Integrated Energy System Dispatch Considering Carbon Trading Mechanisms and Refined Demand Response for Electricity, Heat, and Gas

Abstract

To realize a carbon-efficient and economically optimized dispatch of the integrated energy system (IES), this paper introduces a highly efficient dispatch strategy that integrates demand response within a tiered carbon trading mechanism. Firstly, an efficient dispatch model making use of CHP and P2G technologies is developed to strengthen the flexibility of the IES. Secondly, an improved demand response model based on the price elasticity matrix and the capacity for the substitution of energy supply modes is constructed, taking into account three different kinds of loads: heat, gas, and electricity. Subsequently, the implementation of a reward and penalty-based tiered carbon trading mechanism regulates the system’s carbon trading costs and emissions. Ultimately, the goal of the objective function is to minimize the overall costs, encompassing energy purchase, operation and maintenance, carbon trading, and compensation. The original problem is reformulated into a mixed-integer linear programming problem, which is solved using CPLEX. The simulation results from four example scenarios demonstrate that, compared with the conventional carbon trading approach, the aggregate system costs are reduced by 2.44% and carbon emissions are reduced by 3.93% when incorporating the tiered carbon trading mechanism. Subsequent to the adoption of demand response, there is a 2.47% decrease in the total system cost. The proposed scheduling strategy is validated as valuable to ensure the low-carbon and economically efficient functioning of the integrated energy system.

1. Introduction

Amidst rapid economic development, the reliance on fossil fuels has led to significant issues, including the diminishment of non-renewable energy sources and the aggravation of climate change worldwide. Consequently, governments have prioritized the advancement of renewable energy sources as a crucial strategy to lead the transition in energy and develop an environmentally conscious society in addressing the fossil energy issues and environmental damage [1,2]. In recent years, the advancement and implementation of IESs have been pivotal in enhancing the consumption of renewable energy and improving energy utilization [3]. Optimized scheduling is an essential prerequisite for energy production, consumption, and balancing supply and demand in an IES. It is also a core element to ensure coordination, complementarity, and the economical operation of the diverse energy subsystems within the system [4,5].

Demand response (DR) can facilitate the synergistic correlation between supply and demand in an integrated energy system, mitigate the disparities between peak and off-peak loads, and enhance the economic efficiency of IES operations [6,7]. Common load demand response can be categorized into substitutable loads, transferable loads, and curtailable loads based on customer-side demand characteristics. Furthermore, based on the response type, it can be grouped into price-based and incentive-based demand responses [8,9]. In an IES, electrical, thermal, gas, and cooling loads exhibit distinct characteristics. Even within the same load category, response behaviors may differ significantly when exposed to varying incentives. Thus, the integration of DR can offer greater flexibility in IES scheduling [10].

In [11], the authors proposed the incorporation of incentive-based DR in microgrid energy management to maximize benefits for participating users. In [12,13], demand response according to time-of-day pricing was incorporated into IES scheduling to facilitate the rational coordination of multiple energy forms to meet consumption needs. In [14], the incorporation of time-of-day tariff-based demand response in an IES with CHP units can alleviate pressure on the power supply and enhance system stability. However, [12,14] only analyzed the demand response of electric loads, without considering other forms of energy loads. In [15,16], a demand response mechanism considering both electric and thermal loads is introduced to optimize integrated energy system dispatch, satisfying users’ energy requirements and enhancing renewable energy utilization. However, the demand response modeling method needs further optimization. In [17], demand response modeling was optimized, but only electric and thermal loads were considered. In [18], a flexible renewable resource model was developed and utilized in the efficient allocation of an IES. However, there are issues with the insufficient refinement of flexible resource classification in demand response and the oversimplified substitution relationships between different energy loads. In [19], it is pointed out that introducing a carbon trading mechanism can enable the low-carbon and economic operation of an IES. In [20], CHP and P2G were incorporated into the IES structure within a carbon trading mechanism, enhancing system’s operational flexibility. While CHP technology markedly enhances the overall efficiency of energy utilization through the simultaneous generation of electricity and heat, P2G technology offers a highly effective solution for conversion and energy storage, proving particularly advantageous for the integration of renewable energy sources. In comparison to other emerging technologies, such as hydrogen, P2G not only offers flexible energy storage capabilities but also assumes a critical role in multi-energy complementary systems. In [21], it is demonstrated that a dispatch scheme combining carbon trading mechanisms and demand response can simultaneously reduce greenhouse gas emissions and overall operational expenses. In [22,23], the traditional carbon trading mechanism was introduced in IES scheduling; however, this mechanism is overly simplistic for modeling carbon trading and costs. Therefore, [24] introduced a tiered carbon trading system in the scheduling plan to stratify carbon trading costs and further reduce emissions while ensuring economic operation. In [25], it was highlighted that the reward and penalty ladder carbon trading mechanism can more effectively stimulate user participation to adopt emission reduction measures. In reference [26], a dispatch model for IESs addressing electricity, heat, and gas under a tiered carbon trading approach was proposed. However, the modeling of carbon trading costs and equipment emissions in this study is insufficiently comprehensive. In [27], the modeling of carbon transaction costs and equipment emissions was optimized and the tiered carbon trading approach with incentives and penalties was introduced. However, neither [26] nor [27] considered demand response, resulting in an inability to regulate the user side. In [28], the DR of electricity, heat, and gas loads within the incentive–penalty ladder carbon trading mechanism was considered, but only load reduction and leveling were addressed, without considering the mutual substitution between loads.

To address the issues highlighted above, this paper suggests an integrated energy system dispatch model that incorporates a carbon trading mechanism and electricity–heat–gas DR, making the following key contributions:

• The integration of CHP and P2G technologies into the IES scheduling model significantly enhances the operational flexibility of the system. CHP (combined heat and power) and P2G (power-to-gas) technologies improve the efficiency of converting and distributing electricity, heat, and gas, thereby optimizing the overall operational efficiency of the system.
• The incorporation of a carbon trading mechanism into IES scheduling thoroughly accounts for the impact of each kind of equipment on carbon emissions. A reward-and-penalty-based tiered carbon trading model is established to effectively mitigate carbon emissions and trading costs. This mechanism incentivizes users to implement additional emission reduction measures, thereby achieving low-carbon operation through tiered rewards and penalties.
• A refined DR model based on the price elasticity matrix is developed, further considering the interplay between electricity, heat, and gas load substitutions. By accounting for each load’s reduction and leveling capabilities, the model maximizes the regulatory potential of flexible resources. This model can dynamically adjust load allocation in response to price signals, thereby enhancing the system’s responsiveness and economic performance.

The subsequent sections of this paper are arranged as follows: Section 2 introduces the structure of the integrated energy system and the demand response model. Section 3 introduces a reward-and-penalty-based tiered carbon trading model. Section 4 presents the scheduling model and solution method for the IES. Section 5 provides a case study with four different scenarios to illustrate the effectiveness of the suggested scheduling strategy. Section 6 concludes the paper.

2. IES Structure

The proposed IES optimization framework is fully aligned with both international and national climate objectives, including the Paris Agreement and China’s dual goals of “carbon peaking” and “carbon neutrality”. Through the integration of carbon trading mechanisms and demand response strategies, the framework effectively contributes to carbon emission reductions across multiple energy sectors, including electricity, heat, and gas. The incorporation of technologies such as CHP and P2G enables the more efficient utilization of energy resources, facilitating the transition toward cleaner, more sustainable energy systems. Additionally, the framework’s capacity to optimize energy dispatch while factoring in carbon costs provides a practical and effective solution for managing carbon emissions, consistent with the national target of peaking emissions by 2030 and attaining carbon neutrality by 2060. This framework not only assists policymakers in designing low-carbon energy systems but also equips industrial sectors with strategic tools to achieve their emission reduction targets, underscoring its practical importance in advancing climate action. The structural framework of the proposed IES is illustrated in Figure 1. The constructed IES structure includes the superior grid, superior gas grid, wind turbines (WTs), and photovoltaic panels (PVs) on the energy supply side, and the combined heat and power (CHP), electric boiler (EB), gas boiler (GB), and power-to-gas (P2G) on the energy conversion side. Specifically, the CHP comprises a gas turbine (GT), an organic Rankine cycle (ORC), and a waste heat boiler (WHB).

2.1. Demand Response Model

The DR model proposed in this study simultaneously addresses the DR of three types of loads: electricity, heat, and gas, thereby optimizing the utilization of flexible resources. These loads are categorized into curtailable loads, shiftable loads, and replaceable loads. Based on load response properties, DR is classified into price-based DR and substitution-based DR. Price-driven demand response loads are further categorized into curtailable loads (CLs) and shiftable loads (SLs).

2.1.1. Price-Based Demand Response

CLs determine whether to scale down their load based on the price at certain points prior to and following the DR. The price elasticity of the demand matrix for curtailable loads is defined as $E_{CL}(i,j)$:

$$E_{CL}(i,j)=\left[\begin{array}{cccc}{e}_{11}^{CL}& 0& \dots & 0\\ 0& e_{22}^{CL}& \dots & 0\\ ⋮& ⋮& \hspace{1em}& ⋮\\ 0& 0& \dots & e_{ij}^{CL}\end{array}\right]$$

(1)

$$e_{ij}^{CL}={\displaystyle \frac{\Delta P_i^{CL}}{P_i^{CL.0}}}{\left({\displaystyle \frac{\Delta {\varphi }_j}{{\varphi }_j^0}}\right)}^{-1}$$

(2)

$e_{ij}^{CL}$ is the element within the elasticity matrix $E_{CL}(i,j)$, representing the elasticity coefficient available of the CL at moment i in relation to the price at moment j. $P_i^{CL.0}$ denotes the initial CL and $\Delta P_i^{CL}$ denotes the variation in CL following DR. ${\varphi }_j^0$ is the original price, and $\Delta {\varphi }_j$ is the variation in price after DR. ${\rho }_j^0$ represents the initial tariff, while ${\rho }_j$ represents the TOU tariff. Therefore, the change in CL after DR at moment i, denoted as $\Delta P_{CL,i}$, can be described as follows:

$$\Delta P_{CL,i}=P_{CL,i}^0[{\displaystyle \sum _{j=1}^{24}{E}_{CL}}(i,j){\displaystyle \frac{{\rho }_j-{\rho }_j^0}{{\rho }_j^0}}]$$

(3)

Shiftable loads (SLs) refer to loads where users respond to prices according to their own needs, enabling flexible adjustments in working hours. The time-of-use (TOU) pricing is used as a signal to guide users in shifting their load from high-demand periods to low-demand periods. The price elasticity matrix for shiftable loads is denoted as $E_{SL}(i,j)$:

$$E_{SL}(i,j)=\left[\begin{array}{cccc}{e}_{11}^{SL}& e_{12}^{SL}& \dots & e_{1j}^{SL}\\ e_{21}^{SL}& e_{22}^{SL}& \dots & e_{2j}^{SL}\\ ⋮& ⋮& \hspace{1em}& ⋮\\ e_{i1}^{SL}& e_{i2}^{SL}& \dots & e_{ij}^{SL}\end{array}\right]$$

(4)

$$e_{ij}^{SL}={\displaystyle \frac{\Delta P_i^{SL}}{P_i^{SL.0}}}{\left({\displaystyle \frac{\Delta {\varphi }_j}{{\varphi }_j^0}}\right)}^{-1}$$

(5)

$e_{ij}^{SL}$ is the element of the elasticity matrix $E_{SL}(i,j)$, representing the elasticity coefficient available of the SL at moment i in relation to the price at moment j. $P_i^{SL,0}$ represents the initial SL, and $\Delta P_i^{SL}$ denotes the variation in SL following DR. Therefore, the change in SL after DR, denoted as $\Delta P_{SL,i}$, can be described as follows:

$$\Delta P_{SL,i}=P_{SL,i}^0[{\displaystyle \sum _{j=1}^{24}{E}_{SL}}(i,j){\displaystyle \frac{{\rho }_j-{\rho }_j^0}{{\rho }_j^0}}]$$

(6)

2.1.2. Replacement Demand Response

The alternative demand response strategy seeks to optimize overall energy efficiency by coordinating the substitution of electric, heating, and gas loads. The core concept involves leveraging the price elasticity of each load to flexibly adjust their timing and usage, thereby reducing total operating costs and enhancing system stability. The following description specifically addresses the mutual substitution of electric, heating, and gas loads.

(1)

Mutual Replacement of Electric and Heating Loads

Mutual replacement of electric and heating loads occurs when users, guided by the prices of electricity and heat, adjust between electric and heat loads. For example, users can increase the electric load and replace part of the heat load with electric equipment during periods of low electricity prices. Conversely, when heat prices are low, users can cut down on electrical load and boost the use of heating load. The replaceable load (RL) can be described as follows:

$$\Delta P_i^{RL,e}=-{\xi }_{e,h}\Delta P_i^{RL,h}$$

(7)

$${\xi }_{e,h}={\displaystyle \frac{{\eta }_e{\lambda }_e}{{\eta }_h{\lambda }_h}}$$

(8)

where $\Delta P_i^{RL,e}$ and $\Delta P_i^{RL,h}$ represent the amounts of electric RL and heating RL, respectively. Here, ${\xi }_{e,h}$ represents the electric heat substitution factor, ${\eta }_e$ and ${\eta }_h$ denote the substitution efficiencies for electric and heating energy, and ${\lambda }_e$ and ${\lambda }_h$ indicate the thermal values per unit of electric and heating energy, respectively.

(2)

Mutual Replacement of Electric and Gas loads

Mutual replacement of electric and gas loads occurs when users, guided by electricity and gas prices, adjust between electric and gas loads. For example, when electricity prices are low, users can increase electric loads and use electrical equipment to replace some of the gas loads. Conversely, when gas prices are low, users can reduce the electric load and increase the use of gas loads. The RL can be described as follows:

$$\Delta P_i^{RL,e}=-{\xi }_{e,g}\Delta P_i^{RL,g}$$

(9)

$${\xi }_{e,g}={\displaystyle \frac{{\eta }_e{\lambda }_e}{{\eta }_g{\lambda }_g}}$$

(10)

where $\Delta P_i^{RL,e}$ and $\Delta P_i^{RL,g}$ represent the amounts of electric RL and gas RL, respectively. ${\xi }_{e,g}$ represents the electric gas substitution factor. ${\eta }_e$ and ${\eta }_g$ denote the electric and gas substitution efficiencies, while ${\lambda }_e$ and ${\lambda }_g$ are the thermal values of electric and gas energy, respectively.

3. Carbon Trading Mechanism Model

The carbon emissions trading mechanism is a policy instrument designed to control and reduce greenhouse gas emissions through market-based tools. The core of the mechanism involves the establishment of legal carbon emission credits and their trade in a specialized carbon market. In practice, the administration initially distributes a specific amount of emission allowances to emission sources, such as energy suppliers, free of charge. If the actual emissions of carbon from the energy suppliers are lower than the issued credits, they can sell the excess trading credits at the prevailing carbon market price and obtain financial gains. This mechanism regulates the cost of carbon emissions through market supply and demand, incentivizes enterprises to reduce emissions, and ultimately drives down overall carbon emissions.

3.1. Initial Carbon Emission Assignment

The allocation of initial carbon allocation in an IES comprises four components: the electricity acquired from the superior grid, GT, GB, and gas load. Consequently, the carbon credits of the IES can be expressed as follows:

$$E^I=E^{grid}+E^{GT}+E^{GB}+E^{gload}$$

(11)

$$E^{grid}={\epsilon }_e{\displaystyle \sum _{i=1}^T{P}_i^{grid}}$$

(12)

$$E^{GT}={\epsilon }_h{\displaystyle \sum _{i=1}^T({\epsilon }_{e,h}{P}_i^{GT,e}+}{P}_i^{GT,h})$$

(13)

$$E^{GB}={\epsilon }_h{\displaystyle \sum _{i=1}^T{P}_i^{GB}}$$

(14)

$$E^{gload}={\epsilon }_{gload}{\displaystyle \sum _{i=1}^T{P}_i^{gload}}$$

(15)

Here, $E^I$ represents the initial carbon emission allowance; $E^{grid}$, $E^{GB}$, $E^{GT}$, and $E^{gload}$ denote the carbon emission allowances for power purchased from the superior grid, GB, GT, and gas loads, respectively. $P_i^{grid}$ is the power purchased from the higher level, and ${\epsilon }_e$ is the unremunerated carbon emission allowance per unit of electricity. $P_i^{GT,e}$ and $P_i^{GT,h}$ are the electric power and heat power of the GT, respectively; ${\epsilon }_h$ is the unremunerated carbon emission entitlement for each unit of heat; ${\epsilon }_{e,h}$ is the conversion factor from electricity generation to heat generation; $P_i^{GB}$ is the GB heat power; $P_i^{gload}$ is the power of the gas load; and ${\epsilon }_{gload}$ is the unremunerated carbon emission entitlement of the gas load.

3.2. Actual Carbon Emissions

The consumption of electricity and gas serves as a pivotal determinant of the carbon emissions across the entire energy framework. Moreover, in power-to-gas (P2G) technology, carbon dioxide is utilized as a fundamental raw material during converting electricity into natural gas. The carbon dioxide used in the P2G process should be encompassed within the carbon trading system. Additionally, carbon emissions resulting from gas loads are also considered. Consequently, the effective carbon emissions of the IES can be articulated as described below:

$$E^A=E^{grid,a}+E^{gload,a}+(G^{GT}+G^{GB}-G^{P2G}){\epsilon }_g$$

(16)

$$G^{GT}={\displaystyle \sum _{i=1}^T\frac{P_i^{e,GT}}{{\eta }_{GT,e}{\lambda }_{gas}}}+{\displaystyle \sum _{i=1}^T\frac{P_i^{h,GT}}{{\eta }_{GT,h}{\lambda }_{gas}}}$$

(17)

$$G^{GB}={\displaystyle \sum _{i=1}^T\frac{P_i^{GB}}{{\eta }_{GB}{\lambda }_{gas}}}$$

(18)

$$G^{P2G}={\displaystyle \sum _{i=1}^T\frac{P_i^{P2G}{\eta }_{P2G}}{{\lambda }_{gas}}}$$

(19)

$$E^{grid,a}={\epsilon }_p{\displaystyle \sum _{i=1}^T{P}_i^{grid}}$$

(20)

$$E^{gload,a}={\epsilon }_q{\displaystyle \sum _{i=1}^T{P}_i^{glood}}$$

(21)

where $E^A$ denotes the actual carbon emissions; ${\epsilon }_g$, ${\epsilon }_p$, and ${\epsilon }_q$ represent the carbon emission coefficients for gas consumption, purchased electricity, and gas load, respectively; $G^{GT}$ indicates the gas consumption of the GT; ${\eta }_{GT,e}$ and ${\eta }_{GT,h}$ denote the efficiencies of the GT in electricity and heat production; ${\lambda }_{gas}$ refers to the calorific value of natural gas; $G^{GB}$ signifies the gas consumption of the GB; ${\eta }_{GB}$ denotes the heat production efficiency of the GB; $G^{P2G}$ represents the amount of absorbed gas in the P2G process; $P_i^{P2G}$ is the electricity consumed by the P2G process; ${\eta }_{P2G}$ refers to the electricity-to-gas efficiency of the P2G process; $E^{grid,a}$ denotes the actual carbon emissions associated with purchased electricity; and $E^{gload,a}$ represents the actual carbon emissions from the gas load.

3.3. Laddered Carbon Trading Mechanism

The study establishes a tiered carbon trading system with rewards and penalties grounded on a unified ladder carbon trading framework, predicated on the correlation between $E^A$ and $E^I$. To mitigate carbon dioxide emissions, the difference between $E^A$ and $E^I$ is bifurcated into several intervals. When negative, it indicates that $E^A$ is below $E^I$, allowing the IES to sell the surplus quota for a profit; when positive, it signifies that $E^A$ is above $E^I$, necessitating that the IES purchase additional quotas to meet its demand. The greater the excess, the higher the carbon trading cost. In summary, the model of the tiered carbon trading system with rewards and penalties is articulated as follows:

$$C_{CO2}=\left\{\begin{array}{l}-\gamma (2+3\omega )\upsilon +\gamma (1+3\omega )(E^A-E^I+2\upsilon ),E^A-E^I\le -2\upsilon \\ -\gamma (1+\omega )\upsilon +\gamma (1+2\omega )(E^A-E^I+\upsilon ),-2\upsilon <E^A-E^I\le -\upsilon \\ \gamma (1+\omega )\left(E^A-E^I\right),-\upsilon <E^A-E^I\le 0\\ \gamma \left(E^A-E^I\right),0<E^A-E^I\le \upsilon \\ \gamma (1+\rho )(E^A-E^I-\upsilon )+\gamma \upsilon ,\upsilon <E^A-E^I\le 2\upsilon \\ \gamma (1+2\rho )(E^A-E^I-2\upsilon )+(2+\rho )\gamma \upsilon ,2\upsilon <E^A-E^I\le 3\upsilon \\ \gamma (1+3\rho )(E^A-E^I-3\upsilon )+(3+3\rho )\gamma \upsilon ,3\upsilon <E^A-E^I\le 4\upsilon \\ \gamma (1+4\rho )(E^A-E^I-4\upsilon )+(4+6\rho )\gamma \upsilon ,4\upsilon <E^A-E^I\end{array}\right.$$

(22)

$C_{CO2}$ denotes the carbon trading cost; $\gamma$ signifies the base rate for carbon trading; $\rho$ represents the rate of price advancement; $\upsilon$ indicates the length of the carbon emission interval; and $\omega$ is the incentive factor.

4. IES Scheduling Model

4.1. Objective Function

In this paper, the purpose of lowering the total operating cost is achieved through the implementation of DR and a stepped carbon trading mechanism. The total operating cost comprises energy purchase costs, operation and maintenance costs, carbon trading costs, and compensation costs.

$$\min f=f_{buy}+f_{op}+f_{C{O}_2}+f_{DR}$$

(23)

(1)

Cost of purchasing energy

$$f_{buy}={\displaystyle \sum _{i=1}^T{p}_{e,i}{P}_{e,buy}\left(i\right)}+{\displaystyle \sum _{i=1}^T{p}_{g,i}{P}_{g,buy}\left(i\right)}$$

(24)

where $P_{e,buy}(i)$ and $P_{g,buy}(i)$ represent the power of electricity and gas purchased; $p_{e,i}$ and $p_{g,i}$ denote the electricity and gas price, respectively.

(2)

Operation and maintenance costs

$$f_{op}={\displaystyle \sum _{i=1}^T{\displaystyle \sum _{t=1}^9{\omega }_t{P}_{t,i}}}$$

(25)

where t takes values from 1, 2, …, 8, and 9 to represent the GT, WHB, ORC, EB, GB, ES, GS, HS, and the P2G process, respectively. Here, ${\omega }_t$ is the O&M cost coefficient of equipment t, and $P_{t,i}$ is the output power of equipment t.

(3)

Carbon trade costs

Carbon trade costs are detailed in Equation (22).

(4)

Compensation costs

$$f_{DR}={\displaystyle \sum _{i=1}^T\left[{\zeta }_R\left(\left|\Delta P_i^{RL,e}\right|+\left|\Delta P_i^{RL,h}\right|+\left|\Delta P_i^{RL,g}\right|\right)+{\zeta }_S\left(\left|\Delta P_{\mathit{SL},i}^e\right|+\left|\Delta P_{\mathit{SL},i}^g\right|+\left|\Delta P_{\mathit{SL},i}^h\right|\right)\right]}$$

(26)

where ${\zeta }_R$ and ${\zeta }_S$ represent the compensation cost coefficients for shiftable and substitutable loads, respectively.

4.2. Constraint

(1)

Electric power balance constraints

$$P_i^{WT}+P_i^{PV}+P_i^{e,buy}+P_i^{e,CHP}+P_i^{e,ch}-P_i^{e,P2G}-P_i^{e,EB}-P_i^{e,dis}=P_i^{e,load}+\Delta P_{CL,i}^e+\Delta P_{SL,i}^e+\Delta P_i^{RL,e}$$

(27)

$P_i^{WT}$ and $P_i^{PV}$ represent the power generated by the WT and PV, respectively. $P_i^{e,CHP}$ is the power produced by the CHP unit; $P_i^{e,ch}$ and $P_i^{e,dis}$ are the ES’s charge and discharge electric power, respectively; $P_i^{e,P2G}$ is the power consumed by the P2G process; $P_i^{e,EB}$ is the power consumed by the EB; $P_i^{e,load}$ is the amount of electric loads before Demand response (DR); and $\Delta P_{\mathit{CL},i}^e$, $\Delta P_{SL,i}^e$, and $\Delta P_i^{RL,e}$ are the electric load amounts of the CL, SL, and RL after DR, respectively.

(2)

Heat power balance constraints

$$P_i^{h,CHP}+P_i^{h,EB}+P_i^{h,GB}+P_i^{h,ch}-P_i^{h,dis}=P_i^{h,load}+\Delta P_{CL,i}^h+\Delta P_{SL,i}^h+\Delta P_i^{RL,h}$$

(28)

$P_i^{h,CHP}$ represents the heat power of the CHP unit; $P_i^{h,EB}$ and $P_i^{h,GB}$ are the heat production powers of the EB and GB, respectively; $P_i^{h,ch}$ and $P_i^{h,dis}$ are the HS’s charge and discharge heat power, respectively; $P_i^{h,load}$ is the amount of heat load before DR; and $\Delta P_{CL,i}^h$, $\Delta P_{SL,i}^h$, and $\Delta P_i^{RL,h}$ are the heat load amounts of the CL, SL, and RL after DR, respectively.

(3)

Gas power balance constraints

$$P_i^{g,buy}+P_i^{g,ch}+P_i^{g,P2G}-P_i^{g,CHP}-P_i^{g,GB}-P_i^{g,dis}=P_i^{g,load}+\Delta P_{CL,i}^g+\Delta P_{SL,i}^g+\Delta P_i^{RL,g}$$

(29)

$P_i^{g,buy}$ represents the purchased power; $P_i^{g,ch}$ and $P_i^{g,dis}$ are the charging and discharging powers of the GS; $P_i^{g,CHP}$ is the gas consumption power of the CHP unit; $P_i^{g,P2G}$ is the gas production power of the P2G system; $P_i^{g,GB}$ is the gas consumption power of the GB; $P_i^{g,load}$ is the gas loading capacity before DR; and $\Delta P_{CL,i}^g$, $\Delta P_{SL,i}^g$, and $\Delta P_i^{RL,g}$ are the gas load amounts of the CL, SL, and RL after DR, respectively.

(4)

CHP constraints

$$P_i^{e,CHP}=P_i^{e,GT}+P_i^{e,ORC}$$

(30)

$$P_i^{h,CHP}=P_i^{h,GT}{\beta }_i{\tau }_{WHB}$$

(31)

$$P_i^{e,ORC}=P_i^{h,GT}{\alpha }_i{\delta }_{ORC}$$

(32)

$$P_i^{e,GT}=P_i^{g2e,CHP}{\tau }_{GT}^e$$

(33)

$$P_i^{h,GT}=P_i^{g2h,CHP}{\tau }_{GT}^h$$

(34)

$$P_i^{g,CHP}=P_i^{g2e,CHP}+P_i^{g2h,CHP}$$

(35)

$${\alpha }_i+{\beta }_i=1$$

(36)

$$0\le {\alpha }_i,{\beta }_i\le 1$$

(37)

The constraint on the electric power production of the CHP unit, denoted as $P_i^{e,CHP}$, encompasses two components: the power generated by the GT and the power produced by the ORC. The constraint on the heat production of the CHP unit, represented as $P_i^{h,CHP}$, includes the heat generated by the WHB, which is accounted for as part of the CHP’s total heat production. The electric power production of the ORC at time i is indicated by $P_i^{e,ORC}$. The heat power production of the GT at time i is denoted as $P_i^{h,GT}$. The proportion of the residual heat from the GT allocated to the ORC is represented by ${\alpha }_i$. The electric power generation efficiency of the ORC is denoted by ${\delta }_{ORC}$. The heat conversion efficiency of the WHB is indicated by ${\tau }_{WHB}$. The gas consumption power for gas-to-electricity and gas-to-heat conversions are denoted by $P_i^{g2e,CHP}$ and $P_i^{g2e,CHP}$, respectively. The efficiencies of gas-to-electricity and gas-to-heat conversions are represented by ${\tau }_{GT}^e$ and ${\tau }_{GT}^h$, respectively. The calorific value of natural gas, denoted as ${\lambda }_{gas}$, is 9.88 kWh/m³.

(5)

P2G constraints

$$0\le P_i^{P2G}\le P^{P2G,\max }$$

(38)

$$\left|P_i^{P2G}-P_{i-1}^{P2G}\right|\le r_{P2G}$$

(39)

The parameter $P^{P2G,\max }$ represents the upper output limit of the P2G process; the parameter $r_{P2G}$ denotes the maximum ramp rate of the P2G process.

(6)

EB constraints

$$0\le P_i^{EB}\le P^{EB,\max }$$

(40)

$$\left|P_i^{EB}-P_{i-1}^{EB}\right|\le r_{EB}$$

(41)

The parameter $P^{EB,\max }$ represents the upper output limit of the EB; the parameter $r_{EB}$ denotes the maximum ramp rate of the EB.

(7)

GB constraints

$$0\le P_i^{GB}\le P^{GB,\max }$$

(42)

$$\left|P_i^{GB}-P_{i-1}^{GB}\right|\le r_{GB}$$

(43)

The parameter $P^{GB,\max }$ represents the upper output limit of the GB; the parameter $r_{GB}$ denotes the maximum ramp rate of the GB.

(8)

GT constraints

$$0\le P_i^{GT}\le P^{GT,\max }$$

(44)

$$\left|P_i^{GT}-P_{i-1}^{GT}\right|\le r_{GT}$$

(45)

The parameter $P^{GT,\max }$ represents the upper output limit of the GT; The parameter $r_{GT}$ denotes the maximum ramp rate of the GT.

(9)

ORC constraints

$$0\le P_i^{ORC}\le P^{ORC,\max }$$

(46)

$$\left|P_i^{ORC}-P_{i-1}^{ORC}\right|\le r_{ORC}$$

(47)

The parameter $P^{ORC,\max }$ represents the upper output limit of the ORC; the parameter $r_{ORC}$ denotes the maximum ramp rate of the ORC.

(10)

Energy storage constraints

Three different kinds of energy storage devices are incorporated into the IES to further increase its operating flexibility: electrical, thermal, and gas. These storage systems are modeled uniformly due to the inherent similarities in their respective energy storage mechanisms.

$$0\le P_i^{n,dis}\le P_i^{n,dis,\max }{\tau }_i^{dis}$$

(48)

$$0\le P_i^{n,ch}\le P_i^{n,ch,\max }{\tau }_i^{ch}$$

(49)

$${\tau }_i^{ch}+{\tau }_i^{dis}\le 1$$

(50)

$$S_{i+1}^n=S_i^n+{\eta }^{n,ch}{P}_i^{n,ch}-{\eta }^{n,dis}{P}_i^{n,dis}$$

(51)

$$S^{n,\min }\le S_i^n\le S^{n,\max }$$

(52)

$$S_0^n=S_T^n$$

(53)

Here, the letter n stands for electrical, thermal, and gas energy storage devices, respectively; the maximum power for charging and discharging is represented by $P_i^{n,dis,\max }$ and $P_i^{n,ch,\max }$; the binary variables ${\tau }_i^{dis}$ and ${\tau }_i^{ch}$ represent the energy storage device’s charging and discharging states; the energy stored in the energy storage device is denoted by the symbol $S_i^n$; ${\eta }^{n,ch}$ and ${\eta }^{n,dis}$ denote the charging and discharging efficiencies; $S^{n,\min }$ and $S^{n,\max }$ indicate the energy storage device’s top and lower capacity limitations.

The comprehensive structure of the constraints is depicted in Figure 2.

4.3. Solution Method

The IES scheduling model, which is stated as a mixed-integer linear programming (MILP) problem, incorporates DR and a tiered carbon trading system. It is discussed in this study. Therefore, MATLAB and CPLEX are utilized to solve the model. First, the established IES model is supplemented with data on wind power and photovoltaic inputs, as well as heat, gas, and electricity demands. Subsequently, the parameters of each unit are incorporated. Finally, the model aims to minimize the overall cost, which derives the best scheduling strategy for each unit given the restrictions of power balance and unit-specific constraints. The program flow chart is shown in Figure 3.

5. Case Analysis

5.1. Parameter Setting

An industrial park in the north that operates for 24 h a day, seven days a week, with an hourly unit of operation is the focus of this study.

Table 1. Parameters of energy conversion equipment.

Equipment Name	Power Upper and Lower Limits (kW)	Energy Conversion Efficiency	Operational Costs (CNY/kW)	Maximum Ramp Rate (kW/min)
GT	[0, 4000]	0.3/0.45	0.04	15
GB	[0, 1500]	0.8	0.025	15
EB	[0, 1000]	0.8	0.025	10
P2G	[0, 600]	0.6	0.02	5
ORC	[0, 600]	0.8	0.015	5
WHB	[0, 500]	0.8	0.015	5

presents the parameters of the energy conversion equipment within the IES, whereas

Table 2. Parameters of energy storage equipment.

Equipment Name	Initial Capacity (kWh)	Maximum Capacity (kWh)	Maximum Charge/Discharge Power (kW)	Charge/Discharge Efficiency	Operational Costs (CNY/kW)
ES	80	400	300	0.95/0.90	0.018
GS	50	400	300	0.95/0.90	0.016
HS	50	400	300	0.95/0.90	0.016

presents the specs of the energy storage equipment. Parameters pertaining to the carbon trading mechanism are also included in

Table 3. Carbon trading-related parameters.

Parameter	Value	Parameter	Value
${\epsilon }_e$	424 g/kwh	${\epsilon }_p$	968 g/kwh
${\epsilon }_h$	432 g/kwh	${\epsilon }_g$	504 g/kwh
${\epsilon }_{gload}$	210 g/kwh	${\epsilon }_q$	320 g/kwh
$\upsilon$	2000 kg	$\gamma$	0.25 CNY/kg
$\rho$	0.25	$\omega$	0.2

. Figure 4 illustrates the electrical load, thermal load, gas load, and the power generated by wind and photovoltaic sources. The TOU pricing for electricity procured from the main grid and the gas obtained from the primary gas grid is depicted in Figure 5a and Figure 5b, respectively. Prior to incorporating DR, the IES sells electricity at 0.78 CNY/kWh, gas at 0.36 CNY/kWh, and heat at 0.67 CNY/kWh. Fixed loads constitute 50% of the total load, with the SL, RL, and CL comprising 35%, 10%, and 5%, respectively. Four different scenarios have been created for comparison analysis in order to look at how the IES developed in this study will be affected by the inclusion of DR and the carbon trading system.

Scenario 1 utilizes the traditional carbon trading mechanism without DR consideration.

Scenario 2 utilizes the traditional carbon trading mechanism with DR consideration.

Scenario 3 employs the laddered carbon trading mechanism without DR consideration.

Scenario 4 employs the laddered carbon trading mechanism with DR consideration.

5.2. Scenario Comparison

Figure 6 illustrates the initial and TOU prices of energy purchased by users from the IES before and after considering DR. As depicted in Figure 6a, the peak hours for gas prices are from 6:00 to 12:00 and 18:00 to 21:00, while the valley hours are from 13:00 to 17:00 and 22:00 to 24:00. As shown in Figure 6b, the peak hours for heat prices occur between 4:00 and 6:00, 12:00 and 14:00, and 19:00 and 24:00, with valley hours occur from 1:00 to 3:00. As illustrated in Figure 6c, the peak hours for electricity prices are from 8:00 to 11:00 and 20:00 to 22:00, with valley hours span from 1:00 to 7:00.

The gas load, heat load, and electricity load, respectively, are shown in Figure 7a–c), both before and after taking DR into account, as well as the variations in each kind of load. Some of the gas load is moved to low gas price hours during high gas price hours (6:00–12:00 and 18:00–21:00). During periods of high gas prices and low electricity prices (6:00–7:00, 12:00, and 19:00), some gas loads are converted to electricity loads. Conversely, during periods of low gas prices and high electricity prices (22:00), some electricity loads are converted to gas loads. During high heat price periods (4:00–6:00, 12:00–14:00, and 19:00–24:00), a portion of the heat load is shifted to low heat price periods. During periods of high heat prices and low electricity prices (4:00–5:00 and 13:00–14:00), some heat loads are converted to electricity loads. During periods of low heat prices and high electricity prices (8:00–11:00), a portion of the electric load is converted to heat load. During high tariff hours (8:00–11:00 and 20:00–22:00), a part of the electricity demand is moved to hours with reduced tariffs, resulting in a curtailment of electric load.

The overall balances of thermal, electrical, and gas power in Scenario 4 are shown in Figure 8a, Figure 8b and Figure 8c, respectively. As shown in Figure 8a, The thermal energy requirement is mostly satisfied by the CHP and GB during the hours of 1:00–3:00 and 7:00–18:00, with the HS storing any spare thermal energy. During the periods of 4:00–6:00 and 19:00–24:00, the thermal energy demand is at its highest. Therefore, to satisfy the thermal energy requirement, EB heat generation and HS heat release are also required in addition to the CHP and GB.

As depicted in Figure 8b, during the periods of 1:00–3:00, 7:00–8:00, and 12:00–17:00, the power demand is lower, and it can be met by the CHP, WT, and PV alone, with excess power stored by the P2G system and the ES. During the peak periods of 4:00–6:00, 9:00–11:00, and 19:00–24:00, in addition to the CHP, PV, and WT, the power consumption of the EB and peak demand can be met by purchasing power and discharging the ES. At 22:00, the P2G system needs to store energy for the conversion from electricity to gas. As shown in Figure 8c, the gas demand, along with the GB and CHP consumption, is primarily met by purchased gas, while the P2G process and the GS help reduce the amount of purchased gas.

The power balance of thermal, electrical, and gaseous energy in Scenario 3 are shown in Figure 9a, Figure 9b and Figure 9c, respectively. Each load is left as a raw load without load peak changing since DR is not taken into account. As a consequence, every device’s output is impacted, raising the overall cost.

The simulation results for the four scenarios are presented in

Table 4. Costs and carbon emissions for the four scenarios.

Scenario	Total Cost (CNY)	Energy Purchase Cost (CNY)	Operation and Maintenance Cost (CNY)	Carbon Trading Cost (CNY)	Compensation Cost (CNY)	Carbon Emissions (kg)
1	50,198.48	42,943.32	3106.01	4149.15	0	41,728.50
2	49,091.90	41,846.35	2855.85	3908.94	480.76	40,616.06
3	48,973.47	42,582.87	2989.67	3400.93	0	40,085.71
4	47,875.11	41,422.73	2833.51	3258.62	360.25	38,715.46

, with the total cost for Scenario 1 reaching CNY 50,198.48. This is attributed to the lack of consideration for DR and the ladder carbon trading mechanism, resulting in the inflexible scheduling of the IES. In comparison to Scenario 1, Scenario 2 incorporates DR, which alters users’ energy consumption habits and shifts part of the load to periods with lower energy prices. Additionally, electric, thermal, and gas loads can be substituted with lower-cost alternatives, enhancing the flexibility of IES scheduling, reducing operational pressure on equipment, and lowering O&M costs by 8% and total costs by 2.2%. When comparing Scenario 3 to Scenario 1, the stepped carbon trading mechanism in Scenario 3 reduces carbon emissions by 3.94%, decreases carbon trading costs by 18%, and lowers total costs by 2.44%. When DR and the stepped carbon trading system are coupled, Scenario 4’s total costs and carbon emissions are reduced by 2.24% and 3.42%, respectively, compared to Scenario 3’s.

In summary, this paper’s suggested stepped carbon trading method successfully lowers emissions of carbon and carbon trading expenses. Additionally, the introduction of DR rationalizes the scheduling of each device within the IES, thereby significantly reducing its operation and maintenance costs. Thus, the scheduling technique described in this study effectively meets low-carbon and economic goals.

6. Discussion

The discussion is divided into two key sections: addressing the uncertainty of user behavior and examining the limitations of the current model.

A significant challenge for the practical implementation of demand response models lies in the inherent unpredictability of user behavior. Users’ energy consumption patterns are influenced by a multitude of factors, such as price volatility, climate variability, and individual preferences. These behavioral fluctuations can result in suboptimal demand response outcomes, thereby diminishing dispatch efficiency and compromising the carbon reduction goals of the integrated energy system. To address this uncertainty, future research could explore the integration of probabilistic models or stochastic optimization techniques to simulate varying user demand scenarios, thereby enhancing the model’s robustness. Moreover, leveraging machine learning algorithms and advanced load forecasting models could offer deeper insights into the complex patterns of user behavior and significantly enhance forecasting accuracy. Finally, the development of more flexible and targeted demand response incentives may help mitigate the scheduling challenges posed by unpredictable user behavior to a certain extent.

While the proposed IES optimization framework offers promising results, several limitations should be acknowledged. First, the use of MILP may introduce significant computational complexity, especially when scaling up to larger systems or incorporating more detailed constraints. This could potentially limit the real-time adaptability of the model in dynamic or fast-changing environments. Furthermore, the real-world application of the proposed model requires comprehensive and accurate data on energy demand, supply, and carbon pricing, which may not always be readily available or reliable. Data uncertainty or unavailability could affect the robustness and accuracy of the optimization results. Addressing these limitations in future research, such as through the use of advanced algorithms or machine learning techniques for load forecasting, could enhance both the computational efficiency and the practical applicability of the system.

7. Conclusions

To enhance the economic efficiency of IES operation and optimize the overall carbon emissions of the system, this paper proposes a scheduling strategy that integrates DR and a stepped carbon trading mechanism. The precise findings drawn from the simulation results mentioned above are as follows:

• The mutual substitution between the loads of electricity, heat, and gas as well as the shiftable and curtailable loads of each are covered by the suggested DR approach. This method accomplishes peak shaving and valley filling goals while lowering the operating strain on every piece of IES equipment.
• In comparison to conventional carbon trading schemes, the ladder mechanism decreases carbon emissions more efficiently and makes low-carbon system operation easier.
• By integrating DR into the ladder trading of the carbon mechanism, the IES’s operating and maintenance expenses as well as energy purchase prices may be decreased, all while lowering the system’s carbon emissions. The IES performs more economically and in terms of carbon emissions thanks to this modification.

Future research will explore the integration of carbon capture technologies to further optimize the IES. Additionally, multi-objective optimization algorithms will be employed to balance and optimize multiple objectives. Furthermore, the application of machine learning techniques will be explored to improve the load forecasting accuracy in the DR model.