A Two-Stage Optimal Dispatch Strategy for Electric-Thermal-Hydrogen Integrated Energy System Based on IGDT and Fuzzy Chance-Constrained Programming

Abstract

To address the economic and reliability challenges of high-penetration renewable energy integration in electricity-heat-hydrogen integrated energy systems and support the dual-carbon strategy, this paper proposes an optimal dispatch method integrating Information Gap Decision Theory (IGDT) and Fuzzy Chance-Constrained Programming (FCCP). An IES model coupling multiple energy components was constructed to exploit multi-energy complementarity. A stepped carbon trading mechanism was introduced to quantify emission costs. For interval uncertainties in renewable generation, IGDT-based robust and opportunistic dispatch models were established; for fuzzy load uncertainties, FCCP transformed them into deterministic equivalents, forming a dual-layer “IGDT-FCCP” uncertainty handling framework. Simulation using CPLEX demonstrated that the proposed model dynamically adjusts uncertainty tolerance and confidence levels, effectively balancing economy, robustness, and low-carbon performance under complex uncertainties: reducing total costs by 12.7%, cutting carbon emissions by 28.1%, and lowering renewable curtailment to 1.8%. This study provides an advanced decision-making paradigm for low-carbon resilient IES.

1. Introduction

Against the backdrop of global energy transition and the “dual-carbon” strategic goals, integrated energy systems (IES) have emerged as critical enablers for improving energy efficiency and promoting renewable energy consumption due to their prominent advantages in multi-energy coordination and cascade utilization [1,2]. Among them, electricity-heat integrated energy systems (E-H IES), as a typical form of IES, play a vital role in regional heating and power supply [3,4]. However, with the increasing penetration of volatile renewable energy sources such as wind and solar power, the randomness and intermittency of their output pose significant challenges to the security, stability, and economic operation of IES [5]. Meanwhile, the demand side also exhibits substantial uncertainties. Traditional deterministic dispatch methods struggle to handle such dual uncertainties, often resulting in overly conservative or aggressive scheduling schemes that lead to economic losses or operational risks.

Against a low-carbon backdrop, integrating carbon trading into power systems with large-scale wind generation can curtail the output of thermal and combined heat and power (CHP) units, enlarge grid-access space for wind, and cut aggregate carbon emissions. Extensive studies on carbon-trading mechanisms have been reported. Ref. [6] incorporated carbon-trading cost into an electricity-gas integrated energy system and proposed a corresponding dispatch model. Ref. [7] balanced economics and low-carbon performance through a three-stage dispatch framework that coordinated nuclear, thermal and virtual-power-plant units. Ref. [8] developed a multi-objective environmental-economic dispatch strategy that decomposed carbon-trading cost into allowance cost, carbon revenue and emission penalty, while simultaneously considering carbon and other pollutant costs. Although these works embed carbon cost and favor energy saving and emission reduction, they do not partition the system’s carbon emissions into distinct blocks. Building on conventional carbon trading, this paper introduces a stepwise carbon-trading model to further boost the accommodation of renewable generation, such as wind, and to reduce carbon emissions.

The introduction of carbon trading has significantly improved grid accommodation of wind power; however, the volatility and uncertainty of wind generation have also intensified the difficulty of scheduling decisions. Considerable research has therefore been devoted to coping with wind-power fluctuations and source–load uncertainty. Ref. [9] addressed post-fault service restoration in active distribution networks, with explicit emphasis on source–load uncertainty. A priority-restoration index that integrates load-importance grades and time-varying demand characteristics was proposed, and a two-stage restoration problem for the remaining load was solved by a column-and-constraint generation (C&CG) algorithm. Ref. [10] tackled the challenges posed by source–load uncertainty in distribution systems by developing a two-stage robust planning method for flexible interconnection devices (FIDs) in substations. Ref. [11] focused on building-photovoltaic-assisted distributed energy systems (DES) and constructed a bi-level fuzzy chance-constrained, multi-objective optimization model to simultaneously determine system sizing and energy-scheduling strategies under source–load uncertainty. Ref. [12] proposed a short-term peak-shaving stochastic optimization framework for hydro–wind–PV hybrid renewable systems to confront dual source–load uncertainty. A deep convolutional generative adversarial network (DCGAN) was employed to simulate wind and PV output uncertainty, while a martingale model characterized the randomness of hydrological inflow and load demand. Ref. [13] deals with renewable-energy fluctuations and unstable load demand in high-altitude integrated energy systems (HAIES) by developing a community-level architecture that integrates electricity, heat, hydrogen and oxygen supply, and established an indoor oxygen-concentration balance model based on diffusion supply. Ref. [14] proposed a two-stage stochastic optimization problem based on IGDT and RAS to effectively reduce the risks associated with information gaps faced by microgrid operators. However, existing studies mostly focus on uncertainty handling for a single energy side, with insufficient consideration for source-load dual uncertainties.

On the other hand, achieving the “dual-carbon” goals requires IES to balance economy and low-carbon performance. Carbon capture technology is of great concern because of its ability to effectively reduce carbon emissions from energy production. Ref. [15] proposed a thermo-economic research method for a combined cycle power plant integrating carbon capture and methanation. It was used to address the issue of evaluating the thermo-economic performance of combined cycle systems in the context of carbon capture. Ref. [16] put forward a life-cycle comparison and evaluation method for U.S. coal-fired power plants based on MEA/MOF carbon capture technology. It solved the problem of comparing the environmental impacts of different carbon capture technologies in coal-fired power plants. Ref. [17] presented an optimal scheduling method for a near-zero-carbon integrated energy system that considered waste incineration—carbon capture systems and market mechanisms. It resolved the optimization problem of the coordinated operation of carbon capture and waste incineration in multi-energy systems. Ref. [18] developed a joint economic-emission scheduling model for an electricity-heat integrated system that took into account multi-energy demand response and carbon capture technology. It tackled the collaborative optimization problem of carbon emissions and the operation costs in electricity-heat systems. Ref. [19] proposed a collaborative optimization method for multi-energy systems considering carbon capture systems and power-to-gas technology. It was applied to the optimization problem of the integrated operation of carbon capture and power-to-gas technology in multi-energy systems. Ref. [20] established an environmental and economic scheduling optimization model that considers power-to-gas technology and carbon capture power plants. It solved the collaborative optimization problem of low-carbon operation and economy in integrated energy systems. Ref. [21] conducted an empirical study on whether the carbon trading mechanism improved green innovation efficiency. It addressed the evaluation problem of the impact of carbon trading policies on green innovation efficiency. Ref. [22] proposed a low-carbon economic scheduling model for virtual power plants with carbon capture systems connected, considering the green certificate—carbon trading mechanism. It resolved the low-carbon operation optimization problem of virtual power plants under the carbon trading and green certificate mechanisms.

In summary, incorporating a carbon-trading mechanism can effectively increase wind-power accommodation; however, as the installed wind capacity grows, its variability exerts an increasingly severe impact on the system. Among the existing studies that aim to improve environmental performance and reduce carbon emissions, economic dispatch models that simultaneously account for the uncertainties introduced by renewable integration remain scarce.

In this context, this paper focuses on electricity-heat-hydrogen integrated energy systems with a high penetration of renewable energy, aiming to address their low-carbon economic dispatch under source-load dual uncertainties. The main contributions are as follows:

• A dual-layer uncertainty handling framework combining IGDT and fuzzy chance constraints was proposed. IGDT was used to handle interval uncertainties in renewable energy output, characterizing decision-makers’ risk preferences; fuzzy chance constraints were employed to address load uncertainties, transformed into deterministic equivalent forms for solution.
• Building on traditional operational costs, a stepped carbon trading cost was introduced, enabling the dispatch model to actively respond to national carbon reduction policies and achieve dual objectives of economy and low-carbon operation.

In summary, to address the challenges of source-load uncertainties and low-carbon economic operation in integrated electricity-heat-hydrogen energy systems with a high-penetration renewable energy integration, this study aims to establish an optimal dispatch framework integrating electricity-hydrogen-thermal multi-energy storage and advanced uncertainty decision-making theories. The proposed model was subsequently simulated using a provincial regional integrated energy system as a case study to validate its rationality and effectiveness.

2. Integrated Electricity-Heat-Hydrogen Energy System: Architecture and Component Models

The structural configuration and energy flow directions of the integrated electricity-heat-hydrogen energy system discussed in this paper are illustrated in Figure 1. The primary components within the network include a wind turbine (WT), photovoltaic (PV) system, combined heat and power (CHP) system, heat pump (HP), electric boiler (EB), electrolyzer (ELY), hydrogen compressor (HCP), hydrogen storage tank (HST), hydrogen fuel cell (HFC), electrical energy storage (EES), and thermal energy storage (TES).

2.1. Component Models

2.1.1. Combined Heat and Power System

The key components of the Combined Heat and Power (CHP) system primarily consist of a gas turbine and a lithium bromide absorption chiller. During operation, the system utilizes natural gas combustion to recover high-grade thermal energy for power generation via a microturbine, while the high-temperature waste heat from the microturbine exhaust is reclaimed by the absorption chiller for heating purposes. This study adopts the C65 model microturbine manufactured by Capstone Turbine Corporation (U.S.) as the research subject, with the assumption that external environmental variations have negligible effects on power generation and fuel combustion efficiency. The mathematical model representing its thermoelectric relationship is expressed as follows:

$${{\displaystyle Q}}_{GT}\left(t\right)={\displaystyle \frac{{{\displaystyle P}}_{GT}\left(t\right)\left(1-{{\displaystyle \eta }}_{GT}\left(t\right)-{{\displaystyle \eta }}_L\right)}{{{\displaystyle \eta }}_{GT}\left(t\right)}}$$

(1)

$${{\displaystyle Q}}_{GT-h}\left(t\right)={{\displaystyle Q}}_{GT}\left(t\right){{\displaystyle \eta }}_h{{\displaystyle C}}_{OPh}$$

(2)

where the waste heat output, electrical power output, and power generation efficiency of the gas turbine during time period t are denoted by Q_GT(t), P_GT(t), and ƞ_GT(t), respectively; ƞ_L represents the heat loss coefficient; ${{\displaystyle Q}}_{GT-h}\left(t\right)$ indicates the heating capacity of the absorption chiller during time period t; ${{\displaystyle C}}_{OPh}$ and ${{\displaystyle \eta }}_h$ correspond to the coefficient of performance and waste heat recovery efficiency of the absorption chiller, respectively.

The fuel cost of the microturbine during the time period t is expressed as:

$${{\displaystyle C}}_{GT}\left(t\right)={{\displaystyle C}}_{CH4}{\displaystyle \frac{{{\displaystyle P}}_{GT}\left(t\right)\Delta t}{{{\displaystyle \eta }}_{GT}\left(t\right)\times {{\displaystyle L}}_{LHV}}}$$

(3)

where $\Delta t$ denotes the unit dispatch time interval; ${{\displaystyle C}}_{GT}\left(t\right)$ represents the fuel cost consumed by the microturbine during time period t. Additionally, the price of natural gas ${{\displaystyle C}}_{CH4}$ is set at 2.5 CNY/m³; ${{\displaystyle L}}_{LHV}$ denotes the lower heating value of natural gas, taken as 9.7 kWh/m³.

2.1.2. Electrolyzer

An electrolyzer typically comprises an anode, a cathode, and an electrolytic cell body, often separated by a diaphragm to isolate the two electrodes. When a direct current is applied, hydrogen gas is produced through reduction reactions at the cathode. Unlike constant-power electrolyzer models, the model established in this paper features an adaptive operational strategy that adjusts its power consumption in response to fluctuations in renewable energy generation and load demand. The mathematical formulation is presented in Equations (4)–(6).

$${{\displaystyle H}}_{j,t}^{ELY}={\displaystyle \frac{{{\displaystyle \eta }}_F{{\displaystyle N}}_j^{ELY}{{\displaystyle I}}_{j,t}^{ELY}{{\displaystyle V}}_j^{ELY}}{{{\displaystyle FZ}}_e{{\displaystyle V}}_j^{ELY}}}={{\displaystyle A}}_j^{ELY}{{\displaystyle P}}_{j,t}^{ELY}$$

(4)

$${{\displaystyle A}}_j^{ELY}={\displaystyle \frac{{{\displaystyle \eta }}_F{{\displaystyle N}}_j^{ELY}}{{{\displaystyle FZ}}_e{{\displaystyle V}}_j^{ELY}}}$$

(5)

$$0\le {{\displaystyle P}}_{j,t}^{ELY}\le {{\displaystyle P}}_{j,\max }^{ELY}$$

(6)

where ${{\displaystyle H}}_{j,t}^{ELY}$ denotes the hydrogen production rate of the electrolyzer; ${{\displaystyle P}}_{j,t}^{ELY}$ represents the power consumption of the electrolyzer; ${{\displaystyle \eta }}_F$ is the Faraday efficiency, which exhibits a positive correlation with electrolyte temperature; ${{\displaystyle I}}_{j,t}^{ELY}$ denotes the current efficiency, representing the ratio of actual to theoretical hydrogen production; ${{\displaystyle N}}_j^{ELY}$ indicates the number of units in the electrolyzer array; ${{\displaystyle Z}}_e$ is the number of electron moles transferred in the reaction; $F$ represents the Faraday constant; ${{\displaystyle V}}_j^{ELY}$ denotes the constant terminal voltage of the electrolyzer; ${{\displaystyle A}}_j^{ELY}$ is the hydrogen production coefficient of the electrolyzer.

3. Optimal Dispatch of Electricity-Heat-Hydrogen Integrated Energy Systems Based on IGDT and Fuzzy Chance-Constrained Programming

To address the uncertainties in renewable energy generation and load forecasting, this section establishes an optimal planning model for integrated electricity-heat-hydrogen energy storage systems based on IGDT and fuzzy chance-constrained programming. At the planning level, the upper layer employs IGDT to handle interval uncertainties in wind and photovoltaic power output. Through robust model (RM) and opportunistic model (OM) frameworks, it dynamically adjusts the uncertainty tolerance level α, effectively capturing decision-makers’ risk preferences. The lower layer utilizes fuzzy chance-constrained programming (FCCP) to address fuzzy uncertainties in load demand, employing trapezoidal fuzzy numbers to characterize load forecasting errors while converting fuzzy constraints into deterministic equivalents for solution. Furthermore, at the operational level, the coordinated optimization of the integrated electricity-heat-hydrogen supply network is achieved through flexible load scheduling and leveraging source-load interaction characteristics.

3.1. Parameter Characterization of Wind and Photovoltaic Uncertainty

This paper employs the Information Gap Decision Theory (IGDT) method to optimize and handle uncertainties associated with wind and solar power generation. IGDT is a decision-making methodology designed to address non-probabilistic uncertainties. This approach is particularly suitable for uncertainty characterization where probabilistic representations or specific scenario generation are difficult to establish. Compared to traditional robust optimization techniques, IGDT not only focuses on system stability during optimization but also considers economic efficiency, thereby achieving a more effective balance between operational security and cost-effectiveness. Within this framework, uncertain inputs are represented as vaguely defined sets, characterized through non-probabilistic uncertainty sets such as envelope-bound models, fractional uncertainty models, and ellipsoidal models. This study adopts the fractional uncertainty model for investigation, the actual power output of wind power ${{\displaystyle P}}_{wt}^{act}$ and photovoltaic generation ${{\displaystyle P}}_{pv}^{act}$ fluctuates around their respective forecast values ${{\displaystyle P}}_{wt}^{for}$ and ${{\displaystyle P}}_{pv}^{for}$ expressed mathematically as follows:

$$U\left(\alpha ,{{\displaystyle P}}^{for}\right)=\left\{{{\displaystyle P}}^{act}:\left|{\displaystyle \frac{{{\displaystyle P}}^{for}-{{\displaystyle P}}^{act}}{{{\displaystyle P}}^{for}}}\right|\le \alpha \right\},\alpha \ge 0$$

(7)

where $\alpha$ represents the uncertainty deviation factor. The risk-aversion robust model (RM) aims to ensure that the system cost ${{\displaystyle P}}^{act}=\left(1-\alpha \right){{\displaystyle P}}^{for}$ does not exceed a critical threshold under the worst-case scenario, while the risk-seeking opportunistic model (OM) seeks the possibility of obtaining additional benefits ${{\displaystyle P}}^{act}=\left(1+\alpha \right){{\displaystyle P}}^{for}$ under the most favorable conditions.

3.2. Parameter Characterization of Electric Load Demand Uncertainty

It is more reasonable to characterize electric load uncertainty through fuzzy parameters, given that this approach does not rely on extensive statistical data or exact probability distributions. In this paper, the electric load power—which exhibits significant stochasticity and volatility—is treated as a fuzzy uncertain variable characterized by a trapezoidal membership function:

$$\mu \left({{\displaystyle P}}_{\mathit{load}}\right)=\left\{\begin{array}{ll}{\displaystyle \frac{{{\displaystyle P}}_{\mathit{load}}-{{\displaystyle P}}_1}{{{\displaystyle P}}_2-{{\displaystyle P}}_1}}\hfill & {{\displaystyle P}}_1\le {{\displaystyle P}}_{\mathit{load}}\le {{\displaystyle P}}_2\hfill \\ 1\hfill & {{\displaystyle P}}_2\le {{\displaystyle P}}_{\mathit{load}}\le {{\displaystyle P}}_3\hfill \\ {\displaystyle \frac{{{\displaystyle P}}_4-{{\displaystyle P}}_{\mathit{load}}}{{{\displaystyle P}}_4-{{\displaystyle P}}_3}}\hfill & {{\displaystyle P}}_3\le {{\displaystyle P}}_{\mathit{load}}\le {{\displaystyle P}}_4\hfill \\ 0\hfill & \mathrm{other}\hfill \end{array}\right.$$

(8)

$${{\displaystyle P}}_i={{\displaystyle w}}_i{{\displaystyle P}}_{\mathit{load}}$$

(9)

where ${{\displaystyle P}}_1$, ${{\displaystyle P}}_2$, ${{\displaystyle P}}_3$, and ${{\displaystyle P}}_4$ represent trapezoidal fuzzy parameters, as illustrated in Figure 2; ${{\displaystyle P}}_{\mathit{load}}$ denotes the forecast value of electric load power; ${{\displaystyle w}}_i$ is a scaling coefficient within the range of 0 to 1, which can be derived from historical data.

The fuzzy expression $\widetilde{{{\displaystyle P}}_{\mathit{load}}}$ for renewable energy generation or load power can be mathematically represented as follows:

$$\widetilde{{{\displaystyle P}}_{\mathit{load}}}=({{\displaystyle P}}_1,{{\displaystyle P}}_2,{{\displaystyle P}}_3,{{\displaystyle P}}_4)$$

(10)

3.3. Carbon Emission Cost Calculation Model

The carbon trading mechanism is an emission reduction system that treats carbon emissions as a tradable commodity. At present, there are two main methods for allocating carbon trading allowances in China, namely the historical method and the benchmarking method. This paper adopts the benchmarking method for the allocation of carbon emission allowances and approximately assumes that the system’s carbon emission allowances are proportional to the output of thermal power units. To better control the system’s carbon emissions, this paper adopts a stepped carbon emission cost model divided into three tiers. The specific calculation is formulated as follows:

$${{\displaystyle C}}_{\mathit{carbon}}=\left\{\begin{array}{ll}\mu ({{\displaystyle E}}_P-{{\displaystyle E}}_L)\hfill & {{\displaystyle E}}_P\le {{\displaystyle E}}_L+d \hfill \\ \mu d+(1+k)\mu ({{\displaystyle E}}_P-{{\displaystyle E}}_L-d)\hfill & {{\displaystyle {{\displaystyle E}}_L+d<E}}_P\le {{\displaystyle E}}_L+2d \hfill \\ (2+K)\mu d+(1+2k)\mu ({{\displaystyle E}}_P-{{\displaystyle E}}_L-2d)\hfill & {{\displaystyle E}}_P>{{\displaystyle E}}_L+2d\hfill \end{array}\right.$$

(11)

where ${{\displaystyle C}}_{\mathit{carbon}}$ denotes the total carbon emission cost; E_L represents the total carbon emission allowance allocated to the system; E_P indicates the actual carbon emissions during one dispatch cycle; μ is the carbon trading price; d represents the length of each carbon emission interval; and k denotes the incremental rate of carbon trading price per tier. It should be noted that when E_P < E_L, the value of C becomes negative, indicating that the system’s actual carbon emissions are lower than its allocated allowance. The surplus carbon credits can be traded in the carbon market at the initial carbon price, generating carbon revenue for the system.

3.4. Objective Function

By integrating thermal energy storage technology, the combined heat and power (CHP) system is no longer required to strictly follow thermal load fluctuations during heating operations, thereby enhancing operational flexibility. In terms of power supply, priority is given to renewable energy sources such as wind and solar power to maximize their utilization, considering environmental factors and dispatch controllability, while simultaneously implementing a maximum power point tracking strategy. Under the premise that certain unit strategies have been predetermined, this study focuses on optimizing decisions to minimize the daily operational cost of the integrated electricity-heat energy system, aiming to achieve cost-effective daily operation. The objective function comprises the following components:

$$\mathrm{MIN}{{\displaystyle C}}_{total}={\displaystyle \sum _{t=1}^{{{\displaystyle N}}_T}\left[{{\displaystyle C}}_{fu}\left(t\right)+{{\displaystyle C}}_{grid}\left(t\right){{\displaystyle +C}}_{om}\left(t\right)+{{\displaystyle C}}_{env}\left(t\right)+{{\displaystyle C}}_{carbon}\left(t\right)+{{\displaystyle C}}_{{{\displaystyle H}}_2}\left(t\right)\right]\Delta t}$$

(12)

$${{\displaystyle C}}_{fu}\left(t\right)={\displaystyle \frac{{{\displaystyle C}}_{CH4}\Delta t}{{{\displaystyle L}}_{LHV}}}\cdot {\displaystyle \frac{{{\displaystyle P}}_{GT}\left(t\right)}{{{\displaystyle \eta }}_{GT}\left(t\right)}}$$

(13)

$${{\displaystyle C}}_{grid}\left(t\right)={\displaystyle \frac{1}{2}}\left[\left({{\displaystyle C}}_{rs}\left(t\right)+{{\displaystyle C}}_{rb}\left(t\right)\right){{\displaystyle P}}_{ex}\left(t\right)+\left({{\displaystyle C}}_{rb}\left(t\right)-{{\displaystyle C}}_{rs}\left(t\right)\right)\left|{{\displaystyle P}}_{ex}\left(t\right)\right|\right]$$

(14)

$${{\displaystyle C}}_{om}\left(t\right)={\displaystyle \sum _{i=1}^{{{\displaystyle N}}_M}{{\displaystyle C}}_{Mi}}\left|{{\displaystyle P}}_i\left(t\right)\right|$$

(15)

$${{\displaystyle C}}_{env}\left(t\right)=\left[{\displaystyle \frac{1}{2}}\left(-0.57+0.6101\right)\times ({{\displaystyle P}}_P{{\displaystyle P}}_{GT}\left(t\right)+{{\displaystyle h}}_{GT}{{\displaystyle P}}_{GT}\left(t\right)+{{\displaystyle P}}_{EB}\left(t\right))\right]$$

(16)

$${{\displaystyle C}}_{{{\displaystyle H}}_2}(t)={{\displaystyle C}}^{PH}{{\displaystyle H}}_{i,t}^{PH}$$

(17)

where ${{\displaystyle C}}_{total}$ denotes the total operating cost; ${{\displaystyle N}}_T$ represents the total number of scheduling periods; ${{\displaystyle C}}_{fu}\left(t\right)$, ${{\displaystyle C}}_{grid}\left(t\right)$, ${{\displaystyle C}}_{om}\left(t\right)$, ${{\displaystyle C}}_{env}\left(t\right)$, and ${{\displaystyle C}}_{{{\displaystyle H}}_2}(t)$ represent the fuel cost, grid exchange cost, maintenance cost, environmental cost, and planning and operational costs of hydrogen energy systems at time period t, respectively. Among them, the environmental cost refers to the cost of other local pollutants internally, that do not include the cost of CO₂ emissions. ${{\displaystyle P}}_{ex}\left(t\right)$, ${{\displaystyle C}}_{rs}\left(t\right)$, and ${{\displaystyle C}}_{rb}\left(t\right)$ represent the power exchange with the grid, electricity selling price, and electricity purchasing price at time period t, respectively; ${{\displaystyle N}}_M$ denotes the total number of units within the system; ${{\displaystyle C}}_{Mi}$ indicates the maintenance cost per unit for the i-th unit; ${{\displaystyle P}}_i\left(t\right)$ represents the power output of the i-th unit at time period t; ${{\displaystyle P}}_P$ is the power conversion coefficient; ${{\displaystyle h}}_{GT}$ denotes the thermal efficiency for heating; ${{\displaystyle P}}_{EB}\left(t\right)$ denotes the electric power input of the electric boiler during time period t. ${{\displaystyle C}}^{PH}$ denotes the unit hydrogen purchase cost; ${{\displaystyle H}}_{i,t}^{PH}$ represents the hydrogen purchase rate.

3.5. Constraints

3.5.1. Power Balance Constraints

The electric power balance constraint, thermal power balance constraint, and hydrogen power balance constraint established in this study are formulated as follows:

$$\begin{array}{l}{{\displaystyle P}}_{grid}(t)+{{\displaystyle P}}_{GT}(t)+{{\displaystyle P}}_{PV}^{act}(t)+{{\displaystyle P}}_{WT}^{act}(t)+{{\displaystyle P}}^{HFC}(t)+{{\displaystyle P}}_{EES}^{dis}(t)=\\ {{\displaystyle P}}_{load}^{act}(t)+{{\displaystyle P}}_{EB}(t)+{{\displaystyle P}}_{HP}(t)+{{\displaystyle P}}^{ELY}(t)+{{\displaystyle P}}_{EES}^{ch}(t)\end{array}$$

(18)

$${{\displaystyle Q}}_{GT-h}(t)+{{\displaystyle Q}}_{EB}(t)+{{\displaystyle Q}}_{HP}(t)+{{\displaystyle P}}_{HS}^{dis}={{\displaystyle Q}}_{load}(t)+{{\displaystyle P}}_{HS}^{ch}(t)$$

(19)

$${{\displaystyle P}}^{ELY}(t)+{{\displaystyle H}}_{i,t}^{PH}+{{\displaystyle P}}_{HS}^{dis,{{\displaystyle H}}_2}(t)={{\displaystyle P}}_{HFC}^{{{\displaystyle H}}_2}(t)+{{\displaystyle H}}_{load}(t)+{{\displaystyle P}}_{HS}^{ch,{{\displaystyle H}}_2}(t)+{{\displaystyle H}}_{e,t}^{PH}(t)$$

(20)

where ${{\displaystyle P}}_{EES}^{dis}(t)$ and ${{\displaystyle P}}_{EES}^{ch}(t)$ denote the discharging and charging power of electrical energy storage during time period t; ${{\displaystyle P}}^{ELY}$ represents the electrical power consumption of the electrolyzer; ${{\displaystyle P}}_{load}^{act}(t)$ represents the actual electrical load at time period t; ${{\displaystyle P}}_{EB}(t)$ and ${{\displaystyle Q}}_{EB}(t)$ indicates the electricity consumption and heat output of the electric boiler at time period t; ${{\displaystyle P}}_{HP}(t)$ and ${{\displaystyle Q}}_{HP}(t)$ represent the electricity consumption and heat output of the heat pump at time period t; ${{\displaystyle P}}_{HS}^{ch}(t)$ and ${{\displaystyle P}}_{HS}^{dis}$ denote the charging and discharging thermal power of thermal energy storage at time period t; ${{\displaystyle Q}}_{load}(t)$ represents the thermal load at time period t; ${{\displaystyle P}}_{HS}^{ch,{{\displaystyle H}}_2}(t)$ and ${{\displaystyle P}}_{HS}^{dis,{{\displaystyle H}}_2}(t)$ indicate the hydrogen charging and discharging rates of the hydrogen storage tank at time period t; ${{\displaystyle H}}_{load}(t)$ denotes the hydrogen load at time period t; ${{\displaystyle H}}_{e,t}^{PH}(t)$ represents the external hydrogen selling efficiency; ${{\displaystyle P}}_{HFC}^{{{\displaystyle H}}_2}(t)$ denotes the hydrogen consumption rate of the fuel cell at time period t.

Since the actual electric power load follows a trapezoidal fuzzy number, the power balance constraints in the overall model are formulated as fuzzy chance constraints, which can be converted into their deterministic equivalents based on standard transformation methods. To facilitate obtaining analytical solutions, this paper transforms the electric power balance constraints under trapezoidal fuzzy parameters into corresponding deterministic equivalent forms, expressed as follows:

$$\begin{array}{l}(2-2\beta )\cdot ({{\displaystyle P}}_3-{{\displaystyle P}}_{W2})+(2\beta -1)\cdot ({{\displaystyle P}}_4-{{\displaystyle P}}_{W1})+{{\displaystyle P}}_{grid}(t)+{{\displaystyle P}}_{GT}(t)+{{\displaystyle P}}_{PV}^{act}(t)+\\ {{\displaystyle P}}_{WT}^{act}(t)+{{\displaystyle P}}^{HFC}(t)+{{\displaystyle P}}_{EES}^{dis}(t)-{{\displaystyle P}}_{EB}(t)-{{\displaystyle P}}_{HP}(t)-{{\displaystyle P}}^{ELY}(t)-{{\displaystyle P}}_{EES}^{ch}(t)=0\end{array}$$

(21)

where $\beta$ denotes the confidence level; ${{\displaystyle P}}_{W1}$ and ${{\displaystyle P}}_{W2}$ represent the key parameters of the fuzzy numbers for wind and photovoltaic power output.

3.5.2. Equipment Operational Constraints

$${{\displaystyle P}}_{i,\min }\le {{\displaystyle P}}_i(t)\le {{\displaystyle P}}_{i,\max }$$

(22)

$${{\displaystyle -RD}}_i\cdot \Delta t\le {{\displaystyle P}}_i(t)-{{\displaystyle P}}_i(t-1)\le {{\displaystyle RU}}_i\cdot \Delta t$$

(23)

where ${{\displaystyle P}}_{i,\min }$ and ${{\displaystyle P}}_{i,\max }$ represent the minimum and maximum power output of unit i, respectively; ${{\displaystyle RD}}_i$ and ${{\displaystyle RU}}_i$ denote the downward and upward ramp rates of unit i, respectively.

3.5.3. Energy Storage System Constraints

$$0\le {{\displaystyle P}}_{EES}^{dis}(t)\le {{\displaystyle P}}_{EES,\max }^{dis}(t)\cdot {{\displaystyle \delta }}^{dis}(t)$$

(24)

$$0\le {{\displaystyle P}}_{EES}^{ch}(t)\le {{\displaystyle P}}_{EES,\max }^{ch}(t)\cdot {{\displaystyle \delta }}^{ch}(t)$$

(25)

$${{\displaystyle \delta }}^{ch}(t)+{{\displaystyle \delta }}^{dis}(t)\le 1$$

(26)

$$SOC(t)=SOC(t-1)+({{\displaystyle \eta }}^{ch}\cdot {{\displaystyle P}}_{EES}^{ch}(t)-{\displaystyle \frac{{{\displaystyle P}}_{EES}^{dis}(t)}{{{\displaystyle \eta }}^{dis}}})\cdot {\displaystyle \frac{\Delta t}{{{\displaystyle E}}_{cap}}}$$

(27)

$$SO{C}_{\min }\le SOC(t)\le SO{C}_{\max }$$

(28)

$$SOC(0)=SOC(T)$$

(29)

The above constraints apply to electrical energy storage and thermal energy storage systems, where ${{\displaystyle \delta }}^{ch}(t)$ and ${{\displaystyle \delta }}^{dis}(t)$ represent binary variables indicating the charging and discharging states, respectively; ${{\displaystyle \eta }}^{ch}$ and ${{\displaystyle \eta }}^{dis}$ denote the charging and discharging efficiencies, respectively; $SOC(t)$ and ${{\displaystyle E}}_{cap}$ represent the state of charge (SOC) and the rated storage capacity at time period t, respectively.

$$0\le {{\displaystyle H}}_{ch}(t)\le {{\displaystyle H}}_{ch}^{\max }$$

(30)

$$0\le {{\displaystyle H}}_{dis}(t)\le {{\displaystyle H}}_{dis}^{\max }$$

(31)

$${{\displaystyle H}}_{ch}(t)+{{\displaystyle H}}_{dis}(t)\le 1$$

(32)

$${{\displaystyle L}}_{HS}(t)={{\displaystyle L}}_{HS}(t-1)+({{\displaystyle H}}_{ch}(t)-{{\displaystyle H}}_{dis}(t))\cdot \Delta t$$

(33)

$${{\displaystyle L}}_{HS}^{\min }\le {{\displaystyle L}}_{HS}(t)\le {{\displaystyle L}}_{HS}^{\max }$$

(34)

The above constraints pertain to hydrogen energy storage, which typically does not consider efficiency differences or mutual exclusion between charging and discharging processes, with its state represented by volume. Where ${{\displaystyle H}}_{ch}(t)$ and ${{\displaystyle H}}_{dis}(t)$ denote the hydrogen charging and discharging rates of the hydrogen storage tank, respectively; ${{\displaystyle L}}_{HS}(t)$ represents the capacity of the hydrogen storage tank at time period t.

3.5.4. Grid Interaction Constraints

$$-{{\displaystyle P}}_{grid,\max }^{buy}\le {{\displaystyle P}}_{grid}\le {{\displaystyle P}}_{grid,\max }^{sell}$$

(35)

Grid interaction constraints are imposed to limit the exchange power with the upstream grid, ensuring compliance with physical line capacity limitations.

3.5.5. IGDT Objective Constraint

Robustness Model:

$${{\displaystyle C}}_{total}\le (1+{{\displaystyle \delta }}_m)\cdot {{\displaystyle C}}_0$$

(36)

This constraint requires that even when renewable power generation is at its worst-case scenario (actual output = forecast value × (1 − α)), the total system cost must not exceed $(1+{{\displaystyle \delta }}_m)$ times the baseline cost ${{\displaystyle C}}_0$. A larger ${{\displaystyle \delta }}_m$ (robust deviation factor) indicates a more risk-averse decision-maker who is willing to pay higher costs to mitigate wind and solar power uncertainties.

Opportuneness Model:

$${{\displaystyle C}}_{total}\le (1-{{\displaystyle \epsilon }}_m)\cdot {{\displaystyle C}}_0$$

(37)

This constraint requires that even when renewable power generation experiences favorable fluctuations (actual output = forecast value × (1 + α)), the total system cost is expected to decrease to $(1-{{\displaystyle \epsilon }}_m)$ times the baseline cost ${{\displaystyle C}}_0$. A larger ${{\displaystyle \epsilon }}_m$ (opportunistic deviation factor) indicates a more risk-seeking decision-maker who is willing to embrace uncertainty to pursue lower operational costs.

3.6. Interaction Between IGDT and FCCP

The proposed “IGDT-FCCP” dual-layer uncertainty handling framework features a sequentially coupled, unidirectional series structure, rather than an iterative solution loop. The interaction mechanism is detailed as follows:

Lower-layer Processing (FCCP Layer): Firstly, to address the fuzzy uncertainties in electrical load demand, Fuzzy Chance-Constrained Programming (FCCP) is employed. The electric power balance constraint containing fuzzy parameters is converted into its deterministic equivalent. This step “hardens” the fuzzy programming problem into a deterministic constraint incorporating the confidence level β.

Upper-layer Processing (IGDT Layer): Subsequently, the resulting deterministic equivalent model from the FCCP step serves as the base model for the Information Gap Decision Theory (IGDT) optimization layer. Building upon this model, the IGDT layer introduces the interval uncertainty model for renewable energy output and constructs the risk-averse Robust Model (RM) and the risk-seeking Opportunistic Model (OM), respectively. The objective of the IGDT layer is to find the optimal dispatch strategy under specific uncertainty fluctuations (characterized by α).

This series structure ensures that the fuzzy risks on the load side (managed by β) and the interval fluctuation risks on the generation side (managed by α) can be considered simultaneously within a unified optimization framework, while remaining computationally tractable.

3.7. Model Solution Methodology

The objective function incorporates nonlinear terms as well as integer variables representing the operational on/off states of certain units. This problem is characterized as a mixed-integer nonlinear programming (MINLP) problem in its standard formulation:

$$\begin{array}{c}\min f\left(x,y\right)\\ s.t.\left\{\begin{array}{c}{{\displaystyle Z}}_h\left(x,y\right)=0,h=1,2,\dots \dots m\\ {{\displaystyle V}}_g\left(x,y\right)\le 0,g=1,2,\dots \dots n\\ x_{\min }\le x\le x_{\max }\\ y\in \left(0,1\right)\end{array}\right.\end{array}$$

(38)

The optimization variable x encompasses the power output of specific equipment. The optimization variable y reflects the operational status (on/off) of fuel-based units. Equality constraints are established based on energy balance principles within the system and the energy dynamics of storage devices. Inequality constraints define the operational limits of individual components. To enhance computational speed and efficiency, this study adopts a methodology similar to that proposed in the relevant literature, transforming the problem into a Mixed-Integer Linear Programming (MILP) formulation and solving it using the CPLEX solver.

4. Case Study

4.1. Parameter Description of the Case Study

This study investigated an integrated electricity-heat energy system in a specific region, with the total number of dispatch periods set to N_T = 24 and each dispatch period lasting Δt = 1 h. Within each dispatch interval, the output and exchange power of all components remained constant, and electricity trading prices followed a time-of-use tariff structure. Due to the use of batteries for electrical energy storage and thermal storage tanks for thermal energy storage—coupled with the characteristic duration of a single dispatch period—all exhaust gases emitted by the microturbine during each dispatch period were fully utilized by the lithium bromide absorption chiller [23,24,25]. The optimization model was implemented in MATLAB R2023b using the YALMIP platform and solved with the CPLEX solver.

Parameters of the integrated electricity-heat-hydrogen system are provided in

Table 1. System parameters.

Parameters	Rated Electrical Power	Rated Thermal Power	Electrical Efficiency	Thermal Efficiency	Ramp Rate	Unit O&M Cost
Values	650 (kW)	500 (kW)	0.35	0.45	50 (kWh)	0.025 (CNY/kWh)

and

Table 2. System parameters.

Parameters	EB	HP	ELY	HFC
Rated Power (kW)	500	200	400	300
Conversion Efficiency	-	-	0.70	0.55
Coefficient of Performance	0.98	3.0	-	-
Ramp Rate (kWh)	50	40	100	80
Unit O&M Cost (CNY/kWh)	0.016	0.025	0.040	0.030

. All controllable units within the system were assumed to be initially in an idle state. The power conversion coefficient was set to 2.53 kWh/m³, the heating efficiency was 0.4, the natural gas price was 2.5 CNY/m³, and the lower heating value (LHV) of natural gas was 9.7 kWh/m³ . The higher heating value (HHV) of hydrogen was 39.4 kWh/kg. The rated capacities of photovoltaic and solar thermal systems are 800 kW and 600 kW, respectively, with unit operation and maintenance costs of 0.0196 CNY/kWh and 0.0235 CNY/kWh [26]. Detailed parameters of the energy storage system are shown in

Table 3. Energy storage systems parameters.

Parameters	EES	TES	HST
Rated Capacity	500	400	50
Rated Power (kW)	150	100	20
Charging/Discharging Efficiency	0.95/0.95	−0.98/0.98	1.00/1.00
Initial State of Charge	0.5	0.5	0.5
Max/Min SOC	0.90/0.10	0.95/0.05	0.95/0.05
Self-Discharge Rate	0.0010	0.0100	0.0001
Unit O&M Cost (CNY/kWh)	0.0018	0.0016	0.0050

, with the initial state of charge set to its minimum level [27,28]. The electricity tariff time periods were divided as follows: peak periods from 10:00 to 15:00 and 18:00 to 21:00; flat periods from 07:00 to 10:00, 15:00 to 18:00, and 21:00 to 23:00; valley periods from 00:00 to 07:00 and 23:00 to 24:00. Time-of-use electricity prices, heat sale prices, and hydrogen prices are illustrated in Figure 3 [29,30].

During the optimization process, the benchmark carbon trading price was set at 50 CNY/t, with a carbon emission interval length of d = 40 t. For each tier increase, the carbon trading price rose by 25% of the benchmark price. The baseline emission factor for the system was 0.75 [31,32].

4.2. Analysis of Dispatch Results for the Case Study

4.2.1. Analysis of Operational Outcomes for the Integrated Electricity-Heat-Hydrogen Energy System

Figure 4 clearly illustrates the spatiotemporal distribution characteristics of source-load in the integrated energy system on a typical day. The upper subplot shows that solar PV generation exhibits a classic unimodal curve, peaking around midday (11:00–13:00), which partially coincides with the period of high electrical load. Wind power output demonstrates greater volatility and anti-peak characteristics, with higher output during the night and early morning. This complementarity between wind and solar generation presents favorable conditions for maximizing the utilization of renewable energy.

The lower subplot displays the heat and hydrogen load profiles. The heat load is higher during the morning and evening peaks, aligning with residential heating patterns. The hydrogen load profile is relatively flat but shows a distinct peak during daytime hours, potentially corresponding to refueling demand for hydrogen fuel cell vehicles or industrial hydrogen consumption peaks. The differences in the shapes and peak timings of the electrical, thermal, and hydrogen load curves highlight the necessity and significant potential of multi-energy coupling systems to perform “peak shaving and valley filling” through energy conversion and storage.

Figure 5 reveals the coordinated operation mechanism of the electricity-heat-hydrogen integrated energy system from an energy flow perspective.

Electrical Power Balance (Top Subplot): The results indicate that the system operation follows the “renewable energy priority” principle. During daytime, solar PV serves as the primary power source, with excess generation capacity utilized for hydrogen production via electrolyzers. The gas turbine (CHP) and fuel cell act as flexible regulation units, primarily operating during peak morning and evening hours when renewable generation is insufficient. Grid interaction and electrical energy storage effectively balance short-term power deficits and surpluses, ensuring power supply reliability.

Thermal Power Balance (Middle Subplot): The Combined Heat and Power (CHP) unit serves as the base heat source, while the electric boiler acts as a crucial peaking heat source, supplementing supply during thermal load peaks. The “heat shifting” functionality of the thermal storage is clearly visible—storing heat during off-peak periods and discharging during peak demand—significantly enhancing the system’s thermal economy.

Hydrogen Balance (Bottom Subplot): The hydrogen energy flow achieves bidirectional “electricity-gas” conversion. Electrolyzers operate during periods of low electricity prices or renewable energy surplus, converting electrical energy into hydrogen for storage. Hydrogen fuel cells then generate electricity during peak load periods, enabling efficient conversion from chemical energy back to electrical energy. The hydrogen storage tank and buy/sell hydrogen actions smooth out supply-demand fluctuations, forming the core of the system’s long-term energy storage capability.

Figure 6 provides an in-depth analysis of the roles played by energy storage facilities across different timescales within the system.

Electrical Energy Storage (Top Subplot): Exhibits high-frequency, short-cycle charge and discharge characteristics. Its primary role is to mitigate minute-to-hour fluctuations of renewable energy and participate in energy arbitrage by charging during low-price periods and discharging during high-price periods, thereby enhancing system economics. Its frequent State of Charge (SOC) variations reflect its positioning for short-term power balance services.

Thermal Energy Storage (Middle Subplot): Its operation cycle is highly correlated with the daily heat load profile, typically cycling on a daily basis. Its charge–discharge behavior demonstrates distinct “peak shaving and valley filling” characteristics—storing heat at night and releasing it during the day. This successfully decouples heat production from heat consumption temporally, alleviates the “heat-led electricity” operation constraint of CHP units, and enhances system dispatch flexibility.

Hydrogen Energy Storage (Bottom Subplot): Demonstrates long-term energy storage capabilities spanning days or weeks. Its charge/discharge rates are slower, but it offers large capacity and long storage duration. Essentially, it converts surplus renewable energy (especially wind power) over hours or days into chemical energy for storage. This energy is utilized during periods of renewable scarcity (e.g., consecutive days without sun or wind), making it a critical technology for ensuring long-term energy balance and achieving high penetration of renewable energy integration.

4.2.2. Comparative Analysis of Different Models

To validate the effectiveness of incorporating the carbon trading mechanism and the IGDT-based fuzzy chance-constrained approach into the proposed dispatch model, four distinct dispatch models were compared based on the aforementioned case study, as is detailed in

Table 4. Different models.

Scenario	Description	Model
S1	Considers only electricity-heat coupling, ignores renewable generation and load uncertainties, and adopts a fixed carbon price.	Conventional deterministic model.
S2	Extends S1 by incorporating IGDT to handle renewable generation uncertainties.	Traditional IGDT model.
S3	Proposed electricity-heat-hydrogen coupled model. Builds upon S1 with the introduction of hydrogen systems and stepped carbon trading but remains deterministic.	Proposed electricity-heat-hydrogen coupled model.
S4	Integrates electricity-heat-hydrogen coupling, IGDT (for renewable uncertainties), fuzzy chance constraints (for load uncertainties), and stepped carbon trading. This represents the model proposed in this study.	Complete proposed model

.

With the parameters configured as IGDT (for renewable uncertainty, α = 0.2) and fuzzy chance constraints (for load uncertainty, β = 0.9), the dispatch results of the four models are illustrated in Figure 7 [33,34].

Analysis of

Table 5. A comparative analysis of system dispatch results under different scenarios is summarized.

Metrics	S1	S2	S3	S4
Total System Cost (CNY)	4150.1	4398.7	3802.4	3624.1
Carbon Emissions (kg)	1256.8	1310.5	982.3	903.7
Curtailment Rate of Renewable Energy (%)	8.7%	5.2%	3.1%	1.8%
Hydrogen Utilization Rate (%)	-	-	76.5%	85.2%
Reserve Cost (CNY)	-	218.6	-	154.3

reveals that the complete proposed model (S4) achieves the lowest total system cost, demonstrating a 12.7% reduction compared to the conventional model (S1). This indicates that the integration of hydrogen energy systems enabled effective energy transfer and value-added applications, while the combined IGDT and fuzzy programming approach for uncertainty management enhanced system robustness with lower reserve costs. Furthermore, S4 achieved the lowest carbon emissions, reducing 28.1% compared to S1, which benefited from the dual emission reduction incentives provided by hydrogen utilization and the stepped carbon trading mechanism. Additionally, S4 exhibited the lowest renewable curtailment rate, as the hydrogen system functions as a large-capacity, long-duration storage solution significantly improving the system’s capability to accommodate fluctuating renewable generation. Finally, while Scenario 3 (S3) already demonstrated substantial advantages, Scenario 4 (S4) further enhanced overall system performance through intelligent uncertainty decision-making, validating the necessity of the proposed modeling framework.

The comparative analysis of system dispatch results under different scenarios is summarized in Table 5.

Additionally, a comprehensive analysis of the MILP model’s computational performance and scalability is presented in

Table 6. Detailed MILP computational performance analysis.

Scenario	Time (s)	Optimality Gap (%)	Iterations	Nodes	Relative Complexity
S1	45.2	0.800	1245	89	1.0
S2	67.8	1.200	1890	156	1.5
S3	82.3	1.500	2345	234	1.8
S4	118.6	1.800	3127	378	2.6

. It shows that, relative to S1, scenario S4 exhibited a 2.6-fold increase in solution time and a 2.6-fold rise in problem complexity, yielding a computational-efficiency ratio (complexity growth/time growth) of 0.99. All model variants were solved within a reasonable time: the most complex instance (S4) required only about two minutes, and the optimality gap remained below 2% for every case, guaranteeing solution quality and reliability. Finally, computational demand grew linearly with problem complexity, providing confidence that the formulation can accommodate considerably larger systems.

4.2.3. Sensitivity Analysis of Uncertainty Parameters

Subfigure (a) in Figure 8 demonstrates that as the robustness deviation factor δ increased (more conservative decision-maker), the total system cost increased, but the maximum uncertainty α that the system can withstand also increased, enhancing robustness. Conversely, as the opportunity deviation factor ε increased (more adventurous decision-maker), the total system cost decreased, but at the expense of robustness (α becomes smaller) to pursue potential benefits. This proves that the IGDT model can provide the decision-makers with a clear risk-cost trade-off curve.

Subfigure (b) in Figure 8 shows that as the confidence level β increased, the total system cost increased monotonically. This is because a higher β required a higher probability of satisfying the fuzzy constraints, necessitating more reserve capacity, leading to reduced economy. Decision-makers can choose an appropriate β value based on the system security requirements and the trade-off between economy and reliability.

4.2.4. Sensitivity Analysis of Carbon Trading Price

To evaluate the impact of carbon policies, this analysis examined the trends in system operating costs and carbon emissions as the benchmark carbon trading price varied from 0 to 120 CNY/ton.

Figure 9 quantifies the impact of the carbon trading price on the total operating cost and CO₂ emissions of the integrated energy system by means of 95% confidence intervals, thereby exposing both the statistical significance and the underlying patterns. Total cost increased monotonically with the carbon price. When the price was below 30 yuan/ton, the slope is gentle, indicating that the system can largely internalize the carbon expense through endogenous optimization measures such as expanding hydrogen utilization. Once the price exceeded 60 yuan/ton, the cost curve steepens and the confidence band widens moderately, revealing greater economic volatility and a shrinking optimization space under stringent carbon policy. CO₂ emissions declined markedly as the carbon price rose, yet the marginal abatement effect diminished. In the 0–40 yuan/ton interval the emission curve is steep and the confidence interval narrow, evidencing that even a modest carbon price reliably accelerated low-carbon transition with stable outcomes. Beyond 60 yuan/ton the curve flattens, and the interval remains tight, implying that the technical abatement potential was nearly exhausted; further price increases confer limited additional emission reductions while deterministically driving up system cost.

4.2.5. Analysis of Hydrogen Energy System Operational Modes

As demonstrated in subfigure (a) in Figure 10, the power curves of the electrolyzer and fuel cell show that the electrolyzer operated mainly during low electricity price periods (night and noon) to consume surplus electricity for hydrogen production; the fuel cell operated during evening peak hours to generate electricity, replacing expensive grid power and gas turbines.

As demonstrated in subfigure (b) in Figure 10, the hydrogen storage state indicates charging during periods of abundant renewable energy and discharging during peak load periods, effectively achieving spatiotemporal energy transfer.

As demonstrated in subfigure (c) in Figure 10, the system power balance shows that the hydrogen system complemented the grid interaction power and renewable energy output well, verifying the dual role of the hydrogen system in “peak shaving and valley filling” and “promoting renewable energy consumption”.

4.2.6. Extreme Uncertainty Performance Test

To test the robustness and effectiveness of the proposed model under extreme uncertainty scenarios—such as severe prediction inaccuracies or extreme weather events—we simulated conditions with exceptionally high uncertainty levels: α = 0.4 (indicating renewable generation forecast deviations of up to ±40%) and β = 0.99 (requiring an extremely high confidence level for load balance). A comparative analysis between the S2 (traditional IGDT) and S4 (complete proposed model) was conducted, evaluating total cost, renewable curtailment rate, and computational time to demonstrate the superiority of the proposed model.

Subfigure (a) in Figure 11 shows that under extreme uncertainty conditions (α = 0.4, β = 0.99), the total cost of the proposed model (S4) was significantly lower than that of the traditional IGDT model (S2), proving its superior economic robustness.

Subfigure (b) in Figure 11 shows that the curtailment rate of the proposed model was significantly lower than that of the traditional model, proving its stronger ability to consume renewable energy.

Subfigure (c) in Figure 11 shows that although the computation time of the proposed model was higher than that of the traditional model, the performance improvement it brings far exceeds the increase in computation cost, proving the rationality of the model complexity.

4.2.7. Analysis of Seasonal Impact Characteristics

To validate the adaptability and effectiveness of the proposed model across different seasons (summer and winter), a comparative analysis between S1 (conventional model) and S4 (complete proposed model) was conducted with α = 0.2, β = 0.9, and a carbon price of 50 CNY/ton.

Subfigure (a) in Figure 12 indicates how the total cost comparison shows that the proposed model (S4) significantly reduces costs compared to the traditional model (S1) in both summer and winter. Although absolute costs are higher in winter due to increased heating demand, the relative advantage of the proposed model is more pronounced, with a cost reduction of 17.1% in winter compared to 12.7% in summer.

As is shown in subfigure (b) in Figure 12, the carbon emissions comparison demonstrates that the proposed model effectively reduced carbon emissions in both seasons. The reduction was more substantial in winter 33.5% than in summer 28.1%, primarily because the hydrogen system more fully replaced fossil fuels during periods of high heating demand in winter.

As is demonstrated in subfigure (c) in Figure 12, the renewable energy penetration rate shows that the proposed model significantly improved the system’s ability to consume renewable energy. The improvement was greater in winter 50.0% than in summer 40.6%, indicating that the hydrogen system better addresses the challenge of greater volatility in renewable energy output during winter.

5. Conclusions

This paper addresses the challenge of economic efficiency, robustness, and low-carbon performance in integrated electricity-heat-hydrogen energy systems by proposing a novel optimal dispatch method that combines Information Gap Decision Theory (IGDT) and Fuzzy Chance-Constrained Programming (FCCP). Through a series of rigorous simulation experiments and analyses, the following key conclusions were drawn:

(1) The proposed “IGDT-FCCP” dual-layer uncertainty handling framework effectively characterizes uncertainties on both the source and load sides. Case studies demonstrate that compared to conventional models, the complete proposed model (S4) reduces total system costs by 12.7%, decreases carbon emissions by 28.1%, and lowers the renewable curtailment rate from 8.7% to 1.8%. The introduction of the hydrogen system contributes approximately 60% of the carbon reduction, proving its critical low-carbon value.

(2) Multi-dimensional comparative experiments across different seasons, risk preferences, and carbon policies validate the universal applicability and superiority of the proposed model. Particularly under winter conditions with high heating demand and extreme uncertainty scenarios, the model demonstrates enhanced robustness and flexibility, with relative performance improvements even exceeding those observed in summer, providing an effective solution to thermal-electric conflicts.

(3) Sensitivity analysis provides system operators with clear risk-cost trade-off curves and decision-making foundations. Decision-makers can scientifically and flexibly balance economic efficiency, reliability, and low-carbon performance based on actual risk preferences (by adjusting α and β) and policy environments, thereby formulating dispatch strategies that best meet current needs.

The proposed model primarily targets the scheduling of integrated energy systems. In the future, this research can be deepened in the following aspects: exploring the coordinated interaction mechanism between electric vehicle (EV) loads and vehicle-to-grid (V2G) technologies—as flexible resources—and the electricity–hydrogen energy system. Consider scaling the model from a single park-level system to a multi-region interconnected integrated energy system and investigate its coordinated scheduling and energy transmission issues. Introduce artificial intelligence technologies, especially deep-learning models, to improve the forecasting accuracy of renewable energy and loads, thereby refining the setting of uncertain parameters and further enhancing the foresight and cost-effectiveness of scheduling strategies.