Optimal Scheduling Considering Carbon Capture and Demand Response under Uncertain Output Scenarios for Wind Energy

Abstract

In light of the uncertainties associated with renewable energy sources like wind and photovoltaics, this study aims to progressively increase their proportion in the energy mix. This is achieved by integrating carbon capture devices into traditional thermal power plants and enhancing demand-side management measures, thereby advancing low-carbon objectives in the energy and electricity sectors. Initially, the research proposes utilizing the K-means clustering algorithm to consolidate and forecast the fluctuating outputs of renewable energies such as wind and photovoltaics. Further, it entails a comprehensive analysis of low-carbon resources on both the supply and demand sides of the electricity system. This includes installing carbon storage and power-to-gas facilities in carbon capture plants to create a versatile operating model that can be synchronized with wind power systems. Additionally, the limitations of carbon capture plants are addressed by mobilizing demand-side response resources and enhancing the system’s low-carbon performance through the coordinated optimization of supply and demand resources. Ultimately, this study develops an integrated energy system model for low-carbon optimal operation, aimed at minimizing equipment investment, carbon emission costs, and operational and maintenance expenses. This model focuses on optimizing the load and supply distribution plans of the electrical system and addressing issues of load shedding and the curtailment of wind and solar power. Validation through three typical scenarios demonstrates that the proposed scheduling method effectively utilizes adjustable resources in the power system to achieve the goal of low-carbon economic dispatch.

1. Introductory

With the burning of fossil fuels leading to an unprecedented increase in carbon dioxide emissions, the power sector is expanding renewable energy sources for sustained environmental protection, with wind and photovoltaic power in particular becoming beacons of hope for the transformation of the energy landscape [1,2]. Wind and photovoltaic (PV) power are energy sources that are crucial in the search for optimal dispatch strategies for integrated energy systems (IES) [3]. Optimal dispatch is essential, serving not only as a prerequisite for energy production and utilization and for maintaining the balance between supply and demand in an integrated energy system (IES), but it is also a key factor in achieving the coordinated, complementary, and economically efficient operation of different energy subsystems in the region [4,5,6,7].

Demand response plays a crucial role in integrated energy systems (IES), where demand response helps to balance supply and demand, improves energy efficiency by promoting staggered consumption and reducing energy waste, and enhances flexibility and resilience [8,9]. Demand response (DR), which serves as a crucial mechanism for regulating resilient electric loads in integrated energy systems (IES), can be categorized into transferable, curtailable, and substitutable loads, reflecting the characteristics of customer-side load demand. Furthermore, it can be classified into price-based DR (PBDR) and incentive-based DR (IBDR), depending on the form of response [10]. However, there are many different loads coupled to each other within the IES, and most of the loads are coupled in a complex way centered on electric loads, such as electricity-to-gas (P2G) and electricity-to-heat. Demand response is only for electric loads, so IES dispatch with DR participation can help to create a more sustainable and efficient energy system while smoothing out renewable energy output volatility [11]. Therefore, it is of great significance to study the optimal scheduling problem of a multi-energy coupled power system with renewable energy participation, and how to make full use of demand-side flexible resources in the power system.

Currently, a large number of studies on the IES optimal scheduling problem considering DR are conducted both at home and abroad. Wang, Lei et al. [12] propose a demand response uncertainty model based on price incentives, which effectively reduces the system operating cost and improves the load condition. Wang, Long et al. [13] explored the relationship between various forms of electric–thermal demand response, electric–thermal coupling capacity, and energy storage in IES, and verified the feasibility and economy of integrated demand response. Liu, Dongyu et al. [14] proposed an optimal dispatch method considering stepped carbon trading combined with demand response, which protects different interest groups and controls carbon emissions while smoothing load fluctuations. Ni, Linna et al. [15] designed an integrated IDR scheme, which induced the rational utilization of multiple energy sources and the efficient consumption of renewable energy. Tang, Wentao et al. [16] analyzed the impacts of DR of transferable loads, curtailable loads, and substitutable load demands on system operations based on the optimal dispatch model of the regional integrated energy system (RIES), and the results showed that the application of demand DR can improve the energy efficiency of the system. The IDR in Yang, Haizhu et al. [17]’s study builds a demand response optimal dispatch model by describing the response of price and substitution response, and the results show that it can satisfy the system supply–demand balance, and at the same time, it can inhibit the stochastic fluctuation of renewable energy and load and improve the stability. Song, Tianli et al. [18] considered a variety of elasticities in line with the characteristics of the load, established different load response models, and simulated and analyzed using the Gurobi solver to reduce the system energy loss and improve the system’s ability to consume renewable energy. Nwulu, Nnamdi I et al. [19] demonstrated the application of incentive-based demand response (IBDR) to the optimal scheduling of a multi-energy coupled integrated energy system (IES) and confirmed the effectiveness of demand response (DR) in reducing stochasticity. However, it should be noted that the introduction of DR may potentially affect user satisfaction.

In the context of carbon neutrality, traditional economic dispatch is being progressively supplanted by low-carbon economic dispatch. Additionally, the carbon trading mechanism is anticipated to more efficiently integrate renewable energy into microgrids. Currently, the low-carbon economic dispatch of integrated energy systems (IES) has undergone extensive research and can be categorized into two approaches: the first involves penalizing the environmental cost of carbon emissions produced by the system, and the second entails trading these emissions in a carbon trading market environment. Under the framework of penalizing carbon emission costs, employing carbon capture devices to sequester carbon dioxide from coal-fired and gas-fired power plants has emerged as a prominent area of research in IES [20]. Liu, Xinghua et al. [21] proposed the addition of carbon capture devices on the basis of traditional thermal power units to form a carbon capture power plant, by capturing the carbon dioxide produced by the traditional device to reduce carbon emissions from the aspect of energy supply, to reduce carbon emissions from the aspect of energy supply, with the addition of a carbon trading mechanism at the same time comparing the total cost of a variety of scenarios and the carbon dioxide emissions. The simulation results verified the feasibility and validity of the proposed model. Yu, Fei et al. [22] proposed a low-carbon optimal scheduling model combining carbon capture and storage technology and wind power uncertainty, incorporating carbon emission costs into traditional economic scheduling and taking into account the economic and low-carbon studies of power production. The simulation results show that it can significantly reduce the total carbon emissions of coal-fired units. He, Liangce et al. [23] proposed a new model and optimal scheduling of cogeneration using power-to-gas (P2G) and carbon capture system (CCS), applying the carbon emission problem of cogeneration combined with the carbon source required by P2G in IES, establishing the operation law of the model, and analyzing its coupling characteristics of electricity, heat, gas, and carbon. Ma, Yiming et al. [24] proposed a low-carbon trading model considering the combination of integrated demand response and carbon trading, interconnecting switchable electricity, and heat and gas loads with multi-step carbon trading, incorporating a single price cost into a variety of elements, and greatly reducing operating costs while effectively reducing carbon emissions. Cui, Yang et al. [25] established a tariff-based demand response model with load volatility as the goal and introduced it into a low-carbon economic dispatch model of an integrated electricity–gas–heat energy system with a carbon capture power plant with the goal of lowest integrated cost, and finally solved it using CPLEX optimization software. The results show that the proposed method can take into account both low carbon and the economy.

The above literature involved studies of DR and carbon emissions singularly or in combination with both, but with the deepening of the research on optimal operation of IES, it often fails to address the intermittency and unpredictability brought by renewable energy sources, such as WT and PV [26], which can affect the efficiency of energy management and lead to suboptimal resource allocation, increased environmental impacts, and rising costs. The examination of Zhao, Shuqiang et al. [27] will use the scene analysis method as a focus of research, with a small number of representative scenes to describe a large number of complex scene characteristics for multiple fluctuations of wind power using the K-means clustering algorithm for rapid classification. This method will ensure the accuracy of the calculation and, at the same time improve the computational efficiency of the scale of the larger scene set reduction. In this context, recognizing the importance of these strategies is crucial to address the gaps in the current research field and to advance the integration of uncertain wind and PV output scenarios. Goh, Hui Hwang et al. [28] developed a renewable energy uncertainty generation scenario analysis methodology that employs a demand response approach to evaluate load demand response and considers carbon capture when modeling microgrids, demonstrating that incorporating as many real-world features as possible can improve the reliability of optimization results. From the above studies, there are fewer IES optimal dispatch studies that consider wind uncertain output scenarios while combining DR and carbon capture, and even when they do, the economics of multiple scenarios are not compared. For this reason, this current study compares the optimal scheduling across multiple scenarios, which include wind-scenic uncertain output scenarios, while concurrently integrating demand-side response and optimizing the cost of carbon emissions. The main contributions of this study are outlined as follows:

(1)

Aiming at the volatility of wind power generation and photovoltaic power generation, combined with the idea of density clustering, K-means clustering is used for scene generation, and typical scenes of wind and photovoltaic power generation are obtained.

(2)

Introducing demand response and establishing the basic structure of a demand-responsive, campus-level integrated energy system that can cut the system’s elastic load while ensuring economy.

(3)

By introducing carbon capture and power-to-gas (P2G) technologies, this study establishes a low-carbon economic operation optimization model for the system. This model significantly enhances the utilization efficiency of new energy, promotes the consumption of wind power, and reduces carbon emissions.

The specific chapter structure is outlined as follows: The first section introduces the general architecture of the integrated energy system (IES). The second section details the mathematical models of the equipment utilized in the industrial park. The third section explores the user demand response within the multi-energy system. The fourth section elucidates the low-carbon dispatch model employed in the integrated energy system. The fifth section is dedicated to case simulations, accompanied by a comprehensive analysis of the simulation results.

2. Basic Architecture of IES

The integrated energy system (IES) is designed to meet the demand-side load requirements for electricity, heat, and other forms consisting of multiple energy inputs, various types of energy conversion equipment, and coupling apparatus. The IES constructed for this study is illustrated in Figure 1. The park-type multi-energy complementary system comprises four main units: the energy production unit, energy conversion unit, energy storage unit, and energy demand unit. The energy production units include photovoltaic (PV), wind power, and thermal power units, as well as integration with the superior power grid. The energy conversion unit encompasses a combined heat and power (CHP) unit, along with internal equipment such as carbon capture equipment (CCS), an electric boiler (EB), and a power-to-gas (P2G) device, which includes an electrolytic cell (EC) and a methane reactor (MR). The energy storage unit primarily consists of a carbon storage tank and a hydrogen storage tank (HS). The energy demand unit encompasses the basic electrical load, basic thermal load, and the electrical demand response load, including both heat and gas load. The architecture of the IES is shown in Figure 1.

3. IES Models for Each Power Supply

3.1. PV Power Modeling

Photovoltaic (PV) power generation system output is mainly affected by unit capacity, light intensity, and ambient temperature, and its mathematical model is shown in the following equation, where the unit parameters are determined:

$$\left\{\begin{array}{l}{P}_{\mathrm{PV}}=A_{\mathrm{PV}}{f}_{\mathrm{PV}}\frac{G_{\mathrm{T}}}{G_{\mathrm{STC}}}\\ P_{PV}^{\min }<P_{PV}<P_{PV}^{\max }\end{array}\right.$$

(1)

where $P_{\mathrm{PV}}$ is the rated capacity of the PV power generation, $A_{\mathrm{PV}}$ is the rated power of the PV unit, $f_{\mathrm{PV}}$ is the photovoltaic conversion rate, $G_{\mathrm{T}}$ is the solar irradiation intensity, and $G_{\mathrm{STC}}$ is the baseline irradiation intensity.

3.2. Wind Turbine Modeling

Wind power is a sustainable, clean, and sustainable resource; however, wind power limits its own application due to its own unstable characteristics. Environmental factors such as wind speed and direction have a great influence on the output of wind energy; thus, the output of wind energy has a strong stochastic characteristic. The output of a wind turbine (WT) [29] is modeled as:

$$P_{WT}=\left\{\begin{array}{cc}0,& v<v_{ci}\mathrm{or}v\ge v_{co}\\ a{v}^3+b{v}^2+cv+d,& v_{ci}\le v\le v_r\\ P_r,& P_r^{\min }<P_r<P_r^{\max }\end{array}\right.$$

(2)

where $P_{WT}$ represents the output power of a single WTG (this paper is configured with 120 wind turbines); $P_r$ represents the rated power of the WTG; $v_{ci}$, $v_r$, $v_{co}$ represent the cut-in, rated, and cut-out wind speeds of the WTGs; and a, b, c, d represent the wind speed parameters.

3.3. Electrically Heated Boilers

The electric boiler (HP) enables the flexible conversion of electrical energy to thermal energy, which is expressed in the conversion relationship:

$$\left\{\begin{array}{l}{P}_{i,\mathrm{HP},\mathrm{h}}=P_{i,\mathrm{HP},\mathrm{e}}{\alpha }_{\mathrm{HP}}\\ P_{i,\mathrm{HP},\mathrm{h}}^{\min }\le P_{i,\mathrm{HP},\mathrm{h}}\le P_{i,\mathrm{HP},\mathrm{h}}^{\max }\end{array}\right.$$

(3)

where $P_{i,\mathrm{HP},\mathrm{h}}$ and $P_{i,\mathrm{HP},\mathrm{e}}$ are the thermal power and electric power in the microgrid at time t, respectively; ${\alpha }_{\mathrm{HP}}$ is the electric heat conversion efficiency of the electric boiler; and $P_{i,\mathrm{HP},\mathrm{h}}^{\min }$ and $P_{i,\mathrm{HP},\mathrm{h}}^{\max }$ are the upper and lower limits of the electric boiler output, respectively.

3.4. CCS Carbon Capture Unit Modeling

Unlike conventional units, thermal generating units (GUs) are retrofitted with carbon capture equipment, which has the function of capturing carbon dioxide, thereby effectively reducing the amount of $C{O}_2$ emissions. The power generation output of a carbon capture unit is characterized by two key indices: net power generation and energy consumption for capture. Among these, thermal generating units possess the capability to recover heat energy. The power relationship can be described as follows:

$$\left\{\begin{array}{c}\begin{array}{c}{P}_{\mathrm{CCS}}=P_{\mathrm{GU}}-P_{\mathrm{D}}-P_{\mathrm{B}}\\ H_{GU}=P_{\mathrm{GU}}{\eta }_{\mathrm{n}}\end{array}\\ V_{GU}=e_{\mathrm{g}i}{P}_{\mathrm{GU}}\\ 0\le {\delta }_i\le 1\\ V_{GU,C{O}_2}=V_{\mathrm{CG}}+{\beta }_{\mathrm{CCS}}{\delta }_i{V}_{\mathrm{G}U}\\ 0\le V_{\mathrm{CCS}}\le {\eta }_{CCS}{\beta }_{\mathrm{CCS}}{e}_{\mathrm{gi}}{P}_{i,\max }^{\mathrm{GU}}\\ P_B={\lambda }_{\mathrm{CCS}}{P}_{\mathrm{CCS}}\end{array}\right.$$

(4)

where $P_{\mathrm{CCS}}$ and $P_{\mathrm{GU}}$ are the total output power and net output power of the CCS unit at time t, respectively; $P_{\mathrm{D}}$ is the fixed energy consumption of the CCS unit; $P_{\mathrm{B}}$ is the operational energy consumption of the CCS unit; $H_{GU}$ represents the thermal energy recovery power of the thermal power unit; ${\eta }_{\mathrm{n}}$ is the electric–thermal conversion coefficient; $V_{GU}$ is the electricity–heat conversion coefficient, which is the total amount of energy produced by the CCS unit at any time; $e_{\mathrm{g}i}$ is the carbon emission intensity of the CCS unit; ${\delta }_i$ is the flue gas split ratio; $V_{GU,C{O}_2}$ is the carbon capture capacity of the CCS unit; $V_{\mathrm{CG}}$ is the carbon capture capacity of the CCS unit supplied by the solution memory; ${\beta }_{\mathrm{CCS}}$ is the carbon capture efficiency; ${\eta }_{CCS}$ is the maximum working condition coefficient of the regeneration tower and the compressor; $P_{i,\max }^{\mathrm{GU}}$ is the maximum technological output of the thermal unit; $P_i^{\mathrm{CCS}}$ is the energy consumption of the capture unit.

3.5. Mathematical Model of P2G System

P2G technology utilizes electricity to produce natural gas, which can efficiently consume clean energy electricity and reduce the cost of gas production in natural gas systems. This paper ignores the compression, storage, and utilization of hydrogen in the P2G system and simplifies the operation of the P2G system into two energy conversion stages: hydrogen production from electrolysis of water and hydrogen methanation. The working principle of the P2G plant is shown in Figure 2:

The mathematical model is shown below:

The relationship between P2G consumption of electricity to produce natural gas is shown in Equation (5):

$$\left\{\begin{array}{l}{E}_{P2G,t,gas}={\varpi }_{P2G}\times P_{i,P2G,t}\\ P_{i,P2G,\min }\le P_{i,P2G,t}\le P_{i,P2G,\max }\end{array}\right.$$

(5)

where $E_{P2G,t,gas}$ is the energy obtained after the conversion of electricity to gas at the moment t; $P_{i,P2G,t}$ is the power required for the process of conversion of electricity to gas at the moment t, which is regarded as an electrical load within the power network; and is the balance of reaction coefficient for the Power to Gas(P2G) equipment.

The energy density of methane, produced from electrochemical gas to natural gas (EGN) processes, is four times higher than that of hydrogen. This allows for direct integration into the natural gas pipeline network for utilization, and it also has good low-carbon capability because of the consumption of $C{O}_2$ to synthesize methane. Therefore, in this paper, P2G specifically refers to the process of converting electricity to natural gas [30]. The above chemical reaction (6) (7) in the equation can be obtained by generating a certain volume of $f_{P2G,t,gas}$, and the consumption of $C{O}_2$ can be expressed as [31]:

$$V_{C{O}_2}=\frac{f_{P2G,t,gas}}{f_{P2G,t,gas}^m}{V}_{C{O}_2}^m$$

(6)

where $f_{P2G,t,gas}^m$ and $V_{C{O}_2}^m$ are the molar gases of methane, $V_{C{O}_2}$ is the amount of methane gas consumed to produce a given volume of methane gas; and $C{O}_2$ is the amount of methane gas consumed to produce a certain volume of methane gas.

3.6. Gas Storage Tanks

In this paper, two gas storage models are established, namely storage $H_2$ and storage $C{O}_2$ models, whose mathematical models are given in the following equation:

$$\left\{\begin{array}{l}{V}_{S,t}=V_{S,t-1}+V_{S,in,t}-V_{S,out,t}\\ V_{S,\min }\le V_{S,t}\le V_{S,\max }\end{array}\right.$$

(7)

where $V_{S,t}$ is the gas storage capacity of the tank during the time period $t$; $V_{S,\min }$ and $V_{S,\max }$ are the upper and lower limits of the tank capacity, respectively; $V_{S,in,t}$ is the gas injection capacity of the tank during the time period; and $V_{S,out,t}$ is the gas output capacity of the tank.

4. Demand Response Model

Integrated demand response (IDR) is introduced into the integrated energy system to regulate the users’ energy use behavior and make the coupling links of supply, demand, and storage closer. The demand response model constructed in this paper is based on the controllability of electricity, gas, and heat loads. The model includes electrical and thermal load substitution and electrical and thermal load transfer to achieve lateral time load transfer. When the joint demand-side response is implemented in a multi-regional energy cluster interconnected system and the users contribute to the system operation to a certain extent, appropriate economic compensation should be given to the multi-energy users. Based on the amount of load adjustment under the joint demand-side response, the cost of energy use compensation is determined as follows:

$$C_{\mathrm{IDSR}}={\displaystyle \sum _m{\displaystyle \sum _t^T\left({\mu }_{\mathrm{cut}}\left|P_{1,t}\right|+{\mu }_{\mathrm{mov}}\left|P_{2,t}\right|\right)}}$$

(8)

where $F_{\mathrm{IDSR}}$ is the compensation cost of joint demand-side response; ${\mu }_{\mathrm{cut}}$ and ${\mu }_{\mathrm{mov}}$ are the compensation cost coefficients of cutting and shifting the unit power load; $P_{1,t}$ and $P_{2,t}$ are the loads cut and shifted by the system at time period t, respectively; and T is the total operation time period. According to the actual needs of the system, the allowable load adjustment amount of the joint demand-side response method is constrained, i.e., the range of adjustable load ratio is given as shown in Equation (9).

$$\left\{\begin{array}{l}0\le \left|P_{1,t}\right|\le {\eta }_1{P}_i(t)\\ -{\eta }_2{P}_i(t)\le \left|P_{2,t}\right|\le {\eta }_2{P}_i(t)\end{array}\right.$$

(9)

where $P_i(t)$ is the load at time t before the joint demand-side response is implemented, and ${\eta }_1$ and ${\eta }_2$ are the proportionality coefficients of demand-side curtailment and transfer, respectively, which are determined by the specific load characteristics.

5. Low-Carbon Dispatch Model for Integrated Energy Systems Considering Demand Response

5.1. Objective Function

The integrated energy system in this paper optimizes the output of each equipment in the system with the objective of minimizing the economic cost and carbon emission cost. The objective function is established as shown in Equation (10).

$$\min F_D=C_{inv}+C_{om}+C_{tari}+C_{tax}-C_{IDSR}$$

(10)

where $F_D$ is the comprehensive cost of the system; $C_{inv}$ is the investment cost of each equipment in the system; $C_{om}$ is the cost of operation and maintenance of the equipment in the system; $C_{tari}$ is the acquisition cost of resources, which consists of the cost of purchasing coal and the revenue from the sale of electricity and natural gas; $C_{tax}$ is the cost of carbon emissions; and $C_{IDSR}$ is the demand-side response compensation cost.

Resource acquisition costs $C_{tax}$ for:

$$C_{tari}=\sum _{t=1}^T(P_{GU,t}{k}_1-E_d{\mathrm{k}}_{\mathrm{ri}}-a{V}_{C{H}_4})$$

(11)

where $P_{GU,t}$ is the power generated by the thermal power unit; $k_1$ is the thermal power unit discount factor; $E_d$ is the electric load; $k_{\mathrm{ri}}$ represents time-of-use electricity pricing; $V_{C{H}_4}$ is the volume of methane generated from the electricity-to-gas system; and a is the methane selling unit price of 5 m³/CNY.

System carbon costs $C_{\mathrm{tax}}$ for:

$$C_{\mathrm{tax}}=\sum _{t=1}^T\left[\left(V_{{\mathrm{CO}}_2,\mathrm{GU}}-V_{{\mathrm{CO}}_2,\mathrm{CCS}}\right)b\right]$$

(12)

where $V_{{\mathrm{CO}}_2,\mathrm{GU}}$ is the carbon emission from coal combustion of thermal power units; $V_{{\mathrm{CO}}_2,CCS}$ is the amount of $C{O}_2$ used in the P2G system; and $\mathrm{b}$ represents the carbon emission cost, set at 0.6 CNY/N.m³.

The controllable load cost in this paper is the cost of dispatching a curtailable, levelized load response. $C_{IDSR}$ for:

$$\left\{\begin{array}{l}{C}_{\mathrm{IDSR}}={\displaystyle \sum _{t=1}^T\left({\displaystyle \sum _{i=1}^{N_{\mathrm{int}}}{c}_{\mathrm{int},i}}{P}_{\mathrm{int},i}{U}_{\mathrm{int},i}\Delta t+\right.}\left.{\displaystyle \sum _{j\in J}{\displaystyle \sum _{i=1}^{N_{\mathrm{tram}}}{c}_{\mathrm{tran},i}}}{P}_{\mathrm{tran},i}{U}_{\mathrm{tran},i}\Delta t\right)\\ J=\left\{U_{\mathrm{tran},i}=1\right\}\end{array}\right.$$

(13)

In the formula, $c_{\mathrm{int},i}$ ,$c_{\mathrm{tran},i}$ are the dispatching costs of the i-th type of load that can be reduced or shifted, respectively (CNY/kW·h); the variables $P_{\mathrm{int},i}$ and $U_{\mathrm{int},i}$ respectively denote the reduction power and response status for the i-th type of reducible load during the time period t; the variables $P_{\mathrm{tran},i}$ and $U_{\mathrm{tran},i}$ respectively represent the power and the response status for the i-th type of transferable load during the time period t; and J is the set of shiftable load responses within the dispatch period.

5.2. Constraints

(1)

Electrical balance constraints

At any moment t, the total power generation of the IES system is equal to the power consumption of the total load:

$$P_{PV,t}+P_{\mathrm{wind},t}+P_{GU,t}=P_{EB,t}+P_{CCS,t}+P_{C{H}_4,t}+P_{d,t}+P_{EL,t}+P_{\mathrm{int},t}-P_{\mathrm{tran},t}$$

(14)

In the formula, $P_{EB,t}$ is the electric power consumption of the electric heating boiler, $P_{CCS,t}$ is the electric power of carbon capture, $P_{EL,t}$ is the electrolyzer power consumption, $P_{\mathrm{int},t}$ is the leveling power, and $P_{\mathrm{tran},t}$ is the cuttable power.

(2)

Thermal equilibrium constraint

$$H_{EB}+H_{GU}\ge H_{\mathrm{d}}$$

(15)

In the formula, $H_{EB}$ is the thermal energy recovery power of thermal power units, $H_{GU}$ is the heat production power of the electric heating boiler, and $H_{\mathrm{d}}$ is the heat load.

(3)

Hydrogen equilibrium constraints

$$G_{EL,\mathrm{t}}+G_{\mathrm{in},\mathrm{t}}=G_{P2G,t}+G_{out,t}$$

(16)

In the formula, $G_{EL,\mathrm{t}}$ represents the hydrogen production power of the electrolysis cell, $G_{\mathrm{in},\mathrm{t}}$ denotes the hydrogen supply power at the coupling end, $G_{P2G,t}$ is the power consumed for hydrogen production in power-to-gas conversion, and $G_{out,t}$ signifies the hydrogen utilization power at the coupling end.

(4)

Carbon balance constraints.

$$P_{CCS,\mathrm{t}}+P_{\mathrm{in},\mathrm{t}}^{{CO}_2}=P_{P2G,t}^{C{O}_2}+P_{out,t}^{{CO}_2}$$

(17)

$P_{CCS,\mathrm{t}}$ is the actual carbon capture power, $P_{\mathrm{in},\mathrm{t}}^{{CO}_2}$ is the coupling end hydrogen supply power, $P_{P2G,t}^{C{O}_2}$ is the electrically converted gas, ${CO}_2$ is the power of hydrogen in the electrically converted gas, and $P_{\mathrm{in},\mathrm{t}}^{C_{O2}}$ is the power used at the coupling end of the power.

5.3. Generation of Scenarios for Wind and Light Output Considering Uncertainty

Photovoltaic and wind power generation is directly affected by the light intensity and wind energy density of the location, resulting in high stochasticity and intermittency of wind power output. It is necessary to consider the above uncertainties in the optimal planning of the IES constructed in this paper; for this reason, this study will use the K-means clustering algorithm based on 8760 h of resource data to generate typical wind power output. Further, these raw data are divided and scalarized. The K-means clustering algorithm is utilized to cluster multiple sets of scenarios to generate typical scenarios as the basis of IES optimization planning, and the flowchart is shown in Figure 3.

5.4. Solution Methods

The optimization model constructed in this paper has been given above; obtaining the optimal capacity of each device is the final goal, and the whole optimization problem belongs to the MILP problem. The logic of the MILP model is clear, applicable, and easy to converge, which is conducive to the global optimization of the capacity allocation. This paper utilizes mathematically accurate algorithms to solve the problem; the simulation process is based on the MATLAB software platform, and the optimization model is programmed in the YALMIP language environment. The optimization model is programmed in the YALMIP language environment and CPLEX is invoked for an efficient solution. Further, based on the above theory and platform, we carry out case studies to validate the model: we set up various scenarios to analyze the optimization results in detail, discuss the influence of optimization preferences on the final results through sensitivity analysis, and analyze the weight ranges of the optimal optimization intervals based on the idea of “cost-performance ratio”.

6. Example Analysis

6.1. Arithmetic Background and Data Processing

An industrial park is used as an example to validate the model. The area is rich in solar and wind energy resources and is suitable for the development of photovoltaic and wind power projects. In order to realize the autonomy and cleanliness of the energy supply, the industrial park proposes to lay out the natural gas–wind–photovoltaic–hydrogen IES constructed in this paper to supply all kinds of loads. The annual 8760 h electricity and heat load data are obtained from the smart meters of the park, and the electricity and heat load data of the park are obtained based on the typical day simulation. Figure 4 shows the distribution of the two types of loads over time in detail.

The local light radiation data and wind speed data are provided by the industrial park, which has several large-scale photovoltaic and wind power projects in the area, and the data are accurate and reliable. Figure 5 shows in detail the distribution of wind energy density and light intensity over time throughout the year. Based on the above historical data, using Gaussian kernel density estimation and K-means clustering algorithm, a total of several sets of typical scenarios about wind power are generated, and the clustering is shown in Figure A1 and Figure A2 in Appendix A due to the limitation of space. Figure 6 only shows the typical intra-day forecast data of wind power and electric load. It is easy to see that the K-means clustering well characterizes the uncertainty and probability distribution of wind power. The parameters are shown in Exhibit A1, the natural gas price is CNY 2.55/m³, and the time-sharing electricity price is shown in Exhibit A2.

In order to verify the economic and environmental benefits of its coupled system, this paper sets up three different scenarios for comparative analysis, and each scenario is as follows: Scenario 1 is the traditional IES economic scheduling without considering the demand-side response for carbon trading; Scenario 2 is the IES economic scheduling considering the demand-side response; and Scenario 3 is the IES economic scheduling considering the demand-side response and carbon trading. According to the above three scenarios, the optimal IES scheduling results are obtained as shown in Figure 7, Figure 8, Figure 9 and Figure 10.

6.2. Analysis of Optimized Scheduling Results

Figure 7 illustrates the balance diagram of each energy source, which is optimally dispatched primarily in Scenario 1. From Figure 7a, it can be seen that PV output is mainly concentrated from 9:00 to 15:00 when there is sufficient light, accounting for 6% of the power generation system at the highest percentage, and the other times of the day are characterized by severe light abandonment, which increases the system operation cost. WTG output is concentrated in the afternoon from 13:00 to 17:00 and at night from 23:00 to 05:00 when the wind density is higher, with the highest percentage of up to 25%. In Scenario 1, which does not consider demand response and carbon trading, thermal power units are an important factor affecting the electric power balance within the IES system, accounting for 33% of the supply side. As shown in Figure 7b, the system heat load is supplied by thermal heat recovery and the electric boiler, and the share of the electric boiler is greater than 25%. In the night time period when the heat load increases, the price of electricity in is 0.382 CNY/kWh, and 0.54 CNY/kWh in the trough and levelized periods due to the increase of wind turbine output. The heat conversion rate of the electric boiler is three times that of the thermal heat recovery, and at this time, if there is more low-carbon emission wind power supply, the heat load is better provided by the low-carbon efficient electric boiler, which can not only reduce the thermal power unit output, cutting the volume of carbon emissions but also can reduce the wind abandonment phenomenon, completing the peak shaving to fill the valley. From Figure 7c, it can be seen in the time period from 4:00 to 20:00 that the hydrogen volume has been in a higher state, and the degree of methanization to hydrogen conversion is low, while in the time periods 00:00–3:00 and 17:00–20:00 h, increased operating costs can be seen by the hydrogen storage equipment intervention work. From Figure 7d, it can be seen that methane volume reaches a high level but corresponds to an increase in the power of the carbon storage equipment, carbon storage gas discharge, and filling, and there are 14 h of high-power work time, which also increased the cost of the system equipment.

Figure 8 displays the optimized scheduling results for Scenario 2. Compared to Scenario 1, the incorporation of demand response, as illustrated in Figure 8a, enables the addition of levelizable and curtailable loads on the supply side. This effectively reduces the total operating cost and the peak-to-valley difference in the load of the integrated energy system. On the load side, in comparison with Scenario 1, the levelizable electric loads in the time period from 03:00 to 12:00 are reduced to zero, and the curves before and after the day-before electric demand response are demonstrated in Figure 9. The DR can partially shift the peak-time load amount to the load valley; the red section represents the reduced electrical load within the microgrid following the demand response. In the peak electricity price, after DR, the electric load reduction is obvious, and at the same time, this part of the load is supplied by additional consumption of low marginal cost and no carbon emission wind power output, which can effectively reduce the carbon emission of the system; in the low electricity price, calling DR resources in the real-time phase can improve the flexibility of the system scheduling to cope with the wind abandonment or loss of load caused by the error of wind power and load forecasting. In Scenario 2, the total electric load decreased by 2.14%, and after demand response optimization, the peak-valley difference of the electric load was significantly reduced. In the peak period of electricity price from 8:00 to 15:00, the electric load power was in the process of moving to the two sides, and there was more consumption of power in the grid valley time as well as new energy power generation. At the same time, the electric load through the leveling can be shifted and cut, and then can be transferred to the other time of the day when the load of the power supply is more adequate (valley hours), further increasing the consumption of renewable energy.

As shown in Figure 8c, the volume of hydrogen is reduced by 10,000 m³ compared to Scenario 1, and the hydrogen conversion is significantly higher, while the hydrogen storage intervention time is reduced by 4 h. Figure 8d shows that the power of the carbon storage equipment is reduced, the carbon storage is deflated and inflated with only 8 h of low-power working time, and the time for the storage tank to intervene in the coupling system is reduced, which results in a reduction in the cost of the system.

Figure 10 shows the optimized scheduling results for Scenario 3. Combining carbon capture and demand response, the power of the equipment is changed in each time period, which is shown in Figure 10a, compared with the previous scenario PV power share increases, accounting for 11% of the supply side in the peak period; at the same time, thermal power decreases, accounting for only 14% of the supply side in the trough period, and there is an increase in the levelizable curtailable electric power in the supply side in each time period, which cuts down the generating equipment’s power. As shown in Figure 11, the power of the coupling equipment, while the supply side of the panning, can cut the increase in electric power to guide the load in the scheduling cycle for panning cuts and to achieve the electric load of the “peak shaving to fill in the valley”, which is relative to the Scenarios 1 and 2 where there are electric load cuts of 10.13% and 8.20%, respectively, in the tariff peak hours.

In the peak period from 8:00 to 15:00, the electric load reduction is more obvious, and the economic benefit increases more significantly. As demonstrated in Figure 10b, compared with Scenario 1, the electric boiler shows an increase in heat supply by 59.38%. This is complemented by a reduction in heat supply from thermal power units due to their operational mode. Concurrently, the intervention of renewable energy sources also increases, considering both the cost of carbon emissions and time-of-use tariffs, thus enhancing the benefits of increased output from electric heating boilers. Furthermore, the decrease in thermal power generation impacts power dispatching during peak electricity consumption times, specifically from 11:00 to 16:00 and 19:00 to 22:00. This period also corresponds to peak electricity pricing. An increase in photovoltaic and wind power generation compensates for the reduced thermal power, thereby reducing the curtailment of wind and solar energy. This strategy, known as “peak shaving and valley filling”, simultaneously reduces the operating costs associated with power dispatching during these periods. As shown in Figure 10c,d, the difference in natural gas volume in Scenario 3 is not large compared to Scenario 2, but the time period for carbon and hydrogen storage filling and discharging in Scenario 3 to intervene in the coupling equipment has been cut by 7 and 4 h compared to Scenarios 1 and 2, respectively, which is directly converted into natural gas by carbon capture and electricity-to-hydrogen conversion equipment; further, the degree of coupling has been increased, and the time period of intervening between the storage equipment and the coupling equipment has been reduced significantly to decrease the system operation cost. The system operation cost is reduced. It can be seen that the optimization model proposed in this paper can effectively optimize the model and analyze the data to develop a reasonable power dispatch plan, which can reduce the peak and valley differences of the system and improve the operating efficiency of the power system.

As can be seen from Figure 12, relative to Scenario 1 after adding demand response and carbon capture, the thermal power unit output of Scenario 3 in the 08:00–19:00 time period of the tariff leveling and peak period is greatly reduced, and the total power is reduced by 32.914%, which reduces the dependence on a single source, and the whole system becomes more resilient and less prone to interruptions. The reduction of the thermal power generation can better integrate variable renewable energy; at the same time, the corresponding overall carbon emissions are reduced, the PV power doubles during the tariff peak period, the utilization rate of PV increases significantly, and the new energy consumption capacity within the system increases. Reduced thermal generation allows for better integration of variable renewable energy sources, providing flexibility in managing demand and supply imbalances; this corresponds to a reduction in overall carbon emissions, a doubling of photovoltaic (PV) power during peak tariffs, a significant increase in PV utilization, an increase in new energy consumption within the system, and an effective constraint on the volatility of the system’s wind and light.

In comparing Scenario 1 with Scenarios 2 and 3, it is observed that the latter incorporates demand response and carbon capture technologies. Specifically, as indicated in

Table 1. Three scenario costs.

Project	Scenario 1	Scenario 2	Scenario 3
Operation and maintenance cost/CNY 10,000	674.99	654.38	642.70
Carbon trading cost/CNY 10,000	-	-	−70.60
Demand response cost/CNY 10,000	-	5.2	5.2
Carbon Capture cost/CNY 10,000	-	-	2.71
Photovoltaic capacity/MW	50	100	100
Total cost/CNY 10,000	674.99	659.58	579.31

, the investment costs for Scenarios 2 and 3 show reductions in operation and maintenance costs by CNY 206,100 and CNY 322,900, respectively. These figures represent decreases of 3.05% and 4.78% in comparison to Scenario 1. Additionally, the capacity for photovoltaic power absorption has doubled in Scenarios 2 and 3. Notably, Scenario 3 not only accounts for load demand response, aiding in peak shaving and valley filling but also achieves a reduction in carbon emission costs by CNY 706,000. This equates to a total cost reduction, compared to Scenarios 1 and 2, of CNY 154,100 and CNY 599,700, respectively, amounting to decreases of 2.28% and 14.18%. These results demonstrate the effectiveness of incorporating carbon trading and demand response in integrated energy systems (IES) for reducing operational costs, thereby validating the proposed dispatch model.

7. Conclusions

Addressing the optimal scheduling problem of the integrated energy system (IES), this study adopts the minimum system operating cost as the objective function. Utilizing the K-means clustering algorithm to categorize scenarios and identify typical output scenarios, it comprehensively incorporates demand response (DR) compensation and carbon trading costs. Consequently, an optimal scheduling model was established, focusing on the demand-side response induced by wind and solar output scenarios in conjunction with the carbon trading mechanism, thereby optimizing the outputs of various equipment within the system. This study’s findings were validated through simulation, leading to the following conclusions:

(1)

The K-means clustering algorithm is applied for scenario division to effectively capture the variability and randomness of wind and photovoltaic power outputs, as well as stochastic loads. This approach involves further random sampling and clustering to establish typical probabilistic scenarios, enabling the optimization planning model to represent uncertainties more accurately, thus yielding more reliable optimization results.

(2)

The proposed electric load DR strategy can effectively alleviate the pressure on energy-supplying equipment during peak hours. DR enables quick and flexible adjustment of user-end load, allowing for the cutting or shifting of part of the load during peak electric energy usage hours. This contributes to maintaining system stability and reducing the operating costs of the system.

(3)

With the introduction of the carbon trading mechanism, renewable energy substantially intervenes in IES, which significantly reduces CO₂ emissions. Throughout the dispatch cycle, compared to the scenario without the carbon trading mechanism, the thermal power unit output is reduced by 32.914%, the system operating cost is reduced by 14.18%, and the carbon emission cost is reduced by CNY 70.6 million. This demonstrates that the introduction of the carbon trading mechanism can enable low-carbon operation of the system and effectively mitigate environmental pollution.