Sustainability-Oriented Multi-Objective Low-Carbon Dispatch for an Electricity–Hydrogen Coupling Multi-Microgrid

Abstract

To enhance the sustainable operation of electricity–hydrogen coupling multi-microgrids (EHCMMG), this study proposes a multi-objective dispatch optimization framework driven by electricity price prediction. Although EHCMMG plays a vital role in renewable energy integration and multi-energy synergy, three major sustainability-related research gaps remain: insufficient consideration of cross-regional, multi-market, and multi-stakeholder interests; inadequate electricity–hydrogen demand response mechanisms; and limited investigation of uncertainty modeling that balances economy and security. To address these issues, this study first designs an EHCMMG architecture that supports electric-hydrogen interactions both within and outside the cluster. An electricity price prediction-driven multi-objective dispatch optimization model oriented toward multiple stakeholders is then proposed. This model incorporates incentive-based electricity–hydrogen demand response and constraints on carbon emissions. Moreover, operational uncertainties arising from renewable energy generation are addressed through the coordinated integration of spinning reserve capacity constraint and chance-constrained programming. The results show that the cluster cost, the market integrated operator (MIO) net revenue, user energy cost, and total carbon emissions are CNY 17.502 million, CNY 12.684 million, CNY 5.556 million, and 8168.126 tons in baseline scenario, respectively. The proposed model effectively balances economic efficiency, operational reliability, and low-carbon performance, thereby enhancing the overall sustainability of the EHCMMG.

1. Introduction

1.1. Background and Motivation

To achieve sustainable energy development, the deployment of clean and renewable wind and solar energy has become key to the energy transition. However, the large-scale integration of these intermittent sources poses significant challenges to power system stability [1]. Hydrogen energy, with its excellent storage and flexible conversion capabilities [2], provides an important pathway for mitigating such fluctuations. Nevertheless, a single electricity–hydrogen coupled system still faces limitations in economies of scale and supply–demand matching. Interconnecting multiple such systems into a cluster can integrate distributed energy resources and enhance flexibility. This study aims to enhance the environmental, economic, and social sustainability of an electricity–hydrogen coupling multi-microgrid (EHCMMG) operations through integrated optimization of electricity–hydrogen coordination, demand response (DR), and carbon emission control.

Furthermore, as energy systems become increasingly complex and interconnected, single-market models have become inadequate to meet development needs. Consequently, multi-market joint trading mechanisms have emerged, which support cross-temporal and cross-form optimization of energy allocation while enhancing the economic efficiency and low-carbon operational performance of energy systems [3]. Meanwhile, DR, as a critical mechanism for improving the flexibility of electricity–hydrogen coupled systems, can effectively balance fluctuations in renewable energy output and smooth peak-valley load variations [4]. Given this context, investigating the optimal dispatch of an EHCMMG under joint electricity–hydrogen multi-market trading and DR holds significant value. For the optimal dispatch of an EHCMMG, three critical issues need to be addressed: (1) how to develop dispatch models integrating cross-regional, multi-market, and multi-stakeholder interests; (2) how to establish an effective response mechanism for electricity–hydrogen loads; (3) how to develop uncertainty-handling methods that balance economic and security objectives.

1.2. Innovations and Contributions

The main innovations and contributions of this paper are summarized as follows:

(1)

Designs an EHCMMG comprising an electricity–hydrogen subsystem and an electricity–hydrogen–electricity subsystem. The cluster facilitates internal bidirectional electricity and hydrogen exchange, enhancing operational flexibility and energy efficiency. In addition, it engages in external electricity and hydrogen markets to balance supply and demand while enabling user participation in integrated electricity–hydrogen DR through incentive mechanisms.

(2)

Develops a multi-objective scheduling optimization model based on electricity price forecasting to balance the interests of multiple stakeholders, including the system itself, external energy suppliers, and end-user. The model simultaneously considers carbon emission constraints, electricity and hydrogen balance constraints, and various forms of incentive-based DR for electricity and hydrogen loads.

(3)

Proposes an integrated modeling method that combines spinning reserve capacity constraints with chance-constrained programming to account for operational uncertainties. This approach enables coordinated optimization of both economic performance and system reliability under uncertain operating conditions.

1.3. Paper Organization

The rest of this paper is organized as follows: Section 2 presents a literature review and identifies the research gaps. Section 3 introduces the system architecture and develops the mathematical models for key devices. Based on this modeling foundation, Section 4 formulates a multi-objective chance-constrained optimal dispatch model. Section 5 conducts electricity price forecasting. Section 6 then integrates the forecasting and dispatch models in a comprehensive case study. Finally, Section 7 concludes with the main findings and provides an outlook for future research.

2. Literature Review

2.1. Optimization Objects and Objectives

In single-objective optimal scheduling research, the minimization of operation costs is commonly adopted as the primary optimization criterion. For instance, in addressing the scheduling problem of wind-photovoltaic ($PV$)-hydrogen integrated energy systems, an improved discrete step transformation method has been applied to reformulate the chance-constrained programming into a mixed-integer linear programming model [5]. Wu et al. [6] established an optimization model targeting the minimization of expected total operational cost for microgrids incorporating hydrogen refueling stations. Tostado-Véliz et al. [7] explicitly considered green hydrogen production constraints in the scheduling model of an isolated microgrid. For microgrids with hydrogen vehicles, MansourLakouraj et al. [8] proposed a scheduling model that incorporated electricity market participation and risk constraints. Wang et al. [9] developed an optimal scheduling model for an integrated wind–$PV$–hydrogen energy station, taking into account carbon capture, power-to-gas conversion, and carbon trading mechanisms. To achieve the economic and secure operation of hydrogen microgrids, Huang et al. [10] developed an optimal scheduling framework based on model predictive control, which incorporates the safety constraints of hydrogen equipment.

Meanwhile, the objective of cost minimization has also been extensively applied in the optimal scheduling of multi-microgrids (MMGs). With the goal of minimizing the expected total cost, Rezaei and Pezhmani [11] developed an optimal operation strategy for an off-grid electricity–hydrogen MMG, taking into account electricity-to-hydrogen conversion, hydrogen storage, and hydrogen loads. Pezhmani et al. [12] considered electricity and natural gas market transactions in their MMG scheduling model. In the context of islanded MMGs, Yang et al. [13] established a cost-minimization model that considered renewable energy consumption constraint and introduced an improved multi-agent consensus algorithm for the solution. Wu et al. [14] optimized the scheduling of a wind-PV-gas turbine (GT) MMG with a distributed algorithm, taking into account internal and external power exchanges. In addition, scholars have also conducted relevant research from the revenue perspective. Specifically, among these studies, Alex et al. [15] formulated and solved an optimization model for scheduling a grid-connected tidal–wind–hydrogen hybrid system. The objective was to maximize revenue, and they employed a genetic algorithm to find the solution. Meanwhile, aiming to maximize expected profit, Rezaei et al. [16] addressed the scheduling problem for a grid-connected combined heat and power MMG by formulating a stochastic mixed-integer linear programming model that incorporated risk and carbon emission constraints.

Moreover, scholars have explored the application of multi-objective optimization in multi-microgrid scheduling. For example, Fang [17] optimized the operation of a hydrogen storage-integrated energy system by employing an improved non-dominated sorting genetic algorithm II (NSGA-II) algorithm to reduce both operation and environmental costs. Xu et al. [18] developed a bi-objective model for multi-energy microgrid operation that minimizes operation cost and carbon emissions while accounting for power-to-hydrogen conversion and electric vehicles. Wang et al. [19] developed a bi-objective optimization model with the dual objectives of maximizing profit for the independent market operator and minimizing costs for the MMG. This model incorporated electricity trading and was solved using a parallel algorithm. Mansouri et al. [20] proposed a multi-microgrid scheduling optimization model that aimed to minimize total operating cost and maximize the consumer comfort index, while considering a high penetration rate of renewable energy. Roustaee and Kazemi [21] developed a multi-objective optimization model for MMG operation targeting the minimization of operation cost, environmental pollution emissions, expected energy not supplied, and voltage deviation.

2.2. Demand Response

DR is a crucial tool in demand-side management. The existing literature has explored its application in single electric power systems, as well as in integrated energy systems involving electricity, heating, and gas. Research in this field can be broadly categorized based on the number of energy types considered.

Several studies have focused solely on electricity load DR. For example, Tostado-Véliz et al. [7] took shiftable electricity loads into account when scheduling an isolated microgrid integrated with hydrogen storage. MansourLakouraj et al. [8] further discussed electricity DR based on time-of-use pricing. Moreover, research has also been conducted on integrated DR models covering two energy carriers, such as electricity-heating or electricity–gas load. In the dispatch and operation of integrated energy systems with multi-agents, Li et al. [22] established an integrated electricity-heating DR model accounting for the shiftable nature of electrical loads and the reducible potential of heating loads. Yuan et al. [23] examined the implementation of price-based integrated electricity–heat DR for scheduling multi-region integrated energy systems. Additionally, Chen et al. [24] proposed an integrated electricity-gas DR-based scheduling optimization model for integrated energy systems, in which energy conversion equipment enables mutual conversion between electricity and gas, thereby enhancing system operational flexibility.

Research has progressed to integrated DR involving three or more types of loads. Fan et al. [25] modeled shiftable and reducible cooling, heating, and electricity loads. Tan et al. [26] further analyzed the impact of such integrated cooling, heating, and electricity DR on park-level integrated energy system operation using a demand elasticity matrix. Lu et al. [27] developed both price-based and substitutable DR models for cooling, heating, electricity, and gas loads in community integrated energy systems. Pan et al. [28] integrated incentive-based DR for cooling, heating, and electricity with price-based DR for electricity and gas in a power-to-gas enabled system. Furthermore, Wang et al. [9] investigated shiftable and interruptible loads across five energy carriers: cooling, heating, electricity, gas, and hydrogen.

2.3. Uncertainty in Renewable Energy Generation

Renewable energy sources like wind and PV power generation are inherently uncertain due to their dependence on variable natural conditions. To address these uncertainties, various optimization approaches, including chance-constrained and robust optimization, have been widely applied. Wu et al. [5] used chance-constrained programming for wind–$PV$–hydrogen integrated energy system scheduling, while Wu et al. [6] employed data-driven chance constraints and distributionally robust optimization to manage uncertainties in both renewable generation and electricity price. Li et al. [29] proposed a data-driven two-stage distributionally robust optimization model for community energy systems, and Xu and Yi [30] applied robust interval optimization to handle renewable generation uncertainties in low-carbon economic dispatch. Moreover, in multi-objective electro-thermal dispatch, Ju et al. [31] integrated autoregressive models and scenario reduction to address wind power uncertainty. Li et al. [32] applied model-free deep reinforcement learning for islanded systems, and Tostado-Véliz et al. [33] utilized info-gap decision theory for day-ahead scheduling. Fan et al. [25] used conditional value-at-risk models to assess wind and PV uncertainties. Tostado-Véliz et al. [7] explored weather impacts using interval optimization.

2.4. Gaps in Previous Research

(1)

The research scope has evolved from single microgrids to MMG. Optimization objectives have expanded from operation cost minimization to profit maximization, carbon emission reduction, and user comfort. However, a collaborative framework for cross-regional, multi-market, and multi-level EHCMMG that simultaneously addresses economic viability, low-carbon transition, and stakeholder equity, is still lacking. Current work often overlooks the heterogeneous objectives of stakeholders such as system operators, market entities, and end-user. Moreover, integrating electricity price forecasting into scheduling models would significantly enhance their practical relevance and decision-support value.

(2)

Single-energy DR focuses on the electricity load, dual-energy DR emphasizes coordinated optimization in coupled systems such as electricity-heating and electricity-gas, and research extends further to the coordinated scheduling of three or more types of loads, covering various response modes such as price-based, incentive-based, and substitution-based mechanisms. However, existing research has not yet thoroughly explored the coordinated response mechanisms of shiftable, transferable, and reducible electricity–hydrogen loads, and the joint control strategies for these diverse flexible resources remain to be further investigated.

(3)

Current research employs a variety of optimization techniques, such as chance-constrained programming, distributionally robust optimization, data-driven methods, and interval optimization, to tackle uncertainties in different operational scenarios. However, a unified methodological framework that integrates chance constraints and spinning reserve capacity constraints to effectively manage uncertainties under deep decarbonization pathways remains to be thoroughly explored.

Based on the above analysis, this paper proposes a scheduling optimization framework that integrates multi-objective optimization, DR, electricity price forecasting, and spinning reserve chance constraints to enhance decision-making accuracy.

3. Structure Description and Mathematical Modeling

3.1. Structure Description

This paper proposes an EHCMMG system comprising two heterogeneous subsystems: an electricity–hydrogen subsystem and an electricity–hydrogen–electricity subsystem. It enables internal bidirectional electricity transmission and hydrogen pipeline distribution, thereby improving energy utilization efficiency and operational flexibility. In addition, the EHCMMG participates in flexible transactions with the external electricity market, allowing the export of surplus power and the procurement of power during shortages. It can also purchase hydrogen from the external hydrogen market in response to supply–demand conditions. Moreover, the EHCMMG supplies both electricity and hydrogen load to users and supports their involvement in coordinated electricity–hydrogen DR through incentive mechanisms. The structure of the proposed EHCMMG is illustrated in Figure 1.

3.2. Mathematical Modeling

(1)

Wind turbine ($WT$)

The power output of $WT$ is difficult to predict accurately due to multiple uncertain factors, such as fluctuations in wind speed and changes in wind direction. Its prediction error model is as follows:

$${\chi }_{WT,t}={\overline{P}}_{WT,t}-P_{WT,t}$$

(1)

where ${\chi }_{WT,t}$ is the prediction error of the $WT$ at time $t$; ${\overline{P}}_{WT,t}$ and $P_{WT,t}$ represent the actual and forecasted power generation of the WT at time $t$, respectively.

(2)

Photovoltaic panel ($PVP$)

The power output of $PVP$ is influenced by factors such as weather conditions, sunlight duration, and seasonal variations, resulting in significant uncertainty as well.

$${\chi }_{PVP,t}={\overline{P}}_{PVP,t}-P_{PVP,t}$$

(2)

where ${\chi }_{PVP,t}$ is the prediction error of the $PVP$ at time $t$; ${\overline{P}}_{PVP,t}$ and $P_{PVP,t}$ represent the actual and forecasted power generation of the $PVP$ at time $t$, respectively.

(3)

Gas turbine ($GT$)

$GT$ generates electricity through natural gas combustion and provides flexible load-adjustment capabilities.

$$P_{GT,t}=Q_{GT,t}\cdot {\eta }_{GT}\cdot L_{NG}$$

(3)

$$0\le P_{GT,t}\le P_{GT}^{\max }$$

(4)

where $P_{GT,t}$ denotes the electricity generated by $GT$ at time $t$; $Q_{GT,t}$ represents the gas consumption of $GT$ at time $t$; ${\eta }_{GT}$ is the generation efficiency of $GT$; $L_{NG}$ stands for the calorific value of the natural gas; $P_{GT,t}^{\max }$ represents the upper bound of $GT$’s power generation.

(4)

Electrolyzer ($EL$)

When electricity is input into $EL$, it triggers the electrochemical decomposition of water molecules, thus accomplishing the conversion of electricity into hydrogen [34].

$$V_{EL,t}={\varphi }_{EL}\cdot P_{EL,t}$$

(5)

where $V_{EL,t}$ is the hydrogen production volume of $EL$ at time $t$; ${\varphi }_{EL}$ is the electricity to hydrogen coefficient; $P_{EL,t}$ denotes the electricity consumption of $EL$ at time $t$.

(5)

Fuel cell ($FC$)

The $FC$ is a device that directly converts chemical energy into electricity via the electrochemical reaction of hydrogen.

$$P_{FC,t}={\varphi }_{FC}\cdot V_{FC,t}$$

(6)

where $P_{FC,t}$ represents the power generation of $FC$; ${\varphi }_{FC}$ is the hydrogen to electricity efficiency of $FC$; $V_{FC,t}$ denotes the hydrogen consumption volume of $FC$ at time $t$.

(6)

Energy storage system ($ESS$)

$ESS$ can optimize the supply–demand balance of the EHCMMG through flexible charge and discharge, thereby improving operational economy and reducing wind and PV power abandonment. In this paper, $ESS$ includes electricity storage ($ES$) and hydrogen tank ($HT$). The essential mathematical model for the $ESS$ is specified as follows [35]:

$$S_{EES,t}=S_{EES,t-1}\cdot (1-{\delta }_{EES})+P_{EES,t}^{ch}\times {\eta }_{EES}^{ch}-P_{EES,t}^{dis}/{\eta }_{ESS}^{dis}$$

(7)

where $S_{EES,t}$ and $S_{EES,t-1}$ represent the stored energy at time $t$ and $t-1$, respectively; ${\delta }_{EES}$ is the loss coefficient of $ESS$; $P_{EES,t}^{ch}$ and $P_{EES,t}^{dis}$ represent the charge and discharge of $ESS$ at time $t$; ${\eta }_{EES}^{ch}$ and ${\eta }_{ESS}^{dis}$ denote the charge and discharge efficiencies of $ESS$.

$$0\le P_{EES,t}^{ch}\le P_{EES}^{ch,\max }$$

(8)

$$0\le P_{EES,t}^{dis}\le P_{EES}^{dis,\max }$$

(9)

$$S_{ESE}^{\min }\le S_{ESS,t}\le S_{ESS}^{\max }$$

(10)

where $P_{EES}^{ch,\max }$ and $P_{EES}^{dis,\max }$ are the maximum values of charge and discharge in a single slot; $S_{ESE}^{\min }$ and $S_{ESS}^{\max }$ are the minimum and maximum values of the stored energy in a single slot.

Moreover, at any given time, $ESS$ can operate only in one direction—either charging or discharging [36].

$$P_{ESE,t}^{ch}\cdot P_{EES,t}^{dis}=0$$

(11)

4. Multi-Objective Chance-Constrained Dispatch Optimization for EHCMMG

4.1. Objectives

Optimization objectives are constructed from three dimensions: the system side, the market side, and the user side. These correspond respectively to the economic, market, and social dimensions of sustainable development, achieving synergistic enhancement through balanced optimization.

(1)

System side

The total cost of the EHCMMG is the cumulative sum of the all subsystems.

$$f_1=C_{sub}={\displaystyle \sum _{i=1}^M{C}_{sub,i}}$$

(12)

where $C_{sub}$ and $C_{sub,i}$ are the cost of the EHCMMG and subsystem $i$, respectively.

The cost of an individual subsystem consists of investment cost, operation and maintenance (O&M) cost, fuel cost, DR cost, transmission cost, and revenues generated from transactions with market integrated operator (MIO), user, and other subsystems.

$$C_{sub,i}=C_{IN,i}+C_{OM,i}+C_{FC,i}+C_{DR,i}+C_{S2S,i}-R_{S2M,i}-R_{S2U,i}-R_{S2S,i}$$

(13)

where $C_{IN,i}$, $C_{OM,i}$, $C_{FC,i}$, $C_{CT,i}$, $C_{DR,i}$, and $C_{S2S,i}$ are investment cost, O&M cost, fuel cost, DR cost, transmission cost of subsystem $i$, respectively; $R_{S2M,i}$ is the trading revenue of subsystem $i$ in the energy market; $R_{S2U,i}$ is energy supply revenue of subsystem $i$ to end user; $R_{S2S,i}$ represents the revenue obtained by subsystem $i$ from participating in inter-subsystem energy trading.

$$C_{IN,i}={\displaystyle \sum _{*}{\mathrm{C}}_{uc,*}\cdot P_{*,i}\cdot CR{F}_{*}}$$

(14)

where ${\mathrm{C}}_{uc,*}$, $P_{*,i}$, and $CR{F}_{*}$ are unit investment cost, installed capacity, and capital recovery factor, respectively.

$$C_{OM,i}={\displaystyle \sum _{t=1}^T\left(\begin{array}{l}{C}_{WT,i,t}+C_{PVP,i,t}+C_{GT,i,t}+C_{EL,i,t}\\ +C_{FC,i,t}+C_{ES,i,t}+C_{HT,i,t}\end{array}\right)}$$

(15)

where $C_{WT,i,t}$, $C_{PVP,i,t}$, $C_{GT,i,t}$, $C_{EL,i,t}$, $C_{FC,i,t}$, $C_{ES,i,t}$ and $C_{HT,i,t}$ are O&M cost of $WT$, $PVP$, $GT$, $EL$, $FC$, $ES$, and $HT$ of subsystem $i$ at time $t$.

$$C_{FC,i}=c_{gas}\cdot {\displaystyle \sum _{t=1}^T{Q}_{GT,i,t}}$$

(16)

where $c_{gas}$ is the price of natural gas per cubic meter.

$$C_{DR,i}={\displaystyle \sum _{t=1}^T\left(c_{SL}.P_{SL,i,t}^{DR}+c_{TL}.P_{TL,i,t}^{DR}+c_{CL}.P_{CL,i,t}^{DR}\right)}$$

(17)

where $c_{SL}$, $c_{TL}$, and $c_{CL}$ are unit compensation prices of shifted, transferred, and curtailed loads, respectively. $P_{SL,t}^{DR}$, $P_{TL,t}^{DR}$, and $P_{CL,t}^{DR}$ denote the load shifted, transferred, and curtailed at time $t$, respectively.

$$R_{S2M,i}={\displaystyle \sum _{t=1}^T\left({\lambda }_{s,ex,t}^e\cdot P_{s,ex,i,t}^e-{\lambda }_{b,ex,t}^e\cdot P_{b,ex,i,t}^e-{\lambda }_{b,ex,t}^h\cdot V_{b,ex,i,t}^h\right)}$$

(18)

where ${\lambda }_{b,ex,t}^e$ and ${\lambda }_{s,ex,t}^e$ represent the electricity purchase price and selling price of each subsystem in electricity market at time $t$, respectively; $P_{s,ex,i,t}^e$ and $P_{b,ex,i,t}^e$ denote the electricity sold and purchased by subsystem $i$ in electricity market at time $t$; ${\lambda }_{b,ex,t}^h$ denotes hydrogen purchase price of each subsystem in hydrogen market at time $t$; $V_{b,ex,i,t}^h$ is the amount of hydrogen bought by subsystem $i$ in electricity market at time $t$.

$$R_{S2U,i}={\displaystyle \sum _{t=1}^T\left({\gamma }_{s,in,t}^e\cdot P_{s,in,i,t}^e+{\gamma }_{s,in,t}^h\cdot V_{s,in,i,t}^h\right)}$$

(19)

where ${\gamma }_{s,in,t}^e$ and ${\gamma }_{s,in,t}^h$ are electricity and hydrogen selling price of subsystem $i$ to end user at time $t$, respectively; $P_{s,in,i,t}^e$ and $V_{s,in,i,t}^h$ are the amount of electricity and hydrogen sold by subsystem $i$ to end user at time $t$, respectively.

$$R_{S2S,i}={\displaystyle \sum _{t=1}^T{\displaystyle \sum _{j=1,j\ne i}^M\left[{\chi }_{wit,t}^e\cdot \left(P_{i,j,t}^e-P_{j,i,t}^e\right)+{\chi }_{wit,t}^h\cdot \left(V_{i,j,t}^h-V_{j,i,t}^h\right)\right]}}$$

(20)

where ${\chi }_{wit,t}^e$ and ${\chi }_{wit,t}^h$ denotes the electricity and hydrogen transaction prices between subsystems at time $t$, respectively; $P_{i,j,t}^e$ and $V_{i,j,t}^h$ denote the amount of electricity and hydrogen sold from subsystem $i$ to subsystem $j$ at time $t$; $P_{j,i,t}^e$ and $V_{j,i,t}^h$ denotes amount of electricity and hydrogen sold from subsystem $j$ to subsystem $i$ at time $t$.

$$C_{S2S,i}=0.5\times {\displaystyle \sum _{t=1}^T{\displaystyle \sum _{j=1,j\ne i}^M\left[P_{tr,i,j}^e\cdot \left(P_{i,j,t}^e+P_{j,i,t}^e\right)+P_{tr,i,j}^h\cdot \left(V_{i,j,t}^h+V_{j,i,t}^h\right)\right]}}$$

(21)

where $P_{tr,i,j}^e$ and $P_{tr,i,j}^h$ denote unit costs for electricity and hydrogen transmission between subsystem $i$ and subsystem $j$, respectively.

(2)

Market side

The net revenue of the MIO is calculated as the difference between transactions cost with the EHCMMG and transmission fees within the internal energy trading network.

$$f_2={\displaystyle \sum _{i=1}^M\left(C_{S2S,i}-R_{S2M,i}\right)}$$

(22)

where $f_2$ is the revenue of the MIO.

(3)

User side

The user energy cost is calculated as the difference between their total energy procurement expenditure and DR compensation revenue.

$$f_3={\displaystyle \sum _{i=1}^M\left(R_{S2U,i}-C_{DR,i}\right)}$$

(23)

where $f_3$ is the user energy cost.

4.2. Constraints

In addition to the mathematical models described in Section 3.2, the remaining constraints encompass network constraints, electricity balance constraints, hydrogen balance constraints, carbon-emission constraints, etc.

(1)

Network constraints

It includes electricity and hydrogen network constraints, covering interactions between subsystems and external markets as well as those among the subsystems.

$$0\le P_{s,ex,i,t}^e\le {\epsilon }_{s,ex,i,t}^e{P}_{s,ex,i}^{e,\max }$$

(24)

$$0\le P_{b,ex,i,t}^e\le {\epsilon }_{b,ex,i,t}^e{P}_{b,ex.i}^{e,\max }$$

(25)

$${\epsilon }_{s,ex,i,t}^e+{\epsilon }_{b,ex,i,t}^e\le 1$$

(26)

where $P_{s,ex,i}^{e,\max }$ and $P_{b,ex.i}^{e,\max }$ represent the maximum allowable amount of electricity that subsystem $i$ can sell to and purchase from the electricity market in a single slot, respectively; ${\epsilon }_{s,ex,i,t}^e$ and ${\epsilon }_{b,ex,i,t}^e$ are all binary state variables.

Similarly, the constraints on electricity and hydrogen transactions among subsystems can be derived.

(2)

Constraints of $EL$ and $FC$ operation

The power input and output of both $EL$ and $FC$ are required to be maintained within their respective rated capacity limits [37].

$$0\le P_{EL,i,t}\le {\epsilon }_{EL,i,t}{P}_{EL,i}^{\max }$$

(27)

$$0\le P_{FC,i,t}\le {\epsilon }_{FC,i,t}{P}_{FC,i}^{\max }$$

(28)

$${\epsilon }_{EL,i,t}+{\epsilon }_{FC,i,t}\le 1$$

(29)

where $P_{EL,i}^{\max }$ and $P_{FC,i}^{\max }$ represents the maximum amount of electricity generated by $EL$ and consumed by $FC$ in subsystem $i$ in a single slot, respectively. ${\epsilon }_{EL,i,t}$ and ${\epsilon }_{FC,i,t}$ are all binary state variables.

(3)

Shiftable load ($SL$) constraints

$SL$ is characterized by temporal flexibility and requires shifting as a whole. SL includes shiftable electricity load ($SEL$) and shiftable hydrogen load ($SHL$).

$$T_{SL}={\displaystyle \sum _{\tau =t}^{t+T_{SL}-1}{v}_{SL,t}},t=s{l}_{-},s{l}_{-}+1,\dots ,s{l}_{+}-T_{SL}+1$$

(30)

$$P_{SL,t}^{DR}=v_{SL,t}\cdot P_{SL,t}^{be}$$

(31)

where $v_{SL,t}$ is the shift state variable at time $t$; $T_{SL}$ represents continuous shift time; $s{l}_{-}$ and $s{l}_{+}$ are lower and upper limits of the shift time window, respectively; $P_{SL,t}^{DR}$ denotes load shifted at time $t$; $P_{SL,t}^{be}$ is the $SL$ before the transfer at time $t$.

(4)

Transferable load ($TL$) constraints

TL exhibits spatial flexibility while maintaining constant total energy consumption. Its dispatch must satisfy both the per-unit-time power transfer limit [38] and the minimum continuous transfer time constraint. $TL$ includes transferable electricity load ($TEL$) and transferable hydrogen load ($THL$).

$$v_{TL,t}{P}_{TL}^{DR,\min }\le P_{TL,t}^{DR}\le v_{TL,t}{P}_{TL}^{DR,\max }$$

(32)

$$v_{TL,t}=0,t\notin [t{r}_{-},t{r}_{+}]$$

(33)

$$\left(v_{TL,t}-v_{TL,t-1}\right)T_{TL}^{\min }\le {\displaystyle \sum _{\tau =t}^{t+T_{TL}^{\min }-1}{v}_{TL,\tau }},t=t{r}_{-},t{r}_{-}+1,\dots ,t{r}_{+}-T_{TL}^{\min }+1$$

(34)

$${\displaystyle \sum _{t=1}^T{P}_{TL,t}^{be}}={\displaystyle \sum _{t=1}^T{P}_{TL,t}^{af}}$$

(35)

where $P_{TL}^{DR,\min }$ and $P_{TL}^{DR,\max }$ denote the minimum and maximum values of the load transferred in a single slot; $v_{TL,t}$ is the transfer state variable at time $t$; $t{r}_{-}$ and $t{r}_{+}$ are upper and lower limits of the transfer time window, respectively; $T_{TL}^{\min }$ represents minimum continuous transfer time; $P_{TL,t}^{be}$ and $P_{TL,t}^{af}$ are the TL before and after the transfer at time $t$, respectively.

(5)

Curtailable load ($CL$) constraints

$CL$ is a type of flexible load that dynamically adjusts to fluctuations in energy demand by actively reducing energy consumption or temporarily suspending operation. $CL$ includes curtailable electricity load ($CEL$) and curtailable hydrogen load ($CHL$).

$$\left(v_{CL,t}-v_{CL,t-1}\right)T_{CL}^{\min }\le {\displaystyle \sum _{\tau =t}^{t+T_{CL}^{\min }-1}{v}_{CL,t}},t=1,2,\dots T-T_{CL}^{\min }+1$$

(36)

$$1\le {\displaystyle \sum _{\tau =t}^{t+T_{CL}^{\max }}\left(1-v_{CL,t}\right)},t=1,2,\dots ,T-T_{CL}^{\max }$$

(37)

$$P_{CL,t}^{DR}=v_{CL,t}\cdot {\alpha }_{CL,t}\cdot P_{CL,t}^{be}$$

(38)

$$P_{CL,t}^{af}=P_{CL,t}^{be}-P_{CL,t}^{DR}$$

(39)

where $v_{CL,t}$ and $v_{CL,t-1}$ are the curtailment state variables at time $t$ and $t-1$, respectively; $N_{CL}^{\max }$ is maximum number of curtailment within a scheduling cycle; $T_{CL}^{\min }$ and $T_{CL}^{\max }$ are minimum and maximum continuous curtailment time, respectively; ${\alpha }_{CL,t}$ is load curtailment ratio at time $t$; $P_{CL,t}^{be}$ and $P_{CL,t}^{af}$ are the $CL$ before and after the curtailment at time $t$, respectively.

(6)

Electricity balance constraints

$$\begin{array}{l}E({\overline{P}}_{WT,t})+E({\overline{P}}_{PVP,t})+P_{GT,i,t}+P_{FC,i,t}+P_{ES,i,t}^{dis}+P_{b,ex,i,t}^e+{\displaystyle \sum _{j=1,j\ne i}^M{P}_{j,i,t}^e}(1-{\eta }_e)\\ =P_{EL,i,t}+P_{ES,i,t}^{ch}+P_{s,ex,i,t}^e+{\displaystyle \sum _{j=1,j\ne i}^M{P}_{i,j,t}^e}(1-{\eta }_e)+P_{s,in,i,t}^e\end{array}$$

(40)

$$P_{s,in,i,t}^e=P_{BEL,i,t}+P_{SEL,i,t}^{af}+P_{TEL,i,t}^{af}+P_{CEL,i,t}^{af}$$

(41)

where $P_{BL,i,t}$ represents the fixed electricity load ($FEL$) of subsystem $i$ at time $t$; ${\eta }_e$ denotes the electricity transmission loss coefficient.

(7)

Hydrogen balance constraints

$$\begin{array}{l}{V}_{EL,i,t}+V_{HT,i,t}^{dis}+V_{b,ex,i,t}^h+{\displaystyle \sum _{j=1,j\ne i}^M{V}_{j,i,t}^h}(1-{\eta }_h)=\\ V_{FC,i,t}+V_{HT,i,t}^{ch}+{\displaystyle \sum _{j=1,j\ne i}^M{V}_{i,j,t}^h}(1-{\eta }_h)+V_{s,in,i,t}^h\end{array}$$

(42)

$$V_{s,in,i,t}^h=V_{BHL,i,t}+V_{SHL,i,t}^{af}+V_{THL,i,t}^{af}+V_{CHL,i,t}^{af}$$

(43)

where $V_{BHL,i,t}$ represents the fixed hydrogen load ($FHL$) of subsystem $i$ at time $t$; ${\eta }_h$ denotes the hydrogen transmission loss coefficient.

(8)

Spinning reserve chance constraints

$$P_r\left\{{\chi }_{WT,i,t}+{\chi }_{PVP,i,t}\le P_{GT,i,t}^{\max }-P_{GT,i,t}\right\}\ge {\alpha }_i$$

(44)

where ${\alpha }_i$ represents confidence levels.

(9)

Carbon emission constraints

Furthermore, the carbon emissions of each subsystem during the scheduling period must not exceed a specified limit.

$${\displaystyle \sum _{t=1}^T\left(e_{GT}\cdot Q_{GT,i,t}+e_{EM}\cdot P_{b,ex,i,t}^e\right)}\le C{E}_i^{\max }$$

(45)

where $e_{GT}$ denotes the carbon emissions produced by burning each cubic meter of natural gas; $e_{EM}$ is carbon emission factor of purchased electricity; $C{E}_i^{\max }$ is the carbon emission cap of subsystem $i$ during the scheduling period.

4.3. Model Solution

To solve the constructed multi-objective optimal scheduling model, the paper transforms it into a weighted single-objective optimal scheduling model. Assuming the weights assigned to the optimization objectives on the system side, market side, and user side are $w_1$, $w_2$, and $w_3$, respectively, the weighted single-objective model is presented as follows.

$$f=w_1{\displaystyle \frac{f_1-f_{s1}}{f_{s1}}}+w_2{\displaystyle \frac{f_{s2}-f_2}{f_{s2}}}+w_1{\displaystyle \frac{f_3-f_{s3}}{f_{s3}}}$$

(46)

where $f_{s1}$, $f_{s2}$, and $f_{s3}$ are all single-objective optimization values.

In addition, the optimization framework of the paper is shown in Figure 2.

5. Electricity Price Prediction Based on TBATS Model

The Trigonometric seasonality, Box–Cox transformation, Auto Regressive Moving Average (ARMA) errors, Trend and Seasonal components (TBATS) model is an advanced composite time series forecasting method that integrates the exponential smoothing state-space framework with an ARMA error correction structure, enabling simultaneous modeling of complex seasonal patterns, non-linear trends, etc. It has been applied to forecast electricity price [39], electric vehicle charging loads [40], carbon dioxide emissions [41], and traffic vehicular [42].

Accurate electricity price forecasting not only improves dispatch efficiency but also supports sustainable market participation by enabling informed trading decisions. In this section, the historical data comprise hourly electricity market clearing prices (24 observations per day) covering 360 trading days, drawn from monthly market datasets over recent years in a province in North China. The TBATS model is trained on these hourly price time series to capture intraday seasonality as well as potential longer-term periodic patterns. The forecasting accuracy is evaluated using three standard error metrics: mean error ($ME$), root mean square error ($RMSE$), and mean absolute error ($MAE$).

$$ME={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n({\hat{\mathrm{y}}}_i-{\mathrm{y}}_i)}$$

(47)

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{({\hat{\mathrm{y}}}_i-{\mathrm{y}}_i)}^2}}$$

(48)

$$MAE={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left|{\hat{\mathrm{y}}}_i-{\mathrm{y}}_i\right|}$$

(49)

where ${\hat{\mathrm{y}}}_i$ and ${\mathrm{y}}_i$ are the predicted and actual electricity prices, respectively; $n$ denotes the sample size.

Moreover, a comparison of the predicted and actual price trends is presented in Figure 3, while the values of error evaluation metrics are shown in

Table 1. Values of error evaluation metrics.

Evaluation Metrics	$\mathbf{Mean} \mathbf{Error} \left(\mathit{ME}\right)$	$\mathbf{Root} \mathbf{Mean} \mathbf{Square} \mathbf{Error} \left(\mathit{RMSE}\right)$	$\mathbf{Mean} \mathbf{Absolute} \mathbf{Error} \left(\mathit{MAE}\right)$
Error value	0.0029	0.0092	0.0072

.

According to Figure 3 and Table 1, the trend of the predicted values is basically consistent with that of the actual values. The error values are all less than 0.01, falling within an acceptable range. Moreover, the results of electricity price prediction for the next 24 h are shown in Figure 4.

According to Figure 4, the highest electricity price within the 24 h is approximately CNY 0.503/kWh, while the lowest is about CNY 0.036/kWh. Furthermore, the electricity price data presented in Figure 3 is adopted, where the price for each hour is defined as the mean of the forecasted values within the corresponding hourly interval. Based on this, the electricity prices are incorporated into the multi-objective dispatch model as time-varying price signals. These signals directly guide the optimal scheduling of generation, storage, conversion, transaction, and DR, thereby determining the cost–emission trade-offs. Accordingly, Figure 4 provides the essential bridge between the forecasting module and the dispatch optimization outcomes.

6. Case Study

6.1. Scenario Setting

To comprehensively evaluate the performance of the proposed EHCMMG dispatch model under different operating conditions, the paper sets different scenarios according to the DR implementation, uncertainty in renewable energy generation, subsystem interconnections, and ESS, with scenario 1 serving as the baseline scenario, as detailed in

Table 2. Multiple dispatch scenarios.

Scenarios	Subsystem Interconnections	Uncertainty	DR	$\mathit{E}\mathit{S}\mathit{S}$
1	√	√	√	√
2		√	√	√
3	√		√	√
4	√	√		√
5	√	√	√

.

6.2. Basic Data

The EHCMMG consists of two subsystems, namely subsystem 1 and subsystem 2. Each subsystem is configured with a variable number of $WT$, $PVP$, $GT$, $EL$, $FC$, $ES$, and $HT$. Figure 5 shows the power output profile of a single $WT$ in each subsystem, while Figure 6 shows the corresponding profile for a single $PVP$. The fixed electricity and hydrogen load profiles are illustrated in Figure 7 and Figure 8, respectively. Moreover, the electricity price forecasts used in this study are sourced from Figure 3. Some other technical parameters are set with reference to [43], and the hydrogen price refers to [44].

6.3. Results and Discussion

In the baseline scenario, Figure 9, Figure 10 and Figure 11 illustrate the electricity supply–demand and interaction characteristics, while Figure 12, Figure 13 and Figure 14 present the hydrogen supply–demand and interactions. In addition, the carbon emissions are presented in Figure 15.

Figure 9 shows that electricity procured from the market constitutes the dominant share of the supply mix, indicating that the optimization strategy primarily relies on the market to satisfy demand when self-generation is either insufficient or not cost-competitive. This is because market electricity is often the most economical option under time-varying prices, whereas local generation is constrained by capacity limits, fuel costs, and emission restrictions. $PVP$ generation is mainly concentrated during daylight hours and peaks around midday, consistent with solar irradiance availability, partially meeting demand and thereby reducing the need for $GT$ dispatch. $WT$ output fluctuates throughout the day and reaches its maximum around hour 14, with the total daily wind power generation exceeding 14.5 MWh. Compared with wind power, the total electricity generated by $GTs$ is relatively low and mainly plays a complementary role. This is due to their relatively high marginal cost and operational constraints, which make sustained or frequent operation uneconomical.

In addition, $FCs$ do not generate electricity in this case, suggesting that, under the adopted parameter settings, their operation is not economically optimal. Meanwhile, the total discharge from $ES$ accounts for only a small proportion of the overall power supply. $ES$ is typically scheduled during specific periods when it provides the greatest system value, such as mitigating short-term supply–demand imbalances, shaving peak residual load, or reducing high-cost generation and market purchases. Its contribution is limited because it can only release previously stored electricity and is further constrained by state-of-charge limits and efficiency losses.

Figure 10 indicates that $EL$ remains constant at 360 kW throughout the 24 h period, suggesting that the hydrogen production process is operated at a steady setpoint rather than being frequently adjusted. In contrast, the charge of $ES$ is highly uneven over time, appearing only in selected hours and reaching its daily maximum during peak charging periods. This intermittent charging behavior is consistent with storage being used as an opportunity-driven flexibility resource.

Another important observation is that no electricity is sold to the market over the entire day. This usually implies that, under the adopted price signals and constraints, exporting is not economically attractive or feasible. Regarding the load composition, $FEL$ dominates the demand profile and fluctuates moderately within a relatively narrow band (approximately 1300–2100 kW). Meanwhile, $SEL$ and $TEL$ are dispatched only during specific hours. Additionally, $CEL$ has the largest total among the three flexible loads, and its total value exceeds the combined total of $SEL$ and $TEL$. A deeper interpretation is that, during certain high-cost or constrained hours, simply shifting or transferring load is not sufficient to maintain system balance, and curtailment becomes the most effective flexibility option.

According to Figure 11, the electricity exchange demonstrates a distinct asymmetric pattern on a typical day: the power transferred from subsystem 2 to subsystem 1 (green curve) is positive for most hours and frequently reaches the upper limit of about 300 kW (e.g., early hours 1–5 and several later intervals such as 8–9, 20, and 23), indicating that the interconnection constraint is often binding, so subsystem 1’s required support is sometimes larger than what the line can deliver. In contrast, the reverse flow from subsystem 1 to subsystem 2 (blue curve) stays at zero throughout the day, implying that subsystem 1 does not experience conditions under which exporting electricity would be economically attractive or feasible under the model’s optimal schedule.

The deeper reasons behind this pattern can be interpreted from an operational and economic perspective. First, the one-way flow indicates that subsystem 2 is a net exporter while subsystem 1 is a net importer, which typically occurs when subsystem 2 has higher effective supply, or subsystem 1 has higher demand (or both). Second, the fact that reverse flow remains zero suggests that even during potential surplus periods in subsystem 1, exporting is outcompeted by alternative uses of electricity or prevented by tighter local constraints.

According to Figure 12, $ELs$ demonstrate a stable hydrogen production capability, providing a continuous and reliable foundation for hydrogen supply within the cluster. This suggests that the $ELs$ are operated close to a fixed set-point. In contrast, HT discharge occurs only in a few specific slots (5, 8, 10, 20, and 23), showing that the tank is not used as a continuous supplier but rather as a flexibility buffer to cover short-term imbalances. Notably, the hydrogen released from $HTs$ reaches its maximum value in slot 20, significantly enhancing the cluster’s hydrogen regulation capability.

In addition, the dominant contribution in most hours comes from hydrogen purchases, but this supply exhibits pronounced temporal variability. Purchases rise sharply during hours 14–16 and 19. Overall, Figure 12 indicates a three-layer strategy for hydrogen supply: $EL$ provides a stable baseline, $HT$ discharge is selectively used for peak-shaving and short-term regulation, and market purchases serve as the primary balancing lever when internal supply is insufficient or not cost-effective.

Figure 13 shows that during the daily scheduling period, $FCs$ remain inactive, indicating that hydrogen is not converted back to electricity. This suggests that $FC$ operation is not cost-effective under the given electricity–hydrogen price signals and efficiency assumptions, or that hydrogen is more valuable for satisfying end-use hydrogen loads than for power generation. Meanwhile, the charge of $HT$ is concentrated in hours 1, 3–4, 14–15, and 19, implying that this charging is not continuous but is scheduled only when the system experiences temporary surplus hydrogen or when charging provides the highest marginal value for later balancing. On the demand side, hydrogen load scheduling exhibits a fine-grained management pattern: $FHL$ constitutes the dominant baseline component across nearly all hours, representing the relatively rigid portion of hydrogen consumption that must be satisfied to maintain system operation. In contrast, $SHL$ is mainly scheduled during hours 14–16 and 19–21, indicating that this load type is likely high-priority but time-selective. $THL$ is dispatched more flexibly across multiple time intervals, suggesting it has looser time-coupling constraints. Notably, $CHL$ emerges from hour 6 and persists until hour 19, indicating that curtailment becomes necessary over an extended period.

According to Figure 14, the hydrogen flow from subsystem 2 to subsystem 1 dominates during most hours (green curve) and reaches a maximum of 300 m³, indicating that the interconnection capacity limit is frequently binding. Moreover, subsystem 2 exports a total of more than 4400 m³ of hydrogen to subsystem 1 over the day, effectively alleviating the hydrogen supply pressure faced by subsystem 1. In contrast, the reverse transfer from subsystem 1 to subsystem 2 is almost negligible, totaling only 65.98 m³ and occurring only at hours 19 and 21. These results confirm that subsystem 2 serves as the primary hydrogen supplier, whereas subsystem 1 is a net importer.

From a deeper operational and economic perspective, this pattern typically emerges because subsystem 2 has higher effective hydrogen availability, while subsystem 1 faces persistent supply constraints and must therefore rely on a combination of local hydrogen production, interconnection imports, and market procurement to satisfy its demand.

Figure 15 indicates that the cluster-level carbon emissions peak at hour 21, when both subsystems exhibit relatively high emissions. Specifically, subsystem 1 has a total daily emission of 11.118 tons, with a maximum of 761.222 kg occurring at hour 7, whereas subsystem 2 has a slightly higher total of 11.261 tons, with a maximum of 656.147 kg occurring at hour 21. This implies that the cluster’s highest-emission hour is driven by a simultaneous elevation in both subsystems, rather than both subsystems individually reaching their own maxima at the same time. Moreover, the emission fluctuations of subsystem 2 appear to be more closely associated with its hydrogen dispatch strategy: as a supplier of low-carbon hydrogen, subsystem 2 supports system-wide balancing through flexible operations, which can shift energy consumption and the corresponding emissions across hours. Overall, these patterns are mainly governed by the marginal supply mix and the coupling between electricity and hydrogen scheduling.

6.4. Multi-Scenario Analysis

The results of multi-scenario analysis are presented in

Table 3. Results of multi-scenario analysis.

Scenarios	Cluster Cost (Million CNY)	MIO Net Revenue (Million CNY)	User Energy Cost (Million CNY)	Total Carbon Emissions (Tons)
1	17.502	12.684	5.556	8168.126
2	27.804	22.564	5.721	6957.788
3	17.548	12.255	5.551	8096.230
4	34.176	40.487	23.172	6746.355
5	19.026	14.120	5.280	7961.262

.

In scenario 1, the cluster cost is CNY 17.502 million, the MIO net revenue is CNY 12.684 million, the user energy cost is CNY 5.556 million, and the total carbon emissions are 8168.126 tons. Comparing scenario 1 with scenario 2 (no interconnection) shows that removing interconnections substantially increases the cluster cost to CNY 27.804 million and raises the MIO net revenue to CNY 22.564 million, while the user energy cost increases only slightly to CNY 5.721 million. Meanwhile, total carbon emissions decrease markedly to 6957.788 tons. Further comparison between scenario 1 and scenario 3 (no uncertainty) suggests that accounting for renewable uncertainty mainly influences the cluster’s dispatch decisions and the MIO’s profitability, whereas its effect on user energy cost and carbon emissions is limited in this case. In addition, comparing scenario 1 with scenario 4 (no DR) reveals that removing DR dramatically increases both the cluster cost and the user energy cost, while the MIO net revenue rises and carbon emissions decrease.

Furthermore, comparing scenario 1 with scenario 5 (no-$ESS$) shows that removing ESS increases the cluster cost to CNY 19.026 million and increases the MIO net revenue to CNY 14.120 million, while reducing the user energy cost to CNY 5.280 million and lowering carbon emissions to 7961.262 tons. This suggests that $ESS$ in the baseline case primarily enhances operational flexibility and economic coordination, but it may also shift energy consumption across time in a way that results in slightly higher user energy costs and total carbon emissions than the no-$ESS$ case. Overall, the multi-scenario results reveal a clear trade-off between economic performance and carbon emissions, highlighting the inherent complexity of achieving sustainability in integrated multi-energy systems.

6.5. Sensitivity Analysis

This section conducts a sensitivity analysis on the installed capacity of the $ESS$, and the corresponding economic and environmental indicators are illustrated in Figure 16.

Figure 16 reveals a systematic trade-off: increasing $ESS$ capacity simultaneously reduces cluster cost and total carbon emission, but it also compresses MIO net revenue and slightly increases user energy cost. This highlights that $ESS$ expansion improves system-level economic–environmental performance, while its distributional impacts across stakeholders (cluster, MIO, and users) depend strongly on market interaction and the underlying cost/revenue allocation rules. Overall, the simultaneous reduction in cluster cost and carbon emission supports long-term decarbonization and efficient operation. By enhancing flexibility, $ESS$ enables higher renewable penetration and improves energy security, but fair market and policy designs are needed to support large-scale deployment.

6.6. Engineering Reference Significance

First, from an engineering perspective, this study provides a quantifiable benchmark for optimal EHCMMG dispatch under an economics–carbon–benefit allocation framework, serving as a baseline for similar multi-energy microgrids under comparable pricing schemes and configurations.

Second, the interconnection channel becomes binding in some periods, and removing either interconnection or DR significantly increases both cluster and user energy costs. In practice, adequate tie-line capacity and enforceable DR should be prioritized.

Third, sufficient ramping headroom and spinning reserve should be maintained by the GT to accommodate short-term supply–demand imbalances and mitigate cost volatility. The confidence level of the chance constraints should be calibrated to the acceptable risk of outage and load shedding.

Fourth, expanding $ESS$ capacity reduces cluster cost and emissions but also reshapes benefit allocation. To realize these gains in practice, settlement rules should be designed alongside $ESS$ deployment to avoid unduly squeezing operator revenue and to improve the practical applicability to investment and dispatch decisions.

7. Conclusions

This study provides a theoretically sound and practically applicable solution for the sustainable dispatch of the EHCMMG. By integrating electricity price prediction, multi-objective optimization, demand response, and uncertainty modeling within a unified framework, the proposed approach simultaneously improves economic efficiency, operational reliability, and low-carbon performance-three pillars of sustainable energy systems. The main conclusions are summarized as follows:

(1)

The price forecast-driven multi-objective optimal scheduling model balances the interests of the system side, market side, and user side. In the baseline scenario, the cluster cost, MIO net revenue, and user energy cost amount to CNY 17.502, 12.684, and 5.556 million, respectively, while total carbon emissions reach 8168.126 tons.

(2)

The interconnection among subsystems enhances the economic efficiency of both the cluster and its users but simultaneously decreases the revenue of the MIO and leads to higher carbon emissions. This trade-off underscores the importance of balancing economic gains with low-carbon objectives in the design of multi-energy systems.

(3)

As the ESS capacity coefficient increases from 1 to 10, the cluster cost decreases by 38.8% and carbon emissions fall by 11.5%. In contrast, the user energy cost rises by 8.9%, and MIO’s net revenue is reduced. Overall, expanding $ESS$ capacity enhances system-wide economic and environmental performance.

Despite these contributions, certain limitations remain. Future research could further enhance the sustainability of EHCMMG by: (i) incorporating hydrogen-based derivatives such as ammonia and methanol to build a more comprehensive multi-energy collaboration framework aligned with the hydrogen industry chain; (ii) adopting advanced uncertainty modeling techniques such as distributionally robust optimization and data-driven forecasting to improve system adaptability under extreme and long-term fluctuation scenarios, thereby reinforcing the resilience and sustainability of MMG operations.