multi-objective	Cost, DR benefit
This paper	Independent profit-seeking storage (E/H/H2)	E–H–Gas–H2 + CCS/P2G	Tiered carbon (endogenous)	Integrated (shiftable/substitutable)	Bi-level → KKT → single-level MILP	Cost, RES utilization, emissions, CO2 capture

Table 1. Comparison of recent works vs. this paper.

Study	Storage Role	Coupling Scope	Carbon Mechanism	DR Modeling	Solution Approach	Scenarios/KPIs
[2]	Attached to IES	E–H (trading)	price-driven	Integrated DR	Single-level OPF/LP	Cost, trading benefit
[3]	Attached to IES	E–H–Gas with CCS–P2G–CHP	Low-carbon dispatch (implicit)	-	Single-level economic dispatch	Cost, emissions
[4]	Attached to IES	E–H–Gas	Tiered carbon trading	-	Multi-time-scale scheduling	Cost, emissions
[6]	Attached to IES	E–H (planning)	Low-carbon park (implicit)	-	Single-level planning	Cost, capacity planning
[10]	Attached to IES	Gas–Electric with H2 storage	-	-	Single-level dispatch	Curtailment, RES utilization
[11]	Attached to IES	E–H–Gas–H2	-	-	Two-stage sizing (economic–safety)	Seasonal H2 sizing
[14]	Attached to IES	Hydrogen-blended gas + multi-type storage	Low-carbon operation	-	Bi-level (units–storage)	Cost, emissions
[15]	Shared H2 storage (quasi-independent)	Park clusters (H2-centric)	-	-	Coordination/valuation	Multi-value assessment
[16]	Attached to IES	CHP–P2G–CCS	Robust low-carbon dispatch	-	Robust optimization	Cost, emissions
[17]	Attached to IES	E–Gas + P2G	-	Integrated DR	Two-stage multi-objective	Cost, DR benefit
This paper	Independent profit-seeking storage (E/H/H2)	E–H–Gas–H2 + CCS/P2G	Tiered carbon (endogenous)	Integrated (shiftable/substitutable)	Bi-level → KKT → single-level MILP	Cost, RES utilization, emissions, CO2 capture

2. Framework for Low-Carbon Coordinated Operation of IES Integrating Generation, Grid, Load, and Storage

2.1. IES Architecture

As a crucial platform for multi-energy coordinated optimisation, the IES facilitates complementary energy supply by coupling various energy carriers, including electricity, heat, gas, and hydrogen. The low-carbon coupled operation framework constructed in this paper incorporates wind power, photovoltaics, Thermal Power Units (TPUs), Combined Heat and Power (CHP) units, Gas Boilers (GBs), Electric Boilers (EBs), Carbon Capture Systems (CCS) and Power-to-Gas (P2G) technology, along with three types of energy storage: electrical, thermal, and hydrogen. Through energy coupling, this system achieves multi-energy complementarity and flexible regulation, with its architecture illustrated in Figure 1.

When renewable energy generation within the IES exceeds local electrical demand, the surplus power is preferentially routed by the storage operator to the electrical storage system, while a portion is converted into hydrogen via an electrolyser and stored in a hydrogen tank. During periods of high electricity prices or high system marginal costs, the stored hydrogen is supplied to a fuel cell to generate power, thereby replacing high-priced purchased electricity and enabling inter-temporal price arbitrage. Concurrently, waste heat from both the electrolysis and fuel cell processes is recovered and stored in a thermal storage tank. This stored heat supplements the supply during peak thermal loads or when conventional heating sources (e.g., gas boilers) are insufficient, thus enhancing overall energy efficiency and supply continuity. Through this integrated operation, the operational value of energy storage as an independent market entity is fully realised.

2.2. Low-Carbon Coupled Operation Mechanism and Model for IES Integrating Generation, Grid, Load, and Storage

2.2.1. Low-Carbon Coupled Operation Mechanism for IES Integrating Generation, Grid, Load, and Storage

To enhance the system’s low-carbon performance and emission reduction effectiveness while ensuring flexibility and sustainability, this study introduces several low-carbon operational mechanisms across the generation, grid, load, and storage domains, as illustrated in Figure 2.

On the generation side, A tiered carbon trading mechanism is implemented to incentivise the reduction in high-carbon energy consumption. This is combined with a post-combustion CCS featuring flue gas splitting to enable flexible capture regulation. Furthermore, a two-stage P2G process absorbs surplus renewable electricity and synergistically utilises CO₂ with the CCS, thereby enhancing low-carbon and flexible supply capabilities.

On the network side: The multi-energy grid (electricity, heat, gas, hydrogen) leverages interactions with energy storage and P2G. At the physical level, this facilitates cross-media energy conversion and peak-valley shifting. At the economic level, a unified carbon price, combined with various energy market prices (for electricity, heat, and gas), forms a tripartite signalling channel of cost, energy, and carbon to optimise power flow and energy distribution.

On the load side, the transferability and substitutability of DR are utilised to reshape the energy consumption curve. Driven by price and carbon signals, demand is shifted across time periods and energy carriers, coordinating with flexible generation to enhance local renewable energy consumption and reduce energy use during high-carbon intervals.

On the storage side: Multiple storage types (electrical, thermal, and hydrogen) are treated as independent, tradable entities. They perform multiple functions, including energy time-shifting, capacity support, provision of reserves, and ramp mitigation. These entities participate in the market across three dimensions, i.e., energy, ancillary services, and carbon reduction revenue, to achieve synergistic gains in both economic efficiency and low-carbon performance.

2.2.2. Model of the IES Low-Carbon Coupled Operation Mechanism

The objective of this study is to achieve a low-carbon economic operation of IESs through the optimal dispatch of hybrid electrical, thermal, and hydrogen storage. For the sake of brevity, the models for fundamental equipment, including electrical supply units (wind turbines, photovoltaics, TPUs, and CHP units) and thermal supply units (CHP, GBs, and EBs), are referenced from [18] and will not be reiterated here. Building upon the framework illustrated in Figure 2, the following sections will present the models for the key equipment integral to the low-carbon coupled operation mechanism.

• Carbon Capture System Model

By integrating post-combustion capture methods with flue gas splitting technology and incorporating a dedicated CO₂ storage tank, this study develops a flue gas splitting-based CCS. This configuration enables flexible regulation of both the carbon capture volume and the system’s overall energy consumption. The corresponding mathematical model is presented in Equation (1) [16]:

$$\left\{\begin{array}{l}{P}_{\mathrm{t}}^{\mathrm{CCS}}=e_{\mathrm{c}}{E}_{\mathrm{t}}^{\mathrm{r}}\\ P_{\mathrm{t}}^{\mathrm{CCS},\mathrm{total}}=P_{\mathrm{t}}^{\mathrm{CCS}}+P^{\mathrm{B}}\\ E_{\mathrm{t}}^{\mathrm{a}}=E_{\mathrm{t}}-e_{\mathrm{t}}^{\mathrm{a}}\\ 0\le P_{\mathrm{t}}^{\mathrm{CCS}}\le P_{\max }^{\mathrm{CCS}}\end{array}\right.$$

(1)

where $P_{\mathrm{t}}^{\mathrm{CCS},\mathrm{total}}$ is the total energy consumption of the CCS system; $P_{\mathrm{t}}^{\mathrm{CCS}}$ is the operating energy consumption incurred during capture; $P^{\mathrm{B}}$ is the fixed baseline energy consumption of the CCS; $e_{\mathrm{c}}$ is the specific energy consumption required to capture a unit mass of CO₂; $E_{\mathrm{t}}^{\mathrm{a}}$ is the amount of CO₂ captured by the CCS at time t; $E_{\mathrm{t}}$ is the total CO₂ emitted by the unit; $P_{\max }^{\mathrm{CCS}}$ is the upper bound on CCS operating energy consumption; $e_{\mathrm{t}}^{\mathrm{a}}$ is the amount of CO₂ directly vented to the atmosphere via the flue-gas bypass at time t.

The solvent storage unit within the CCS is composed of a lean solution tank and a rich solution tank. Adjusting the solution levels in these tanks enables the temporal decoupling of the CO₂ absorption and solvent regeneration processes. The mathematical model for these storage tanks is presented in Equation (2):

$$\left\{\begin{array}{l}{V}_{\mathrm{t}}^{\mathrm{R}}=V_{\mathrm{t}-1}^{\mathrm{R}}+v_{\mathrm{t}}^{\mathrm{R},\mathrm{in}}-v_{\mathrm{t}}^{\mathrm{R},\mathrm{out}}\\ V_{\mathrm{t}}^{\mathrm{L}}=V_{\mathrm{t}-1}^{\mathrm{L}}+v_{\mathrm{t}}^{\mathrm{L},\mathrm{in}}-v_{\mathrm{t}}^{\mathrm{L},\mathrm{out}}\\ v_{\mathrm{t}}^{\mathrm{R},\mathrm{out}}=v_{\mathrm{t}}^{\mathrm{L},\mathrm{in}}\\ v_{\mathrm{t}}^{\mathrm{L},\mathrm{out}}=v_{\mathrm{t}}^{\mathrm{R},\mathrm{in}}\end{array}\right.$$

(2)

where $V_{\mathrm{t}}^{\mathrm{R}}$ is the volume of rich solvent at time t; $V_{\mathrm{t}}^{\mathrm{L}}$ is the volume of lean solvent at time t; $v_{\mathrm{t}}^{\mathrm{R},\mathrm{in}}$ and $v_{\mathrm{t}}^{\mathrm{R},\mathrm{out}}$ are the inflow to and outflow from the rich-solution tank, respectively; $v_{\mathrm{t}}^{\mathrm{L},\mathrm{in}}$ and $v_{\mathrm{t}}^{\mathrm{L},\mathrm{out}}$ are the inflow and outflow from the lean-solution tank, respectively.

2.

Two-Stage P2G Model

To fully leverage the low-carbon benefits of hydrogen, the P2G process is disaggregated into two distinct stages: water electrolysis and methanation. The specific mathematical model for the water electrolysis process is as follows:

Water Electrolysis Process:

$$\left\{\begin{array}{l}{P}_{\mathrm{t}}^{{\mathrm{EW},\mathrm{H}}_2}={\eta }^{\mathrm{EW}}{P}_{\mathrm{t}}^{\mathrm{e},\mathrm{EW}}\\ P_{\min }^{\mathrm{e},\mathrm{EW}}\le P_{\mathrm{t}}^{\mathrm{e},\mathrm{EW}}\le P_{\max }^{\mathrm{e},\mathrm{EW}}\\ \Delta P_{\min }^{\mathrm{e},\mathrm{EW}}\le P_{\mathrm{t}+1}^{\mathrm{e},\mathrm{EW}}-P_{\mathrm{t}}^{\mathrm{e},\mathrm{EW}}\le \Delta P_{\max }^{\mathrm{e},\mathrm{EW}}\end{array}\right.$$

(3)

where $P_{\mathrm{t}}^{\mathrm{e},\mathrm{EW}}$ is the electrical energy input to the electrolytic tank at time t; $P_t^{\mathrm{EW},{\mathrm{H}}_2}$ is the hydrogen energy output from the electrolytic tank at time t; ${\eta }^{\mathrm{EW}}$ is the energy-conversion efficiency; $P_{\min }^{\mathrm{e},\mathrm{EW}}$ and $P_{\max }^{\mathrm{e},\mathrm{EW}}$ are the lower and upper bounds of the electrolytic tank’s input electrical power; $\Delta P_{\min }^{\mathrm{e},\mathrm{EW}}$ and $\Delta P_{\max }^{\mathrm{e},\mathrm{EW}}$ are the downward and upward ramping limits of the electrolytic tank, respectively.

Methanation stage:

$$\left\{\begin{array}{l}{P}_t^{\mathrm{MR},\mathrm{g}}={\eta }^{\mathrm{MR}}{P}_t^{{\mathrm{H}}_2,\mathrm{MR}}\\ P_{\min }^{{\mathrm{H}}_2,\mathrm{MR}}\le P_t^{{\mathrm{H}}_2,\mathrm{MR}}\le P_{\max }^{{\mathrm{H}}_2,\mathrm{MR}}\\ \Delta P_{\min }^{{\mathrm{H}}_2,\mathrm{MR}}\le P_{\mathrm{t}+1}^{{\mathrm{H}}_2,\mathrm{MR}}-P_t^{{\mathrm{H}}_2,\mathrm{MR}}\le \Delta P_{\max }^{{\mathrm{H}}_2,\mathrm{MR}}\end{array}\right.$$

(4)

where $P_{\mathrm{t}}^{\mathrm{MR},\mathrm{g}}$ and $P_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{MR}}$ are the methane output power and the hydrogen input power of the methanation unit at time t, respectively; $P_{\min }^{{\mathrm{H}}_2,\mathrm{MR}}$ and $P_{\max }^{{\mathrm{H}}_2,\mathrm{MR}}$ are the lower and upper bounds of the methanation unit’s output; $\Delta P_{\min }^{{\mathrm{H}}_2,\mathrm{MR}}$ and $\Delta P_{\max }^{{\mathrm{H}}_2,\mathrm{MR}}$ are the downward and upward ramp-rate limits of the methanation unit.

3.

Tiered Carbon Trading Model

In IESs dispatch models guided solely by the minimisation of fuel or energy procurement costs, the externality of carbon emissions is often not effectively internalised. This leads to a dispatch strategy that favours high-carbon generation sources, such as coal-fired units and gas boilers. Concurrently, renewable energy sources are subject to curtailment due to their inherent volatility, while energy storage and demand response lack effective price signals to incentivise their operation. As a result, the system struggles to reconcile economic efficiency with emission reduction targets. Therefore, this paper introduces a tiered carbon trading model to make the carbon constraint explicit and strengthen the economic incentive for emission abatement by applying progressively higher marginal carbon prices to different tiers of excess emissions [3].

The tiered carbon trading mechanism partitions the total required carbon allowances into multiple purchasing intervals. As the volume of purchased allowances increases, the corresponding marginal price for each successive tier becomes higher. The mathematical formulation for the tiered carbon trading model is as follows:

$$C_{{\mathrm{CO}}_2}=\left\{\begin{array}{l}\lambda E_{\mathrm{IES},\mathrm{t}},E_{\mathrm{IES},\mathrm{t}}\le l\\ \lambda (1+\alpha )(E_{\mathrm{IES},\mathrm{t}}-l)+\lambda l,l<E_{\mathrm{IES},\mathrm{t}}\le 2l\\ \lambda (1+2\alpha )(E_{\mathrm{IES},\mathrm{t}}-2l)+(2+\alpha )\lambda l,2l<E_{\mathrm{IES},\mathrm{t}}\le 3l\\ \lambda (1+3\alpha )(E_{\mathrm{IES},\mathrm{t}}-3l)+(3+3\alpha )\lambda l,3l<E_{\mathrm{IES},\mathrm{t}}\le 4l\\ \lambda (1+4\alpha )(E_{\mathrm{IES},\mathrm{t}}-4l)+(4+6\alpha )\lambda l,4l<E_{\mathrm{IES},\mathrm{t}}\end{array}\right.$$

(5)

here $E_{\mathrm{IES},\mathrm{t}}$ is the quantity of carbon allowances traded by the IES at time t; $C_{{\mathrm{CO}}_2}$ is the carbon-trading cost; $\lambda$ is the base carbon-trading price; $l$ is the length of the emissions interval; $\alpha$ is the price escalation rate.

4.

Demand Response Model

DR utilises joint signals and incentives, such as electricity, heat, gas, and carbon prices, to encourage users to autonomously adjust their energy consumption without compromising service quality or comfort, thereby enhancing operational efficiency and reducing carbon intensity. The IES constructed in this paper aggregates multiple types of dispatchable resources, where electricity, heat, and gas loads can undergo both cross-temporal shifting (for peak shaving and valley filling) and cross-carrier substitution within the same time period (e.g., substituting gas-fired heating with electric heating).

In the proposed model, DR operates in synergy with energy storage, P2G, and CCS to reshape the load profile. This coordination aims to increase local renewable energy consumption, suppress the dispatch of high-carbon marginal units, and lower the overall system carbon intensity. Following the methodology in reference [17], the total load is classified into fixed, shiftable, and substitutable types. The value of load type k at time period t is denoted as

$$P_{\mathrm{k},\mathrm{Load}}(t)=P_{\mathrm{k},\mathrm{Load}}^{\mathrm{s},0}(t)+P_{\mathrm{k},\mathrm{Load}}^{\mathrm{p},0}(t)+P_{\mathrm{k},\mathrm{Load}}^{\mathrm{c},0}(t)$$

(6)

where $k\in \{\mathrm{e},\mathrm{h},\mathrm{g}\}$ is the energy carrier: electricity (e), heat (h), and gas (g). $P_{\mathrm{k,Load}}(t)$ is the value of the k-type load at time t; $P_{\mathrm{k},\mathrm{Load}}^{\mathrm{s},0}(t)$ is the fixed component; $P_{\mathrm{k},\mathrm{Load}}^{\mathrm{p},0}(t)$ is the shiftable component; and $P_{\mathrm{k},\mathrm{Load}}^{\mathrm{c},0}(t)$ is the substitutable component.

3. Optimal Dispatch Model of Hybrid Storage in an IES with an Independent Storage Operator

To reflect the independent operational nature of energy storage systems, this paper constructs a bilevel optimal framework with Stackelberg characteristics: the upper level addresses the coordinated dispatch problem for the IES operator, aiming to minimise the total system operating cost, while the lower level deals with the operational capacity configuration of the independent energy storage operator, targeting net profit maximisation. The bilevel optimal logic is illustrated in Figure 3, with the two levels coupled through two types of quantities: one is physical coupling quantities, primarily including the flow and exchange of four energy types- electricity, heat, gas, and hydrogen- as well as power constraints of related equipment in the IES. These quantities are involved in both the upper-level electricity-heat-gas-hydrogen balance and network constraints and determine the lower-level settlement electricity volumes and cost/revenue calculations. The other is environmental signalling quantities, including electricity, heat, and gas prices, carbon quotas, and forecasts of load and renewable energy output. These are passed down from the upper to the lower level, driving the optimal response of energy storage. To improve the efficiency of model solving, this paper employs the strong duality KKT conditions to embed the lower-level optimality into the upper level, forming an equivalent single-level MILP model for unified solution.

In this paper, internal market prices generated by the upper-level IES operator are denoted by ${\eta }_{\mathrm{r}}^{\mathrm{e}}$ (electricity), ${\eta }_{\mathrm{r}}^{\mathrm{h}}$ (heat), ${\eta }_{\mathrm{r}}^{\mathrm{g}}$ (gas) and ${\eta }_{\mathrm{r}}^{{\mathrm{H}}_2}$ (hydrogen). These prices are sent top–down to the lower-level independent storage operator and enter the storage revenue/cost terms. The tiered carbon trading mechanism determines the marginal carbon cost ${\lambda }_t^{\mathrm{C}\mathrm{O}2}$, which feeds into the internal price formation. Settlement constraints at the upper level reconcile physical exchanges decided by storage with monetary payments so that what the ISO earns equals what the IES pays.

3.1. Upper-Level Low-Carbon Operation Model for the IES

The upper-level objective function aims to minimise the total operating cost of the IES while incorporating multiple cost components, including energy procurement, tiered carbon trading, wind/solar curtailment, CCS, and DR compensation. This approach enables unified consideration of carbon constraints and economic objectives within a single framework, demonstrating greater comprehensiveness compared to traditional models that only account for energy procurement or single environmental costs.

Regarding low-carbon mechanism integration, the model embeds the operational principles of flue gas split-flow CCS, two-stage P2G and DR into upper-level decision-making and constraints. This not only enhances local renewable energy consumption capacity but also provides institutionalised interfaces for synergies among different low-carbon measures.

Furthermore, through triple-signal coupling (“price-energy-carbon”) with lower-level entities, the upper level can transmit carbon costs, energy margins, and price expectations downward, thereby guiding hybrid energy storage systems to make optimal responses aligned with overall system objectives.

3.1.1. Objective Function

The specific objective is:

$$F\_\mathrm{upper}=\min (C_{\mathrm{buy}}+C_{{\mathrm{CO}}_2}+C_{\mathrm{DG},\mathrm{cut}}+C_{\mathrm{CCS}}+C_{\mathrm{DR}})$$

(7)

The energy-procurement cost $C_{\mathrm{buy}}$ is:

$$C_{\mathrm{buy}}=\sum _{\mathrm{t}=1}^{\mathrm{T}}{\alpha }_{\mathrm{t}}{P}_{\mathrm{e},\mathrm{buy}}(t)+\sum _{\mathrm{t}=1}^{\mathrm{T}}{\beta }_{\mathrm{t}}{P}_{\mathrm{g},\mathrm{buy}}(t)$$

(8)

where $P_{\mathrm{e},\mathrm{buy}}(\mathrm{t})$ represents the electricity purchased by the IES during time period t (decision variable); $P_{\mathrm{g},\mathrm{buy}}(\mathrm{t})$ denotes the natural gas purchased by the IES during time period t (decision variable); ${\alpha }_{\mathrm{t}}$ and ${\beta }_{\mathrm{t}}$ are the electricity price and natural gas price at time t, respectively.

The calculation method for carbon trading cost $C_{{\mathrm{CO}}_2}$ is detailed in Equation (5).

Curtailment cost $C_{\mathrm{cut}}$ is

$$C_{\mathrm{cut}}={\delta }_{\mathrm{DG}}\sum _{\mathrm{t}=1}^{\mathrm{T}}{P}_{\mathrm{DG},\mathrm{cut}}(\mathrm{t})+{\delta }_{\mathrm{PV}}\sum _{\mathrm{t}=1}^{\mathrm{T}}{P}_{\mathrm{PV},\mathrm{cut}}(\mathrm{t})$$

(9)

where ${\delta }_{\mathrm{DG}}$ and ${\delta }_{\mathrm{PV}}$ represent the penalty costs per unit of curtailed wind and photovoltaic power, respectively; $P_{\mathrm{DG},\mathrm{cut}}(\mathrm{t})$ and $P_{\mathrm{PV},\mathrm{cut}}(\mathrm{t})$ denote the curtailed wind power and photovoltaic power at time t (decision variables), respectively.

The carbon sequestration cost $C_{\mathrm{CCS}}$ is calculated as

$$C_{\mathrm{CCS}}=c_{\mathrm{CCS}}\sum _{\mathrm{t}=1}^{\mathrm{T}}{E}_{\mathrm{t}}^{\mathrm{a}}(\mathrm{t})$$

(10)

where $c_{\mathrm{CCS}}$ denotes the carbon sequestration cost coefficient; $E_{\mathrm{t}}^{\mathrm{a}}(\mathrm{t})$ represents the CO₂ mass captured by the CCS system at time t (decision variable).

The demand response (DR) compensation cost $C_{\mathrm{DR}}$ is given by

$$C_{\mathrm{DR}}=\sum _{\mathrm{k}=1}^3\sum _{\mathrm{t}=1}^{\mathrm{T}}({\delta }_{\mathrm{p}}|\mathsf{\Delta }{P}_{\mathrm{k},\mathrm{Load}}^{\mathrm{p}}(\mathrm{t})|+{\delta }_{\mathrm{c}}|\mathsf{\Delta }{P}_{\mathrm{k},\mathrm{Load}}^{\mathrm{c}}(\mathrm{t})|)$$

(11)

where ${\delta }_{\mathrm{p}}$ and ${\delta }_{\mathrm{c}}$ represent the unit compensation coefficients for shiftable loads and substitutable loads participating in demand response (DR), respectively.

3.1.2. Constraints

1.

Power-balance constraints

The constraints primarily include power balance equations for four energy carriers: electricity, heat, gas, and hydrogen, as formulated below:

$$\begin{array}{l}{P}_{\mathrm{t}}^{\mathrm{e},\mathrm{buy}}+P_{\mathrm{t}}^{\mathrm{EM}}+P_{\mathrm{t}}^{\mathrm{pv}}+P_{\mathrm{t}}^{\mathrm{wind}}+P_{\mathrm{t}}^{\mathrm{E},\mathrm{dis}}+P_{\mathrm{t}}^{\mathrm{CHP}}=\\ P_{\mathrm{t}}^{\mathrm{e},\mathrm{EW}}+P_{\mathrm{t}}^{\mathrm{EB}}+P_{\mathrm{t}}^{\mathrm{CCS}}+P_{\mathrm{e}}^{\mathrm{load}}(\mathrm{t})+P_{\mathrm{t}}^{\mathrm{E},\mathrm{cha}}\end{array}$$

(12)

$$H_{\mathrm{t}}^{\mathrm{CHP}}+H_{\mathrm{t}}^{\mathrm{GB}}+H_{\mathrm{t}}^{\mathrm{EB}}+H_{\mathrm{t}}^{\mathrm{hot},\mathrm{dis}}=P_{\mathrm{h}}^{\mathrm{load}}(\mathrm{t})+H_{\mathrm{t}}^{\mathrm{hot},\mathrm{cha}}$$

(13)

$$P_{\mathrm{t}}^{\mathrm{grid},\mathrm{g}}+P_{\mathrm{t}}^{\mathrm{MR},\mathrm{g}}=P_{\mathrm{t}}^{{\mathrm{CH}}_4,\mathrm{CHP}}+P_{\mathrm{t}}^{{\mathrm{CH}}_4,\mathrm{GB}}+P_{\mathrm{g}}^{\mathrm{load}}(\mathrm{t})$$

(14)

$$P_{\mathrm{t}}^{{\mathrm{EW},\mathrm{H}}_2}+V_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{dis}}=V_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{cha}}+P_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{CHP}}+P_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{GB}}+P_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{MR}}$$

(15)

where $P_{\mathrm{t}}^{\mathrm{e},\mathrm{buy}}$ is electricity purchased by the integrated energy system; $P_{\mathrm{t}}^{\mathrm{EM}}$ is the output of coal-fired generation units (decision variable); $P_{\mathrm{t}}^{\mathrm{pv}}$ and $P_{\mathrm{t}}^{\mathrm{wind}}$ are the output of photovoltaic and wind turbine units, respectively (decision variables); $P_{\mathrm{t}}^{\mathrm{CHP}}$ is the electrical output of the CHP unit (decision variable); $P_{\mathrm{t}}^{\mathrm{E},\mathrm{cha}}$ and $P_{\mathrm{t}}^{\mathrm{E},\mathrm{dis}}$ are the charging and discharging power of the EES (decision variables); $P_{\mathrm{t}}^{\mathrm{e},\mathrm{EW}}$ is the electric power absorbed by the electrolytic tank (decision variable); $P_{\mathrm{t}}^{\mathrm{EB}}$ is the electric power consumed by the electric boiler (decision variable); $P_{\mathrm{t}}^{\mathrm{CCS}}$ is the electric power consumed by the CCS system (decision variable); and $P_{\mathrm{e}}^{\mathrm{load}}(\mathrm{t})$ is the electric load at time t. $P_{\mathrm{h}}^{\mathrm{load}}(\mathrm{t})$ is the thermal load at time t; $H_{\mathrm{t}}^{\mathrm{hot},\mathrm{cha}}$ and $H_{\mathrm{t}}^{\mathrm{hot},\mathrm{dis}}$ are the charging and discharging thermal power of thermal energy storage system (decision variables). $P_{\mathrm{t}}^{\mathrm{grid},\mathrm{g}}$ is the amount of gas purchased by the system (decision variable); $P_{\mathrm{g}}^{\mathrm{load}}$ is the gas load. $P_{\mathrm{t}}^{\mathrm{MR},\mathrm{g}}$ is the CH₄ generated by P2G (decision variables); $V_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{cha}}$ and $V_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{dis}}$ are the Hydrogen charging and discharging volumes of the HES system (decision variables).

2.

TPUs Output Constraints

$$\left\{\begin{array}{l}{P}_{\min }^{\mathrm{C}}\le P_{\mathrm{t}}^{\mathrm{C}}\le P_{\max }^{\mathrm{C}}\\ \Delta P_{\min }^{\mathrm{C}}\le P_{\mathrm{t}}^{\mathrm{C}}-P_{\mathrm{t}-1}^{\mathrm{C}}\le \Delta P_{\max }^{\mathrm{C}}\end{array}\right.$$

(16)

where $P_{\min }^{\mathrm{C}}$ and $P_{\max }^{\mathrm{C}}$ represent the lower and upper limits of TPUs output, respectively; $\Delta P_{\min }^{\mathrm{C}}$ and $\Delta P_{\max }^{\mathrm{C}}$ denote the downward and upward ramping limits of the TPUs, respectively. $P_{\mathrm{t}}^{\mathrm{C}}$ is decision variable.

3.

Wind and PV Generation Constraints

$$\left\{\begin{array}{l}{p}_{\mathrm{t}}^{\mathrm{pv}}=P_{\mathrm{t}}^{\mathrm{pv}}-P_{\mathrm{t}}^{\mathrm{pvc}}\\ 0\le P_{\mathrm{t}}^{\mathrm{pv}}\le P_{\max }^{\mathrm{pv}}\end{array}\right.$$

(17)

$$\left\{\begin{array}{l}{p}_t^{\mathrm{wind}}=P_t^{\mathrm{wind}}-P_t^{\mathrm{windc}}\\ 0\le P_t^{\mathrm{wind}}\le P_{\max }^{\mathrm{wind}}\end{array}\right.$$

(18)

where $P_{\mathrm{t}}^{\mathrm{PV}}$ and $P_{\max }^{\mathrm{PV}}$ are the actual photovoltaic output and its upper limit at time t; $P_{\mathrm{t}}^{\mathrm{pvc}}$ is the curtailed PV power. Similarly, $P_{\mathrm{t}}^{\mathrm{wind}}$ and $P_{\max }^{\mathrm{wind}}$ are the Actual wind power output and its upper limit at time t; $P_{\mathrm{t}}^{\mathrm{windc}}$ is the curtailed wind power.

4.

Payment settlement

The cash flows between the IES and the storage operator are cleared as

$$\left\{\begin{array}{l}Pa{y}_{\mathrm{t}}^{\mathrm{e}}={\eta }_{\mathrm{r}}^{\mathrm{e}}(P_{\mathrm{t}}^{\mathrm{E},\mathrm{dis}}-P_{\mathrm{t}}^{\mathrm{E},\mathrm{cha}})\\ Pa{y}_{\mathrm{t}}^h={\eta }_{\mathrm{r}}^h(H_{\mathrm{t}}^{\mathrm{hot},\mathrm{dis}}-H_{\mathrm{t}}^{\mathrm{hot},\mathrm{cha}})\\ Pa{y}_{\mathrm{t}}^h={\eta }_{\mathrm{r}}^{H_2}(V_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{dis}}-V_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{cha}})\end{array}\right.$$

(19)

where $Pa{y}_{\mathrm{t}}^{\mathrm{e}}$ denotes the electricity payment from the IES to the independent storage at time $t$ (positive when the IES pays the storage). ${\eta }_{\mathrm{r}}^{\mathrm{e}}$ is the internal electricity price (CNY/kWh) decided at the upper level. A positive value of $Pa{y}_{\mathrm{t}}^{\mathrm{e}}$ occurs when discharging exceeds charging; a negative value indicates net purchasing from the IES due to charging. If the model settles on energy rather than power, multiply by the time step $\Delta \mathrm{t}$ (h): $Pa{y}_{\mathrm{t}}^{\mathrm{e}}={\eta }_{\mathrm{r}}^{\mathrm{e}}(P_{\mathrm{t}}^{\mathrm{E},\mathrm{dis}}-P_{\mathrm{t}}^{\mathrm{E},\mathrm{cha}})\Delta \mathrm{t}$ (CNY). Summing over $t$ yields the total electricity cash flow, which equals the storage’s electricity revenue term in the lower-level objective by construction: ${\displaystyle \sum _{\mathrm{t}}}({\mathrm{Pay}}_{\mathrm{t}}^{\mathrm{e}}+{\mathrm{Pay}}_{\mathrm{t}}^{\mathrm{h}}+{\mathrm{Pay}}_{\mathrm{t}}^{{\mathrm{H}}_2})=$ storage revenue recorded at the lower level. The electricity settlement equations for thermal and hydrogen energy storage are analogous to those for electrical energy storage and are therefore omitted for brevity.

5.

DR constraints

The DR constraints are formulated in Equation (6). To reflect field practice we add linear constraints on magnitude, energy-neutrality and ramps.

$$\left\{\begin{array}{l}0\le \mathsf{\Delta }{P}_{\mathrm{k},\mathrm{Load}}^{\mathrm{p}}(\mathrm{t})\le {\alpha }_{\mathrm{k}}^{\mathrm{p}}{P}_{\mathrm{k},\mathrm{Load}}^0(\mathrm{t})\\ 0\le \mathsf{\Delta }{P}_{\mathrm{k},\mathrm{Load}}^{\mathrm{C}}(\mathrm{t})\le {\alpha }_{\mathrm{k}}^{\mathrm{C}}{P}_{\mathrm{k},\mathrm{Load}}^0(\mathrm{t})\end{array}\right.$$

(20)

$$\sum _{\mathrm{t}\in {\mathcal{W}}_k}\left(\mathsf{\Delta }{P}_{\mathrm{k},\mathrm{Load}}^{\mathrm{c}}(\mathrm{t})-\mathsf{\Delta }{P}_{\mathrm{k},\mathrm{Load}}^{\mathrm{p}}(\mathrm{t})\right)=0,\forall k$$

(21)

$$\left\{\begin{array}{l}\left|\mathsf{\Delta }{P}_{\mathrm{k},\mathrm{Load}}^{\mathrm{p}}(\mathrm{t})-\mathsf{\Delta }{P}_{k,\mathrm{Load}}^p(\mathrm{t}-1)\right|\le r_{\mathrm{k}}^{\mathrm{p}}\\ \left|\mathsf{\Delta }{P}_{\mathrm{k},\mathrm{Load}}^{\mathrm{C}}(\mathrm{t})-\mathsf{\Delta }{P}_{\mathrm{k},\mathrm{Load}}^{\mathrm{C}}(\mathrm{t}-1)\right|\le r_{\mathrm{k}}^{\mathrm{C}}\end{array}\right.$$

(22)

where ${\alpha }_{\mathrm{k}}^{\mathrm{p}},{\alpha }_{\mathrm{k}}^{\mathrm{c}}\in (0,1]$ denotes the instantaneous participation cap; ${\mathcal{W}}_{\mathrm{k}}$ is the finite recovery window (set to 24 h in this study); $r_{\mathrm{k}}^{\mathrm{p}}$, $r_{\mathrm{k}}^{\mathrm{C}}$ are the inter-temporal upward and downward ramp limits of DR, respectively. To preserve user comfort, the DR magnitude is bounded at every time step. These constraints render the DR scheme more realistic and implementable.

6.

Other constraints

The tiered carbon-trading constraints are given by Equation (5); The system also includes other device-level constraints, such as the CCS operational constraints in Equations (1) and (2); The P2G unit constraints in Equations (3) and (4).

3.2. Lower-Level Energy Storage Optimal Dispatch Model

The lower-level energy storage dispatch model decouples electricity, thermal, and hydrogen storage from the IES’s centralised ancillary resources as independent operational entities. With the objective of net profit maximisation, the model simultaneously incorporates investment costs and operational revenues (e.g., charging/discharging, heat storage/release, hydrogen production/release) into the objective function, achieving a unified economic characterisation of multiple energy storage types. This approach grants storage systems market-oriented autonomous decision-making authority, fully expanding their value potential and strategic flexibility.

The model establishes operational constraints for electrical, thermal, and hydrogen storage systems based on key parameters, including capacity, power rating, efficiency, self-discharge, and switching states. It meticulously captures cross-temporal energy shifting and efficiency loss mechanisms to ensure engineering feasibility of profit-maximising decisions, while providing independent operators with enhanced arbitrage and dispatch flexibility.

3.2.1. Objective Function

The storage revenues/costs are calculated using upper-level prices ${\eta }_{\mathrm{r}}^{\mathrm{e}}$, ${\eta }_{\mathrm{r}}^{\mathrm{h}}$ and ${\eta }_{\mathrm{r}}^{H_2}$(received as exogenous inputs), alongside the physical decisions.

The specific objective function is formulated as:

$$C_{\mathrm{ESS}}=C_{\mathrm{in}}-C_{\mathrm{cost}}$$

(23)

where

$$\left\{\begin{array}{l}{C}_{\mathrm{in}}={\eta }_{\mathrm{r}}^{\mathrm{e}}{\displaystyle \sum _{t=1}^T}\left(E_{\mathrm{t}}^{\mathrm{cha}}+E_{\mathrm{t}}^{\mathrm{dis}}\right)+{\eta }_{\mathrm{r}}^{\mathrm{h}}{\displaystyle \sum _{t=1}^T}(H_{\mathrm{t}}^{\mathrm{cha}}+H_{\mathrm{t}}^{\mathrm{dis}})\\ C_{\mathrm{cost}}=C_{\mathrm{S}}^{\mathrm{E}}+C_{\mathrm{S}}^{{\mathrm{H}}_2}+C_{\mathrm{S}}^{\mathrm{h}}\end{array}\right.$$

(24)

here, $C_{\mathrm{ESS}}$ is the total revenue of Energy Storage System (ESS); $C_{\mathrm{in}}$ and $C_{\mathrm{cost}}$ denote the operational revenue and investment cost of the ESS, respectively. ${\eta }_{\mathrm{r}}^{\mathrm{e}}$ and ${\eta }_{\mathrm{r}}^{\mathrm{h}}$ are the charging/discharging prices for electricity and thermal energy storage; $E_{\mathrm{t}}^{\mathrm{cha}}$ and $E_{\mathrm{t}}^{\mathrm{dis}}$ are the amounts of electricity charged to and discharged from the ESS. $H_{\mathrm{t}}^{\mathrm{cha}}$ and $H_{\mathrm{t}}^{\mathrm{dis}}$ are the corresponding thermal charge and discharge amounts; $C_{\mathrm{S}}^{\mathrm{E}}$, $C_{\mathrm{S}}^{{\mathrm{H}}_2}$ and $C_{\mathrm{S}}^{\mathrm{h}}$ indicate the investment costs for electricity, hydrogen, and thermal energy storage, respectively.

3.2.2. Constraints

Energy storage devices store excess energy during periods of low load and high renewable energy generation. Their energy time-shifting characteristics can effectively alleviate supply-demand imbalances in the park and address the uncertainty of renewable energy output. The energy storage devices in the ESS include fuel cell storage, hydrogen storage tanks, and thermal storage tanks. While the models for different types of energy storage devices are similar in form, constraints such as capacity and charge/discharge power must be considered.

1.

Fuel Cell Constraints:

The operating power and ramp-rate constraints of the fuel cell are given by:

$$\left\{\begin{array}{l}{S}_{\mathrm{t}}^{\mathrm{E}}=S_{\mathrm{t}-1}^{\mathrm{E}}(1-{\delta }^{\mathrm{E}})+(P_{\mathrm{t}}^{\mathrm{E},\mathrm{cha}}{\eta }^{\mathrm{E},\mathrm{cha}}-{\displaystyle \frac{P_{\mathrm{t}}^{\mathrm{E},\mathrm{dis}}}{{\eta }^{\mathrm{E},\mathrm{dis}}}})\Delta t\\ S_{\min }^{\mathrm{E}}\le S_{\mathrm{t}}^{\mathrm{E}}\le S_{\max }^{\mathrm{E}}\\ 0\le P_{\mathrm{t}}^{\mathrm{E},\mathrm{cha}}\le {\omega }_{\mathrm{t}}^{\mathrm{E},\mathrm{cha}}{P}_{\max }^{\mathrm{E},\mathrm{cha}}\\ 0\le P_{\mathrm{t}}^{\mathrm{E},\mathrm{dis}}\le {\omega }_{\mathrm{t}}^{\mathrm{E},\mathrm{dis}}{P}_{\max }^{\mathrm{E},\mathrm{dis}}\\ 0\le {\omega }_{\mathrm{t}}^{\mathrm{E},\mathrm{cha}}+{\omega }_{\mathrm{t}}^{\mathrm{E},\mathrm{dis}}\le 1\\ S_{\mathrm{t}=0}^{\mathrm{E}}=S_{\mathrm{t}=\mathrm{T}}^{\mathrm{E}}\end{array}\right.$$

(25)

where $S_{\mathrm{t}}^{\mathrm{E}}$ (decision variable),$S_{\min }^{\mathrm{E}}$ and $S_{\max }^{\mathrm{E}}$ represent the state-of-charge and its lower/upper limits for electrical storage at time t; $P_{\mathrm{t}}^{\mathrm{E},\mathrm{cha}}$, $P_{\mathrm{t}}^{\mathrm{E},\mathrm{dis}}$ (decision variables), $P_{\max }^{\mathrm{E},\mathrm{cha}}$ and $P_{\max }^{\mathrm{E},\mathrm{dis}}$ denote the charge/discharge power and their upper limits; ${\delta }^{\mathrm{E}}$ is the self-discharge coefficient; ${\eta }^{\mathrm{E},\mathrm{cha}}$ and ${\eta }^{\mathrm{E},\mathrm{dis}}$ indicate charge/discharge efficiencies; ${\omega }_{\mathrm{t}}^{\mathrm{E},\mathrm{cha}}$ and ${\omega }_{\mathrm{t}}^{\mathrm{E},\mathrm{dis}}$ are binary variables representing charge/discharge states (decision variables); $S_{\mathrm{t}=0}^{\mathrm{E}}$ and $S_{\mathrm{t}=\mathrm{T}}^{\mathrm{E}}$ specify the initial and final states-of-charge.

2.

Hydrogen-tank constraints:

The hydrogen storage level and charge/discharge rate constraints are formulated as:

$$\left\{\begin{array}{l}{V}_{\mathrm{t}}^{{\mathrm{H}}_2}=V_{\mathrm{t}-1}^{{\mathrm{H}}_2}(1-{\delta }^{{\mathrm{H}}_2})+(H_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{cha}}{\eta }^{{\mathrm{H}}_2,\mathrm{cha}}-{\displaystyle \frac{H_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{dis}}}{{\eta }^{{\mathrm{H}}_2,\mathrm{dis}}}})\Delta t\\ V_{\min }^{{\mathrm{H}}_2}\le V_{\mathrm{t}}^{{\mathrm{H}}_2}\le V_{\max }^{{\mathrm{H}}_2}\\ 0\le V_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{cha}}\le {\omega }_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{cha}}{V}_{\max }^{{\mathrm{H}}_2,\mathrm{cha}}\\ 0\le V_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{dis}}\le {\omega }_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{dis}}{V}_{\max }^{{\mathrm{H}}_2,\mathrm{dis}}\\ 0\le {\omega }_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{cha}}+{\omega }_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{dis}}\le 1\\ S_{\mathrm{t}=0}^{{\mathrm{H}}_2}=S_{\mathrm{t}=\mathrm{T}}^{{\mathrm{H}}_2}\end{array}\right.$$

(26)

where $V_{\mathrm{t}}^{{\mathrm{H}}_2}$ (decision variable), $V_{\min }^{{\mathrm{H}}_2}$ and $V_{\max }^{{\mathrm{H}}_2}$ represent the hydrogen storage volume and its lower/upper limits for the hydrogen tank at time t; $V_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{cha}}$, $V_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{dis}}$ (decision variables),$V_{\max }^{{\mathrm{H}}_2,\mathrm{cha}}$ and $V_{\max }^{{\mathrm{H}}_2,\mathrm{dis}}$ denote the hydrogen charging/discharging rates and their upper limits; ${\delta }^{H_2}$ is the self-loss coefficient; ${\eta }^{{\mathrm{H}}_2,\mathrm{cha}}$ and ${\eta }^{{\mathrm{H}}_2,\mathrm{dis}}$ indicate the charging/discharging efficiencies; ${\omega }_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{cha}}$ and ${\omega }_{\mathrm{t}}^{{\mathrm{H}}_2,\mathrm{dis}}$ are binary variables representing the charging/discharging states (decision variables); $S_{\mathrm{t}=0}^{{\mathrm{H}}_2}$ and $S_{\mathrm{t}=\mathrm{T}}^{{\mathrm{H}}_2}$ specify the initial and final hydrogen storage volumes over a scheduling cycle.

3.

Thermal Storage Tank Constraints:

The thermal energy storage level and charge/discharge rate constraints are formulated as:

$$\left\{\begin{array}{l}{H}_{\mathrm{t}}^{\mathrm{hot}}=H_{\mathrm{t}-1}^{\mathrm{hot}}(1-{\delta }^{\mathrm{hot}})+(H_{\mathrm{t}}^{\mathrm{hot},\mathrm{cha}}{\eta }^{\mathrm{hot},\mathrm{cha}}-{\displaystyle \frac{H_{\mathrm{t}}^{\mathrm{hot},\mathrm{dis}}}{{\eta }^{\mathrm{hot},\mathrm{dis}}}})\Delta t\\ H_{\min }^{\mathrm{hot}}\le H_{\mathrm{t}}^{\mathrm{hot}}\le H_{\max }^{\mathrm{hot}}\\ 0\le H_{\mathrm{t}}^{\mathrm{hot},\mathrm{cha}}\le {\omega }_{\mathrm{t}}^{\mathrm{hot},\mathrm{cha}}{H}_{\max }^{\mathrm{hot},\mathrm{cha}}\\ 0\le H_{\mathrm{t}}^{\mathrm{hot},\mathrm{dis}}\le {\omega }_{\mathrm{t}}^{\mathrm{hot},\mathrm{dis}}{H}_{\max }^{\mathrm{hot},\mathrm{dis}}\\ 0\le {\omega }_{\mathrm{t}}^{\mathrm{hot},\mathrm{cha}}+{\omega }_{\mathrm{t}}^{\mathrm{hot},\mathrm{dis}}\le 1\\ S_{\mathrm{t}=0}^{\mathrm{hot}}=S_{\mathrm{t}=\mathrm{T}}^{\mathrm{hot}}\end{array}\right.$$

(27)

where $H_{\mathrm{t}}^{\mathrm{hot}}$ (decision variable), $H_{\min }^{\mathrm{hot}}$ and $H_{\max }^{\mathrm{hot}}$ represent the hydrogen storage volume and its lower/upper limits for the hydrogen tank at time t; $H_{\mathrm{t}}^{\mathrm{hot},\mathrm{cha}}$, $H_{\mathrm{t}}^{\mathrm{hot},\mathrm{dis}}$ (decision variables), $H_{\max }^{\mathrm{hot},\mathrm{cha}}$ and $H_{\max }^{\mathrm{hot},\mathrm{dis}}$ denote the hydrogen charging/discharging rates and their upper limits; ${\delta }^{\mathrm{hot}}$ is the self-loss coefficient; ${\eta }^{\mathrm{hot},\mathrm{cha}}$ and ${\eta }^{\mathrm{hot},\mathrm{dis}}$ indicate the charging/discharging efficiencies; ${\omega }_{\mathrm{t}}^{\mathrm{hot},\mathrm{cha}}$ and ${\omega }_{\mathrm{t}}^{\mathrm{hot},\mathrm{dis}}$ are binary variables representing the charging/discharging states (decision variables); $S_{\mathrm{t}=0}^{\mathrm{hot}}$ and $S_{\mathrm{t}=\mathrm{T}}^{\mathrm{hot}}$ specify the initial and final hydrogen storage volumes over a scheduling cycle.

4. Solving Model

We reformulate the bilevel model by imposing the Karush-Kuhn-Tucker (KKT) conditions of the lower level within the upper level, thereby obtaining a single-level MILP. Following standard linearisation, the continuous lower-level subproblem is linear and convex. Complementarity relations are linearised using the Fortuny-Amat big-M method, with M-values derived from tightened variable bounds to enhance numerical robustness. We solve the KKT-based single-level MILP in Gurobi (via YALMIP) with the following settings: MIPGap = 0.5%, TimeLimit = 3600 s, Presolve = 2, NumericFocus = 3, ScaleFlag = 1, Cuts = 2, Method = 2, MIPFocus = 1, IntFeasTol = 1 × 10⁻⁹, FeasibilityTol = 1 × 10⁻⁸, and OptimalityTol = 1 × 10⁻⁸.

5. Case Study

5.1. Scenario Design

Using operational data from a large-scale industrial park IES as an example, the scheduling cycle T is set to 24 h. The forecasted output curves of renewable generation (wind and PV) and the electricity/heat load demand profiles are shown in Figure 4. The parameters of all equipment and models are presented in

Table 2. Equipment and model parameters.

Parameter Type	Value	Parameter Type	Value
Coal price	800 CNY/ton	Electric boiler	40 MW
gas price	3.5 CNY/m3	Min/max output of thermal power unit	100/40 MW
Electrical output per CHP unit	125 MW	Ramping limits of the thermal power unit	80/−80 MW/h
Thermal output per CHP unit	150 MW	Electrical storage capacity and power	50 MWh/25 MW
Gas boiler output	80 MW	Thermal storage capacity and power	60 MWh/15 MW

.

This study establishes five comparative scenarios for analysis:

Scenario 1: Adopts the most basic IES model without considering DR, energy storage, or tiered carbon trading.

Scenario 2: Builds upon Scenario 1 by incorporating DR to specifically examine its load regulation effect.

Scenario 3: Extends Scenario 2 with a hybrid energy storage configuration, still under unified dispatch by the IES operator (i.e., non-independent storage entity), to verify the combined effect of DR and energy storage.

Scenario 4: Introduces tiered carbon trading based on Scenario 3, with energy storage remaining as a centralised ancillary resource of IES, jointly investigating the low-carbon and economic benefits under the tripartite interaction.

Scenario 5: Further develops Scenario 4 by designating energy storage as an independent operational entity and applying the proposed bi-level optimal method.

5.2. Analysis of IES Operating Costs

First, the operational costs of the IES under the aforementioned five scenarios are validated and comparatively analysed. The statistical results of operational costs are presented in

Table 3. System operating cost results.

Scenario	Total Cost/CNY	Coal Consumption Cost/CNY	Gas Purchase Cost/CNY	Electricity Purchase Cost/CNY	Renewables Utilisation Rate
1	4,298,067	975,228,800	4,290,926	7141	0.791
2	3,419,853	887,642,600	4,301,328	63,211	0.834
3	3,199,424	781,586,964	4,317,435	0	0.929
4	4,405,988	867,929,814	4,085,194	0	0.95
5	3,783,769	995,716,800	3,169,273	0	1

.

As shown in Table 3, Scenario 1 exhibits a relatively high total operational cost at 4,298,100, with a renewable energy utilisation rate of 0.791. After introducing DR in Scenario 2, the total system cost decreases to ¥3,419,900 (a 20.4% reduction compared to Scenario 1), while the renewable utilisation rate improves from 0.791 to 0.834. This demonstrates DR’s positive role in enhancing clean energy integration. Scenario 3 incorporates hybrid energy storage, further reducing operational costs to ¥3,199,400, highlighting the critical function of energy storage in coordinating electric/thermal load regulation and peak shaving. Renewable energy utilisation also becomes more efficient. Although Scenario 4 experiences a slight cost increase (¥4,406,000) due to explicit carbon emission pricing, the carbon-constrained mechanism promotes environmentally friendly dispatch. The renewable utilisation rate rises to 0.950, and overall system emissions are effectively suppressed. With the bi-level optimal mechanism introduced in Scenario 5, the total operational cost drops to ¥3,783,769 (a 14.1% reduction compared to Scenario 4). This cost reduction primarily stems from the independent operation of energy storage, which no longer solely serves IES objectives but instead optimises charging/discharging strategies flexibly: reducing reliance on external grid purchases and maximising profits through market-oriented dispatch.

However, despite the cost reduction in Scenario 5, the independent energy storage operator prioritises economic benefits over low-carbon operation in the absence of strict carbon constraints. Consequently, coal consumption costs increase, revealing a potential trade-off between economic and environmental objectives. Furthermore, the independent storage operator, free from external dispatch targets, can dynamically adjust charging/discharging based on electricity prices and renewable generation fluctuations. This autonomous scheduling eliminates renewable curtailment, achieving full utilisation (renewable rate = 1).

In summary, the proposed hybrid energy storage cooperative optimal method demonstrates superior performance in balancing economic efficiency and operational flexibility, while DR and energy storage significantly enhance renewable utilisation and system efficiency. Nevertheless, without carbon constraints, economic and environmental goals may conflict. Future dispatch strategies should better harmonise low-carbon objectives with economic viability to ensure sustainable development.

5.3. Analysis of Low-Carbon Benefits of the IES

To quantify the carbon emission control effects across different scenarios, Figure 5 presents the carbon emissions from major energy equipment, carbon capture volumes, and the total system carbon emissions under the five operational scenarios described above.

In Scenario 1, total carbon emissions reached 5010.84 tons, with the lowest level of carbon capture at 483.27 tons. Upon the introduction of DR in Scenario 2, emissions declined to 4700.41 tons, representing a reduction of approximately 6.2% compared to Scenario 1. Building upon this, Scenario 3 incorporates the role of energy storage, further decreasing emissions to 4377.90 tons: a 12.6% reduction from the baseline. In Scenario 4, the inclusion of a tiered carbon pricing mechanism results in total emissions of 4465.41 tons, while the carbon capture amount increases significantly to 618.53 tons.

Scenario 5 integrates multiple mechanisms: independent energy storage, bi-level optimisation, DR, CCS, and carbon trading, achieving a total system carbon emission of 4206.49 tons, the lowest among all scenarios and approximately 804.35 tons (16.1%) lower than in Scenario 1. The carbon capture level in Scenario 5 also rises to 835.42 tons, the highest across all cases. This improvement is primarily attributed to the independent storage operator’s price- and carbon-driven autonomous charge/discharge strategy, which, combined with DR reshaping the load curve, enables the substitution of high-carbon generation during periods of high marginal carbon cost. Furthermore, under carbon pricing constraints, the marginal benefits of low-carbon technologies are amplified, thereby achieving the dual low-carbon objective of “lowest emissions + highest carbon capture.”

These findings highlight that Scenario 5 demonstrates the synergistic advantages of multi-mechanism integration and market-based energy storage operation, positioning it as the most carbon-effective configuration among all the examined cases.

5.4. Benefit Analysis of Independently Operated Hybrid Storage

The economic contribution of energy storage systems to integrated energy systems varies under different optimal dispatch methods. Therefore, we have conducted a statistical analysis of the total costs, total revenues, and net benefits of electricity, heat, and hydrogen storage systems for Scenarios 3 to 5. The results are presented in

Table 4. Storage Benefit Analysis.

Scenario	Total Storage Cost/CNY	Total Storage Revenue/CNY	Net Revenue/CNY
3	30,809.45	204,133.25	173,323.80
4	28,587.59	198,658.63	170,071.04
5	190,342.40	527,587.60	337,245.20

:

According to the results in Table 4, the benefits of energy storage in Scenario 3 and Scenario 4 are relatively similar, with both demonstrating significantly higher storage revenues compared to their corresponding costs. In Scenario 4, after the introduction of the carbon trading mechanism, the carbon emission constraints partially limited the system’s dispatch flexibility, resulting in a reduced marginal contribution from energy storage. Consequently, the net profit declined to ¥170,071.04. Nevertheless, Scenario 4 outperformed in terms of carbon capture (618.53 tons) and system-wide carbon emission reduction (4465.41 tons). This indicates that, under multi-objective dispatch, energy storage can sacrifice part of its economic gains in exchange for improved low-carbon system performance. It is an outcome that reflects a trade-off optimal strategy of “environmental benefit over profit”.

In Scenario 5, energy storage is upgraded from a system-dependent asset to an independent market participant. Although the initial investment and the scale of installation and operation were considerably increased, raising the total storage cost to ¥190,342.40, the revenues still significantly outweighed the costs. This was achieved by improving local utilisation of renewable energy, enhancing system flexibility, reducing carbon emissions, and leveraging electricity price arbitrage. The net profit in this scenario reached ¥337,245.20. The core advantage lies in the bi-level optimal framework, which grants energy storage greater autonomy in scheduling and arbitrage, thereby achieving a synergistic benefit of “enhanced economic efficiency + optimal clean energy integration.” On one hand, the system’s reliance on high-carbon energy sources such as coal and natural gas is reduced, significantly lowering emissions; on the other, the increased flexibility enhances system stability and the ability to accommodate renewable generation fluctuations under high renewable penetration levels. These results robustly demonstrate the comprehensive economic and environmental value of independent energy storage systems.

Figure 6 and Figure 7 show the optimized scheduling results of the electrical energy storage and the system’s electrical power balance, respectively. Evidently, the EES follows a price-spread arbitrage mechanism: it charges at low prices and discharges at high prices. Scenarios 3 and 4 show higher unit economic efficiency, with Scenario 4 offering improved benefit–cost ratios and return on investment under carbon constraints. In Scenario 5, although electricity storage as an independent operator generates higher absolute net profits, investment and operational costs also increase accordingly.

In comparison, as is shown in Figure 8 and Figure 9, thermal energy storage yields lower direct returns than electrical storage but exhibits significant system-level synergistic value. It flattens thermal loads and stabilises CHP operation by shifting heat supply from off-peak to peak periods, thus alleviating the output pressure on GBs. In Scenario 4, carbon constraints further magnify the positive effects of electric-thermal coupling. In Scenario 5, in conjunction with electrical storage, power-to-heat conversion becomes more seamless; however, the expansion in scale leads to a marginal decline in unit efficiency.

Hydrogen storage demonstrates a threefold value: renewable absorption, energy conversion, and low-carbon benefits. It absorbs excess electricity during low-price or curtailed periods through hydrogen production, achieving energy vector transformation and generating terminal value via external sales or process substitution. Additionally, replacing carbon-based fuels with hydrogen contributes directly to emission reductions. Figure 10 and Figure 11 present the optimised scheduling results for hydrogen energy storage. In Scenario 5, the independence and scaling-up of hydrogen storage further enhance its arbitrage and low-carbon benefits, significantly improving the local utilisation of renewables and the temporal matching between generation and load.

5.5. Sensitivity to Storage Capacity

We scale the rated capacities of the three storage types—electrical (EES), thermal (TES), and hydrogen (HES)—by factors {0.50, 0.75, 1.00, 1.25, 1.50,1.75, 2.0}, re-solve the model for each case, and extract the ISO profit of each storage as well as the sum across the three technologies. Figure 12a shows per-technology ISO profit vs. capacity factor. HES exhibits a pronounced knee around 1.0–1.25×: profit surges when the capacity passes this threshold and then slightly tapers, suggesting that a binding constraint along the P2G-H2 utilisation-CCS chain is relaxed. In contrast, EES/TES display nearly flat or gently declining trends, implying that their limits are non-binding under the current price signals and coupling settings. Figure 12b plots the total ISO profit (EES + TES + HES), which increases markedly up to near 1.25 and then shows diminishing returns. Practically, this identifies 1.0–1.25 as a reasonable sizing range for storage expansion in the industrial-park case, while further expansion delivers smaller incremental value.

6. Conclusions

This study addresses the inherent trade-offs among low-carbon operation, economic efficiency, and system flexibility within IESs and proposes a Stackelberg bi-level optimal model in which energy storage is scheduled independently by a third-party operator. The primary innovations of the model are reflected in the following aspects:

(1)

Methodological Innovation: The model breaks away from the traditional centralised storage dispatch paradigm by integrating multiple types of energy storage under an independent operator framework. This approach significantly enhances the dispatchability and marketability of ESS within coupled energy networks.

(2)

Structural Incentive Design: Through upper–lower-level game-theoretic coordination, energy storage simultaneously serves the IES-level system objectives while maintaining its own arbitrage capability in response to price signals such as electricity price, carbon price, and DR. This forms an incentive-compatible structure that aligns system-level optimality with individual-level profitability.

(3)

Performance Outcomes: Case studies demonstrate that independently optimised energy storage scheduling not only reduces IES operational costs and carbon emissions but also improves renewable energy utilisation and increases net storage revenue. It thereby offers a viable pathway toward dynamically balancing economic performance and low-carbon objectives, while enhancing system-level operational flexibility.

Although configuring storage as an independent operator can substantially improve the economics of IESs and facilitate local absorption of renewables, further advances are needed to address uncertainty under high renewable penetration. First, an integrated, multi-time-scale “planning-operation-control” configuration framework should be developed to co-ordinate electrical, thermal, and hydrogen storage, jointly with P2G and CCS coupling links, thereby enabling cross-carrier complementarity and seasonal load shifting. Second, prices from multiple markets—carbon, green certificates, capacity, and ancillary services—should be endogenised in sizing and dispatch decisions; Stackelberg game formulations and mechanism design can be employed to ensure incentive compatibility between the independent storage operator and the IES operator, with extensions to multi-park sharing, coalition-based configuration, and benefit allocation. Pursuing these directions may yield a replicable and scalable paradigm for storage planning that balances low-carbon objectives, economic efficiency, and flexibility, thereby supporting a high-quality, low-carbon transition of park-level multi-energy systems.