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.
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].
where
is the uncertainty parameter;
is the decision variable;
is the objective function;
and
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.
where
,
are the predicted power of WT and PV;
,
are the actual power of WT and PV;
,
are the power fluctuation of WT and PV, respectively; the formula for both are shown below.
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).
where
is the combined uncertainty;
,
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.
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.
where
is the optimal economic operating cost of the IES with uncertainty equal to 0;
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.
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.
where
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:
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 intervals by taking the segmentation point according to the desired accuracy.
Step 2: Add the
continuous auxiliary variable
with the
binary-type auxiliary variable
and satisfy Equation (38).
Step 3: Replace the nonlinear function with the linear expression shown in Equation (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 displays the operational characteristics of the system’s equipment;
Table 2 displays the cost of time-shared power;
Table 3 displays the real carbon emission model; and
Table 4 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
kg/kW·h. Similarly, the carbon emission allowance per unit of natural gas consumed by a natural gas-fired unit is
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 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.