Multi-Energy Coordination Strategy for Islanded MEMG with Carbon-Gas Coupling and Demand Side Responses

Abstract

Multi-energy microgrids are emerging technologies to facilitate the integration of distributed energy resources and decarbonisation of various energy consumptions. To assist in the low-carbon and efficient operation of multi-energy microgrids, this paper proposes a multi-energy coordination method for an electricity-heat-gas microgrid which integrates technologies of carbon-gas coupling (CGC) and demand side response (DSR). The carbon capture system–power-to-gas unit and water electrolyser (WE) are jointly employed to capture carbon emissions from combined heat-and-power units for methane synthesis, enabling the CGC and reducing carbon emissions and reliance on external gas supply. Then, incentive-based DSR schemes are implemented for both electricity and heat loads, leveraging the demand-side flexibility to further enhance the use of renewable generation. The operation of CGC and DSR units is co-optimised to minimise the penalties related to renewable generation curtailments and carbon emissions subject to a set of constraints including demand-side comfort coefficients. Compared to a traditional microgrid with neither CGC nor DSR, the joint implementation of CGC and DSR is estimated to reduce the total operational cost and carbon emissions of microgrid by over 20% and 40%, respectively, and increase the use of renewable generation by about 19%, illustrating the effectiveness of the proposed coordination method together with CGC and DSR technologies in reducing microgrid operating costs and carbon emissions while improving the share of renewables.

1. Introduction

To facilitate the efficient operation and systematic management of distributed energy resources (DERs), microgrid technology has gradually emerged as an innovative paradigm within modern power systems. A microgrid is generally referred to as a localised, small-scale power system that integrates diverse forms of DERs, such as renewable generation units, in conjunction with energy storage systems and local loads. Through the application of scheduling strategies and advanced control mechanisms, a microgrid can achieve a high degree of energy self-sufficiency. This enables it to function independently in an islanded mode, securing local electricity supply in the event of upstream grid faults. In addition, a microgrid can be seamlessly connected to the external utility grid, where it acts as a vital component of the bulk power system. In this grid-connected mode, the microgrid can contribute to the stability, reliability, and operational flexibility of large-scale electric networks, demonstrating its dual capability of both local autonomy and system-level support.

Traditional microgrids typically only feature a single energy source and rely heavily on fossil fuel, resulting in substantial renewable generation curtailment and elevated carbon emissions. They generally achieve certain operational flexibility through the deployment of fast-acting generators and/or energy storage systems (ESSs). In contrast, a multi-energy microgrid (MEMG) integrates multiple energy carriers such as electricity, heat and gas, which enable more flexible operation and significantly improve renewable energy utilisation and overall energy efficiency [1]. Multiple energy carriers can be produced simultaneously by co- or tri-generation units, a carbon capture system (CCS) with power-to-gas (P2G) units, fuel cells, electrolysers, etc. [2]. Due to the complex coupling nature and different operational characteristics of multiple energy sources, it is necessary to develop multi-energy coordination strategies to ensure the efficient and economic operation of MEMGs.

References [3,4,5,6] investigate optimization and scheduling strategies for MEMGs from different perspectives. Reference [3] applies a Stackelberg game model to ancillary services, achieving improved economy, peak shaving, and user comfort. Reference [4] integrates a thermoelectric-coupled CHP model and a simplified gas network with demand response for intraday electricity–gas co-scheduling. Reference [5] employs a reinforcement-learning-based differential evolution algorithm for multi-energy flow scheduling, reducing industrial energy costs. Reference [6] proposes an optimal dispatch strategy for grid-connected and islanded MEMGs, realizing integrated optimization of electricity–heat–cooling systems and energy storage. References [7,8,9] focus on energy trading in MEMGs, addressing ancillary services, network reconfiguration, and risk aversion.

However, most of the research above focuses primarily on economic dispatch while disregarding renewable curtailment caused by the uncertainty of wind and solar generation [10,11] and overlooking the environmental implications of carbon emissions. These shortcomings lead to underutilization of renewable resources and excessive reliance on fossil-fuel-based units, thereby limiting the sustainability of multi-energy systems. The coordinated scheduling of multi-energy systems that simultaneously considers the penalty of curtailment renewable energy curtailment and the carbon emissions remain open issues that require further investigation to achieve both efficient renewable accommodation and low-carbon operation.

To address global climate challenges, low-carbon operation of MEMGs has gained increasing attention. References [12,13,14,15,16,17] examine low-carbon operation of MEMGs under various carbon-related mechanisms and optimization strategies. Reference [12] develops a distributed ADMM-based DC optimal power flow model incorporating carbon trading, enabling coordinated economic–environmental dispatch. References [13,14] integrate carbon trading into multi-energy system scheduling frameworks, achieving joint optimization of system cost and carbon-emission performance. Reference [15] proposes a two-step diffusion strategy combining carbon trading and green certificate mechanisms with a piecewise linear carbon-pricing model to enhance renewable-energy utilization. Reference [16] formulates a stochastic multi-objective sizing model that minimizes total cost and carbon emissions while explicitly considering battery-degradation effects. Reference [17] establishes a multi-energy coupling framework embedding carbon-emission flow modeling and carbon-capture units, offering improved emission-reduction capability for integrated energy systems.

However, these studies mainly achieve carbon reduction through mechanisms such as carbon trading, green certificate incentives, and stepped carbon pricing. While these approaches effectively constrain emissions and enhance renewable energy utilization, they predominantly focus on the supply side with limited attention to the demand side. The absence of DSR consideration restricts the system’s ability to exploit flexible load resources for peak shaving, renewable absorption, and carbon mitigation; therefore, the coordinated integration of DSR with low-carbon scheduling remains an important research issue, deserving further investigation to achieve a more balanced and flexible operation of MEMGs.

References [18,19,20,21,22] examine demand-side response (DSR) mechanisms from different perspectives, focusing on user flexibility modelling, optimisation strategies, and behavior characterization. Reference [18] introduces DSR as a mechanism that reshapes user consumption through dynamic pricing and economic incentives. Reference [19] proposes a distributed multi-objective optimisation scheme for incentive-based DSR, balancing profit, comfort and environmental goals with reduced communication needs. Reference [20] applies time-of-use DSR to energy-hub scheduling to improve multi-carrier coordination and reduce overall energy use. While most MEMG studies consider only electric-side DSR with simplified heat-load modelling, reference [21] develops a multi-energy demand-response exchange mechanism that jointly coordinates electric and gas flexibility. Reference [22] presents a graph-attention-based temporal elasticity model to depict user behavior responses under varying prices and assess DSR accuracy.

However, these studies provide valuable analyses of DSR mechanisms but do not refine the categorization of flexible loads, often adopting coarse or unified modeling approaches that fail to distinguish between different types of load flexibility. Moreover, most existing works focus exclusively on economic optimisation and overlook the influence of user comfort coefficients, leaving the quantitative relationship between comfort levels and operational costs insufficiently explored in the current literature. The comparative analysis of the main referenced literature is presented in

Table 1. Comparative Analysis of the Reviewed Literature.

References	DSR	Carbon Cost	CGC	User Comfort
[3,6,9,11,14]	Not considered	Not considered	Not considered	Not considered
[5,7,10,12,16]	Not considered	Stepped carbon cost [5,7,10,16] Carbon market [12]	Not considered	Not considered
[4,20]	Electric and heat DSR, without load classification [4] Electric DSR only, without load classification [20]	Not considered	Not considered	Not considered
[15,21]	Electric DSR only, without load classification [15] Electric and gas DSR, with load classification [21]	Stepped carbon cost [15] Carbon market [21]	Not considered	Not considered
[8,19]	Electric and heat DSR, with load classification [8] Electric DSR only, with load classification [19]	Not considered	Not considered	Considered
[13]	Electric, heat and cool DSR, without load classification	Carbon market	Not considered	Considered
[17]	Not considered	Stepped carbon cost	CCS-P2G is considered	Not considered

.

To solve these challenges, this paper develops a comprehensive optimisation framework for the low-carbon operation of multi-energy microgrids (MEMGs). Specifically, a multi-energy coordination model is proposed by integrating a stepped carbon-penalty mechanism with demand-side response (DSR) and carbon–gas coupling (CGC) technologies. Compared with existing studies that mainly address electricity–heat–gas coordination or treat CCS, P2G, and water electrolysis (WE) units as isolated components, this work establishes a multi-energy framework considering CGC that embeds CCS–WE–P2G into the real-time dispatch layer as flexible conversion units. Furthermore, an incentive-based DSR model is developed, where daily loads are divided into basic, shiftable, and curtailable categories, and corresponding price compensation and incentive mechanisms are introduced under user comfort constraints. Compared with conventional simplified DSR models that focus only on electric loads or neglect comfort impacts, the proposed model provides a more comprehensive and fine-grained representation of load flexibility. In addition, the interaction between user comfort and economic performance is quantitatively examined, revealing the variation in total operating cost under different comfort levels. By coupling the carbon-market pricing signal with the stepped carbon-penalty mechanism, the proposed model realizes an integrated low-carbon scheduling strategy that links energy flow and carbon flow. Within this framework, the inherent flexibility of DSR together with the dynamic conversion characteristics of CCS–P2G and WE are exploited to improve the absorption of wind and photovoltaic (PV) power and reduce reliance on external natural gas.

• Main Contributions:

(1) An electricity–heat–gas–carbon-hydrogen framework with CGC coupling is formulated, integrating CCS, P2G and WE units. The combined heat and power (CHP) unit is equipped with CCS to capture CO₂ emissions, while the WE unit produces hydrogen from renewable electricity. The captured CO₂ and generated H₂ are subsequently converted into methane through the P2G methanation process. This configuration establishes a closed carbon–gas–hydrogen cycle, effectively enhancing carbon utilization and reducing dependence on the external natural gas grid. Unlike previous studies that treat CCS, WE, and P2G as independent post-processing modules, the proposed framework embeds them into the real-time dispatch layer as flexible conversion units, enabling dynamic coupling among electricity, gas, and carbon flows.

(2) An incentive-based DSR model for electric and heat loads is developed to fully exploit load flexibility under user comfort constraints. The daily load is classified into basic, shiftable, and curtailable loads, and based on the flexibility characteristics of different load types, price compensation and price incentive mechanisms are designed for curtailable and shiftable loads, respectively, encouraging consumers to actively adjust their energy consumption. A comfort coefficient constraint is incorporated to maintain user satisfaction while ensuring economic operation. Furthermore, the effect of varying user comfort levels on total operating cost is quantitatively analyzed, revealing the inherent trade-off between user comfort and system economy. Additional simulations under different user comfort levels are conducted to further verify this relationship, demonstrating that higher comfort requirements reduce system flexibility and lead to a gradual increase in total operating cost. Compared with traditional single-energy DSR models, the proposed strategy achieves coordinated electric–heat flexibility management, significantly improving system adaptability and cost efficiency.

(3) A stepped carbon penalty mechanism is embedded into the optimization model. By associating the carbon penalty cost with dispatch decisions of each generation unit, the system internalizes emission costs and dynamically regulates overall carbon output. The proposed piecewise penalty function better represents marginal emission costs than linear formulations, thereby driving low-carbon scheduling behaviors and strengthening the environmental–economic trade-off within multi-energy coordination.

Comprehensive simulations validate the effectiveness and superiority of the proposed strategy. Compared with the base case without CGC and DSR participation, the proposed model increases renewable energy utilization by 19.03%, reduces total carbon emissions by 46.26%, and lowers overall operating cost by 17.56%, thereby demonstrating the synergistic benefits of flexible conversion units and demand-side coordination.

2. Structure of MEMG

In MEMG, the principal energy carriers are electricity, heating energy, and natural gas. The schematic of a typical MEMG, encompassing subsystems for energy generation, conversion, storage, and consumption, is shown in Figure 1.

The multi-energy microgrid (MEMG) achieves continuous and reliable energy supply through the coordinated integration of multiple energy sources. The structural configuration of the MEMG considered in this study is illustrated in Figure 2. The system comprises an input interface capable of grid-connection with external natural gas networks, as well as direct utilization of renewable energy from wind turbines (WTs) and photovoltaic (PV) units. On the demand side, the output interface is designed to simultaneously meet users’ requirements for electricity, heating, and natural gas.

Within the energy conversion subsystem, several key components are incorporated, including a combined heat and power (CHP) unit, a gas boiler (GB), a micro-gas turbine (MT), a power-to-gas (P2G) unit, and a WE. The CHP unit not only generates electricity but also recovers waste heat for heating, thereby realizing efficient cogeneration. The inclusion of electric storage (ES) and heat storage (HS) further enhances the flexibility of system operation and improves the overall efficiency of energy utilization by providing peak-shaving and load-balancing capabilities.

Moreover, the model integrates a carbon capture system (CCS) with the CHP unit. The captured CO₂ is subsequently directed into the P2G process, where it is combined with hydrogen produced by the WE to synthesize methane. This process not only reduces net carbon emissions but also provides a supplementary source of natural gas, thereby decreasing reliance on external gas procurement and enhancing the sustainability of the entire MEMG system.

2.1. Energy Storage System

The crucial function of energy storage system (ESS) lies in its ability to balance energy consumption and production, thereby facilitating equilibrium between energy supply and demand [23]. In this paper, energy storage is classified into two types, electric storage (ES) and heat storage (HS).

ES is currently primarily employed to mitigate the impacts of renewable generation uncertainty on power system operations [24]. For HS, its primary role is to decouple the electric heat coupling of the CHP unit by storing surplus heat produced during power generation, thereby enhancing the operational flexibility of the power system. When the heat output from the CHP and GB units cannot be fully utilized, it can be temporarily stored in the heat storage system, thereby enabling temporal shifting of heat energy and enhancing its utilization efficiency. Its operating model is analogous to that of electric storage.

Beyond conventional electric and heat storage, modern integrated energy systems encompass multiple energy carriers with inherent storage capabilities. Hydrogen storage plays a vital role in long-term energy balance through reversible processes of water electrolysis and fuel cell conversion, effectively facilitating seasonal utilization of renewable energy. Compressed air energy storage and flywheel energy storage are typically employed for short- and medium-term frequency regulation and power balancing. In addition, the linepack capacity of natural gas pipelines serves as an important form of virtual storage, where dynamic pressure regulation enables short-term gas storage and release, contributing to system energy balance and operational security [25].

Different storage technologies exhibit distinct mechanisms and temporal characteristics. Electric and heat storage are suitable for short-term scheduling and local energy balancing, whereas hydrogen storage and linepack are more appropriate for long-term energy smoothing and system security enhancement. Considering the spatial–temporal scale of the studied islanded microgrid, this paper focuses on the scheduling flexibility and multi-energy coupling effects of electric and heat storage, while future work will incorporate gas-side linepack dynamics and hydrogen storage modeling to further improve the representation of coordinated and low-carbon energy management.

Accordingly, the ESS models are expressed by (1).

$$\left\{\begin{array}{c}{P}_{ES,n}\left(t\right)={\lambda }_c{P}_{ES,n}^{cha}\left(t\right){\eta }_{ES,n}^{cha}-{\displaystyle \frac{{\lambda }_d{P}_{ES,n}^{dis}\left(t\right)}{{\eta }_{ES,n}^{dis}}},\forall t\in T_{ES}\\ 0⩽P_{ES,n}^{cha}\left(t\right)⩽P_{ES,n}^{max},\forall t\in T_{ES}\\ 0⩽P_{ES,n}^{dis}\left(t\right)⩽P_{ES,n}^{max},\forall t\in T_{ES}\\ S_n\left(t\right)=S_n\left(t-1\right)\ast \left(1-{\eta }_{ES,n}^{los}\right)+P_{ES,n}\left(t\right),\forall t\in T_{ES}\\ S_n\left(1\right)=S_n\left(T\right)\\ {\lambda }_c,{\lambda }_d\in \left[\mathrm{0,1}\right]\\ {\lambda }_c+{\lambda }_d⩽1\\ S_n^{\mathrm{m}\mathrm{i}\mathrm{n}}⩽S_n\left(t\right)⩽S_n^{\mathrm{m}\mathrm{a}\mathrm{x}},\forall t\in T_{ES}\\ n\in \left[ES,HS\right]\\ 0\le T_{ES}\le 24\end{array}\right.$$

(1)

where ${\eta }_{ES,n}^{cha} \mathrm{a}\mathrm{n}\mathrm{d} {\eta }_{ES,n}^{dis}$ denote the charging and discharging rates of the ESS, respectively, $P_{ES,n}^{cha}$, $P_{ES,n}^{dis}$ denote the charging and discharging power of the ESS, respectively,${\lambda }_c,{\lambda }_d$ are the binary indicators for charging and discharging of the ESS, respectively. $S_n$ denotes the current state of charge (SOC) of the ESS.

The ESS model describes the charging and discharging behavior and the corresponding energy balance over time. The output power of the ESS at each time period is determined by its charging and discharging power, where the charging and discharging states are controlled by binary variables and constrained by their respective maximum limits. The SOC is updated based on its previous value, the charging and discharging power, and the energy-loss coefficient, while being required to remain cyclically consistent over the scheduling horizon and confined within the allowable minimum and maximum capacity limits.

2.2. Power Generation Unit

This study considers three types of gas turbine power generation units—MT, GB, CHP and WE, with the detailed models specified by (2).

$$\left\{\begin{array}{c}{P}_t^{MT}={\eta }_{MT}{H}_{gas}{G}_t^{MT},\forall t\in T\\ H_t^{GB}={\eta }_{GB}{H}_{gas}{G}_t^{GB},\forall t\in T\\ P_t^{CHP}={\eta }_e^{CHP}{H}_{gas}{G}_t^{CHP},\forall t\in T\\ {\lambda }_{\mathrm{m}\mathrm{i}\mathrm{n}}^{CHP}\le {\displaystyle \frac{H_t^{CHP}}{P_t^{CHP}}}\le {\lambda }_{\mathrm{m}\mathrm{a}\mathrm{x}}^{CHP},\forall t\in T\end{array}\right.$$

(2)

where, ${\eta }_{MT}$, ${\eta }_{GB}$ and ${\eta }_e^{CHP}$ denote the generation efficiencies of MT, GB, CHP units, respectively, $H_{gas}$ is the calorific value of natural gas. ${\lambda }_{min}^{CHP}$ and ${\lambda }_{max}^{CHP}$ are the minimum and maximum electric-to-heat output ratios of the CHP units, respectively.

The model describes the energy conversion relationships of MT, GB, and CHP units. MT, GB, and CHP convert natural gas into electric or heat output according to their respective energy-conversion efficiencies. The CHP unit produces both electricity and heat simultaneously, and its electric-to-heat ratio is constrained within specified bounds to ensure that the CHP operates within its feasible coupling region. This constraint reflects the inherent coupling characteristics between the electric and heat outputs of the CHP unit.

2.3. Carbon-Gas Coupling Unit

The CGC unit in this study consists of CCS, WE, and P2G units. CCS can sequester the CO₂ produced during the operation of the generation unit. In addition to reducing carbon emissions, the captured CO₂ can be utilized to produce other energy carriers, thereby enhancing byproduct utilization. In this study, the carbon capture unit captures CO₂ emitted by the CHP unit and combines with H₂ produced by WE, in conjunction with the P2G system, converts the CO₂ into methane to supplement the natural gas demand of the multi-energy microgrid [25].

The detailed model is formulated by (3).

$$\left\{\begin{array}{c}0\le E_t^{CCS}\le {\alpha }^{CCS}{e}_g^{CCS}{P}_{i,t}^{CHP},\forall t\in T\\ P_{CCS,t}^{OP}={\lambda }^{CCS}{E}_{{CO}_2,t}^{CCS},\forall t\in T\\ 0\le E_{{CO}_2,t}^{P2G}\le E_{{CO}_2,t}^{CCS},\forall t\in T\\ G_{{CH}_4,t}=\varpi E_{{CO}_2,t}^{P2G},\forall t\in T\\ P_{P2G,t}={\eta }^{P2G}{G}_{{CH}_4,t},\forall t\in T\\ 0\le P_{CCS,t}^{OP}\le P_{CCS,\mathrm{m}\mathrm{a}\mathrm{x}}^{OP},\forall t\in T\\ 0\le P_{P2G,t}\le P_{P2G,\mathrm{m}\mathrm{a}\mathrm{x}},\forall t\in T\\ P_{WE,t}={\eta }_{WE}{H_2}_t^{WE},\forall t\in T\\ 0\le {H_2}_t^{WE}\le 4·G_{{CH}_4,t},\forall t\in T\end{array}\right.$$

(3)

where $P_{CCS,t}^{OP}$ denotes the operating power of the carbon capture unit, ${\lambda }^{CCS}$, ${\alpha }^{CCS}$ and $e_g^{CCS}$ are the unit’s energy-consumption coefficient, capture-ratio coefficient and carbon-emission coefficient, respectively. $P_{\mathrm{P}2\mathrm{G},t}$ is the output power of the power-to-gas unit, ${\eta }^{P2G}$ and $G_{{\mathrm{C}\mathrm{H}}_4,t}$ are the P2G energy-conversion efficiency and the volume of methane produced, and $E_{{CO}_2,t}^{CCS}$ represents the total amount of CO₂ captured, $E_{{CO}_2,t}^{P2G}$ is the fraction of captured CO₂ allocated to the P2G process. $P_{\mathrm{P}2\mathrm{G},max}$ and $P_{CCS,max}^{OP}$ denote the maximum operating power of the P2G and CCS units, ${H_2}_t^{WE}$ denotes the value of H₂ produced in WE, $P_t^{WE}$ denotes the operating power of WE unit, respectively.

The CGC model describes the multi-energy conversion relationships among CCS, P2G, and WE units. CCS captures the CO₂ generated from the fuel consumption of the CHP unit, with the captured amount determined by the capture ratio and the carbon-emission coefficient. A portion of the captured CO₂ is processed within CCS, while the remainder is supplied to the P2G unit for methane synthesis. P2G converts CO₂ into CH₄ according to its energy-conversion efficiency and operates within its maximum power limit. Meanwhile, WE converts electricity into H₂, providing the necessary hydrogen for methane synthesis, where the hydrogen production depends on the operating power and efficiency of the WE unit.

2.4. Demand Response Model

Incentive-based demand response (IBDR) is a mechanism designed to encourage users to actively cooperate with microgrid operation through financial compensation or reward measures. The underlying principle is to employ incentive signals to influence user behavior, prompting them to voluntarily curtail loads during periods of power scarcity or to shift part of their consumption to alternative time slots. This strategy not only alleviates supply pressure in isolated microgrids and enhances operational reliability and stability but also facilitates renewable energy integration by guiding users to increase consumption during periods of high wind power and PV generation. Consequently, IBDR improves overall energy-utilization efficiency and contributes to the low-carbon and sustainable operation of microgrids.

Conventional DSR models generally account only for electric load participation. However, heat loads as an equally essential component can also take part in DSR regulation. Therefore, the DSR model developed in this study simultaneously considers the incentive-based demand response of both electric and heat loads. On the user side, loads are categorized into fixed and flexible types, with flexible loads further subdivided into curtailable and shiftable classes.

Curtailable loads refer to demand-side devices or services, such as televisions and air conditioners, that can be temporarily reduced within a designated response window in exchange for financial compensation, without significantly affecting users’ comfort or daily activities. In this study, the curtailable electric loads mainly include lighting and electronic devices such as computers and televisions, while the curtailable heat loads primarily consider a portion of domestic hot water demand. The mathematical formulations of the curtailable electric and heat load models are expressed in Equations (4) and (5), respectively.

$$L_{E,cur,\mathrm{m}\mathrm{i}\mathrm{n}}^{t_C^E} \le \mid \Delta L_{E,cur}^{t_C^E}\mid \le L_{E,cur,\mathrm{m}\mathrm{a}\mathrm{x}}^{t_C^E},\forall t_C^E\in T_C^E$$

(4)

where $\Delta L_{E,cur}^{t_C^E}$ denotes the quantity of curtailable electric loads, $T_C^E$ denotes the time cycle for curtailable electric loads, it is described detailed in Section 5.1.

$$L_{H,cur,\mathrm{m}\mathrm{i}\mathrm{n}}^{t_C^H} \le \mid \Delta L_{H,cur}^{t_C^H}\mid \le L_{H,cur,\mathrm{m}\mathrm{a}\mathrm{x}}^{t_C^H},\forall t_C^H\in T_C^H$$

(5)

where $\Delta L_{H,cur}^{t_C^H}$ denotes the quantity of curtailable heat loads, $T_C^H$ denotes the time cycle for curtailable heat loads, it is described detailed in Section 5.1.

Shiftable loads refer to demand-side appliances or services, such as washing machines and water heaters, that can be rescheduled to other times at equal or lower levels through price incentives without significantly disrupting normal usage patterns. In this study, the shiftable electric loads mainly include air conditioners and other flexible electric appliances, while the shiftable heat loads primarily consider domestic hot water used for bathing and other flexible heat loads. The mathematical formulations of the shiftable electric and heat load models are expressed in Equations (6) and (7), respectively.

$$L_{E,sft,\mathrm{m}\mathrm{i}\mathrm{n}}^{t_S^E} \le \mid \Delta L_{E,sft}^{t_S^E}\mid \le L_{E,sft,\mathrm{m}\mathrm{a}\mathrm{x}}^{t_S^E},\forall t_S^E\in T_S^E$$

(6)

where $\mathsf{\Delta }{L}_{E,sft}^{t_S^E}$ denotes the quantity of shiftable electric loads, $T_C^E$ denotes the time cycle for shiftable electric loads, it is described detailed in Section 5.1.

$$L_{H,sft,\mathrm{m}\mathrm{i}\mathrm{n}}^{t_S^H} \le \mid \Delta L_{H,sft}^{t_S^H}\mid \le L_{H,sft,\mathrm{m}\mathrm{a}\mathrm{x}}^{t_S^H},\forall t_S^H\in T_C^H$$

(7)

where $\mathsf{\Delta }{L}_{H,sft}^{t_S^H}$ denotes the quantity of shiftable heat loads, $T_C^H$ denotes the time cycle for shiftable heat loads, it is described detailed in Section 5.1.

The post-response electric and heat load in DSR is formulated by (8) and (9).

$$L_{E,af}^t=L_E^t-\left(L_{E,cur}^{t_C^E}+\Delta L_{E,sft}^{t_S^E}\right),\forall t\in T$$

(8)

where $L_E^t$ denotes the total electric load prior to demand response.

$$L_{H,af}^t=L_H^t-\left(\Delta L_{H,cur}^{t_C^H}+\Delta L_{H,sft}^{t_S^H}\right),\forall t\in T$$

(9)

where $L_H^t$ denotes the total heat load prior to demand response.

Demand side comfort coefficient (DSCC) refers to the impact of demand response by expressing the ratio of the post-response load to the original total load. A lower DSCC indicates greater load shifting, while a value closer to 1 indicates minimal disruption to user consumption patterns. The DSCC model is formulated by (7).

$$DSCC=\left\{1-\left[{\displaystyle \frac{\sum _{t_C^E,t_S^E}\left(L_{E,cur}^{t_C^E}+\Delta L_{E,sft}^{t_S^E}\right)}{\delta ·L_E^t}}+{\displaystyle \frac{\sum _{t_C^H,t_S^H}\left(\Delta L_{H,cur}^{t_C^H}+\Delta L_{H,sft}^{t_S^H}\right)}{\delta ·L_H^t}}\right]\right\}$$

(10)

where $\delta$ denotes the number of energy carriers participating in DSR, this paper considers electric and heat.

3. Carbon Market Model

The carbon emission trading mechanism is a typical mechanism in the carbon market. It refers to the allocation of free carbon emission credits to energy producers based on their historical carbon output. These carbon emission credits are tradable on a dedicated carbon market to achieve effective emission control. If the actual carbon emission of energy producers exceeds their allocated allowances, it is required to buy additional credits from the market.

In this paper, the energy producers are CHP, MT, and GB units. Among these, the CHP unit is one of the primary heat producers, which can operate with a higher capacity to satisfy simultaneous electric and heat demands. It consequently has the largest carbon emission. To mitigate these emissions, the CCS system is integrated with the CHP unit.

Electric output from the CHP may be converted into its heat-equivalent value, and the carbon emissions associated with heat output from the CHP can be estimated by using its electric output [26].

The specific model for carbon emission and carbon emission credits is formulated by (11)–(13).

$$E_{d,t}^{CHP}+{\sigma }_{gas}\left(P_t^{MT}+H_t^{GB}\right),\forall t\in T$$

(11)

$$E_{d,t}^{CHP}={\sigma }_{gas}\left({\displaystyle \frac{{\phi }_{H,CHP}\left(1-{\phi }_{P,CHP}\right)P_t^{CHP}}{{\phi }_{P,CHP}}}+\phi P_t^{CHP}\right)$$

(12)

where $E_{d,t}^{Gen}$ denote the carbon emission of energy generation, $E_{d,t}^{CHP}$ denotes the carbon emission of the CHP unit, ${\sigma }_{gas}$ denotes the carbon emission coefficient of gas, ${\phi }_{P,CHP}$ and ${\phi }_{H,CHP}, \phi$ denote the electric generation coefficient, heat generation coefficient and the transformation coefficient from electric to heat of CHP, respectively, $H_{grid,t}^r$ and $P_{grid,t}^r$ denote heat and electric power sold back by the microgrid to the upstream network.

The actual carbon emission participating in the carbon market is formulated by (13).

$$E_{market}=E_{d,t}^{Gen}-E_{{CO}_2,t}^{CCS}-E_c,\forall t\in T$$

(13)

where $E_{market}$ denotes the carbon emissions subject to the carbon emissions stepped penalty, $E_c$ is the carbon emission credits allocated to MEMG. In this paper, a stepped emissions carbon penalty mechanism [17] is formulated by (14).

$$C_{carbon}=\left\{\begin{array}{c}{p}^c{E}_{market} \\ 0\le E_{market}\le d\\ p^c\left(1+x\right)\left(E_{market}-d\right)+p^{c}d\\ d\le E_{market}\le 2d\\ p^c\left(1+2x\right)\left(E_{market}-2d\right)+p^c\left(2+x\right)d\\ 2d\le E_{market}\le 3d\\ p^c\left(1+3x\right)\left(E_{market}-3d\right)+p^c\left(3+3x\right)d\\ 3d\le E_{market}\le 4d\\ p^c\left(1+4x\right)\left(E_{market}-4d\right)+p^c\left(4+6x\right)d\\ E_{market}\ge 4d\end{array}\right.$$

(14)

where $p^{\mathrm{c}}$ be the base penalty unit price, $x$ the additional penalty coefficient. The difference between actual emissions and the carbon allowance is partitioned into up to five equal-length intervals, each of length $d$. If the excess does not exceed $d$, the penalty is calculated at the base unit price $p^{\mathrm{c}}$, if the excess exceeds the first interval, then for each additional full interval of length $x{p}^{\mathrm{c}}$, For example, if a generation unit’s actual emissions exceed its carbon allowance by $1.4d$ the first $d$ is penalized at the base rate $p^{\mathrm{c}}$, whereas the excess $0.4d$ is penalized at ($1+x)p^{\mathrm{c}}$.

4. MEMG Optimal Configuration Model

4.1. Objective Functions

In the multi-energy microgrid model, to achieve optimal economic operation while satisfying demand-side user comfort requirements, this paper sets economic optimality as the objective and imposes user comfort constraints alongside the economic goal. $F$ denotes the economic objective function.

It should be noted that, unlike large-scale AC/DC hybrid microgrids where network-constrained formulations are commonly required [27], the system studied in this work is a small-scale islanded MEMG. Owing to its short feeders and compact topology, the network can be equivalently represented as a single-node system, in which voltage limits and line-capacity constraints are inherently satisfied by the system’s structural design and equipment ratings. Therefore, power-flow constraints for the electric or heat networks are not included in the objective-function formulation. Instead, the model focuses on three economic components: operational cost, renewable curtailment penalty cost, and carbon-emission cost.

$$\mathrm{m}\mathrm{i}\mathrm{n}F=\min \left(C_{op}+C_{pu}+C_{carbon}\right)$$

(15)

where $C_{op}$ denote, the operation cost, $C_{pu}$ denote the penalty cost for wind power and PV curtailment, $C_{carbon}$ denote the carbon penalty cost.

$$C_{op}=C_{grid}+C_S+C_{gen}+C_{DR}+C_{CCS-P2G}$$

(16)

where $C_{grid},{ C}_S, C_{gen}, C_{DR}$ and $C_{CP}$ denote, respectively, the cost of energy purchase from the external grid, the operation cost of the energy storage system, the operation cost of the generation unit, the DSR incentive and compensation cost and the operating cost of the CCS-P2G unit.

(1) Cost of energy purchase

$$C_{grid}=\sum _t\left(c_e{P}_{grid,t}+c_g{G}_{grid,t}\right), \forall t\in T$$

(17)

(2) Cost of energy storage

$$C_S=\sum _{n\in \left[ES,HS\right]}{c}_{S,n}\sum _t{P}_{S,n}\left(t\right),\forall t\in T$$

(18)

$$P_{S,n}\left(t\right)=P_{ES,n}^{cha}\left(t\right)+P_{ES,n}^{dis}\left(t\right),n\in \left[ES,HS\right]$$

(19)

(3) Cost of energy generation

$$C_{gen}=\left[\begin{array}{c}{\displaystyle \sum _t}{c_{PV}P}_t^{PV}+{\displaystyle \sum _t}{c_{WT}P}_t^{WT}+{\displaystyle \sum _t}{c}_{GB}{H}_t^{GB}\\ +{\displaystyle \sum _t}{c}_{CHP,e}(P_t^{CHP}+H_t^{CHP}) +{\displaystyle \sum _t}{c_{MT}P}_t^{MT}\end{array}\right],\forall t\in T$$

(20)

(4) Cost of CCS-P2G operation

$$C_{CCS-P2G}=\sum _t\left(c_{CCS}{P}_{CCS,t}^{OP}+c_{P2G}{P}_{P2G,t}+c_{WE}{P}_{WE,t}\right),\forall t\in T$$

(21)

(5) Cost of DSR incentive and compensation

$$C_{DR}=\sum _{m\in \left[E,H\right]}\left(c_{cut}\Delta L_{m,cur}^{t_1}+c_{sft}\Delta L_{m,sft}^{t_2}\right),\forall t_1\in T_{cur},t_2\in T_{sft}$$

(22)

(6) Cost of wind power and PV curtailment

$$C_{pu}=\sum _t{\mu }_w\left(P_t^{WT}-P_{t,\mathrm{m}\mathrm{a}\mathrm{x}}^{WT}\right)+\sum _t{\mu }_{pv}\left(P_t^{PV}-P_{t,\mathrm{m}\mathrm{a}\mathrm{x}}^{PV}\right),\forall t\in T$$

(23)

where $c_e$ and $c_g$ denote the unit costs of purchasing electric and natural gas from the external grid, respectively, $P_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d},t}$ and $G_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d},t}$ denote the electric and natural gas purchased from the external grid, $c_{S,n}$ denotes the unit operating cost of the electric and heat storage system, $c_{PV},c_{WT},c_{GB},c_{CHP}$ and $c_{MT}$ denote the unit operating costs of PV, WT, GB, CHP, MT. $c_{CCS},c_{P2G}$ and $c_{WE}$ denote the unit operating costs of CCS, P2G and WE $c_{cur}$ denotes the unit compensation cost of curtailable loads, $c_{sft}$ denotes the unit incentive cost of shiftable loads.

4.2. Constraints

Output power Constraints of Generation Units are formulated by (24).

$$\left\{\begin{array}{c}0\le P_t^{PV}\le P_{t,\mathrm{m}\mathrm{a}\mathrm{x}}^{PV},\forall t\in T\\ 0\le P_t^{WT}\le P_{t,\mathrm{m}\mathrm{a}\mathrm{x}}^{WT},\forall t\in T\\ P_{\mathrm{m}\mathrm{i}\mathrm{n}}^{CHP}\le P_t^{CHP}\le P_{\mathrm{m}\mathrm{a}\mathrm{x}}^{CHP},\forall t\in T\\ P_{\mathrm{m}\mathrm{i}\mathrm{n}}^{MT}⩽P_t^{MT}⩽P_{\mathrm{m}\mathrm{i}\mathrm{n}}^{MT},\forall t\in T\\ H_{\mathrm{m}\mathrm{i}\mathrm{n}}^{GB}\le H_t^{GB}\le H_{\mathrm{m}\mathrm{a}\mathrm{x}}^{GB},\forall t\in T\end{array}\right.$$

(24)

where $P_{t,max}^{PV}$, $P_{t,max}^{WT}$, $P_{max}^{CHP}$, $P_{min}^{MT}$ and $H_{max}^{GB}$ denote the maximum output capacities of the PV, WT, CHP, MT, and GB units, respectively. $P_{min}^{CHP}$, $P_{min}^{MT}$ and $H_{min}^{GB}$ denote the minimum out capacities of the CHP, MT and GB units, respectively.

Ramping up Constraints are formulated by (25).

$$\left\{\begin{array}{c}-R{D}^{MT}\le P_t^{MT}-P_{t-1}^{MT}\le R{U}^{MT},\forall t\in T\\ -R{D}_e^{CHP}\le P_t^{CHP}-P_{t-1}^{CHP}\le R{U}_e^{CHP},\forall t\in T\\ -R{D}_h^{CHP}\le H_t^{CHP}-H_{t-1}^{CHP}\le R{U}_h^{CHP},\forall t\in T\\ R{D}^{GB}\le H_t^{GB}-H_{t-1}^{GB}\le R{U}^{GB},\forall t\in T\end{array}\right.$$

(25)

where $R{U}^{MT},R{U}_e^{CHP},R{U}_h^{CHP}$ and $R{U}^{GB}$ denote the ramp-rate coefficients of the MT, the electric output of the CHP, the heat output of the CHP unit, and the GB unit, respectively.

The demand side comfort constraint is formulated by (26).

$$DSC{C}_{\mathrm{m}\mathrm{i}\mathrm{n}}\le DSCC\le 1$$

(26)

The Electric Power Balance Constraint is formulated by (27).

$$P_{grid,t}+P_t^{CHP}+P_t^{MT}+P_t^{WT}+P_t^{PV}+P_{S,ES}^{dis}\left(t\right)=L_{E,af}^t+P_{S,ES}^{cha}\left(t\right),\forall t\in T$$

(27)

Heat Power Balance Constraint is formulated by (28).

$$H_t^{CHP}+H_t^{GB}+P_{S,HS}^{dis}\left(t\right)=L_{H,af}^t+P_{S,HS}^{cha}\left(t\right),\forall t\in T$$

(28)

Gas Power Balance Constraint is formulated by (29).

$$G_{grid,t}+G_t^{C{H}_4}+P_{S,GS}^{dis}\left(t\right)=L_G^t+G_t^{MT}+G_t^{GB}+G_t^{CHP}+P_{S,GS}^{cha}\left(t\right),\forall t\in T$$

(29)

The overview of the proposed optimization framework, including variables, constraints, objectives and optimal results are shown in Figure 3.

5. Results

5.1. Test System and Parameters

This paper employs YALMIP and CPLEX within MATLAB (2024a) for simulation. The configured electric–heat–gas multi-energy microgrid includes PV, WT, CHP, GB, ESS, and CCS-P2G, and incorporates demand response. The cost of purchasing electricity from the main grid is set at 0.20 CNY/kWh for 1–7 h, 0.53 CNY/kWh for 8–10 h, 16–18 h, and 21–23 h, and 0.82 CNY/kWh at all other times and the cost of gas procurement is 0.35 CNY/kWh.

All gas-fired units are constrained by ramp-rate limits of ±10% of their maximum capacity. Main parameters in

Table 2. Main Parameters in MEMG.

Parameter	Value	Parameter	Value
$P_{\mathrm{m}\mathrm{i}\mathrm{n}}^{CHP}$	100 kW	${\sigma }_{gas}$	564.7 g
$P_{\mathrm{m}\mathrm{a}\mathrm{x}}^{CHP}$	200 kW	${\eta }_{WE}$	4.5
$P_{\mathrm{m}\mathrm{i}\mathrm{n}}^{MT}$	70 kW	$e^{CCS}$	564.7 g
$P_{\mathrm{m}\mathrm{a}\mathrm{x}}^{MT}$	150 kW	${\alpha }^{CCS}$	0.9
$S_n^{\mathrm{m}\mathrm{i}\mathrm{n}}$	40 kW	${\eta }^{P2G}$	0.9
$S_n^{\mathrm{m}\mathrm{a}\mathrm{x}}$	100 kW	$\varpi$	0.0002
$H_{\mathrm{m}\mathrm{i}\mathrm{n}}^{GB}$	100 kW	${\lambda }^{CCS}$	0.00024
$H_{\mathrm{m}\mathrm{a}\mathrm{x}}^{GB}$	200 kW	${\eta }_{ES n}^{dis}$	0.9
$p^{\mathrm{c}}$	0.0012 ¥	${\eta }_{ES n}^{cha}$	0.9
$d$	15,000 g	${\eta }_{ES n}^{los}$	0.01
$x$	0.4	$c_{S,ES}$	0.003 ¥
$c_{PV}$	0.003 ¥	$c_{S,ES}$	0.003 ¥
$c_{WT}$	0.0032 ¥	$c_{GB}$	0.012 ¥
$c_{MT}$	0.015 ¥	$c_{CCS}$	0.1 ¥
$c_{CHP}$	0.018 ¥	$c_{P2G}$	0.07 ¥
$c_{cut,E}$	0.3 ¥	$c_{cut,H}$	0.3 ¥
$c_{sft,E}$	0.05 ¥	$c_{sft,H}$	0.05 ¥
$c_{mov,E}$	0.05 ¥	$ICS{I}_{\mathrm{m}\mathrm{i}\mathrm{n}}$	0.96
${\mu }_w$	0.35 ¥	${\mu }_{PV}$	0.35 ¥
$H_{gas}$	11.7	${\lambda }_{\mathrm{m}\mathrm{i}\mathrm{n}}^{CHP}$	0.5
${\lambda }_{\mathrm{m}\mathrm{a}\mathrm{x}}^{CHP}$	1.1	$\delta$	2

.

For DSR, electric loads are categorized into curtailable and shiftable types, with response windows of 20–24 h, 5–21 h, and 4–18 h, respectively (time constraints apply only to shiftable loads). The shiftable electric load is further divided into three segments: the first requires a continuous 2-h response within its designated window, the second requires a continuous 3-h response, and the third necessitates a continuous 5-h response within its available time frame. Heat DSR likewise comprises both curtailable and shiftable loads. The shiftable heat load is scheduled to respond once for a continuous 3-h period within the window of 5–19 h. For all curtailable loads, the minimum curtailable proportion is set to 20% of their respective maximum capacity. Within the 24-h scheduling horizon, curtailable loads are required to be activated during no fewer than eight time periods.

The demand-side electric and heat loads are illustrated in Figure 4, while the gas load is represented in the gas-power-balance diagram for each scenario. Both the electric and heat loads are divided into baseline and flexible components. In the figure, “Equivalent” denotes the equivalent maximum load, “Fixed” represents the inflexible baseline load; and “Shiftable” and “Curtailable” correspond to the flexible portions of the load associated with shiftable and curtailable categories, respectively.

5.2. Case Information

Four representative cases are defined to investigate the effects of the CCS-P2G unit and DSR on the multi-energy microgrid. The stepped carbon-penalty mechanism is applied in all cases and is henceforth omitted for brevity.

Case 1: The traditional MEMG model considers only WT, PV, and other generation units while neglecting the participation of demand-side and carbon-gas coupling mechanisms.

Case 2: The MEMG model with demand-side flexible loads scheduling without CCS-P2G equipment. The flexibility of demand-side flexible loads enables the enhancement in more effective wind power and PV generation utilization rates, thereby reducing the output requirements of other generation units and carbon emissions.

Case 3: The MEMG model with CCS-P2G unit and WE unit but without demand-side flexible load scheduling. As a flexible load, the CCS-P2G unit can change its operating power to enhance wind power and PV generation utilization, capture CO₂ and promote carbon–gas coupling for methane synthesis.

Case 4: The MEMG model proposed in this paper involves both the participation of demand-side and carbon-gas coupling mechanisms, in which the demand-side flexible load scheduling, CCS-P2G and WE unit are involved.

To provide a more comprehensive analysis, Section 5.3 compares the operational scheduling result diagrams of Case 1 and Case 4. The objective is to visually illustrate the differences in system dispatch characteristics, renewable energy absorption, and unit operation stability between the traditional MEMG and the proposed low-carbon model. Subsequently, Section 5.4 conducts a comparative analysis of all four cases in terms of quantitative indicators such as renewable utilization rate, carbon emissions, and total system cost, aiming to further evaluate the effectiveness of different flexible resources and validate the advantages of the proposed method.

5.3. Comparison and Analysis for Case 1 and Case 4

The different structures of Case 1 and Case 4 are shown in Figure 5, where Case 4 is distinguished by the addition of the CGC and DSR, and the electric power balance for Case 1 and Case 4 are shown in Figure 6. From the viewpoint of power balance and flexible resources, the ESS in Case 1 undertakes intensive and frequent charge–discharge cycling, characterized by large charging during valley periods (1–5 h, 14 h) or when WT and PV generation is abundant, and discharging during peak-demand periods (12 h, 19–22 h) to meet the load requirements. This behavior indicates that storage acts as the sole flexibility resource, simultaneously fulfilling the dual role of renewable absorption and peak supply. However, the limited rated capacity and power of the ESS restrict its temporal-shifting ability, resulting in a narrow regulation margin. Consequently, when the renewable output exceeds the local demand during extended valley hours (3–11 h, 23–24 h), the surplus electricity cannot be fully absorbed, leading to substantial renewable curtailment. The over-reliance on a single flexibility source also forces the ESS to operate close to its cycling limits, potentially increasing degradation and further weakening its ability to respond to subsequent fluctuations.

In Case 4, the CCS–WE–P2G chain and the DSR are incorporated in addition to the ESS. These resources act as controllable loads whose power consumption can be dynamically adjusted to follow renewable availability. During valley hours, the CCS–WE–P2G cluster operates as an adaptive sink for surplus wind and solar electricity, driving CO₂ capture, hydrogen production, and methane synthesis. This not only absorbs renewable oversupply but also forms a conversion pathway from intermittent renewable energy to fuel. As a result, the burden on the ESS is markedly alleviated, with its charge–discharge amplitude and frequency both reduced, extending its effective lifetime and improving system reliability.

The interaction between DSR and generation scheduling provides additional coordination. Transferable loads within DSR are shifted from peak to off-peak intervals, increasing valley consumption and further smoothing the net demand curve. Reducible loads are curtailed during peak hours under incentive signals, directly lowering the required generation output. These behaviors collectively compress the peak–valley gap and enhance the temporal alignment between renewable generation and demand. During prolonged low-price hours (1–12 h, 14–18 h, 23–24 h), the CCS–WE–P2G units operate near rated power, forming a persistent renewable-consuming load that effectively stabilizes the system balance and minimises curtailment losses.

From the generation-side perspective, Case 1 shows steep ramp-ups of MT units at 21 h and pronounced fluctuations in CHP output around 13 h and 21 h, reflecting the lack of coordinated flexibility. In Case 4, with DSR and CCS–WE–P2G support, only a moderate CHP increase at 21 h is observed, and the outputs of all major units remain comparatively smooth. This improvement is mainly attributed to the mutual regulation between flexible sources and flexible demands. When renewable production rises, CCS–WE–P2G and ESS absorb the excess; when generation declines, shifted loads and residual storage discharge complement the deficit. Such bidirectional coordination forms a self-balancing mechanism that minimises ramping stress and fuel consumption.

On the demand side, Case 4 demonstrates a clear redistribution of consumption. At peak-hour (12–15 h, 20–22 h) loads are effectively suppressed, while valley-hour loads (5–11 h, 23–24 h) increase significantly. The DSR mechanism thus exhibits both responsiveness and sustainability, repeatedly adjusting load profiles without compromising overall comfort, as bounded by the demand-side comfort coefficient. The smoother aggregated load curve enhances system stability, reduces the need for frequent generator start-ups, and improves operational economics. These findings confirm that coordinated utilisation of DSR, CCS–WE–P2G, and ESS achieves an integrated flexibility framework capable of simultaneously improving renewable utilisation, reducing curtailment, and stabilizing generation scheduling.

The heat power balance for Case 1 and Case 4 are shown in Figure 7. Comparison of Case 1 and Case 4 in terms of heat balance, form perspective of heating units’ operation, in Case 1, the outputs of GB and CHP units fluctuate considerably: heating supply decreases significantly during load valley hours (e.g., 5–8 h, 22–24 h) while rising sharply in peak hours (e.g., 11–14 h, 17–21 h). By contrast, Case 4 shows much smaller variations in heating output, with only a notable ramp-up at 21 h. This improvement can be attributed to the introduction of demand-side response (DSR) on the heat load side. Specifically, reducible loads effectively reduce the overall demand level, while transferable loads shift part of the peak heating demand to valley periods, thereby smoothing the load profile and alleviating the scheduling burden of heating units.

From the perspective of flexible scheduling, Case 1 relies solely on the heat storage system for adjustment. The storage charges during valley periods (e.g., 8–10 h, 15–17 h) and discharges during peaks (e.g., 11–14 h, 18–21 h) to balance demand. However, the excessive peak–valley gap and strong demand fluctuations exceed the limited regulation capacity of storage, forcing frequent and volatile adjustments of heating units. In Case 4, benefiting from the smoothing effect of DSR, the load curve is substantially improved, enabling the heat storage system to operate more stably within its constraints. During valley hours (e.g., 7–10 h, 15–18 h), storage performs significant charging, while discharging occurs in peak hours (e.g., 12–14 h, 19–21 h). Through this charge–discharge process, demand can be effectively balanced without relying on large fluctuations in unit output.

From the perspective of load profile characteristics, Case 4 demonstrates marked reductions in heating demand during peak hours (11–14 h, 18–21 h) due to reducible loads, while transferable loads shift part of the peak demand to valleys, leading to a smoother overall load profile. Compared with Case 1, the DSR in Case 4 plays a pronounced regulatory role, not only realizing peak shaving and valley filling, but also enhancing the flexibility, stability, and economic efficiency of system operation.

The gas power balance for Case 1 and Case 4 are shown in Figure 8. In Case 4, the coordination of DSR, CCS–P2G, and WE units introduces additional flexibility on the gas side and enables more effective temporal adjustment of energy conversion processes. These components collectively regulate gas consumption by coupling electricity and heat operations with the gas network. During valley hours, surplus renewable electricity is converted through the WE–P2G pathway into methane, which supplements the gas supply and partially offsets external procurement. When system demand increases, the stored or self-produced methane is utilised to sustain stable operation of gas-fired units, thereby mitigating sharp ramping requirements. As a result, the gas consumption profile becomes smoother, and the total volume of natural gas required by MT, GB, and CHP units decreases markedly compared with Case 1.

From the generation-side perspective, Case 1, which lacks DSR, CCS–P2G, and WE participation, displays strong fluctuations in the gas consumption of MT and CHP units, reflecting the absence of coordinated flexibility. In contrast, Case 4 achieves synchronised regulation among gas-consuming and electricity-producing units, supported by renewable-driven gas conversion. The coordinated interaction among these subsystems reduces the amplitude of gas-flow variation and lowers the instantaneous demand peaks, thereby improving fuel utilisation and maintaining stable combined energy dispatch.

From the perspective of gas-supply structure, Case 1 depends entirely on external natural gas procurement, resulting in a higher purchase level and limited autonomy. In Case 4, while part of the gas demand is still supplied by external sources, the inclusion of the P2G unit enables partial methane self-production that diversifies the supply portfolio. This configuration reduces dependence on upstream gas markets, enhances system self-sufficiency, and contributes to a lower overall procurement cost. The integration of CCS–P2G, WE, and DSR therefore establishes a hybrid gas–electric–heat coordination mechanism that supports renewable absorption, stabilises gas consumption, and promotes both economic efficiency and low-carbon operation across the scheduling period. The electric and heat loads in Case 4 after DSR are shown in Figure 9.

5.4. Scheduling Results of Each Case

The dispatch results for the four cases are summarized in

Table 3. The operational cost simulation results for the four Cases.

Cases	Total Cost (¥)	Carbon Cost (¥)	RE Curtailment Cost (¥)
Case 1	7541.7063	956.6260	410.7545
Case 2	7495.9874	880.2002	407.5158
Case 3	6324.6196	242.5403	13.1644
Case 4	6218.5719	191.9422	0.2768

and

Table 4. The remaining simulation results for the four Cases.

Cases	Net Carbon Emission (g)	WT-PV Utilization Rate (%)
Case 1	529,687.83	80.96
Case 2	505,192.38	81.11
Case 3	300,814.20	99.39
Case 4	284,596.85	99.99

. Comparing Case 2 and Case 4, the introduction of CCS–P2G and WE units in Case 4 results in an 18.88% increase in renewable energy utilization, a 43.67% reduction in net carbon emissions, and a 17.54% decrease in total system cost. These improvements are primarily attributed to the CCS unit capturing CO₂ emissions from CHP units and subsequently converting the captured CO₂ into methane through P2G technology, thereby reducing both external natural gas purchases and carbon emission costs. In addition, the CCS–P2G and WE units act as flexible loads that effectively absorb renewable energy during valley periods, substantially reducing wind and solar curtailment and consequently enhancing the system’s economic and environmental performance.

When comparing Case 3 and Case 4, renewable energy utilization in Case 4 increases by a further 0.63%, while net carbon emissions and total cost decrease by 5.39% and 1.68%, respectively. This incremental improvement can be ascribed to the incorporation of DSR alongside CCS–P2G and WE. During periods of pronounced load fluctuation (e.g., 23–24 h), renewable energy absorption is particularly challenging. However, under the regulation of DSR, part of the peak demand is shifted to low-demand hours, thereby elevating valley load levels. Supported by the coordinated operation of CCS–P2G, WE, and ESS, this adjustment enables the full utilization of renewable energy that would otherwise be curtailed. Furthermore, DSR contributes to a smoother load profile by narrowing peak–valley differences, mitigating generation-unit output fluctuations, and reducing the overall dispatch level compared with Case 3. As a result, carbon emissions and gas-purchase costs are further lowered, leading to an additional reduction in total system cost.

Comparing Case 1 and Case 4, renewable energy utilization in Case 4 improves by 19.03%, net carbon emissions decline by 46.26%, and total system cost decreases by 17.56%. This superior performance arises from the joint participation of CCS–P2G, WE, and DSR. The CCS unit captures CO₂ emissions from CHP units and, through P2G conversion, synthesizes methane, thereby reducing dependence on external gas supply and lowering emission levels. Meanwhile, the P2G and WE units function as flexible loads that absorb surplus WT/PV generation during valley hours, significantly enhancing renewable energy utilization. On the demand side, DSR implements peak shaving and valley filling, whereby reducible loads relieve peak demand pressure and transferable loads shift part of the demand to valley hours, resulting in a smoother load curve.

Overall, Case 4 achieves the most favorable system performance. The coordinated operation of CCS–P2G, WE, and DSR not only enhances renewable energy integration and reduces net carbon emissions but also strengthens system stability and cost effectiveness. These results verify that the collaborative participation of multiple flexible resources is key to achieving high renewable energy penetration and promoting low-carbon, efficient system operation.

In this MEMG system, the overall energy balance and supply stability rely entirely on local generation units and flexible resources. As the DSCC increases, the allowable range of load adjustment becomes more restricted, reducing the flexibility of demand-side response and leading to a smaller peak-to-valley difference in the load profile. The comparison of total costs under different DSCC levels is shown in

Table 5. Comparison of costs under different DSCC levels in Case 4.

Case 4	DSCC	Total Cost
Best DSCC level	96.11%	6218.5719
Upper DSCC level	97.11%	6227.4435
Upper DSCC level	98.11%	6241.5985

. Under this condition, the system exhibits two main operational characteristics:

First, the output of gas-fired units slightly increases. With a smaller peak–valley gap, the peak-shaving capability weakens, and the system must rely more on MT and CHP units to compensate for load variations and maintain stable electricity–heat coupling. Because the islanded microgrid cannot purchase electricity from the external grid, gas-fired units become the primary means of balancing supply and demand. Consequently, a higher comfort constraint leads to a moderate rise in unit output, resulting in additional fuel consumption and operating cost.

Second, the CGC system tends to operate at higher power during low-load periods. As the load curve becomes flatter, the valley demand increases, requiring the CCS–WE–P2G chain to enhance its power output to absorb surplus renewable generation from wind and photovoltaic sources. This intensified operation helps mitigate renewable curtailment and maintain internal energy balance, but it also raises the energy consumption and operating cost of the CGC system.

6. Conclusions and Future Work

This paper develops an electric–heat–gas low-carbon MEMG enhanced by a stepped carbon-penalty mechanism, an incentive-based demand response (DSR) scheme, and the coupling of the CHP unit with a CCS–P2G unit, thereby further reducing carbon emissions and improving overall energy utilization efficiency. Comparative analysis across four scenarios demonstrates that, through flexible curtailment, deferral, and shifting of demand-side loads, the utilization rates of wind and PV generation are significantly improved, which in turn reduces the penalty costs associated with renewable curtailment. Meanwhile, the smoothing of gas-turbine output fluctuations facilitates more stable operation, leading to reductions in both carbon emissions and operational expenditures.

Moreover, by employing CCS to capture CO₂ emissions from the CHP unit and synthesizing methane via the P2G unit, reliance on upstream methane supply is reduced, gas procurement costs are lowered, and carbon emissions together with corresponding penalty costs are substantially curtailed. The integration of the WE unit further strengthens this process: electricity from surplus wind and PV generation is utilized to produce hydrogen, which subsequently reacts with captured CO₂ in the P2G unit to synthesize methane. In this way, the coordinated operation of WE, CCS, and P2G units not only absorbs renewable electricity that would otherwise be curtailed but also facilitates large-scale CO₂ conversion into fuel, forming a self-sufficient and low-carbon internal circulation within the microgrid boundary.

Furthermore, as a dispatchable load, the CCS–P2G process dynamically consumes surplus electricity during periods of high renewable generation, while the WE provides a direct conversion pathway from electricity to hydrogen, thereby enhancing renewable absorption and improving system flexibility. The joint action of DSR, CHP, CCS, P2G, and WE ensures a tri-objective benefit of lowering total system cost, reducing carbon emissions, and increasing renewable energy utilization.

In addition, a sensitivity analysis on the demand-side comfort coefficient (DSCC) reveals that higher comfort requirements narrow the available flexibility of DSR and reduce the range of load adjustment, resulting in a smaller peak-to-valley difference in the load profile. Under this condition, the system must rely more on gas-fired units such as MT and CHP to compensate for load fluctuations, slightly increasing fuel consumption and operating cost. Simultaneously, the CGC system operates at higher power during low-load periods to absorb surplus renewable output, which enhances renewable utilization but also raises energy consumption within the system. Therefore, a trade-off exists between user comfort and operational economy. Properly setting DSCC can balance comfort satisfaction and system efficiency, achieving both stable operation and economic optimization.

For future research, several extensions will be pursued to further enhance the practical applicability of the proposed framework. First, when operating in grid-connected mode, the microgrid interacts dynamically with the upstream network, and the resulting bidirectional power exchange, external price signals, and renewable fluctuations introduce additional operational challenges. Future work will therefore develop a coordinated scheduling model for grid-connected operation, including islanded–grid-connected switching strategies and multi-regional energy coordination, to enable more positive and seamless integration of microgrids into larger networks. Second, the stochastic nature of renewable energy becomes even more critical under grid-connected conditions. To improve forecasting accuracy and reduce dispatch risks, future work will incorporate refined short-term forecasting models for wind and photovoltaic generation. Third, as the coupling among electricity, heat, and gas networks deepens, future studies will integrate optimal power flow formulations for multi-energy carriers, enabling joint optimisation of electric, heat, and gas flow constraints while accounting for power quality, voltage stability, and feasibility issues in grid-connected operation. Finally, in terms of flexible resource coordination, adaptive control and real-time dispatch strategies will be explored to enhance the system’s ability to respond promptly to load variations, renewable fluctuations, and external uncertainties, thereby improving the controllability and operational resilience of the microgrid.