Economic Dispatch of Integrated Energy Systems Considering Wind–Photovoltaic Uncertainty and Efficient Utilization of Electrolyzer Thermal Energy

Abstract

Currently, high levels of output stochasticity in renewable energy and inefficient electrolyzer operation plague IESs when combined with hydrogen energy. To address the aforementioned issues, an IGDT-based economic scheduling strategy for integrated energy systems is put forth. Firstly, this strategy establishes an IES consisting of coupled electricity, heat, hydrogen, and gas taking the hydrogen production electrolyzer’s thermal energy utilization into account. Second, to minimize the system’s overall operating costs, a deterministic scheduling model of the IES is built by taking into account the stepped carbon trading mechanism and the integrated demand response. Lastly, an optimal dispatch model is built using the information gap decision theory under the two strategies of risk aversion and risk seeking, taking into account the uncertainty of renewable energy generation. CPLEX is the solver used to solve the proposed model. After taking into account the effective use of thermal energy from the electrolyzer and loads demand response, the results show that the system carbon emission is reduced by 2597.68 kg and the operating cost is lowered by 44.65%. The IES scheduling model based on IGDT can effectively manage costs while maintaining system risk control, all while accommodating decision-makers’ varying risk preferences. This study can provide a useful reference for the research related to the scheduling of the IES low-carbon economy.

1. Introduction

Promoting the use of renewable energy sources and developing various uses for hydrogen energy is crucial from a practical standpoint when it comes to the “dual-carbon” aim and the green energy transition [1]. Several heterogeneous energy sources and conversion equipment can be combined by integrated energy systems (IESs) to satisfy the various demands of loads and offer a solution to encourage the use of energy efficiently and renewable energy sources [2,3].

Because of its high energy density, huge storage capacity, and high utilization rate, hydrogen energy can be used as a long-term energy storage system [4,5]. Simultaneously, IES carbon reduction goals can be achieved by the use of hydrogen energy, which is clean and environmentally benign [6]. Reference [7] proposes a wind–hydrogen energy system model, consisting of a wind turbine power generation system and a hydrogen storage system, and optimizes the configured capacity of the hydrogen storage system with the objective function of minimizing the system investment cost, operation, and maintenance cost. Reference [8] proposes an integrated energy system integrating hydrogen and electricity, considering both the operating costs of the system and the environmental costs associated with the buyback for constructing an optimal scheduling model for the coupled electricity–hydrogen–carbon system. Reference [9], an integrated energy system with wind turbines (WT), solar panels, and hydrogen storage systems, was built. A multi-objective day-ahead optimal scheduling model for the system was established, considering both the system’s operating costs and environmental costs comprehensively. NSGA-Ⅱ was then used to solve the problem. Reference [10] reduces the carbon emissions of the system by diversifying the utilization of hydrogen energy within the framework of green certificate trading mechanisms, focusing on energy applications. Reference [11] built an integrated electricity, heat, hydrogen, and gas energy system to lower carbon emissions and increase the use of renewable energy sources. This study did just that by utilizing hydrogen energy to enhance the system’s use of renewable energy sources and to realize the synergistic interaction between various energy sources. Utilizing the extended duration and high capacity that hydrogen energy storage can provide, the aforementioned study elaborates on integrating hydrogen energy storage into IESs to achieve hydrogen–electricity hybridization. However, during operation, the hydrogen fuel cell (HFC) and electrolyzer (EL) will unavoidably produce heat, and none of the literature [7,8,9,10,11] addressed the use of this portion of the heat, leading to energy waste in the system.

Reference [12] examined various methods of utilizing hydrogen energy, along with the physical attributes of each type of hydrogen storage mechanism. For the integrated thermoelectric hydrogen system, a two-layer optimization model is suggested, with the lower layer optimizing the system operation scheme and the upper layer determining the equipment capacity of the hydrogen energy system. Reference [13] describes the construction of an optimal scheduling model for a wind–photovoltaic–electricity–hydrogen storage integrated energy system. This model takes into account waste heat recovery from the HFC to promote the application of clean energy, such as wind–photovoltaic–hydrogen energy, within the park’s integrated energy system. Reference [14] suggests designing an integrated energy system in conjunction with hydrogen energy to achieve a synergistic supply of heat, cold, and electricity. It also establishes the ideal configuration for the integrated energy system by thoroughly assessing its energy, economics, environment, and grid dependence. The waste heat recovery from fuel cells was examined in reference [15], which also created an IES for combined biomass–photovoltaic–hydrogen energy and assessed the system’s performance from the energy–exergy–economy–environment standpoint.

As of right now, fuzzy optimization [16], stochastic optimization [17], and robust optimization [18] are the three primary types of approaches used to address the internal uncertainties of IESs. To solve numerous uncertainty problems in wind power integrated multi-energy systems, reference [19,20] developed an IES scheduling model based on fuzzy planning. However, fuzzy optimization is inherently subjective due to the necessity of selecting the membership function to describe uncertainty and its potential implications. A stochastic optimization approach was presented in reference [21] to address the unpredictability of renewable energy units in a microgrid and enhance system performance. A stochastic optimization-based optimal scheduling model for a combined wind–hydro system was created in reference [22] to address the deterministic nature of wind power output. However, stochastic optimization heavily relies on probabilistic models of uncertain quantities because it is grounded in probabilistic analysis. To address the uncertainties surrounding renewable energy sources, reference [23] created a coordination network and energy planning model for an IES utilizing robust optimization. A two-stage resilient optimal configuration model is proposed in reference [24] that examines the effects of various system uncertainties on both the configuration cost and the system’s running costs. References [25,26] employ a two-stage distributionally robust optimization approach to manage uncertainties in renewable energy and load demand within the system. Based on the range of variations in a given uncertainty, robust optimization selects the worst perturbation scenarios, resulting in overly conservative outcomes and suboptimal system economics. In contrast to the previously mentioned techniques, Information Gap Decision Theory (IGDT) exhibits the ability to establish the intended objective, optimize the range of fluctuation for uncertain parameters, and demonstrate strong adaptability when the probability distribution or fuzzy affiliation function of uncertain parameters is not known [27,28].

This paper aims to address the aforementioned issues by enhancing the energy utilization efficiency of hydrogen energy equipment within the system and mitigating the impact of source-load uncertainty on IES scheduling. Firstly, the operation framework of the IES is established by considering demand response, the stepped carbon trading mechanism, and the thermoelectric characteristics of EL. Second, the IES low-carbon economic dispatch model was established with the goal of minimizing the system costs associated with energy purchase, stepped carbon trading, and penalties for wind and light abandonment. Lastly, the IGDT method was used to discuss the uncertainty of WT and PV, and the risk-seeking and risk aversion models were created based on the decision-makers’ respective levels of risk preference. The original model must be converted into a mixed-integer linear model and solved in MATLAB using the CPLEX solver because the generated model is nonlinear. The effectiveness of the proposed model is verified by setting up different scenarios to analyze the scheduling results.

2. Operational Framework for IES

2.1. Structure of IES

The IES’s operating framework is depicted in Figure 1, with an emphasis on the EL’s efficient use of thermal energy. The system integrates energy supply equipment with multiple energy sources to meet its internal energy requirements. The three primary components of the IES model developed in this study are the energy supply unit, energy conversion and storage unit, and energy consumption unit, as seen in Figure 1. The energy supply unit of the system is made up of wind turbine (WT), photovoltaic (PV), the electricity grid, and the gas network. The energy conversion unit contains an EL, HFC, methane reactor (MR), combined heat and power (CHP), and gas boiler (GB). The energy storage unit has battery energy storage (BES), a hydrogen storage tank (HST), thermal storage tank (TST), and gas storage tank (GST).

The majority of the energy used to produce hydrogen in the EL and electricity in HFC is lost as heat, making the current electricity–hydrogen–electricity conversion process inefficient. As a result, recovering the working waste heat from the EL and HFC using a waste heat recovery device is crucial to increasing their energy conversion efficiency and making the most of hydrogen energy’s low-carbon and clean qualities.

The IES’s demand for thermal energy will be met by CHP, GB, EL, and HFC through the realization of hydrogen energy equipment cogeneration. This would lower the GB and CHP’s need for natural gas during the peak hours of thermal energy demand. The heat storage tank efficiently increases the stability and flexibility of the system’s energy supply and can further lower the system’s carbon emissions if the heat generated by the system is more than the heat load requirement.

2.2. Mathematical Models

2.2.1. Electrolyzer

The EL is a crucial device for converting electrical energy into hydrogen by employing the chemical principle of water electrolysis. Throughout this process, a portion of the energy dissipates as heat. Hence, the waste heat produced during electrolysis can be captured with a waste heat recovery device to enhance the energy efficiency of the EL [29]. At the moment, alkaline anion exchange membranes, high-temperature solid oxide with alkaline water electrolysis, and proton exchange membrane water electrolysis are the three primary technical pathways for producing hydrogen from electrolyzed water. Due to its advantages of mature technology, low cost, and long service life, the alkaline EL has become the most widely used equipment for producing hydrogen. In this paper, an alkaline EL is used for water electrolysis to produce hydrogen. The alkaline EL mathematical model is represented by the following equation [30].

$$\left\{\begin{array}{l}{P}_{\mathrm{EL}, {\mathrm{H}}_2}(t)={\eta }_{\mathrm{EL}}{P}_{\mathrm{e},\mathrm{EL}}(t)\\ P_{\mathrm{EL}, \mathrm{h}}(t)=(1-{\eta }_{\mathrm{EL}})P_{\mathrm{e},\mathrm{EL}}(t)\\ P_{\mathrm{e},\mathrm{EL}}^{\min }⩽P_{\mathrm{e},\mathrm{EL}}(t)⩽P_{\mathrm{e},\mathrm{EL}}^{\max }\\ \Delta P_{\mathrm{e},\mathrm{EL}}^{\min }⩽P_{\mathrm{e},\mathrm{EL}}(t+1)-P_{\mathrm{e},\mathrm{EL}}(t)⩽\Delta P_{\mathrm{e},\mathrm{EL}}^{\max }\end{array}\right.$$

(1)

where $P_{\mathrm{e},\mathrm{EL}}(t)$ is the electrical energy input to the EL, ${\eta }_{\mathrm{EL}}$ is the energy conversion efficiency of the EL, in this paper, the value is 0.87; $P_{\mathrm{EL}, {\mathrm{H}}_2}(t)$ is the hydrogen production power of the EL; $P_{\mathrm{EL}, \mathrm{h}}(t)$ is the thermal energy output from the EL; $P_{\mathrm{e},\mathrm{EL}}^{\min }$ and $P_{\mathrm{e},\mathrm{EL}}^{\max }$ are the lower and upper limits of the electrical energy input to the EL, respectively; $\Delta P_{\mathrm{e},\mathrm{EL}}^{\max }$, $\Delta P_{\mathrm{e},\mathrm{EL}}^{\min }$ are the upper and lower limits of the climbing power of the EL, respectively.

2.2.2. Hydrogen Fuel Cell

As a hydrogen–electricity conversion device within the system, HFCs can be utilized for combined heat and power generation, as they produce significant heat energy alongside electrical output. Given the adjustable electric and thermal energy conversion efficiencies of HFC, this study aims to enhance energy supply flexibility by constructing a mathematical model that incorporates an adjustable electric-to-thermal ratio [31]. The mathematical model is shown below [30].

$$\left\{\begin{array}{l}{P}_{\mathrm{HFC}, \mathrm{e}}(t)={\eta }_{\mathrm{HFC}}^e{P}_{{\mathrm{H}}_2, \mathrm{HFC}}(t)\\ P_{\mathrm{HFC}, \mathrm{h}}(t)={\eta }_{\mathrm{HFC}}^h{P}_{{\mathrm{H}}_2, \mathrm{HFC}}(t)\\ P_{{\mathrm{H}}_2, \mathrm{HFC}}^{\min }\le P_{{\mathrm{H}}_2, \mathrm{HFC}}(t)\le P_{{\mathrm{H}}_2, \mathrm{HFC}}^{\max }\\ \Delta P_{{\mathrm{H}}_2, \mathrm{HFC}}^{\min }\le P_{{\mathrm{H}}_2, \mathrm{HFC}}(t+1)+P_{{\mathrm{H}}_2, \mathrm{HFC}}(t)\le \Delta P_{{\mathrm{H}}_2, \mathrm{HFC}}^{\max }\\ {\kappa }_{\mathrm{HFC}}^{\min }\le P_{\mathrm{HFC}, \mathrm{h}}(t)/P_{\mathrm{HFC}, \mathrm{e}}(t)\le {\kappa }_{\mathrm{HFC}}^{\max }\end{array}\right.$$

(2)

where $P_{\mathrm{HFC}, \mathrm{e}}(t)$, $P_{\mathrm{HFC}, \mathrm{h}}(t)$ are the electrical energy and thermal energy output from the HFC, respectively; ${\eta }_{\mathrm{HFC}}^e$, ${\eta }_{\mathrm{HFC}}^h$ are the power generation efficiency and thermal efficiency of the HFC, respectively, the values are 0.55, 0.4, respectively; $P_{{\mathrm{H}}_2, \mathrm{HFC}}(t)$ is the hydrogen consumption power of HFC; $P_{{\mathrm{H}}_2, \mathrm{HFC}}^{\max }(t)$, $P_{{\mathrm{H}}_2, \mathrm{HFC}}^{\min }(t)$ are the upper and lower limits of the hydrogen input to the HFC, respectively; $\Delta P_{{\mathrm{H}}_2, \mathrm{HFC}}^{\max }(t)$, $\Delta P_{{\mathrm{H}}_2, \mathrm{HFC}}^{\min }(t)$ are the upper and lower limits of the climbing power of the HFC, respectively; ${\kappa }_{\mathrm{HFC}}^{\min }$ and ${\kappa }_{\mathrm{HFC}}^{\max }$ are the lower and upper limits of the thermoelectric ratio of the HFC.

2.2.3. Methane Reactor

The MR utilizes hydrogen from the EL and CO₂ from the IES for methanation, which is a mathematical model represented as follows.

$$\left\{\begin{array}{l}{P}_{\mathrm{MR}, \mathrm{g}}(t)={\eta }_{\mathrm{MR}}{P}_{{\mathrm{H}}_2, \mathrm{MR}}(t)\\ P_{{\mathrm{H}}_2, \mathrm{MR}}^{\min }⩽P_{{\mathrm{H}}_2,\mathrm{MR}}(t)⩽P_{{\mathrm{H}}_2, \mathrm{MR}}^{\max }\\ \mathsf{\Delta }{P}_{{\mathrm{H}}_2, \mathrm{MR}}^{\min }⩽P_{{\mathrm{H}}_2, \mathrm{MR}}(t+1)-P_{{\mathrm{H}}_2,\mathrm{MR}}(t)⩽\mathsf{\Delta }{P}_{{\mathrm{H}}_2, \mathrm{MR}}^{\max }\end{array}\right.$$

(3)

where $P_{\mathrm{MR}, \mathrm{g}}(t)$ is the natural gas power output from the MR; ${\eta }_{\mathrm{MR}}$ is the energy conversion efficiency of the MR, the value is 0.6; $P_{{\mathrm{H}}_2, \mathrm{MR}}(t)$ is the hydrogen consumption power of the MR; $P_{{\mathrm{H}}_2, \mathrm{MR}}^{\max }$, $P_{{\mathrm{H}}_2, \mathrm{MR}}^{\min }$ are the upper and lower limits of the hydrogen energy input to the MR, respectively; and $\mathsf{\Delta }{P}_{{\mathrm{H}}_2, \mathrm{MR}}^{\max }$, $\mathsf{\Delta }{P}_{{\mathrm{H}}_2, \mathrm{MR}}^{\min }$ are the upper and lower limits of the creep power of the MR, respectively.

2.2.4. Adjustable Thermoelectric Ratio CHP

Natural gas is burned in CHP for cogeneration. Because conventional CHP may only operate in “heat by electricity” or “heat by electricity” modes, their fixed cogeneration ratio restricts their operational flexibility. Adjustable thermoelectric ratio CHP can adjust the thermoelectric ratio according to the real-time situation of thermal and electric loads by controlling the pumping ratio of the turbine and the angle of the inlet guide vane, the mathematical model of which is shown below.

$$\left\{\begin{array}{l}{P}_{\mathrm{CHP}, \mathrm{e}}(t)={\eta }_{\mathrm{CHP}}^{\mathrm{e}}{P}_{\mathrm{g}, \mathrm{CHP}}(t)\\ P_{\mathrm{CHP}, \mathrm{h}}(t)={\eta }_{\mathrm{CHP}}^{\mathrm{h}}{P}_{\mathrm{g}, \mathrm{CHP}}(t)\\ P_{\mathrm{g}, \mathrm{CHP}}^{\min }\le P_{\mathrm{g},\mathrm{CHP}}(t)\le P_{\mathrm{g}, \mathrm{CHP}}^{\max }\\ \Delta P_{\mathrm{g}, \mathrm{CHP}}^{\min }\le P_{\mathrm{g}, \mathrm{CHP}}(t+1)-P_{\mathrm{g}, \mathrm{CHP}}(t)\le \Delta P_{\mathrm{g}, \mathrm{CHP}}^{\max }\\ {\kappa }_{\mathrm{CHP}}^{\min }\le P_{\mathrm{CHP}, \mathrm{h}}(t)/P_{\mathrm{CHP}, \mathrm{e}}(t)\le {\kappa }_{\mathrm{CHP}}^{\max }\end{array}\right.$$

(4)

where $P_{\mathrm{CHP}, \mathrm{e}}(t)$, $P_{\mathrm{CHP}, \mathrm{h}}(t)$ are the electrical and thermal energy output of the CHP; ${\eta }_{\mathrm{CHP}}^{\mathrm{e}}$, ${\eta }_{\mathrm{CHP}}^{\mathrm{h}}$ are the electrical and thermal energy conversion efficiency of the CHP; $P_{\mathrm{g}, \mathrm{CHP}}(t)$ is the natural gas power input to the CHP; $P_{\mathrm{g}, \mathrm{CHP}}^{\max }$, $P_{\mathrm{g}, \mathrm{CHP}}^{\min }$ are the upper and lower limits of the natural gas power input to the CHP; $\Delta P_{\mathrm{g}, \mathrm{CHP}}^{\max }$, $\Delta P_{\mathrm{g}, \mathrm{CHP}}^{\min }$ are the upper and lower limits of the ramp power of the CHP; ${\kappa }_{\mathrm{CHP}}^{\max }$, ${\kappa }_{\mathrm{CHP}}^{\min }$ are the upper and lower limits of the CHP’s thermoelectricity ratio, respectively.

2.2.5. Gas Boiler

The GB produces a large amount of heat energy by burning natural gas, which is mathematically modeled as shown in the following equation.

$$\left\{\begin{array}{l}{P}_{GB,h}(t)={\eta }_{GB}^h{P}_{g,GB}(t)\\ P_{g,GB}^{\min }\le P_{g,GB}(t)\le P_{g,GB}^{\max }\\ \Delta P_{g,GB}^{\min }\le P_{g,GB}(t+1)-P_{g,GB}(t)\le \Delta P_{g,GB}^{\max }\end{array}\right.$$

(5)

where $P_{GB,h}(t)$ stands for the heat energy output of the GB; ${\eta }_{GB}^h$ for the heat efficiency of the GB, the value is 0.92; $P_{g,GB}(t)$ for the GB consumption of natural gas power; $P_{g,GB}^{\min }$, $P_{g,GB}^{\max }$ for the lower and upper limits of the heat power output of the GB; $\Delta P_{g,GB}^{\min }$, $\Delta P_{g,GB}^{\max }$ for the lower and upper limits of the climbing power of the GB.

2.2.6. Energy Storage System

Energy storage devices in the IES include BES, HST, GST, and TST, which are modeled using a generic approach due to the similarity of their energy charging and discharging processes, as shown in the following equation.

$$W_s(t)=W_s(t-1)(\begin{array}{c}1-{\delta }_s\end{array})+(\begin{array}{c}{\eta }_{\mathrm{s},\mathrm{cha}}{P}_{\mathrm{s},\mathrm{cha}}(t)-{\displaystyle \frac{P_{\mathrm{s},\mathrm{dis}}(t)}{{\eta }_{\mathrm{s},\mathrm{dis}}(t)}})\mathsf{\Delta }t\end{array}$$

(6)

where $s$ is the type of energy, $W_s(t)$ is the energy stored in the energy storage device; ${\delta }_s$ is the energy self-loss rate; ${\eta }_{\mathrm{s},\mathrm{cha}}$, ${\eta }_{\mathrm{s},\mathrm{dis}}$ are the charging and discharging efficiency of the energy storage device, respectively; $\mathsf{\Delta }t$ is the time interval.

2.3. Stepped Carbon Trading Model

A carbon trading mechanism is a system of trading that permits the market-based purchase and sale of carbon emission rights [32]. To reduce greenhouse gas emissions, the mechanism can support the commercialization of carbon credits, which will optimize the energy mix of the IES. Each source of carbon emissions is first given a specific amount of carbon credits by the regulator. Producers generate and release energy based on the credits that have been assigned to them. Producers can sell the leftover credits on the carbon market if their actual carbon emissions are less than the credits they have been allotted; if their actual emissions are more than the credits they have been allotted, they must buy more carbon credits. The carbon emission right quota model, the real carbon emission model, and the stepped carbon emission trading model are the three key parts of the stepped carbon trading model [33].

2.3.1. Carbon Emission Allowance Model

The IES developed in this study has three different kinds of carbon emission sources: GB, CHP, and purchased power from the upper grid. This study’s unpaid quota carbon quota approach is predicated on the idea that all power purchases from the upper grid originate from coal-fired units that produce energy.

$$\left\{\begin{array}{l}{E}_{\mathrm{IES}}=E_{\mathrm{e},\mathrm{bay}}+E_{\mathrm{CHP}}+E_{\mathrm{GB}}\\ E_{\mathrm{e},\mathrm{bay}}={\chi }_{\mathrm{e}}{\displaystyle \sum _{t=1}^T}{P}_{\mathrm{e},\mathrm{bay}}(t)\\ E_{\mathrm{CHP}}={\chi }_{\mathrm{g}}{\displaystyle \sum _{t=1}^T}(P_{\mathrm{CHP},\mathrm{e}}(t)+P_{\mathrm{CHP},\mathrm{h}}(t))\\ E_{\mathrm{GB}}={\chi }_{\mathrm{g}}{\displaystyle \sum _{t=1}^T}{P}_{\mathrm{GB},\mathrm{h}}(t)\end{array}\right.$$

(7)

where $E_{\mathrm{IES}}$, $E_{\mathrm{e},\mathrm{bay}}$, $E_{\mathrm{CHP}}$, $E_{\mathrm{GB}}$ are the carbon credits of the IES, purchased power from the upper grid, CHP, and GB, respectively; ${\chi }_{\mathrm{e}}$, ${\chi }_{\mathrm{g}}$ are the carbon credits per unit of electricity consumed by coal-fired units and per unit of gas consumed by natural gas-fired units, respectively; $P_{\mathrm{e},\mathrm{bay}}(t)$ is the amount of power purchased from the upper grid; and $T$ is the scheduling cycle.

2.3.2. Real Carbon Emissions Modeling

The real carbon emissions are predicted as indicated by the following equation, as part of the CO₂ created by the IES during the hydrogen-to-natural-gas conversion process is absorbed by the MR.

$$\left\{\begin{array}{l}{E}_{\mathrm{IES},\mathrm{a}}=E_{\mathrm{e},\mathrm{buy},\mathrm{a}}+E_{\mathrm{total},\mathrm{a}}-E_{\mathrm{MR},\mathrm{a}}\\ E_{\mathrm{e},\mathrm{buy},\mathrm{a}}={\displaystyle \sum _{t=1}^T(a_1+b_1{P}_{\mathrm{e},\mathrm{buy}}(t)+c_1{P}_{\mathrm{e},\mathrm{buy}}^2(t))}\\ E_{\mathrm{total},\mathrm{a}}={\displaystyle \sum _{t=1}^T(a_2+b_2{P}_{\mathrm{total}}(t)+c_2{P}_{\mathrm{total}}^2(t))}\\ P_{\mathrm{total}}(t)=P_{\mathrm{CHP}, \mathrm{e}}(t)+P_{\mathrm{CHP}, \mathrm{h}}(t)+P_{\mathrm{GB}, \mathrm{h}}(t)\\ E_{\mathrm{MR}, \mathrm{a}}={\displaystyle \sum _{t=1}^T\varpi P_{\mathrm{MR}, \mathrm{g}}(t)}\end{array}\right.$$

(8)

where $E_{\mathrm{IES},\mathrm{a}}$, $E_{\mathrm{e},\mathrm{buy},\mathrm{a}}$ are the actual carbon emission from the IES and power purchased from the higher grid, respectively; $E_{\mathrm{total},\mathrm{a}}$ is the total actual carbon emission from CHP, GB, and MR; $E_{\mathrm{MR},\mathrm{a}}$ is the amount of CO₂ absorbed by the MR during its operation; $P_{\mathrm{total}}(t)$ is the equivalent output power of CHP, GB, and MR; $a_1$, $b_1$, $c_1$ and $a_2$, $b_2$, $c_2$ are the parameters for calculating the carbon emissions of coal-fired units and natural gas-consuming energy equipment, respectively, and are the parameters for the CO₂ absorbed during the conversion of natural gas by the MR.

2.3.3. Stepped Carbon Emissions Trading Model

The actual carbon allowances for the IES to participate in the carbon trading market can be derived from the IES’s carbon credit allowances and actual carbon emissions, as shown in the following equation.

$$E_{\mathrm{IES}, \mathrm{t}}=E_{\mathrm{IES}, \mathrm{a}}-E_{\mathrm{IES}}$$

(9)

where $E_{\mathrm{IES}, \mathrm{t}}$ is the amount of carbon credits traded by the IES.

This study uses a ladder pricing technique to separate various purchasing intervals and further limit the carbon emissions of the IES. The price of the response interval increases with the amount of carbon permits purchased. The stepped carbon transaction costs are shown in the following equation.

$$C_{{\mathrm{CO}}_2}=\left\{\begin{array}{ll}\lambda E_{IES,t}& E_{IES,t}\le l\\ \lambda (1+\alpha )(E_{IES,t}-l)+\lambda l& l\le E_{IES,t}\le 2l\\ \lambda (1+2\alpha )(E_{IES,t}-2l)+\lambda (2+\alpha )l& 2l\le E_{IES,t}\le 3l\\ \lambda (1+3\alpha )(E_{IES,t}-3l)+\lambda (3+3\alpha )l& 3l\le E_{IES,t}\le 4l\\ \lambda (1+4\alpha )(E_{IES,t}-4l)+\lambda (4+4\alpha )l& E_{IES,t}\ge 4l \end{array}\right.$$

(10)

where $C_{{\mathrm{CO}}_2}$ is the stepped carbon transaction cost; $\lambda$ is the carbon transaction base price; $l$ is the length of the carbon emission interval; and $\alpha$ is the price growth rate.

2.4. Demand Response Model

The loads in the IES consist of heat, electricity, and gas. The flexibility of gas loads is not taken into account in this article. Electricity and heat loads include base loads and transferable loads. The base load is an uncontrollable load, which responds totally to the user’s demand, and the system cannot change the mode and time of its energy usage. To ensure that the total loads of the entire cycle after the transfer stay the same as it did before, the transferable loads can be dynamically altered for each period of energy consumption.

2.4.1. Demand Response for Electric Loads

Demand response refers to regulating the system load in the power system through pricing mechanisms and incentives to optimize the load curve and ensure stable system operation. In order to achieve the goal of reducing or shifting electric loads, this study employs price-based demand response for electric loads, charging fixed tariffs differently according to the period of energy consumption, and assisting users in changing their power usage habits [34]. The relationship between energy prices and demand is depicted by a price elasticity matrix. The energy usage cycle is split into three time periods: peak, flat, and valley. In this paper, demand response is modeled using the price elasticity matrix method, where the price elasticity matrix is expressed as follows [35].

$$E=\left[\begin{array}{cccc}{\epsilon }_{11}& {\epsilon }_{12}& \cdots & {\epsilon }_{1\mathrm{t}}\\ {\epsilon }_{21}& {\epsilon }_{22}& \cdots & {\epsilon }_{2t}\\ ⋮& ⋮& & ⋮\\ {\epsilon }_{t1}& {\epsilon }_{t2}& \cdots & {\epsilon }_{tt}\end{array}\right]$$

(11)

$${\epsilon }_{ii}={\displaystyle \frac{\mathsf{\Delta }{L}_i}{L_i}}{({\displaystyle \frac{\mathsf{\Delta }{p}_i}{p_i}})}^{-1}$$

(12)

$${\epsilon }_{ij}={\displaystyle \frac{\mathsf{\Delta }{L}_i}{L_i}}{({\displaystyle \frac{\mathsf{\Delta }{p}_j}{p_j}})}^{-1}$$

(13)

where ${\epsilon }_{ii}$ and ${\epsilon }_{ij}$ are the coefficients of auto-elasticity and cross-elasticity, respectively; $L_i$ represents the quantity of electricity demanded in time $i$; $\mathsf{\Delta }{L}_i$ denotes the relative increment of quantity demanded; $p_i$ and $\Delta p_i$ stand for the tariffs and their increments in time $i$; $p_j$ and $\Delta p_j$ denote the tariffs and their increments in time $j$.

Customer demand for electric loads can be categorized into fixed electric loads and transferable electric loads. Combined with the price elasticity matrix shown in Equation (14), the demand response model for electric loads is presented below.

$$\left\{\begin{array}{l}{P}_{\mathrm{e}\_\mathrm{load}}(t)=P_{\mathrm{e}\_\mathrm{load}}^{\mathrm{fhl}}(t)+P_{\mathrm{e}\_\mathrm{load}}^{\mathrm{shift}}(t)=L_i+L_{i}E{\displaystyle \frac{\Delta p_i}{p_i}}\\ 0\le P_{\mathrm{e}\_\mathrm{load}}^{\mathrm{shift}}(t)\le P_{\mathrm{e}\_\mathrm{load}, \max }^{\mathrm{shift}}(t)\\ {\displaystyle \sum _{t=1}^T{P}_{\mathrm{e}\_\mathrm{load}}^{\mathrm{shift}}(t)\Delta t=W_{\mathrm{e}\_\mathrm{load}}^{\mathrm{shift}}}\end{array}\right.$$

(14)

where $P_{\mathrm{e}\_\mathrm{load}}^{\mathrm{fhl}}(t)$ represents the fixed electric load; $P_{\mathrm{e}\_\mathrm{load}}^{\mathrm{shift}}(t)$ denotes the transferable electric load; $P_{\mathrm{e}\_\mathrm{load}, \max }^{\mathrm{shift}}(t)$ is the upper limit of the transferable electric load; $W_{\mathrm{e}\_\mathrm{load}}^{\mathrm{shift}}$ signifies the total amount of transferable electric load; and $\Delta t$ is the time step, set at 1 h.

2.4.2. Demand Response for Heat Loads

Hot water loads are the primary ones for which demand response is taken into account since heat loads involve temporal delay and fuzzy perception characteristics. The primary heat load regulator that keeps the water’s temperature within an acceptable range is temperature.

$$\left\{\begin{array}{l}{P}_{\mathrm{h}\_\mathrm{load}, \min }(t)\le P_{\mathrm{h}\_\mathrm{load}}(t)\le P_{\mathrm{h}\_\mathrm{load}, \max }(t)\\ P_{\mathrm{h}\_\mathrm{load}, \min }(t)=\gamma {\rho }_w{V}_c(t)\left(T_{h,\min }-T_{h,in}\right)\mathsf{\Delta }t\\ P_{\mathrm{h}\_\mathrm{load}, \max }(t)=\gamma {\rho }_w{V}_c(t)\left(T_{h,\max }-T_{h,in}\right)\mathsf{\Delta }t\end{array}\right.$$

(15)

where $P_{\mathrm{h}\_\mathrm{load}}(t)$ is the heat loads power; $P_{\mathrm{h}\_\mathrm{load}, \max }(t)$, $P_{\mathrm{h}\_\mathrm{load}, \min }(t)$ are the upper and lower limits of the heat loads power, respectively; $\gamma$ is the specific heat capacity of water; ${\rho }_w$ is the density of water; $V_c(t)$ is the volume of cold water injected; $T_{h,\max }$, $T_{h,\min }$ are the upper and lower limits of water temperature, respectively; $T_{h,in}$ is the initial water temperature.

The heat loads can be categorized into fixed heat loads and transferable heat loads with the expression shown in the following equation.

$$\left\{\begin{array}{l}{P}_{\mathrm{h}\_\mathrm{load}}(t)=P_{\mathrm{h}\_\mathrm{load}}^{\mathrm{fhl}}(t)+P_{\mathrm{h}\_\mathrm{load}}^{\mathrm{shift}}(t)\\ 0\le P_{\mathrm{h}\_\mathrm{load}}^{\mathrm{shift}}(t)\le P_{\mathrm{h}\_\mathrm{load}, \max }^{\mathrm{shift}}(t)\end{array}\right.$$

(16)

$${\displaystyle \sum _{t=1}^T{P}_{\mathrm{h}\_\mathrm{load}}^{\mathrm{shift}}(t)\Delta t=W_{\mathrm{h}\_\mathrm{load}}^{\mathrm{shift}}}$$

(17)

where $P_{\mathrm{h}\_\mathrm{load}}^{\mathrm{fhl}}(t)$ is the fixed heat load; $P_{\mathrm{h}\_\mathrm{load}}^{\mathrm{shift}}(t)$ is the transferable heat load; $P_{\mathrm{h}\_\mathrm{load}, \max }^{\mathrm{shift}}(t)$ is the upper limit of the transferable heat loads; $W_{\mathrm{h}\_\mathrm{load}}^{\mathrm{shift}}$ is the total amount of transferable heat loads.

3. IES Optimal Economic Scheduling Model

3.1. Objective Function

The primary objective of this study is to assess the overall operational cost of the IES, which includes considerations of the system’s energy procurement costs, stepped carbon trading expenses, and costs associated with wind and photovoltaic curtailment, as shown in the following equation.

$$C=\min (C_{\mathrm{buy}}+C_{{\mathrm{CO}}_2}+C_{\mathrm{cut}})$$

(18)

where $C_{\mathrm{buy}}$ is the cost of purchasing energy; $C_{{\mathrm{CO}}_2}$ is the cost of carbon trading; $C_{\mathrm{cut}}$ is the wind and photovoltaic curtailment cost.

The combined cost of purchased gas and electricity constitutes the system’s purchased energy costs, which are determined using the following equation.

$$C_{\mathrm{buy}}=C_{\mathrm{e}, \mathrm{buy}}+C_{\mathrm{g}, \mathrm{buy}}$$

(19)

$$\left\{\begin{array}{l}{C}_{\mathrm{e}, \mathrm{buy}}={\displaystyle \sum _{t=1}^T}{\alpha }_t{P}_{\mathrm{e},\mathrm{buy}}(t)\\ C_{\mathrm{g}, \mathrm{buy}}={\displaystyle \sum _{t=1}^T}{\beta }_t{P}_{\mathrm{g},\mathrm{buy}}(t)\end{array}\right.$$

(20)

where ${\alpha }_t$ is the electricity price in period $t$; $P_{\mathrm{e},\mathrm{buy}}(t)$ is the quantity of electricity purchased; ${\beta }_t$ is the gas price in period $t$; and $P_{\mathrm{g},\mathrm{buy}}(t)$ is the quantity of gas purchased.

Equation (10) displays the system carbon trading cost calculation, while the following shows the wind and photovoltaic curtailment cost.

$$C_{\mathrm{cut}}={\delta }_{\mathrm{WT}}\sum _{t=1}^T{P}_{\mathrm{WT},\mathrm{cut}}(t)+{\delta }_{\mathrm{PV}}\sum _{t=1}^T{P}_{\mathrm{PV},\mathrm{cut}}(t)$$

(21)

where ${\delta }_{\mathrm{WT}}$, ${\delta }_{\mathrm{PV}}$ are the unit cost of wind curtailment and unit cost of photovoltaic curtailment; $P_{\mathrm{WT},\mathrm{cut}}(t)$, $P_{\mathrm{PV},\mathrm{cut}}(t)$ are the wind curtailment cost and photovoltaic curtailment cost, respectively.

3.2. Restrictive Condition

3.2.1. WT and PV Unit Output Constraints

$$\left\{\begin{array}{l}0⩽P_{\mathrm{WT}}(t)⩽P_{\mathrm{WT}}^{\max }\\ 0⩽P_{\mathrm{PV}}(t)⩽P_{\mathrm{PV}}^{\max }\end{array}\right.$$

(22)

where $P_{\mathrm{WT}}^{\max }$, $P_{\mathrm{PV}}^{\max }$ are the upper limits of WT and PV output, respectively.

3.2.2. Energy Storage Unit Operational Constraints

$$\left\{\begin{array}{l}{W}_{s, \min }⩽W_s(t)⩽W_{s, \max }\\ 0⩽x_{s, \mathrm{cha}}(t)+x_{s, \mathrm{dis}}(t)⩽1\\ x_{s, \mathrm{cha}}(t)P_{s, \mathrm{cha}}^{\min }⩽P_t^{s,\mathrm{cha}}(t)⩽x_{s, \mathrm{cha}}(t)P_{s, \mathrm{cha}}^{\max }\\ x_{s, \mathrm{dis}}(t)P_{s, \mathrm{dis}}^{\min }⩽P_t^{s, \mathrm{dis}}(t)⩽x_{s, \mathrm{dis}}(t)P_{s, \mathrm{dis}}^{\max }\\ x_{s, \mathrm{cha}}(t)P_{s, \mathrm{cha}}^{\mathrm{down}}⩽P_{s, \mathrm{cha}}(t)-P_{s, \mathrm{cha}}(t-1)⩽x_{s, \mathrm{cha}}(t)P_{s, \mathrm{cha}}^{\mathrm{up}}\\ x_{s, \mathrm{dia}}(t)P_{s, \mathrm{dia}}^{\mathrm{down}}⩽P_{s, \mathrm{dia}}(t)-P_{s, \mathrm{dia}}(t-1)⩽x_{s, \mathrm{dai}}(t)P_{s, \mathrm{dia}}^{\mathrm{up}}\\ W_1^s=W_T^s\end{array}\right.$$

(23)

where $W_{s, \max }$, $W_{s, \min }$ are the upper and lower energy storage limits of the energy storage device; $x_{s, \mathrm{cha}}$, $x_{s, \mathrm{dis}}$ are the charging flag bit and discharging flag bit of the energy storage device; $P_{s, \mathrm{cha}}^{\max }$, $P_{s, \mathrm{cha}}^{\min }$ are the upper and lower energy storage power limits; $P_{s, \mathrm{dis}}^{\max }$, $P_{s, \mathrm{dis}}^{\min }$ are the upper and lower energy discharge power limits; $P_{s, \mathrm{cha}}^{\mathrm{up} }$, $P_{s, \mathrm{cha}}^{\mathrm{down}}$ are the upper and lower energy storage climbing power limits; $P_{s, \mathrm{dis}}^{\mathrm{up} }$, $P_{s, \mathrm{dis}}^{\mathrm{down}}$ are the upper and lower energy discharge climbing power limits; $W_1^s$, $W_T^s$ are the initial value and the end value of the energy storage device in a scheduling cycle, respectively.

3.2.3. Purchased Energy Power Constraints

$$\left\{\begin{array}{l}0⩽P_{\mathrm{e}, \mathrm{buy}}\left(t\right)⩽P_{\mathrm{e}, \mathrm{buy}}^{\max }\\ 0⩽P_{g, \mathrm{buy}}\left(t\right)⩽P_{g, \mathrm{buy}}^{\max }\end{array}\right.$$

(24)

3.2.4. Electric Power Balance Constraints

$$P_{\mathrm{e},\mathrm{buy}}\left(t\right)+P_{\mathrm{WT}}\left(t\right)+P_{\mathrm{PV}}\left(t\right)+P_{\mathrm{CHP},\mathrm{e}}\left(t\right)+P_{\mathrm{HFC},\mathrm{e}}\left(t\right)+P_{\mathrm{e},\mathrm{dis}}\left(t\right)=P_{\mathrm{e}\_\mathrm{load}}^{\mathrm{fhl}}(t)+P_{\mathrm{e}\_\mathrm{load}}^{\mathrm{shift}}(t)+P_{\mathrm{e},\mathrm{EL}}\left(t\right)+P_{\mathrm{e},\mathrm{cha}}\left(t\right)$$

(25)

where $P_{\mathrm{e},\mathrm{cha}}\left(t\right)$, $P_{\mathrm{e},\mathrm{dis}}\left(t\right)$ are the electric storage charging power and discharging power, respectively.

3.2.5. Thermal Power Balance Constraints

$$\begin{array}{l}{P}_{\mathrm{HFC},\mathrm{h}}\left(t\right)+P_{\mathrm{CHP},\mathrm{h}}\left(t\right)+P_{\mathrm{GB},\mathrm{h}}\left(t\right)+P_{\mathrm{EL},\mathrm{h}}\left(t\right)+P_{\mathrm{h},\mathrm{dis}}\left(t\right)=P_{\mathrm{h}\_\mathrm{load}}^{\mathrm{fhl}}(t)+\\ P_{\mathrm{h}\_\mathrm{load}}^{\mathrm{shift}}(t)+P_{\mathrm{h},\mathrm{cha}}\left(t\right)\end{array}$$

(26)

where $P_{\mathrm{h},\mathrm{cha}}\left(t\right)$, $P_{\mathrm{h},\mathrm{dis}}\left(t\right)$ are the TST heat storage power and exothermic power, respectively.

3.2.6. Gas Power Balance Constraints

$$P_{\mathrm{g},\mathrm{buy}}\left(t\right)+P_{\mathrm{MR},\mathrm{g}}\left(t\right)+P_{\mathrm{g},\mathrm{dis}}\left(t\right)=P_{\mathrm{g},\mathrm{Load}}\left(t\right)+P_{\mathrm{g},\mathrm{cha}}\left(t\right)+P_{\mathrm{g},\mathrm{CHP}}\left(t\right)+ P_{\mathrm{g},\mathrm{GB}}\left(t\right)$$

(27)

where $P_{\mathrm{g},\mathrm{cha}}\left(t\right)$, $P_{\mathrm{g},\mathrm{dis}}\left(t\right)$ are the GST filling power and deflating power, respectively; $P_{\mathrm{g},\mathrm{Load}}\left(t\right)$ is for the gas loads.

3.2.7. Hydrogen Equilibrium Constraints

$$P_{{\mathrm{EL}, \mathrm{H}}_2}(t)+P_{{\mathrm{H}}_2,\mathrm{dis}}(t)=P_{{\mathrm{H}}_2,\mathrm{MR}}(t)+P_{{\mathrm{H}}_2,\mathrm{HFC}}(t)+P_{{\mathrm{H}}_2,\mathrm{cha}}(t)$$

(28)

where $P_{{\mathrm{H}}_2,\mathrm{cha}}\left(t\right)$, $P_{{\mathrm{H}}_2,\mathrm{dis}}\left(t\right)$ are the hydrogen charging power and hydrogen discharging power of the HST, respectively.

4. IGDT-Based IES Optimized Scheduling Model

This study uses IGDT to predict the uncertainty in the amplitude of wind power fluctuation, to address the stochastic and intermittent character of wind and solar power output. The aim is to study the effect of uncertain parameters on the IES and to quantify the error between the predicted and actual values of uncertain parameters, provided that the preset objectives are met. The equation below illustrates a typical IGDT model [36,37].

$$\left\{\begin{array}{l}\min C(U,x)\\ \mathrm{s}.\mathrm{t}. H(U,x)=0\\ G(U,x)\ge 0\end{array}\right.$$

(29)

where $U$ is the uncertainty parameter; $x$ is the decision variable; $C(U,x)$ is the objective function; $H(U,x)$ and $G(U,x)$ are the equality constraints and inequality constraints, respectively.

This study characterizes the uncertainty of WT and PV output using the envelope constraint. The equation below displays the interval uncertainty model for solar and wind power.

$$\left\{\begin{array}{l}U({\alpha }_{\mathrm{WT}},P_{\mathrm{WT}, \mathrm{pr}}(t))=\left\{P_{\mathrm{WT}}(t):(1-{\alpha }_{\mathrm{WT}})P_{\mathrm{WT}, \mathrm{pr}}(t)\le P_{\mathrm{WT}}(t)\le (1+{\alpha }_{\mathrm{WT}})P_{\mathrm{WT}, \mathrm{pr}}(t)\right\}\\ U({\alpha }_{\mathrm{PV}},P_{\mathrm{PV}, \mathrm{pr}}(t))=\left\{P_{\mathrm{PV}}(t):(1-{\alpha }_{\mathrm{PV}})P_{\mathrm{PV}, \mathrm{pr}}(t)\le P_{\mathrm{PV}}(t)\le (1+{\alpha }_{\mathrm{PV}})P_{\mathrm{PV}, \mathrm{pr}}(t)\right\}\end{array}\right.$$

(30)

where $P_{\mathrm{WT}, \mathrm{pr}}(t)$, $P_{\mathrm{PV}, \mathrm{pr}}(t)$ are the predicted power of WT and PV; $P_{\mathrm{WT}}(t)$, $P_{\mathrm{PV}}(t)$ are the actual power of WT and PV; ${\alpha }_{\mathrm{WT}}$, ${\alpha }_{\mathrm{PV}}$ are the power fluctuation of WT and PV, respectively; the formula for both are shown below.

$$\left\{\begin{array}{l}{\alpha }_{\mathrm{WT}}={\displaystyle \frac{(P_{\mathrm{WT}, \mathrm{pr}}-P_{\mathrm{WT}})}{P_{\mathrm{WT}, \mathrm{pr}}}}\\ {\alpha }_{\mathrm{PV}}={\displaystyle \frac{(P_{\mathrm{PV}, \mathrm{pr}}-P_{\mathrm{PV}})}{P_{\mathrm{PV}, \mathrm{pr}}}}\end{array}\right.$$

(31)

In this paper, considering uncertainties from both WT and PV, IGDT leads to an increase in the number of objectives in the model when dealing with multiple uncertain variables. This consequently escalates the complexity of solving the model. Therefore, this paper employs a linear weighting approach to aggregate the uncertainties of WT and PV, as shown in Equation (32).

$$\phi ={\kappa }_{\mathrm{WT}}{\alpha }_{\mathrm{WT}}+{\kappa }_{\mathrm{PV}}{\alpha }_{\mathrm{PV}}$$

(32)

where $\phi$ is the combined uncertainty; ${\kappa }_{\mathrm{WT}}$, ${\kappa }_{\mathrm{PV}}$ are the weighting factors for WT uncertainty and PV uncertainty, respectively. The impact of wind uncertainty and PV uncertainty on the system is proportional to the total power they generate; specifically, the larger the total power generated, the greater the weighting factor. The formula for calculating the weighting factor is shown in the following equation.

$$\left\{\begin{array}{l}{\kappa }_{\mathrm{WT}}={\displaystyle \frac{{\displaystyle \sum _{t=1}^T{P}_{\mathrm{WT}}(t)}}{{\displaystyle \sum _{t=1}^T(P_{\mathrm{WT}}(t)+P_{\mathrm{WT}}(t))}}}\\ {\kappa }_{\mathrm{PV}}={\displaystyle \frac{{\displaystyle \sum _{t=1}^T{P}_{\mathrm{PV}}(t)}}{{\displaystyle \sum _{t=1}^T(P_{\mathrm{PV}}(t)+P_{\mathrm{PV}}(t))}}}\end{array}\right.$$

(33)

4.1. IGDT Scheduling Model Based on Risk Aversion

The goal of the risk aversion approach is to enhance the degree of uncertainty while gaining the ability to minimize risk at the expense of increased operating costs. The IDGT scheduling model based on risk aversion is shown in the following equation.

$$\left\{\begin{array}{l}\max \phi \\ \max C\le (1+{\beta }_{\mathrm{RM}})C_0\\ P_{\mathrm{WT}}^{\mathrm{ture}}(t)\in U({\alpha }_{\mathrm{WT}},P_{\mathrm{WT}}(t))\\ P_{\mathrm{PV}}^{\mathrm{ture}}(t)\in U({\alpha }_{\mathrm{PV}},P_{\mathrm{PV}}(t))\\ H(U,x)=0\\ G(U,x)\ge 0\end{array}\right.$$

(34)

where $C_0$ is the optimal economic operating cost of the IES with uncertainty equal to 0; ${\beta }_{\mathrm{RM}}$ is the cost deviation parameter under the risk aversion strategy.

The two-layer planning model in Equation (34) shows the maximum uncertainty when the costs do not exceed expectations, and the lower layer represents the operating costs that must not exceed the expected costs when the actual output of renewable energy varies within the uncertainty interval. Operating costs rise with increasing uncertainty. Therefore, the two-tier planning model can be changed to a single-tier planning model, as shown in the following equation.

$$\left\{\begin{array}{l}\max \phi \\ \max C\le (1+{\beta }_{\mathrm{RM}})C_0\\ P_{\mathrm{WT}}^{\mathrm{ture}}(t)=U({\alpha }_{\mathrm{WT}},P_{\mathrm{WT}}(t))\\ P_{\mathrm{PV}}^{\mathrm{ture}}(t)=U({\alpha }_{\mathrm{PV}},P_{\mathrm{PV}}(t))\\ H(U,x)=0\\ G(U,x)\ge 0\end{array}\right.$$

(35)

4.2. IGDT Scheduling Model Based on Risk Seeking

The goal of the risk-seeking strategy is to enable the decision-maker to use uncertainty as a tool for cost cutting. Considering the need to satisfy scheduling decision-makers while seeking opportunities for cost reduction despite increased risks, the IGDT optimization model is obtained, as shown in the following equation.

$$\left\{\begin{array}{l}\max \phi \\ \max C\le (1-{\beta }_{\mathrm{OM}})C_0\\ P_{\mathrm{WT}}^{\mathrm{ture}}(t)\in U({\alpha }_{\mathrm{WT}},P_{\mathrm{WT}}(t))\\ P_{\mathrm{PV}}^{\mathrm{ture}}(t)\in U({\alpha }_{\mathrm{PV}},P_{\mathrm{PV}}(t))\\ H(U,x)=0\\ G(U,x)\ge 0\end{array}\right.$$

(36)

where ${\beta }_{\mathrm{OM}}$ is the cost deviation parameter under the risk-seeking strategy.

By applying the model transformation procedure in Section 4.1, the model presented in Equation (36) can be changed into a single-layer optimization model, as indicated by the following equation:

$$\left\{\begin{array}{l}\max \phi \\ \max C\le (1-{\beta }_{\mathrm{OM}})C_0\\ P_{\mathrm{WT}}^{\mathrm{ture}}(t)=U({\alpha }_{\mathrm{WT}},P_{\mathrm{WT}}(t))\\ P_{\mathrm{PV}}^{\mathrm{ture}}(t)=U({\alpha }_{\mathrm{PV}},P_{\mathrm{PV}}(t))\\ H(U,x)=0\\ G(U,x)\ge 0\end{array}\right.$$

(37)

4.3. Model Linearization Process

The economic dispatch model of the IES, developed in this study to consider uncertainties in wind and solar power generation and efficient heat utilization of the EL, is formulated as a mixed-integer nonlinear model. It needs to be transformed into a mixed-integer linear model. For Equation (8), linearization is performed using piecewise linear approximation. The linearization process is outlined as follows.

Step 1: The original function is divided into $Q$ intervals by taking the $Q+1$ segmentation point $\left[r_1,r_2,\cdots ,r_{Q+1}\right]$ according to the desired accuracy.

Step 2: Add the $Q+1$ continuous auxiliary variable $\left[w_1,w_2,\cdots ,w_{Q+1}\right]$ with the $Q$ binary-type auxiliary variable $\left[z_1,z_2,\cdots ,z_{Q+1}\right]$ and satisfy Equation (38).

$$\left\{\begin{array}{l}{w}_1+w_2+\cdots +w_{Q+1}=1\\ z_1+z_2+\cdots +z_Q=1\\ w_1\ge 0,w_2\ge 0,\cdots ,w_{Q+1}\ge 0\\ w_1\le z_1,w_2\le z_1+z_2,\cdots ,w_{Q+1}\le z_Q\end{array}\right.$$

(38)

Step 3: Replace the nonlinear function with the linear expression shown in Equation (39).

$$\left\{\begin{array}{l}{P}_{\mathrm{e},\mathrm{buy}}={\displaystyle \sum _{q=1}^{Q+1}}{w}_q{r}_q\\ E_{\mathrm{e},\mathrm{buy},\mathrm{a}}={\displaystyle \sum _{q=1}^{Q+1}}{w}_q{E}_{\mathrm{e},\mathrm{buy},\mathrm{a}}(r_q)\end{array}\right.$$

(39)

Since Equation (10) is already a piecewise function, step 1 above can be omitted, and steps 2 and 3 can be combined for linear transformation.

The model proposed in this paper has been transformed into a mixed-integer linear model through segmented linearization. Therefore, the proposed model will be implemented in the MATLAB R2022b environment, and the CPLEX solver will be utilized to solve the problem. Compared to other solvers, CPLEX exhibits superior accuracy and robustness in solving linear programming problems, enabling rapid identification of optimal solutions for the optimization model.

5. Calculus Analysis

5.1. Parameter Setup

An arithmetic example is set up for verification in order to confirm the validity of the economic dispatch model proposed in this study considering the IES. Figure 2 and Figure 3 depict the load data and scenery forecasts within the IES. The optimized scheduling is executed in a 24 h cycle.

Table 1. Main equipment parameters.

Device	Capacity (kW)	Climbing Constraints (%)
EL	500	20
HFC	250	20
CHP	600	20
MR	250	20
GB	300	20
BES	450	20
TST	450	20
HST	200	20
GST	200	20

displays the operational characteristics of the system’s equipment;

Table 2. Time-sharing tariff.

Times (h)	Price of Electricity (CNY)
01:00–07:00, 23:00–24:00	0.38
08:00–11:00, 15:00–18:00	0.68
12:00–14:00, 19:00–22:00	1.20

displays the cost of time-shared power;

Table 3. Modeling of real carbon emissions.

Power Consumption Type			Gas Consuming Type
$a_1$	$b_1$	$c_1$	$a_2$	$b_2$	$c_2$
36	−0.38	0.0034	3	−0.004	0.001

displays the real carbon emission model; and

Table 4. Deterministic model optimization results.

	Scenario 1	Scenario 2	Scenario 3	Scenario 4
$E_{\mathrm{IES}}$ (kg)	4233.70	2819.94	2896.87	1636.02
$C_{{\mathrm{CO}}_2}$ (CNY)	1212.64	756.22	780.27	409.00
$C_{\mathrm{e}, \mathrm{buy}}$ (CNY)	715.68	808.26	0	0
$C_{\mathrm{g}, \mathrm{buy}}$ (CNY)	5695.11	4102.78	5510.46	3942.74
$C_{\mathrm{cut}}$ (CNY)	238.68	104.65	63.30	0
$C$ (CNY)	7862.11	5771.92	6354.03	4351.75

displays the price of natural gas, which is 0.35 CNY/kw·h. The cost per unit of wind and photovoltaic curtailment is 0.2 CNY/kW·h, and the carbon emission allowance per unit of electricity consumed by a coal-fired unit is ${\chi }_{\mathrm{e}}=0.798$ kg/kW·h. Similarly, the carbon emission allowance per unit of natural gas consumed by a natural gas-fired unit is ${\chi }_{\mathrm{g}}=0.385$ kg/kW·h [30,38].

The following six scenarios are set up for comparison in order to assess the superiority of the IES scheduling model put forward in this research.

Scenario 1: The IES does not take into account the working waste heat utilization of the EL, the demand response, or the uncertainty of the scenery output;

Scenario 2: The IES considers the utilization of operating waste heat from the EL without considering the demand response and without considering the uncertainty of the scenery output;

Scenario 3: The IES does not take into account the working waste heat utilization of the EL and considers the demand response without taking into account the scenario output uncertainty;

Scenario 4: The IES considers the utilization of operating waste heat from the electrolysis tanks, taking into account the demand response and disregarding the scenery output uncertainty;

Scenario 5: The IES considers the use of operating waste heat from the EL, considers the demand response, takes into account the WT and PV output uncertainty, and uses a risk aversion model for optimization;

Scenario 6: The IES considers the use of operating waste heat from the EL, considers demand response, takes into account the WT and PV output uncertainty, and uses a risk-seeking type for optimization.

5.2. Analysis of Deterministic Model Simulation Results

Scenarios 1 to 4 are solved under the deterministic model, and the results obtained are shown in Table 4.

5.2.1. Analysis of the Impact of EL Heat Use on the IES

The effective use of heat energy in the EL is taken into account in Scenarios 2 and 4, as indicated in Table 4. In comparison to Scenario 1, Scenario 2 lowers carbon emissions by 1413.76 kg, lowers the cost of carbon trading by 37.64%, lowers the cost of buying gas by 27.96%, raises the cost of buying electricity by 12.9%, and lowers the overall cost by 26.59%. Scenario 4 represents a reduction of 43.52% in carbon emissions, 47.58% in carbon trading expenses, 28.45% in gas purchase expenses, and 31.51% in total expenditures as compared to Scenario 3.

The efficient utilization of heat energy from the EL effectively reduces system carbon emission costs, as well as minimizes expenses associated with purchasing gas and penalties for WT and PV curtailment. This leads to a significant reduction in the total operating costs of the system.

Figure 4 and Figure 5 depict the scheduling outcomes for Scenarios 1 and 2, respectively. Figure 4b indicates that the primary heat production equipment of the IES are the HFC and the CHP. When the TST releases heat energy and the GB is used as a backup heat source, the heat demand of the IES is comparatively high between the hours of 1 and 10. The IES’s thermal energy requirement is mostly satisfied by CHP, HFC, and EL, as shown in Figure 5b. During the 2–7 h when there is a high demand for thermal energy, the GB only produces a tiny amount of energy.

The primary cause of the reduction in Scenario 2 carbon emissions and system expenses is the consideration of the EL’s heat utilization, which lowers the output of the system’s gas-consuming equipment while simultaneously increasing the EL’s efficiency of use and electrical energy demand, both of which enhance the system’s capacity to use wind energy while raising the system’s power purchases.

5.2.2. Analysis of Demand Response on the IES

Figure 6 and Figure 7 depict the variations in thermal and electric loads following IES demand response. After considering price-based demand response for electric loads, users can adjust their energy consumption strategies based on electricity prices during different time periods. This allows them to select suitable time periods to meet their energy requirements, thereby enhancing both their own energy efficiency and the overall power utilization rate of the system. The electric loads undergo a temporal shift due to price-based demand response; however, the overall loads before and after the shift remain unchanged. Figure 3 illustrates how a price-based demand response controls the electric loads profile. The lowest power costs occur during the 1–7 h and 24 h when the IES’s electric energy demand increases by 13.03% and 10.57%, respectively. Customers adjust their energy usage strategies to shift loads to periods with lower electricity prices during the 8–11 and 17–22 periods, as these are times when electricity prices are higher. As can be observed from Figure 8a, sufficient PV and WT generation occurs during the 12–16 h to increase the system’s wind energy consumption rate, leading to an increase in the electric load demand of the IES during this period following optimization.

This study sets the transferable heat loads to account for 10% of the total heat loads to ensure the comfort of users’ energy use, since users have greater reliability requirements for heat loads. The total loads in the loads curve’s peak hours drop by 6.32%, the total loads in the trough hours rise by 7.50%, and the peak-to-valley difference drops from 388.8 kW to 293.98 kW following the demand response of the thermal loads, as shown in Figure 7. This demonstrates that a tendency of peak shaving follows the demand response in the heat loads curve.

Table 4 illustrates that, when the demand response of the electric and heat loads is taken into consideration, Scenario 4 lowers its carbon emissions by 1183.92 kg when compared to Scenario 2, lowers the cost of bought gas by 3.90%, and lowers the total cost by 24.60%. When Figure 5b and Figure 8b are compared, it is evident that the IES, which takes into account the high desired utilization of EL heat, reduces the system’s natural gas demand because heat loads shift in the 2–6 h, which removes the need for GB outlets and increases the number of HFC outlets in the 12–16 h. It has been demonstrated that demand response can maximize the benefits of CHP equipment and improve the system’s capacity for carbon reduction.

5.3. IGDT-Based IES Scheduling Analysis

The deviation coefficients have an impact on the IES optimal scheduling findings that are based on IGDT.

Table 5. Calculation of the coefficient of deviation.

Risk-Seeking Strategy			Risk Aversion Strategy
Operational Cost (CNY)	Uncertainty	Deviation Factor	Uncertainty	Operational Cost (CNY)
4351.75	0	0	0	4351.75
4264.71	0.0186	0.02	0.0184	4438.78
4177.68	0.0376	0.04	0.0364	4525.82
4090.64	0.0583	0.06	0.0545	4612.85
4003.61	0.0851	0.08	0.0712	4699.89
3916.57	0.1327	0.10	0.0877	4786.92

presents the operating costs and uncertainty solution outcomes for two techniques: one based on a risk-seeking strategy and the other on a risk aversion strategy for decision optimization, each with varying deviation coefficients.

With a deviation coefficient of 0.02 as an example, when the IES’s dispatch is biased toward conservatism—that is, when risk aversion is selected—the corresponding uncertainty is 0.0184 and the operating cost is 4438.78 CNY. This means that when the real-time scenery output fluctuates within the positive 0.0184 range and below, it can guarantee that the IES’s operating cost is not greater than 4438.78 CNY at this deviation coefficient.

The corresponding uncertainty is 0.0186, and the operating cost is 4264.71 CNY when IES scheduling is biased toward opportunistic and a risk-seeking strategy is selected. In other words, when real-time scenery output fluctuates within the range of negative 0.0186 and above, it can be guaranteed that the IES operating cost is not higher than 4264.71 CNY at this deviation factor.

From a system operation perspective, using the operating cost of 4351.75 CNY at a deviation factor of 0 as a benchmark, it is evident that under a risk-seeking strategy, the minimum acceptable uncertainty of the IES increases with rising deviation coefficient, while the intervals of wind turbine and PV unit outputs continue to narrow. This risk-seeking behavior escalates system operational risk, concurrently reducing operational costs to a minimum of 3916.57 CNY. The compressed intervals reflect the balance between increased risk and lowered costs. Under the risk-seeking strategy, the decision-maker can release up to an upper limit of 435.18 CNY in the cost space. If the operating costs continue to decrease beyond this threshold, the system may fail due to changes in the operating mechanism stemming from excessive risk. The upper limit of the IES’s operating costs under the risk aversion strategy is 4786.92 CNY, with decision-makers reserving a maximum of 435.71 CNY for effective risk management.

Figure 9 and Figure 10 illustrate the trends in operational cost and uncertainty with deviation factor. An increase in the system’s scenic output uncertainty has a favorable effect on reducing the operating cost of the system under the risk-seeking strategy. Here, uncertainty is inversely related to operating cost and positively correlated with the deviation coefficient. Simultaneously, as uncertainty grows, so does the system’s risk.

The deviation factor rises together with the level of uncertainty and system operation expenses under the risk aversion strategy. The reason for this is that when utilizing a risk aversion scheduling technique, the decision-maker fights the impact of uncertainty on the system by raising operating costs since they feel that uncertainty may adversely move the objective under that direction of deviation.

6. Discussion

This paper focuses on enhancing the energy efficiency of an EL within an IES by recovering and utilizing its waste heat to meet heat load demands. It leverages the flexible characteristics of electric and thermal loads, allowing them to participate in demand response as flexible loads. This reduces pressure on energy supply during peak consumption hours, effectively improving the system’s economic and low-carbon characteristics. The study considers uncertainties associated with WT and PV, using IGDT theory to offer decision-makers with varying risk preferences a theoretical basis for selecting optimal scheduling strategies.

This paper serves as a valuable reference for research in the field of low-carbon economic dispatch in an IES, considering the impact of uncertainty. However, there are still aspects that require further research and expansion.

• This paper presents a basic simulation of thermal energy recovery from an EL and an HFC. The IES optimal scheduling model developed in this study will be enhanced in the future by more accurately modeling the thermal energy utilization of the EL and HFC, and by developing a comprehensive approach to thermal energy recovery.
• The paper does not consider the ladder gas price; however, in our future work, we plan to include it in the study and conduct a comprehensive analysis of the system’s carbon emissions and economic costs.
• In the future, we will continue to investigate uncertainties on both the source and load sides in the IES, thoroughly evaluate the advantages and disadvantages of current uncertainty approaches, and more comprehensively integrate theoretical findings with real-world implementations.
• In this paper, the optimal scheduling of the system under several typical day situations is not examined, as only one set of wind and load data is chosen. Different typical day scenarios exhibit varying wind and solar production, along with cooling, heating, and electric demands. These variations lead to different IES scheduling strategies. To gain a deeper understanding of IES scheduling algorithms across various typical day scenarios, we intend to expand the dataset in future work.
• In this paper, day-ahead scheduling has been conducted with a time scale of 1 h. Future research will explore intraday scheduling, incorporating real-time phases to optimize the IES across multiple time scales.

7. Conclusions

The integrated demand response of loads and the effective use of thermal energy from electrolysis tanks are taken into account in this study’s proposal for an IES low-carbon economic dispatch strategy. An IES dispatch model is constructed based on the IGDT under the two strategies of risk aversion and risk seeking, which can fulfill the risk preferences of different decision-makers, in order to balance the equilibrium of IES risk management and operating expenses. The simulation leads to the following conclusions:

• The efficient use of waste heat generated by the EL in the IES can improve energy efficiency, relieve pressure on the heat supply during peak heat load hours, and lessen the IES’s reliance on GB and CHP, all of which lower the system’s carbon emissions. When using the EL thermal energy-efficient utilization model, the system’s carbon output is decreased by 1413.76 kg and its operating costs are lowered by 26.59% when compared to the standard EL utilization model;
• When heat, electricity, gas, and hydrogen energy sources are coupled internally in the IES, the electric loads and heat loads act as flexible loads that can engage in demand response. This allows the electric loads to be transferred in a way that is reasonable based on the price of electricity, effectively reducing the heat loads’ peak and valley differences and increasing the system’s energy use flexibility. After considering the demand response of the loads, the carbon emission of the system is reduced by 1138.92 kg and the operating cost is reduced by 24.60%;
• IGDT is employed to simulate the uncertainty of WT and PV fluctuations and to quantify the error between predicted and actual values of WT and PV outputs. The IGDT-based IES optimal scheduling model can derive two scheduling strategies, risk seeking and risk aversion, that satisfy the risk preferences of decision-makers. This model achieves a balance between IES risk control and operational costs while effectively addressing the stochastic nature of WT and PV outputs.