Optimization Scheduling Method for Integrated Energy System Considering Weight Sensitivity and Flexible Load

Abstract

The multiobjective optimization problem in the integrated energy system (IES) is crucial for achieving optimal scheduling of the system. This paper proposes a weight optimization method for IES scheduling based on the weight sensitivity (WS) index. First, an IES coupling network model is established, considering the network structure of the power grid, natural gas network, and heating network. The time-of-use price is determined based on generation resources to guide the demand for flexible load (FXL). Next, the weights of the multiobjective function are optimized using the coefficient of variation of the WS index. The analytic hierarchy process (AHP) is utilized to achieve multiobjective function weight optimization, considering environmental friendliness and installed capacity. The optimal scheduling model is solved using CPLEX, and the results of different weight optimization methods are compared. The change in the carbon emission (CE) index under the increasing permeability trend is analyzed, and the guiding effect of intraday prices based on power generation resources on FXL is studied. The simulation results demonstrate that: (1) Single-objective weight optimization based on the WS index reduces the objective function value by 0.47%, and the objective function value based on AHP, considering multiobjective weight optimization, decreases by 10.31%, indicating that the WS index is suitable for comprehensive weight optimization. (2) As the IES permeability increases by 46.31%, the IES CE decreases by 94.69%, and the demand for energy storage increases by 7.32%. (3) Under the guidance of time-of-use prices based on power generation resources, 51.47% of FXL autonomously shifts power consumption time, reducing electricity purchase fees by 24.61%. This paper provides valuable insights for utilizing the WS index to optimize IES scheduling.

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

1. Introduction

The integrated energy system (IES) has garnered significant attention for its capacity to efficiently utilize various forms of energy and capitalize on their complementary characteristics [1, 2], the complexity of scheduling tasks within the energy network stems from diverse energy sources, and adaptable energy conversion processes [3]. In this competitive landscape, the effectiveness and efficiency of IES optimal scheduling outcomes hinge on successfully optimizing multiobjective functions involving multiple stakeholders.

In the context of the IES, integrating power generation, consumption, and various energy service providers necessitates the consideration of an increasingly diverse range of factors during the scheduling optimization process [4]. These factors add complexity to the task and underscore the necessity of comprehensive consideration when devising optimal scheduling strategies for IES. Addressing the fluctuations in power generation due to the rise in renewable energy (RE) penetration rate, attention has been drawn to the scheduling of energy storage power stations. Sun et al. [5] considers fuel cells, batteries, thermal storage, and heat pumps, composing a micro combined heat and power (CHP) system. It leverages the advantages of energy storage to enhance the overall efficiency and sustainability performance of the system. Chen et al. [6] studied an electric gas thermal IES system that includes integrated demand response (IDR), virtual energy storage (VES), and RE. By establishing VES, the operational efficiency and RE penetration level of power plants were improved. Chen et al. [7] explores the application and scheduling methods of shared energy storage (SES) in IES systems, utilizing ES to reduce IES operating costs and improve RE consumption. But the working mode of ES is not limited to this. Due to the flexible characteristics of charging and discharging of ES, ES can not only serve as a flexible resource to improve the operational efficiency of energy networks, but also participate in energy trading as an important profit-making entity. On the other hand, with the advancement of low-carbon energy networks, carbon emission (CE) indicators have gradually become an important factor that IES needs to consider [8]. Xu et al. [9] proposed an integrated scheduling study for low-carbon park IES, which improved the overall reliability and energy efficiency of the system. Huang et al. [10] studied a multi-energy complementary model based on conditional value at risk (CVaR), and studied the optimal scheduling results of IES under different conditions when considering demand response and CEs. Liu et al. [11] established a two-level scheduling model based on the CE flow model to study the incentive effect of IES carbon trading.

Due to the multi-agent architecture in IES, the selection of optimization methods in IES scheduling work will affect the rationality and accuracy of scheduling results [12]. The swarm intelligence optimization algorithm is a typical type of optimization algorithm that achieves optimization iteration by imitating biological behavior [13]. Nemati, Braun, and Tenbohlen [14] studies the economic scheduling problem in microgrids based on genetic algorithms and mixed integer linear programming (MILP), improving the limitations of MILP network topology. Yang et al. [15] established a cogeneration system based on a typical industrial park and solved the model using chaotic particle swarm optimization algorithm. However, in research, it was found that due to the multiobjective nonlinear characteristics of IES, swarm intelligence optimization algorithms are prone to dimensional disasters [16]. In order to solve multiobjective optimization problems, pareto frontier methods have received widespread attention. Deb et al. [17] proposed a sorting principle for pareto frontiers, and the proposed pareto frontiers improvement scheme focuses more on the optimal solution neighborhood. Wang et al. [18] proposes multiobjective cross entropy (MOCE) by combining cross entropy and importance sampling techniques, transforming uncertainty into deterministic constraints, and the method has universality for multiobjective algorithms. However, the pareto frontier method places more emphasis on the ideal situation in the process of seeking the optimal solution [19]. In order to consider the competition and rational choices of different entities in the actual operation of the network, game theory has received extensive research [20, 21]. Ma et al. [22] used an optimization model based on Stackelberg game to establish a cogeneration microgrid model and implemented microgrid electricity pricing based on differential evolution heuristic algorithm. Chen et al. [23] uses noncooperative games to achieve the optimal operational strategy of a comprehensive energy system and uses the characteristics of noncooperative games to depict the interest relationships between multiple regions. The above methods have shown good results in scheduling optimization between different agents and can depict the cooperation and competition relationships between different agents. Sun and You [24] discusses the application of machine learning and data-driven control in the context of increasing system scale and uncertainty, demonstrating the advantages and future development potential of machine learning and data-driven over traditional model–based approaches in terms of flexibility, economy, and other aspects. However, they do not pay attention to the relationship between the weight of multiobjective function indicators and the value of the objective function. On the other hand, the increasing complexity of the IES network structure also makes the solution of the IES scheduling problem more challenging.

With the increasing participation of various entities in energy trading within the IES, optimizing the multiobjective function while considering a variety of indicators becomes the central challenge in IES optimal scheduling. In traditional IES optimization and scheduling studies, there is a lack of consideration for network architecture. However, due to the expansion of IES, the impact of the network structure of the energy system on IES can no longer be ignored. To address this issue, this paper establishes a network model for IES and studies the optimization scheduling problem of IES considering the impact of power flow. Based on this, innovative ideas for multiobjective weight optimization and the positive effects of flexible loads (FXLs) on IES are discussed. This paper focuses on optimizing the scheduling of the IES with a specific emphasis on its network structure. It starts by investigating the relationship between the objective weight and the objective function value in the multiobjective function and proposes an IES optimal scheduling method based on the weight sensitivity (WS) index to optimize the objective function weight. The effects of single-objective optimization weight and multiobjective optimization weight are compared when considering the WS index, and the influence mechanism of the CE index and FXL on IES scheduling is discussed. In contrast to other optimization methods, this paper introduces a novel weight optimization approach based on the WS indicator, which extracts WS characteristics from the results of single-objective optimization calculations and utilizes evaluation methods for comprehensive assessment to achieve weight optimization. This approach has the potential to enhance the efficiency of weight allocation for multiobjective functions. The research findings presented in this paper will provide valuable insights for subsequent IES scheduling through multiobjective function optimization weight. The main contributions of this paper are as follows:

1. Based on the IES optimal scheduling model of the electricity–gas–heat node coupling network, the CE model considering RE CE, thermal power generation (TPG) CE, ES CE, and IES CE in construction and operation is established. The CE index is added to the IES multiobjective function optimization weight, and the change of CE and the growth of ES demand in the process of RE permeability improvement are studied.

2. This paper proposes an IES multiobjective function weight optimization method based on WS index, analyzes the advantages and disadvantages of WS index in the process of optimizing the objective function, optimizes the multiobjective function weight based on a single WS index, further uses analytic hierarchy process (AHP) to optimize the multiobjective function weight combined with environmental friendliness and installed capacity, compares the differences between the two methods in the optimization of the objective function value, and gives suggestions and potential research directions for further study of WS index in multiobjective function optimization work.

3. The guiding mechanism of FXL power purchase behavior based on time-of-use price is established to simulate the trading scenario in which power users choose their own time-of-use and power demand. The time-of-use price based on the fluctuation of power generation is used to realize the time sequence transfer of the peak energy demand of IES, and the significant role of FXL in alleviating the pressure of IES power supply and reducing the power purchase fee of users is analyzed.

The remaining chapters of this paper are arranged as follows: The second section introduces the IES coupling network model and equipment model, providing the mathematical model for the IES network, objective function, and constraint conditions. The third section analyzes the influencing factors of multiobjective function optimization, defines the WS index, presents objective function optimization ideas, and outlines the research methods for index comparison. The fourth section presents the simulation results of the IES coupling network, summarizes the application effects and potential areas of the WS index in optimizing the objective function weight, discusses the impact of permeability on the IES CE index, and analyzes the guiding effect of intraday power prices based on energy supply fluctuations on FXL behavior. The fifth section concludes by summarizing the contributions and findings of this paper. The variables used in this article are shown in Table A1.

2. IES Modeling

The IES model proposed in this article encompasses the integration of the power network, natural gas network, and heating network. These three energy networks are interconnected and mutually supportive, allowing for the efficient utilization of energy during peak or low-demand periods. Moreover, the IES model incorporates the use of ES and FXL, which play crucial roles in alleviating energy supply pressures during peak demand periods. The ES helps store excess energy during low-demand periods for later use, while the FXL enables the flexible adjustment of energy consumption patterns to match supply and demand. These features enhance the overall resilience and reliability of the IES model, ensuring a balanced and optimized energy supply.

2.1. IES Network Model

In IES, the energy characteristics of different networks make their complementarity more prominent. Energy is transmitted between multiple networks through CHP and electric boiler (EB). The architecture and interrelationships of each network are shown in Figure 1.

[figure(s) omitted; refer to PDF]

The IES architecture shown in Figure 1 is divided into three energy networks: electricity, natural gas, and heat. The power system includes TPG, photovoltaic (PV), wind power (WP), and CHP as power sources, with loads including field load (FML) and FXL. Gas source (GS) is used for gas supply in the natural gas system, while gas load (GL) and CHP are used as natural GLs. In the heating system, CHP, heat source (HS), and EB are used as HSs for heating, while heat load (HL) is the consumer of heat.

In the IES established in this article, mathematical models of each device are established to characterize their energy transmission behavior in different energy networks. CHP and EB are the main energy exchange devices, while ES and FXL mainly play a role in storing and transferring energy in a timely manner.

2.1.1. CHP

The CHP unit includes two parts: a gas turbine and a waste heat filter. While the gas turbine generates electricity, the waste heat boiler uses waste heat for heating, which can achieve simultaneous production of electricity and heat and improve gas utilization efficiency. In this article, the CHP unit is based on power generation and consumes natural gas to achieve power and heat supply.

2.1.2. ES

ES has diverse application scenarios in the comprehensive energy system model, such as suppressing the volatility of new energy generation, reducing load fluctuation pressure through peak shaving and valley filling processes, and considering low power grid prices for buying, selling, and arbitrage [25]. The ES model established in the article is an electrochemical ES. In order to achieve the research and optimization of the objective function weight in the article, the application mode of the ES is not limited, but is controlled through the setting of the objective function weight.

2.1.3. EB

In order to strengthen the energy conversion method and flexibility from the power system to the thermal system, make the connections between different networks closer, and improve energy utilization efficiency, EB [26] are added to achieve the conversion of power to thermal power.$$\begin{array}{}\text{(1)}& H_{\text{EB}}=P_{\text{EB}}{\eta }_{EB},\end{array}$$where P_EB is the power consumption of the EB, H_EB is the heat generated by the EB, and η_EB is the efficiency of EB in converting electricity to heat.

2.1.4. Nature Gas Compressor

Natural gas compressors usually include gas compressors and electric compressors. Due to the low energy required for compressor operation, which does not affect the analysis of the results in this article, a simplified compressor model is used, ignoring the energy consumed. The expression is formulated as:$$\begin{array}{}\text{(2)}& p_j={\rho }_c{p}_n,\end{array}$$where p_j and p_n are the pressures at the outlet and inlet of the compressor, respectively, and ρ_c is the compression ratio of the compressor, which is constant without considering the consumption characteristics.

2.2. Objective Function

The optimization objective of this article is to minimize the objective function, which takes into account the influence of various factors such as power generation, consumption, energy service provision, and new energy power generation aggregator. The variables are set as weights of eight indicators, and the greater the weight, the greater the tendency towards this indicator. The objective function are formulated as:$$\begin{array}{}\text{(3)}& \begin{array}{c}\text{MIN}F=r_1{f}_{\mathrm{c},\mathrm{T}}+r_2{f}_{\mathrm{c},\mathrm{E}}+r_3{f}_{\mathrm{c},\mathrm{N}}+r_4{f}_{\mathrm{C}}+r_5{f}_{\mathrm{c},\mathrm{L}}+r_6{f}_{\mathrm{m},\mathrm{T}}+r_7{f}_{\mathrm{m},\mathrm{N}}+r_8{f}_{\mathrm{m},\mathrm{E}}\end{array}.\end{array}$$

r₁ to r₈ represent the weights of different objective functions and are also the key to the multiobjective optimization problem discussed in this paper. f_c,T, f_c,E, f_c,N, f_C, f_c,L, f_m,T, f_m,N, and f_m,E are the TPG cost, ES cost, RE energy abandonment, CE, TPG profit, ES profit, RE profit, and FXL cost, respectively.

2.2.1. Cost and Benefits of TPG

$$\begin{array}{}\text{(4)}& f_{\mathrm{T}}=C_{\mathrm{b},\mathrm{T}}+C_{\mathrm{o},\mathrm{T}},\end{array}$$$$\begin{array}{}\text{(5)}& C_{\mathrm{o},\mathrm{T}}=\sum _{i=1}^{24}{m}_{\mathrm{c}}{P}_{\mathrm{T}}^t,\end{array}$$$$\begin{array}{}\text{(6)}& f_{\mathrm{m},\mathrm{T}}=\sum _{t=1}^{24}{m}_{\mathrm{p}}^t{P}_{\mathrm{T}}^t,\end{array}$$where f_T and f_m,T are the cost and revenue of TPG, respectively. C_b,T and C_o,T are the construction and operating costs of TPG, respectively. $P_T^t$ is the power generated by the TPG during the t period. m_c is the unit power generation cost of TPG. $m_p^t$ is the time-of-use electricity price during the t period.

2.2.2. Cost and Benefits of ES

The cost of ES includes construction costs and operation and maintenance costs, benefiting from purchasing electricity at low prices and selling electricity at high prices are formulated as:$$\begin{array}{}\text{(7)}& f_{\mathrm{c},\mathrm{E}}=\frac{C_{\mathrm{b},\mathrm{E}}+C_{\mathrm{o},\mathrm{E}}\cdot r\cdot {1+r}^L}{{1+r}^L-1},\end{array}$$$$\begin{array}{}\text{(8)}& C_{\mathrm{b},\mathrm{E}}=\frac{m_{\mathrm{P}}\cdot P_{\mathrm{E},\mathrm{N}}+m_{\mathrm{S}}\cdot S_{\mathrm{E},\mathrm{N}}}{L},\end{array}$$$$\begin{array}{}\text{(9)}& C_{\mathrm{o},\mathrm{E}}=\frac{\sum _{i=1}^{n_{\mathrm{E}}}\sum _{t=1}^{24}{C}_{\mathrm{R}}\cdot m_{\mathrm{S}}\cdot S_{\mathrm{E},\mathrm{N}}}{{1+r}^L},\end{array}$$$$\begin{array}{}\text{(10)}& f_{\mathrm{m},\mathrm{E}}=\sum _{t=1}^{24}{m}_{\mathrm{p}}^t{P}_{\mathrm{E}}^t,\end{array}$$where f_c,E is the cost of ES. C_b,E and C_o,E are the construction and maintenance costs of ES, respectively. r is the discount rate. L is the payback period of ES investment. m_p and m_s are the unit price of power and capacity of the ES, respectively. C_R is the conversion coefficient between the operation and maintenance costs of ES and the unit capacity unit price. S_E,N and P_E,N are ES rated capacity and ES rated power. n_E is the number of ES.

2.2.3. Energy Abandonment Rate (AR) and Income of RE

The RE consumption and revenue indicators represent the utilization rate of RE power generation and the revenue of RE itself, its constraints are formulated as [27]:$$\begin{array}{}\text{(11)}& f_{\mathrm{c},\mathrm{N}}=\sum _{i=1}^{n_{\text{PV}}}{P}_{\text{PV},\max }^t-P_{\text{PV},i}^t+\sum _{i=1}^{n_{\text{WP}}}{P}_{\text{WP},\max }^t-P_{\text{WP},i}^t,\end{array}$$$$\begin{array}{}\text{(12)}& f_{\mathrm{p},\mathrm{N}}=\sum _{i=1}^{n_{\text{PV}}}{C}_{\mathrm{b},\text{PV},i}^t+\sum _{i=1}^{n_{\text{WP}}}{C}_{\mathrm{b},\text{WP},i}^t,\end{array}$$$$\begin{array}{}\text{(13)}& f_{m,N}=\sum _{t=1}^{24}{m}_{\mathrm{p}}^t{P}_{\mathrm{N},\text{PV}}^t+\sum _{t=1}^{24}{m}_{\mathrm{p}}^t{P}_{\mathrm{N},\text{WP}}^t-f_{\mathrm{p},\mathrm{N}},\end{array}$$where f_c,N, f_p,N, and f_m,N are RE power abandonment penalty, RE cost, and RE power sales profit, respectively. $C_{b,PV,i}^t$ and $C_{b,\wp ,i}^t$ are RE construction costs and RE power generation and sales profits. $P_{PV,\max }^t$, $P_{PV,i}^t$, $P_{\wp ,\max }^t$, and $P_{\wp ,i}^t$ are the maximum generation power of PV and WP and the generation power during t period. n_PV and n_WP are the number of PV and WP.

2.2.4. Consumer Side Electricity Purchase Cost

The cost of purchasing electricity on the user side includes the cost of purchasing electricity for fixed loads and FXL.$$\begin{array}{}\text{(14)}& f_{\mathrm{c},\mathrm{L}}=\sum _{t=1}^{24}{m}_{\mathrm{p}}^t{P}_{\mathrm{L},i}^t+P_{\mathrm{L},\text{FXL}}^t,\end{array}$$where f_c,L is the electricity purchase cost of power users. $P_{L,i}^t$ and $P_{L,FXL}^t$ are the fixed load and FXL electricity demand during time t.

Due to the fact that the electricity consumption on the load side is not a fixed data in practical applications, some civil loads may generate flexible electricity demand based on changes in electricity prices [28]. Therefore, the load in this article is divided into two parts: fixed load and FXL. The fixed load demand has a fixed electricity demand at different times within 24 h, while FXL has a constant electricity consumption within 24 h, but the electricity consumption time is chosen by the user, such as the autonomous charging behavior of smart appliances [29]. Therefore, the load model in this article are formulated as [30]:$$\begin{array}{}\text{(15)}& P_{\mathrm{L}}^t=P_{\mathrm{L},\mathrm{F}}^t+P_{\mathrm{L},\mathrm{a}}^t,\end{array}$$$$\begin{array}{}\text{(16)}& P_{\mathrm{L},\mathrm{a}}=\sum _{t=1}^{24}{P}_{\mathrm{L},\mathrm{a}}^t,\end{array}$$where $P_L^t$ is the hourly power consumption of power users. $P_{L,F}^t$ and $P_{L,a}^t$ are the power of FML and FXL. P_L,a is the total electricity demand of FXL within 24 h, and the total electricity demand of FXL cannot be changed.

This paper employs linear programming methods to allow the FXL to autonomously select electricity usage times throughout the day. The advantage of this approach is that it reduces the total electricity costs for the FXL, while enabling the IES to schedule the use of electrical energy during periods of energy redundancy for the FXL, thereby, enhancing the overall energy utilization efficiency of the system.

2.2.5. CE

In this article, IES CE mainly includes the construction and operation CE of the power generation side, the construction and operation CE of ES, and the operation CE of functional systems.$$\begin{array}{}\text{(17)}& \begin{array}{c}{f}_{\mathrm{c}}=C_{\mathrm{T},\mathrm{b}}^{\mathrm{c}}+C_{\mathrm{T},\mathrm{o}}^{\mathrm{c}}+C_{\mathrm{g},\mathrm{o}}^{\mathrm{c}}+C_{\text{PV},\mathrm{b}}^{\mathrm{c}}+C_{\text{WP},\mathrm{b}}^{\mathrm{c}}+C_{\mathrm{E},\mathrm{o}}^{\mathrm{c}}+C_{\mathrm{s},\mathrm{o}}^{\mathrm{c}}\end{array},\end{array}$$where f_c is the IES CE. $C_{T,b}^c$, $C_{T,o}^c$, $C_{g,o}^c$, $C_{PV,b}^c$, $C_{\wp ,b}^c$, $C_{E,o}^c$, and $C_{s,o}^c$ are CE from TPG construction, TPG operation, natural gas and thermal system operation, PV and WP construction, ES operation, and grid operation.

2.3. IES Optimization Scheduling Constraints

2.3.1. Power Network Constraints

To ensure the energy balance of the power generation side, consumption side, and equipment losses in the power grid, the power balance constraints of the power grid are formulated as [31]:$$\begin{array}{}\text{(18)}& \text{Power\hspace{0.17em}balance}:P_{i,j}^t-P_L^t-P_{PV}^t-P_{WP}^t-P_T^t-P_{CHP}^t+P_b^t+P_E^t+P_{load}^t=0,\end{array}$$$$\begin{array}{}\text{(19)}& \text{Voltage\hspace{0.17em}constraint}:{\nu }_{\min }\le {\nu }_i^t\le {\nu }_{\max },\end{array}$$$$\begin{array}{}\text{(20)}& \text{Current\hspace{0.17em}constraint}:I_{\min }\le I_i^t\le I_{\max },\end{array}$$where $P_{i,j}^t$ and $P_L^t$ are the line flow power and user power from node i to node j. v_max, v_min, $v_i^t$, I_max, I_min, and $I_i^t$ are the upper limit of the node voltage and current after relaxation, node voltage, and line current in t period, respectively.

The ES constraint needs to consider the charge discharge characteristics, power and capacity constraints, and discharge depth constraints. The specific constraints are formulated as:$$\begin{array}{}\text{(21)}& \text{ES\hspace{0.17em}power\hspace{0.17em}balance\hspace{0.17em}constraint}:S_{E,1}=S_{E,24},\end{array}$$$$\begin{array}{}\text{(22)}& \text{ES\hspace{0.17em}charge\hspace{0.17em}discharge\hspace{0.17em}depth\hspace{0.17em}constraint}:c_{\min }\times S_{E,N}\le S_E^t\le c_{\max }\times S_{E,N},\end{array}$$$$\begin{array}{}\text{(23)}& \text{ES\hspace{0.17em}power\hspace{0.17em}constraint}:-P_{\max }\le P_{\mathrm{E}}^t\le P_{\max },\end{array}$$$$\begin{array}{}\text{(24)}& \text{ES\hspace{0.17em}ampere\hspace{0.17em}hour\hspace{0.17em}constraint}:P_{\mathrm{E}}\le c_{\mathrm{r}}\times S_{\mathrm{E},\mathrm{N}},\end{array}$$where S_E,N and $S_E^t$ are ES rated capacity and ES capacity state, respectively. c_min and c_max are the upper and lower limits of ES SoC power. c_r is the charge discharge rate of ES. P_max and $P_E^t$ are the upper limit of ES power and the charging power of ES in t period, respectively.

The fixed generation model is adopted for RE and the daily RE generation curve is generated based on historical data as the maximum generation power of RE, limiting the actual generation power of RE to controllable constraints are formulated as:$$\begin{array}{}\text{(25)}& \text{WP\hspace{0.17em}output\hspace{0.17em}constraint}:0\le P_{\text{PV}}^t\le P_{\text{PV},\max },\end{array}$$$$\begin{array}{}\text{(26)}& \text{PV\hspace{0.17em}output\hspace{0.17em}constraint}:0\le P_{\text{WD}}^t\le P_{\text{WD},\max },\end{array}$$where P_PV,max and P_WP,max are the maximum power generation of PV and WP, respectively.

2.3.2. Natural Gas Network Constraints

The natural gas transportation model used in this paper includes natural GS, natural gas pipeline, compressor, and natural GL. Among them, the natural GS provides natural gas for the natural GL in the natural gas network, and the natural gas pipeline plays the role of transporting natural gas. Due to the pressure drop effect during natural gas transmission, compressors are installed along the natural gas pipeline to keep the gas node pressure within the allowable range and reduce the possibility of gas transmission blockage during peak GL [32]. Figure 2 show the relationship of each part as:

[figure(s) omitted; refer to PDF]

The natural gas network constraints are formulated as:$$\begin{array}{}\text{(27)}& \text{Natural\hspace{0.17em}gas\hspace{0.17em}balance}:g_{\mathrm{L}}^t+g_{\text{CHP}}^t-g_{\mathrm{s}}^t-g_{i,j}^t=0,\end{array}$$$$\begin{array}{}\text{(28)}& \text{Pipe\hspace{0.17em}air\hspace{0.17em}pressure\hspace{0.17em}constraint}:u_i^t-u_i^{t-1}=n_{1,i,j}{g}_{i,j}^t+g_{j,i}^t,\end{array}$$$$\begin{array}{}\text{(29)}& \text{Barometric\hspace{0.17em}coupling\hspace{0.17em}constraint}:g_{i,j}^t=n_{2,i,j}\sqrt{{u_m^t}^2-{u_n^t}^2},\end{array}$$$$\begin{array}{}\text{(30)}& \text{Nodal\hspace{0.17em}pressure\hspace{0.17em}constraint}:u_{\min }\le u_i^t\le u_{\max },\end{array}$$$$\begin{array}{}\text{(31)}& \text{Flow\hspace{0.17em}direction\hspace{0.17em}constraint}:u_i^t\ge u_j^t,\end{array}$$where $g_L^t$, $g_{CHP}^t$, $g_s^t$, and $g_{i,j}^t$ are the gas consumption of natural GL, CHP gas consumption, GS output, and natural gas flow input at nodes. u_max, u_min, and $u_i^t$ are the upper and lower pressure limits of node i of the natural gas network and the pressure in period t, respectively. $g_{i,j}^t$ is the natural gas flow from pipeline i to pipeline j in period t. n_1,i,j and n_2,i,j are pipeline characteristic parameters.

2.3.3. Heating Network Constraints

In the heating network, multiple HSs supply heat to the load at the same time, and the heating medium is the include heat supply pipe and water return pipe. The structure of the heating network is shown in Figure 3 [33].

[figure(s) omitted; refer to PDF]

In the heating network, the hot water is delivered to the HL through the supply pipe. After the heating is completed, the hot water with reduced temperature is delivered to the HS through the return pipe for heating to realize the heating cycle. The constraints of heating network are formulated as [34]:$$\begin{array}{}\text{(32)}& \text{Network\hspace{0.17em}equilibrium\hspace{0.17em}equation}:H_{\mathrm{S}}^t+H_{\text{CHP}}^t+H_{\text{EB}}^t-H_{\mathrm{L},\mathrm{p}}^t-H_i^t=0,\end{array}$$$$\begin{array}{}\text{(33)}& \text{Pipe\hspace{0.17em}heat\hspace{0.17em}loss}:H_{\mathrm{L},\mathrm{p}}^t=C_w{\eta }_{\mathrm{L}}{T}_{\text{in}}^t-T_{\text{out}}^t,\end{array}$$$$\begin{array}{}\text{(34)}& \text{EB\hspace{0.17em}output\hspace{0.17em}constraint}:H_{\text{EB},\min }\le H_i^t\le H_{\text{EB},\max },\end{array}$$$$\begin{array}{}\text{(35)}& \text{CHP\hspace{0.17em}generation\hspace{0.17em}equation}:P_{\text{CHP}}={\eta }_{\mathrm{g},\mathrm{p}}{g}_{\text{CHP}},\end{array}$$$$\begin{array}{}\text{(36)}& \text{Residual\hspace{0.17em}heat\hspace{0.17em}recovery\hspace{0.17em}equation}:H_{\mathrm{t}}=1-{\eta }_{\mathrm{L}}-{\eta }_{\mathrm{l}}/{\eta }_{\mathrm{L}}{P}_{\text{CHP}},\end{array}$$$$\begin{array}{}\text{(37)}& \text{CHP\hspace{0.17em}heating\hspace{0.17em}equation}:H_{\text{CHP}}=H_{\mathrm{t}}{\eta }_{\mathrm{r}}{\eta }_{\mathrm{h}},\end{array}$$where $H_{\text{S}}^t,H_{\text{CHP}}^t,H_{\text{EB}}^t,H_{\text{L,p}}^t,\text{and}{H}_i^t$, respectively, represent heat loss and HL from HS, CHP, EB, heat supply pipe, and water return pipe. C_w is the heat capacity of water. η is the heat loss coefficient of the pipeline. $T_{\text{in}}^t\text{\hspace{0.17em}and\hspace{0.17em}}{T}_{\text{\hspace{0.17em}out}}^t$ are the inlet water temperature and outlet water temperature of the pipeline, respectively. H_EB,min and H_EB,max are the upper and lower limits of EB output, respectively. P_CHP is the CHP power generation. g_CHP is the natural gas consumption. H_t and H_CHP are waste heat generated by CHP and CHP waste heat heating. η_L, η_l, η_r, and η_h are power generation efficiency and heat dissipation coefficient of CHP, waste heat recovery efficiency, and heating efficiency of waste heat boiler.

The power flow models of the electricity grid, natural gas grid, and heating network considered in this paper operate independently to supply energy. Energy conversion and mutual support are achieved through EB and CHP systems. Due to the differing peak demands and energy consumption characteristics of various types of energy, the three supply networks can complement each other to achieve efficient energy utilization.

2.3.4. Price Fluctuation Mechanism Based on Generation Resources

In IES, the power generation in a single period directly determines the power supply capacity to users. However, when the RE permeability in IES increases, the increase of power generation fluctuation will lead to the further increase of power supply peak valley difference. In this paper, in order to study the effect of price guidance on reducing the pressure of power supply during peak demand, a price fluctuation mechanism based on time of day generation resources is established. The time-of-use price formulation rules in this paper are formulated as:$$\begin{array}{}\text{(38)}& \text{Calculate\hspace{0.17em}total\hspace{0.17em}power\hspace{0.17em}generation}:P_{\text{sum}}^t=P_{\text{PV}}^t+P_{\text{WD}}^t-P_{\mathrm{T}}^t-P_{\text{CHP}}^t,\end{array}$$$$\begin{array}{}\text{(39)}& \begin{array}{c}\text{Calculate\hspace{0.17em}fluctuation\hspace{0.17em}coefficient}\text{:}{C}_{\mathrm{P}}^t=1-2P_{\text{sum}}^t-P_{\mathrm{L},\max ,\mathrm{h}}^t+P_{\mathrm{L},\min ,\mathrm{h}}^t/P_{\mathrm{L},\max ,\mathrm{h}}^t+P_{\mathrm{L},\min ,\mathrm{h}}^t,\end{array}\end{array}$$$$\begin{array}{}\text{(40)}& \text{Calculate\hspace{0.17em}intraday\hspace{0.17em}electricity\hspace{0.17em}price}:m_{\mathrm{p}}^t=C_{\mathrm{p},\mathrm{c}}{C}_{\mathrm{P}}{m}_{\mathrm{b}},\end{array}$$where $P_{\text{sum}}^t,P_{L,\max ,h}^t,\text{\hspace{0.17em}and\hspace{0.17em}}{P}_{L,\min ,h}^t$ are the total power generation during t period, the historical maximum load, and the historical minimum load within a day, respectively. $C_p^t$ and C_p,c are the price fluctuation coefficient and the price fluctuation conversion coefficient, respectively. $m_P^t$ and m_b are time-of-use price and benchmark price in t period, respectively.

3. A Multiple Indicator Weight Optimization Model Considering WS

In the process of optimizing the objective function of the IES, there is a conflict of interest among different energy operators, users, and energy suppliers. Therefore, only considering the objective function index of an interest subject in the study will lead to the corresponding tendency of the results. In order to solve this problem, the cost and benefit indicators of multiple stakeholders are considered as the objective function, so that the benefit distribution in the power grid is more balanced. In this paper, the multi-index weight is optimized to realize the benefit distribution of multiple stakeholders. In the process of benefit distribution, the sensitivity of different stakeholders to the weight in the objective function, the status of CEs, the importance to the energy network, and the installed capacity are comprehensively considered.

3.1. The Influencing Factors of Objective Function Optimization

In IES optimization scheduling work, the diversity of objective functions also determines that their scheduling results are influenced by more factors, including objective function dimensions, physical meanings, operating modes, et cetera, which need to be considered when optimizing the weight of objective functions.

3.1.1. WS

Due to the existence of diversified indicators from the generation side, consumption side, and energy service providers in the objective function, the dimensions, physical meanings, and propensity towards energy allocation of each indicator are different. This also results in different degrees of improvement in the weight of different indicators by the comprehensive energy system. In order to take this WS into account in the comprehensive optimization of the objective function, a WS index is set, so that the sensitive index can obtain greater weight, thereby, improving the utilization efficiency of scheduling resources in the comprehensive energy system.

3.1.2. IES CE

In the optimal dispatch of IES, for example, power generation stations, energy service providers, and users have their own clear trading objectives, that is, to improve their own profits or reduce their own power purchase costs. Therefore, their objectives can be clearly modeled and solved in the optimal dispatch. However, although the CE index has no clear profit target, its impact on the environment is difficult to ignore [35], so the CE index should be considered as an important index for the weight optimization of the objective function in IES scheduling.

3.1.3. Installed Capacity

Due to differences in installed capacity among different power plants, such as TPG, PV, WP, et cetera, the cost and benefits in the objective function will also vary in order of magnitude. In order to avoid equipment such as ES that is relatively small in installed capacity being masked by equipment such as large power plants, small equipment cannot gain in the weight optimization of the objective function. Therefore, it is necessary to consider it as one of the factors in determining the weight of the objective function.

3.2. Weight Optimization Method Based on WS Index in IES

There is a variety of interest competition in IES, so when optimizing the objective function, we can not simply consider some indicators in IES, but need to optimize the comprehensive weight of the indicators involved in the competition, and WS is an important indicator in the weight optimization of the objective function. WS here means that when a single-objective is used as the objective function, the IES operation results under the single-objective optimal condition can be obtained through simulation. Therefore, multiple IES operation results under different index optimal conditions can be obtained by running different indexes as the single-objective function. At this time, comparing these results, it can be found that when different indicators are used as single-objective functions, the change range of the same indicator is not the same, that is, under the optimal operation conditions of other indicators, the indicator is greatly optimized, that is, the WS of the indicator is large, while some other indicators cannot be greatly optimized even under the optimal operation conditions, that is, the WS of the indicator is small. At this time, allocating too much weight of the objective function to the index with small WS for optimal scheduling will not achieve the desired optimization effect, which will cause a waste of IES resources. Therefore, it is necessary to optimize the weight of the objective function according to WS, so as to obtain more reasonable IES scheduling results.

The weight optimization method based on WS proposed in this paper uses the coefficient of variation C_WS to express the importance of WS index, and its calculation method are formulated as:$$\begin{array}{}\text{(41)}& d_{i,j}^{\mathrm{N}}=d_{i,j}/\sum _{i=1}^n{d}_{i,j},\end{array}$$$$\begin{array}{}\text{(42)}& {\sigma }_j=\sum _{i=1}^n{d}_{i,j}/n,\end{array}$$$$\begin{array}{}\text{(43)}& {\mu }_j=\sqrt{\sum _{i=1}^n{d_{i,j}-{\sigma }_i}^2},\end{array}$$$$\begin{array}{}\text{(44)}& C_{\text{WS},i}={\sigma }_i/{\mu }_i,\end{array}$$$$\begin{array}{}\text{(45)}& w_i=C_{\text{WS},i}/\sum _{i=1}^n{C}_{\text{WS},i},\end{array}$$where $d_{i,j}^N$ and d_i,j are the normalized value and original value of the j-th index when the i-th index is a single-objective function. Normalizing the index can reduce the calculation error caused by different dimensions of the index. n is the number of indicators. σ_i and μ_i are the mean and standard deviation of the index, respectively. C_WS,i and w_i are coefficient of variation and weight of the i-th index, respectively.

3.3. Comprehensive Weight Optimization Based on AHP

In order to compare the effect of taking WS as a single-objective optimization weight and considering multiple indicators, AHP method is used to optimize the objective function combined with WS, environment friendly index and equipment installed capacity index in IES. In the process of AHP decision weight, the criteria layer indicators include WS, environmental friendliness, and equipment installed capacity. The scheme layer considers TPG cost, ES cost, RE power abandonment, IES CE, TPG profit, ES profit, RE profit, and user electricity purchase fee. The judgment matrices at different levels are set according to the calculation results and some expert experience. The process of AHP method is shown in Table 1.

Table 1

Optimal scheduling algorithm based on AHP to optimize the weights of IES multiobjective functions.

Step	Pseudocode
Step 1	Initialize IES network data, intraday price, input Dv // initialize IES parameters and input the AHP check vector Dv.
Step 1	For i = 1 to n do Z (X,f (xi)) → Min f (xi)do CPLEX → X → Z(X,f (xi)), i = 1,2,…,n end For // calculate IES scheduling results under each single-objective function.
Step 3	Sort {wii = 1,2,…,n}, build Dp,jdg // the scheme layer judgment matrix Dp,jdg established according to WS index.
Step 4	Sort {gii = 1,2,…,n} and {cii = 1,2,…,n}, build Dg,jdg and Dc,jdg // established the scheme layer judgment matrix Dg,jdg and Dc,jdg.
Step 5	Sort R = {w g c}, build Dr. // the criterion level judgment matrix WS established according to criterion level index.
Step 6	For i = 1 to m calculate {λi, Ai, i = 1,2,…,m}, λiRi = AiRi.Ri = Dv (n), Ci = (λi-n)/ (n−1), CR = Ci/Ri.if CR < 0.1Pass consistency check, continue the next cycle.else return to step 3.end if.end For. // single hierarchical sort and consistency check.
Step 7	Calculate λr, Ar, λrDr = ArDr.Rr = Dv (m), Cr = (λr-m)/ (m−1), CR = Cr/Rr.if CR < 0.1Pass consistency check, continue the next step.else return to step 5.end if. // criterion layer consistency check.For i = 1 to n wi = 0.For j = 1 to mwi = wi + Ar (j)${\hspace{0.17em}}^{\ast }$Ai (j).end For.end For.W = (w1,w2,…,wn). // hierarchical total sort.
Step 8	Output W = (w1,w2,…,wn). // output AHP weight optimization results.

In this paper, the weight optimization process of single WS index and multi-index objective function based on AHP is shown in Figure 4.

[figure(s) omitted; refer to PDF]

As shown in Figure 4, after two different weight optimization schemes, the comparison of the results can be used to analyze the role of WS index in the weight optimization process and the precautions when studying WS index.

4. Case Studies

The IES coupling network model in this article includes a tripartite coupling of the power grid, natural gas network, and heating network, and the interconnection between different energy networks is achieved through energy conversion equipment. In this paper, under the equality and inequality constraints of Equations (18)–(40), and with Equation (3) as the optimization objective, the proposed model is formulated as a linear programming problem, and the proposed model is solved on the Yalmip platform in Matlab 2020A with the CPLEX solver.

4.1. Data Input

The IES model used in this article includes the power grid (IEEE 39-bus system [36]), the heating network (6-node heating system [37]), and the natural gas network (Belgian high caloric 20-node natural gas system [38]). In order to conduct the research in this article, multiple ES, RE, and FXL were added on the basis of the original calculation examples, resulting in a RE penetration rate of 41.57% in the power grid. The RE data comes from the real data of a certain PV and WP station in a certain year. The impact of time-of-use electricity prices based on energy supply on IES energy architecture was considered, and IES optimization scheduling considering CE and FXL under high penetration rates was studied. In the calculation example, the power system includes a total of 10 generator units, with a total installed capacity of 6967 MW and a total power load of 5941.5 MW. There are a total of six GSs and nine GLs in the natural gas network. Seven conventional GLs and two gas turbine generator loads, total load 2.4608 Mm³. The heating network includes one CHP unit, one EB, and three heating loads, with a total load of 50 MW. The main power generation equipment data in IES is shown in Table 2.

Table 2

IES main power generation equipment data.

Node	Equipment	Power cap (MW)	Unit CE (t/MWh)	Operation cost (yuan/MWh)
30	CHP	250	0.522	180
31	TPG	650	0.856	250
32	WP	650	0.0095	200
33	CHP	632	0.522	180
34	TPG	508	0.856	250
35	PV	650	0.086	160
36	TPG	560	0.856	250
37	CHP	540	0.522	180
38	TPG	830	0.856	250
39	TPG	1000	0.856	250

The simulation example architecture in this article is shown in Figure 5.

[figure(s) omitted; refer to PDF]

The ES in this example is constructed at nodes 10, 20, and 32, and the ES capacity is 50 MW/200 MWh. Node 32 is the WP node and node 35 is the PV node. The load at nodes 4, 8, 20, and 29 is FXL. The load fluctuation and RE fluctuation characteristic curve in this paper are shown in Figure 6.

[figure(s) omitted; refer to PDF]

The RE characteristic curve in Figure 6 is the RE power generation fluctuation characteristic curve obtained by clustering the annual power generation data of a RE station. It can be seen that due to the influence of meteorological factors associated with time, PV generation is concentrated in the time period of [9,19], while WP generation has a certain output in 24 h, but more power is generated in the time period of [0,5] and [12,24]. RE generation shows the characteristics of irregular time series fluctuation. The load of power grid, natural gas network, and heating network fluctuated continuously within 24 h. Due to the office power consumption in the daytime and the household power consumption in the evening, the power demand of power grid was relatively large in [7,23] time period. Due to the fact that families cook at noon and night, the gas network has a large demand for natural gas in [7,13] and [17,23] periods. However, due to the greater demand for heat supply at night, the heat demand of the heat supply network in [23,24] and [0,4] is larger, and there is a complementary relationship between the energy demand of the three networks. The power flow characteristics of the three networks are independent of each other, but energy form conversion and interaction can be achieved through EB and CHP systems. To ensure the basic living needs of users, the natural GL and HL cannot be reduced, while the electricity load adopts a demand response mode.

4.2. Optimization of Weights for Multiple Indicator Objective Functions

In order to obtain the power generation cost of TPG, CHP power generation cost, ES operation and maintenance cost, RE power abandonment, CE, FXL electricity fee, ES profit, RE profit, and WS of TPG profit indicators, each indicator was operated as a single-objective function and the results shown in Table 3 were obtained.

Table 3

IES single-objective function optimization results.

Single-objective function	TPG cost (10,000 yuan)	ES cost (10,000 yuan)	RE energy abandonment (%)	CE (t)	TPG profit (10,000 yuan)	ES profit (10,000 yuan)	RE profit (10,000 yuan)	FXL cost (10,000 yuan)
TPG cost	207.40	7.20	0	9226.78	378.24	6.45	362.41	2842.29
ES cost	608.81	0	0	10056.24	415.52	32.44	362.41	2798.82
RE energy abandonment	779.30	5.89	0	16329.18	407.65	5.19	362.41	3058.88
CE	560.00	3.00	0	8593.41	555.68	2.50	362.41	3065.85
TPG profit	974.43	4.20	20.22	15202.89	800.01	3.56	75.85	3226.76
ES profit	535.36	36.00	0	9303.57	411.37	32.44	362.41	2757.37
RE profit	779.23	5.89	0	9806.19	407.65	5.19	362.41	3058.88
FXL cost	358.27	7.20	61.59	12513.86	348.69	6.45	298.70	2142.14

In Table 3, boldface values represent metrics functioning as individual optimization targets. When IES scheduling is carried out with a single-objective as the objective function, the index shows a better optimization effect than that not listed as the objective function. In order to compare the optimization effect of each index under different dimensions, each index is normalized to take out the influence of dimensions. The optimization range of each index is shown in Figure 7.

[figure(s) omitted; refer to PDF]

The pole in Figure 7 represents the index represented by the single-objective function. It can be clearly seen that the single-objective optimization has too obvious tendency. For example, TPG power generation tends to be minimized, while the power supply of TPG is mostly undertaken by RE, so the AR of RE generation is reduced to 0%. On the other hand, when TPG profit was taken as the optimization target, TPG profit was 80.012 million yuan, an increase of 2.12 times, so the RE power AR increased by 79.79%. The reason for this result is that there is a certain redundancy in generation resources in IES, but users’ power consumption does not lack the source of power, so the objective function weight is the main reason affecting the utilization rate of different types of generation resources. The ES dispatching results also show the same rule. This significant change reflects the serious tendency of single-objective optimization. Therefore, in the process of optimization, the participants of benefit distribution should be considered as a whole, and the results obtained can have application value. Comparing TPG profit, RE profit, and ES profit index, we can find that the WS volatility relationship of the three is ES (0.92) > RE (0.79) > TPG (0.53).

Based on the above WS index differences, the results shown in Table 4 can be obtained by using Equations 41–45 to optimize the weights of multiobjective functions. It is important to note that in certain extreme cases, if indicators are chosen improperly, there is a risk of excessive optimization of specific indicators, which can adversely affect the overall performance of the system. In such situations, it is necessary to perform single-objective calculations on the objective function and keep the sensitivity of the weights among the objective functions within acceptable limits to avoid excessive optimization of specific indicators. However, only considering WS will lead to the neglect of some indicators insensitive to weight. For example, when ES with small installed capacity is used as the objective function, its optimization range is larger than its own installed capacity, but the optimization range of TPG and RE at the generation side is smaller than its own installed capacity. On the other hand, since CE is a nonprofit indicator, insufficient consideration is given to CE in optimization. In order to reduce the difference of WS indicators among different indicators, further research is carried out in combination with the AHP. In order to consider WS while examining the environment friendly and avoid the poor optimization effect caused by small equipment capacity, WS, environment friendly index, and installed capacity index are optimized as the judgment indicators of AHP criterion layer. The WS index is used to enhance the utilization of weights in multiobjective optimization problems, while the environmental index promotes energy conservation and low-carbon operation of the IES. The installed capacity indicator is used to ensure consistency among devices with different installed capacities. It should be noted that the criteria-level indicators can be adjusted based on needs in different application scenarios. The AHP conducts a comprehensive evaluation of the single-objective weight schemes based on the criteria-level indicators, and subsequently optimizes the weights of multiple objective functions according to the differences in evaluations. The AHP optimization results are shown in Table 4 and Figure 8.

[figure(s) omitted; refer to PDF]

Table 4

Comparison of indicator weights.

Number	1	2	3	4
Index	TPG cost	ES cost	RE AR	CE
Nomalized w	0.125	0.125	0.125	0.125
WS optimization w	0.107	0.282	0.083	0.045
AHP optimization w	0.071	0.231	0.157	0.033
Number	5	6	7	8
Index	TPG profit	ES profit	RE profit	FXL
Nomalized w	0.125	0.125	0.125	0.125
WS optimization w	0.083	0.286	0.083	0.031
AHP optimization w	0.048	0.331	0.106	0.024

The weight of the objective function shown in Table 4 is the weight optimization result after considering WS. At this time, the weight change of the objective function is shown in Figure 8. It can be seen that when only considering WS index, ES cost and profit weight decreased by 73.60% and 73.92%, respectively. The reason is that ES capacity is small, and the optimization effect of optimizing ES index weight on the function is poor for WS index. When AHP is used for comprehensive optimization, ES cost and profit weight are optimized by 5.99 times and 9.16 times, respectively. The reason for such a significant increase is that the installed capacity of ES is smaller than that of RE and TPG, so the weight decreases when only WS index is considered. When the weight of installed capacity optimization is additionally considered, the weight of ES is compensated. At the same time, because the operation of ES is conducive to the access operation of RE, when considering the environment friendly index, ES has also been optimized. On the other hand, because the FXL electricity tariff index was not the focus of optimization in the process of AHP optimization, the index weight was reduced by 92.23%. CE index and RE index are related to environment friendly index, but RE AR punishment is more closely related to environment friendly index. Less RE AR means higher utilization of RE, which reduces CE, so its weight increases by 40.73%, while CE includes TPG CE, ES CE, RE CE, et cetera, so CE index is not positively related to environment friendly index, which reduces the weight of CE index by 84.29%.

According to the weight calculation after optimization, the optimal scheduling objective function results of IES are obtained, and the data of each index value increase or decrease are calculated, as shown in Figure 9.

[figure(s) omitted; refer to PDF]

In Figure 9, the comparison of scheduling results after AHP comprehensive weight optimization and WS index weight optimization shows that the weight optimization results based on WS show that TPG profit and FXL power purchase fee increase by 0.22% and 0.23%, respectively, while CE decreases by 0.29%. At this time, the value of the objective function decreases by 0.47% without increasing any power generation or ES resources. This is because, in all the objective functions, due to their different dimensions and physical meanings, the optimization ranges of the objective functions that can be obtained under the premise of obtaining the same weight optimization are also different, and the WS index effectively enlarges the sensitivity to weight changes and tends to allocate more weight resources to the indicators with high sensitivity.

Comparing the WS index and the AHP considering WS with normalized weights, the sum of the percentage improvement in the numerical optimization of indicators was found to be 22.87% for WS index optimization alone, whereas it increased to 60.57% when AHP, incorporating WS, further optimized the indicators. After considering WS index, environment friendly index and installed capacity and using AHP method to optimize the weight, it is found that the weight of CE index in AHP optimization result is smaller, so the proportion of CE in the objective function increases by 5.48%, while the proportion of other indexes decreases by 5.46%. The scheduling results after AHP optimization weight show that the objective function value is reduced by 10.31% compared with the normalized weight. Although the CE proportion increases, the CE value decreases by 19,592.94 t, the IES CE value decreases instead. The reason is that the impact of environment friendly index on IES scheduling results lies in the increase of RE weight, but since CE includes TPG CE, the CE weight is reduced under the combined effect of environment friendly index and installed capacity index, but the scheduling results are significantly better, so all indexes have been optimized in all aspects, which is reflected in the reduction of the value of each index and the overall reduction of the objective function. Compared with the single-objective optimization weight of WS index, the IES scheduling results at this time not only comprehensively consider the environmental factors, installed capacity and WS index, but also the objective function is worth more optimization.

By comparing the reasons, it can be found that the optimization direction of weight optimization results when considering WS index is relatively single, and the optimization of objective function value is achieved only by increasing WS higher index weight. The AHP method additionally considers the environment friendly index and the installed capacity index, and its optimization results include the optimization of the scheduling results of RE, TPG, ES, and other equipment. While enlarging the WS index, the scheduling results initially have a certain degree of selectivity, and the optimization results can optimize the objective function value in all aspects compared with the single WS index optimization, so the IES scheduling results of AHP optimization weight are comprehensively optimal compared with the single WS index.

By comparing the normalized weight, the weight optimization based on WS index and the comprehensive weight optimization scheduling based on AHP method show that: (1) The weight optimization method based on WS index variation coefficient can reduce the objective function value without increasing the investment of IES planning, and the objective function value in this example is reduced by 0.47%. (2) By combining subjective and objective weighting methods such as AHP, comprehensive weight optimization can be achieved by combining WS indicators and other indicators (such as environment friendly index, installed capacity index, etc.). The value of the objective function in this example increases by 10.31%, and the IES scheduling results can selectively optimize the scheduling results of some key equipment in the system, with better optimization results and stronger selectivity. (3) Comparing the WS indicator with the AHP method, it is evident that WS represents a fully objective approach to weight optimization. AHP, on the other hand, generates the evaluation of multiobjective weights under expert guidance. When the interrelationships between multiple metrics are unclear, the WS indicator is more applicable, whereas, with rich expert experience, combining AHP with the WS indicator can enhance weight optimization.

4.3. Trends in CE Changes in High Permeability IES

Due to the inclusion of equipment such as TPG, RE, and ES in IES, the CO₂ emissions generated cannot be ignored. In the objective function weight optimization of this article, CE indicators include emissions from IES power generation equipment, energy service providers, energy networks, et cetera. By comparing the IES scheduling results with and without considering CE indicators, the CE results shown in Table 5 can be obtained.

Table 5

CE impact on IES.

Index	PV CE (t)	WP CE (t)	GS CE (t)
Considering CE	17724.60	2066.25	626.69
Not considering CE	17724.60	2066.25	1177.63
Difference	0	0	550.94
Index	IES operation CE (t)	TPG CE (t)	ES CE (t)
Considering CE	34363.79	51338.76	403.20
Not considering CE	34771.63	51939.64	403.20
Difference	407.84	600.88	0

From Table 5, it can be seen that the consideration of CE indicators can have a significant effect on IES scheduling work, effectively reducing the system’s CE level. Among them, the most significant reduction effect is GS CE, IES running CE, and TPG CE. The portion of GS CE reduction is the energy supply from CHP units to the power grid and heating network. While TPG CE decreased, PV and WP did not increase power generation, indicating that FXL and ES reduced their demand for TPG power generation through temporal transfer of electricity demand.

By analyzing the composition of CE, it can be found that the CE in IES mainly come from RE power generation, TPG power generation, and CE generated during IES operation. Among them, TPG CE accounts for the largest proportion, and due to its nonrenewable nature and low efficiency in carbon resource utilization, TPG has gradually been replaced by RE in recent years. In order to study the impact of different RE permeability on IES CE, adjust RE permeability in the calculation example and make statistics on RE, TPG power generation and CE, and get the results shown in Figures 10 and 11.

[figure(s) omitted; refer to PDF]

In Figure 10, it can be seen that as the penetration rate of RE increases from 19.17% to 65.48%, the main body of CE in IES gradually changes from TPG to RE. During this process, the total power generation of IES remains basically unchanged, while the total CE of IES decreases by 94.69%. The reason is that RE mainly focuses on construction CE, and this article ignores the small amount of CE generated during RE operation, while TPG generates a large amount of CE during operation. Figure 11 shows that, while the penetration rate of IES has increased by 46.31%, the total profit of ES has increased by 7.32%. This indicates that the increase in RE leads to an increase in IES power generation volatility and ES can provide support for RE’s power generation volatility. On the other hand, the intensified power generation fluctuations will increase the price fluctuations of the time-of-use electricity price and ES will gain more benefits through low-priced charging and high-priced discharge. From this, it can be seen that the increase in RE penetration rate has also increased the demand for ES by IES.

The research on the total power generation and CE of RE and TPG under different penetration rates shows that: (1) An increase in RE penetration rate can effectively reduce IES CE. (2) When building RE power plants with the goal of reducing CE, the operating CE of WP are lower than those of PV. (3) ES can serve as an important means of regulating fluctuations in RE power generation, and an increase in RE penetration rate is also beneficial for ES operators to increase ES profits.

4.4. The Regulatory Effect of FXL on Supply and Demand Balance Based on Electricity Price Guidance

For FXL, due to its self selected characteristics, it has a good regulatory effect. This article uses a price guidance mechanism to guide changes in electricity prices as a guide for FXL time series transfer. On the other hand, the transfer characteristics of FXL also benefit the flexible scheduling of IES. Therefore, this article establishes a price guided FXL demand transfer mechanism and compares the scheduling results of IES with and without FXL, as shown in Figure 12.

[figure(s) omitted; refer to PDF]

The red and green curves in Figure 12 represent the daily load demand without considering FXL and considering FXL, respectively, while the blue bar chart represents the time-of-use electricity price based on electricity generation. It can be seen that in the impression of time-of-use electricity prices [3,10] and [20,24] are high electricity price periods, while [11,19] is low electricity price period. It can be clearly observed that when considering FXL, FXL undergoes a significant transfer phenomenon, as FXL, under the influence of the time-of-use electricity price, utilizes its own temporal transfer characteristics to pursue cheaper electricity. By comparing the differences in daily power supply demand and electricity purchase fees between FXL and non FXL, Figure 13 is obtained.

[figure(s) omitted; refer to PDF]

From Figure 13, it can be seen that FXL has shifted its electricity demand from high electricity price periods to low electricity price periods in order to reduce electricity purchase fees, thereby, achieving the goal of reducing electricity bills. Among all FXL, 51.47% of them transferred their own electricity usage period. At this time, the electricity purchase fees of FXL and no FXL were calculated, and it was found that the daily electricity bills of FXL were 239,000 yuan, while the daily electricity bills of no FXL were 317,000 yuan. Through FXL’s independent choice of electricity purchase time, the electricity bills were reduced by 24.61%. On the other hand, due to the fact that the fluctuation of the time-of-use electricity price is determined by the amount of power generation resources in the text, the load transfer behavior of FXL corresponding to the time-of-use electricity price can effectively regulate and alleviate the energy shortage caused by the fluctuation of IES power generation resources.

By establishing a time-of-use electricity price based on power generation resources, it was found that FXL, as a flexible user side scheduling resource, can achieve the goal of users spontaneously transferring electricity load peaks through price guidance. The strategy of establishing a price guidance mechanism will affect the scheduling results of FXL. The time-of-use electricity price based on generation resources used in this article is more effective in alleviating the power supply pressure during peak periods in the network.

5. Conclusion

In the face of increasing penetration rates of RE sources in the generation side of the IES, the growing participation in power trading, and the unpredictability of user electricity consumption, optimization and scheduling of the IES face new challenges. To address these challenges, this article proposes a weight optimization method for the multiobjective function based on the WS index. The article also analyzes the changes and impacts of CE in the IES under different permeabilities of RE sources. By examining the role of FXL in IES scheduling, the study sheds light on the importance of flexible energy consumption patterns in optimizing the overall system performance.

1. In this example, without increasing the planning and construction investment of the IES system, the objective function value is optimized by 0.47%. By incorporating the WS method and considering additional environment friendly and installed capacity indexes using AHP, the objective function of the scheduling result is further reduced by 10.31%. The multiobjective function optimization method based on the WS index is suitable for optimizing and scheduling complex systems with different dimensions and physical meaning indexes. Weight optimization based on the WS indicator is suitable for scenarios where the interrelationships between multiple objectives are unclear. However, when experts have extensive experience in the same problem, subjective and objective combined evaluation methods such as AHP can be used. By integrating WS indicators with other metrics to optimize weights, better results in objective function optimization can be achieved.

2. As a green power generation mode, the volatility of RE will lead to further differences between peak and trough power supply and demand in IES. The calculation example in this paper demonstrates that when the IES permeability increases by 46.3%, the IES CE decreases by 94.69%, and the profit from energy storage increases by 7.32%. The construction of ES and the implementation of an electricity price guidance mechanism based on generation fluctuation on the load side to guide FXL’s power purchase behavior are two feasible supporting measures. How IES quantifies and encourages the supporting role of ES and FXL to ensure the sustainable and favorable development of the ES industry and energy market is the research goal for future studies.

3. This paper guides the electricity purchase behavior of FXL through a time-of-use pricing mechanism based on generation capacity fluctuations. The simulation shows that 51.47% of FXL’s power demand exhibits time sequence transfer characteristics, reducing FXL’s power purchase price by 24.61%, and relieving the energy supply pressure of IES during peak energy demand periods. Although this time-of-use pricing strategy effectively transfers energy demand in the appropriate time sequence, the time-of-use pricing established in this paper solely based on power generation fluctuations does not consider the supply and demand balance of the actual energy market. Incorporating real-time supply and demand balance fluctuations in establishing TOU prices is the focus of future research endeavors.

Acknowledgments

This work was supported by National Natural Science Foundation of China (Game control–based planning and simulation modeling of coupled optical storage hydrogen production system) (Grant 52277211) and Research Start-up Fund of North China University of Technology (Research on High Precision Simulation and Advanced Control Strategy of Optical Storage Green Hydrogen System) (Grant 110051360022XN107-03).

Appendix

Table A1

The meaning of parameters and variables.

Nomenclature
Indices
fT	TPG cost
Cb,T	TPG construction cost
Co,T	TPG operation cost
fm,T	TPG profit
fc,E	ES cost
Cb,E	ES construction cost
Co,E	ES operation cost
fc,N	RE Power curtailment penalty
fp,N	RE cost
fm,N	Profit from RE power sales
$C_{\mathrm{b},\text{PV},i}^t$	RE construction cost
$C_{\mathrm{b},\text{WP},i}^t$	Profit from RE power sales
fc,L	Electricity purchase expenses of power users
fc	IES CE
$C_{\mathrm{T},\mathrm{b}}^{\mathrm{c}}$	TPG construction CE
$C_{\mathrm{T},\mathrm{o}}^{\mathrm{c}}$	TPG operation CE
$C_{\mathrm{g},\mathrm{o}}^{\mathrm{c}}$	Operation CE of natural gas system and thermal system
$C_{\text{PV},\mathrm{b}}^{\mathrm{c}}$	PV construction CE
$C_{\text{WP},\mathrm{b}}^{\mathrm{c}}$	WP construction CE
$C_{\mathrm{E},\mathrm{o}}^{\mathrm{c}}$	ES operation CE
$C_{\mathrm{s},\mathrm{o}}^{\mathrm{c}}$	IES operation CE
Variables
PEB	EB consumed electric power
$P_{\mathrm{T}}^t$	TPG power in t period
$P_{\text{PV},i}^t$	PV generation power in t period
$P_{\text{WP},i}^t$	WP generation power in t period
$P_{\mathrm{L},i}^t$	Power demand of FML in t period
$P_{\mathrm{L},\text{FXL}}^t$	Power demand of FXL in t period
HEB	EB thermogenesis
pj	Compressor outlet pressure
pn	Compressor inlet pressure
$P_{i,j}^t$	Line flow power from node i to node j
$P_{\mathrm{L}}^t$	Consumer power
$P_{\mathrm{E}}^t$	Charging power of ES in t period
$P_{\text{sum}}^t$	Total power generation in t period
$P_{\mathrm{L},\max ,\mathrm{h}}^t$	Daily historical maximum load
$P_{\mathrm{L},\min ,\mathrm{h}}^t$	Daily historical minimum load
$P_{\mathrm{L}}^t$	Hourly power consumption of power users
$P_{\mathrm{L},i}^t$	FML power
$P_{\mathrm{L},\text{FXL}}^t$	FXL power
$v_i^t$	Node voltage in t period
$I_i^t$	Line current in t period
$S_{\mathrm{E}}^t$	ES state of charge
$g_{\mathrm{L}}^t$	Natural gas load gas consumption
$g_{\text{CHP}}^t$	CHP gas consumption
$g_{\mathrm{s}}^t$	Output of natural gas source
$g_{i,j}^t$	Node input natural gas flow
$u_i^t$	Nodal pressure in t period
$g_{i,j}^t$	Natural gas flow of pipelines i to j in t period
$H_{\mathrm{S}}^t$	Heat source heating
$H_{\text{CHP}}^t$	CHP heating
$H_{\text{EB}}^t$	EB heating
$H_{\mathrm{L},\mathrm{p}}^t$	Pipe heat loss
$H_i^t$	Heat for heat load
$T_{\text{in}}^t$	Inlet water temperature of pipeline
$T_{\text{out}}^t$	Outlet water temperature of pipeline
PCHP	CHP generation power
gCHP	Natural gas consumption by CHP
Ht	Waste heat generated by CHP
HCHP	CHP waste heat heating
σ	Mean value
μ	Standard deviation
CWS	Index variation coefficient
w	Index weight
Parameters
ηEB	EB electric heat transfer efficiency
ρc	Compressor compression ratio
mc	TPG unit generation cost
$m_p^t$	Time-of-use price in t period
mp	ES power unit price
ms	ES capacity unit price
r	Discount rate
L	ES payback period of investment
CR	Es operating cost conversion coefficient
SE,N	ES rated capacity
PE,N	ES rated power
nE	ES quantity
nPV	PV quantity
nWP	WP quantity
vmax	Upper limit of node voltage after relaxation
vmin	Lower limit of node voltage after relaxation
Imax	Upper limit of node current after relaxation
Imin	Lower limit of node current after relaxation
cmin	ES SOC Power cap
cmax	ES SOC lower power limit
cr	ES charge and discharge ratio
Pmax	ES power cap
PPV,max	PV maximum generating power
PWP,max	WP maximum generating power
umax	Node i upper pressure limit
umin	Node i lower pressure limit
Cw	The heat capacity of water
η	Pipe heat loss coefficient
HEB,min	The upper limit of EB output
HEB,max	The lower limit of EB output
ηL	CHP generation efficiency
ηl	CHP heat dissipation coefficient
ηr	Waste heat recovery efficiency of waste heat boiler
ηh	Heating efficiency of waste heat boiler
$C_{\mathrm{P}}^t$	Price fluctuation coefficient
Cp,c	Conversion coefficient of price fluctuation
mb	Benchmark price in t period
PL,a	Total power demand of FXL within 24 h

References

[1] M. Mohammadi, Y. Noorollahi, B. Mohammadi-ivatloo, H. Yousefi, "Energy Hub: From a Model to a Concept—A Review," Renewable and Sustainable Energy Reviews, vol. 80, pp. 1512-1527, DOI: 10.1016/j.rser.2017.07.030, 2017.

[2] T. Jiang, H. Deng, L. Bai, R. Zhang, X. Li, H. Chen, "Optimal Energy Flow and Nodal Energy Pricing in Carbon Emission-Embedded Integrated Energy Systems," CSEE Journal of Power and Energy Systems, vol. 4 no. 2, pp. 179-187, DOI: 10.17775/CSEEJPES.2018.00030, 2018.

[3] J. Wang, S. You, Y. Zong, C. Træholt, Y. Zhou, S. Mu, "Optimal Dispatch of Combined Heat and Power Plant in Integrated Energy System: A State of the Art Review and Case Study of Copenhagen," Energy Procedia, vol. 158, pp. 2794-2799, DOI: 10.1016/j.egypro.2019.02.040, 2019.

[4] H. Hu, X. Sun, B. Zeng, D. Gong, Y. Zhang, "Enhanced Evolutionary Multi-Objective Optimization-Based Dispatch of Coal Mine Integrated Energy System With Flexible Load," Applied Energy, vol. 307,DOI: 10.1016/j.apenergy.2021.118130, 2022.

[5] L. Sun, Y. Jin, J. Shen, F. You, "Sustainable Residential Micro-Cogeneration System Based on a Fuel Cell Using Dynamic Programming-Based Economic Day-Ahead Scheduling," ACS Sustainable Chemistry & Engineering, vol. 9 no. 8, pp. 3258-3266, DOI: 10.1021/acssuschemeng.0c08725, 2021.

[6] C. M. Chen, X. Deng, Z. Zhang, "Optimal Day-Ahead Scheduling of Multiple Integrated Energy Systems Considering Integrated Demand Response, Cooperative Game and Virtual Energy Storage," IET Generation, Transmission & Distribution, vol. 15 no. 11, pp. 1657-1673, DOI: 10.1049/gtd2.12124, 2021.

[7] C. Chen, Y. Li, W. Qiu, "Cooperative-Game-Based Day-Ahead Scheduling of Local Integrated Energy Systems With Shared Energy Storage," IEEE Transactions on Sustainable Energy, vol. 13 no. 4, pp. 1994-2011, DOI: 10.1109/TSTE.2022.3176613, 2022.

[8] S. Wang, S. Wang, Q. Zhao, S. Dong, H. Li, "Optimal Dispatch of Integrated Energy Station Considering Carbon Capture and Hydrogen Demand," Energy, vol. 269,DOI: 10.1016/j.energy.2023.126981, 2023.

[9] W. Xu, W. Han, H. Z. Jin, Y. Bai, H. Liu, "Research on Optimal Scheduling of Integrated Energy System in Low-Carbon Parks Based on Demand Response," International Journal of Low-Carbon Technologies, vol. 18, pp. 433-442, DOI: 10.1093/ijlct/ctad020, 2023.

[10] Y. M. Huang, N. Wang, Q. Chen, "Multi-Energy Complementation Comprehensive Energy Optimal Dispatch System Based on Demand Response," Process Integration and Optimization for Sustainability, vol. 7 no. 5, pp. 1157-1166, DOI: 10.1007/s41660-023-00335-w, 2023.

[11] Z. Liu, H. Xing, Y. Luo, Y. Ye, Y. Shi, "Low-Carbon Economic Dispatch of an Integrated Energy System Based on Carbon Emission Flow Theory," Journal of Electrical Engineering & Technology, vol. 18 no. 3, pp. 1613-1624, DOI: 10.1007/s42835-022-01298-7, 2023.

[12] D. R. Song, W. Q. Meng, M. Dong, "A Critical Survey of Integrated Energy System: Summaries, Methodologies and Analysis," Energy Conversion and Management, vol. 266,DOI: 10.1016/j.enconman.2022.115863, 2022.

[13] Q. Zheng, Y. Gu, Y. Liu, J. Ma, M. Peng, "Chaotic Particle Swarm Algorithm-Based Optimal Scheduling of Integrated Energy Systems," Electric Power Systems Research, vol. 216,DOI: 10.1016/j.epsr.2022.108979, 2023.

[14] M. Nemati, M. Braun, S. Tenbohlen, "Optimization of Unit Commitment and Economic Dispatch in Microgrids Based on Genetic Algorithm and Mixed Integer Linear Programming," Applied Energy, vol. 210, pp. 944-963, DOI: 10.1016/j.apenergy.2017.07.007, 2018.

[15] Y. Yang, M. Hu, M. Wei, Y. Wang, M. Zhou, Y. Ma, "Research on Optimization of Linkage Operation of Integrated Energy System in Industrial Parks Based on Chaotic Particle Swarm Algorithm," .

[16] Y. Chen, F. Lou, Y. Jiang, Q. Ye, N. Wang, G. Ying, "A Modified Particle Swarm Optimization Based Algorithm for the Energy Management Strategy of a Regional Integrated Energy System," pp. 3014-3020, .

[17] K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, "A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II," IEEE Transactions on Evolutionary Computation, vol. 6 no. 2, pp. 182-197, DOI: 10.1109/4235.996017, 2002.

[18] L. Wang, Q. Li, R. Ding, M. Sun, G. Wang, "Integrated Scheduling of Energy Supply and Demand in Microgrids Under Uncertainty: A Robust Multi-Objective Optimization Approach," Energy, vol. 130 no. 1,DOI: 10.1016/j.energy.2017.04.115, 2017.

[19] R. Mei, T. Wu, D. J. Geng, "Multi-Objective Optimization of Integrated Energy System Based on Improved NSGA-II Algorithm," pp. 1721-1726, .

[20] Y. Li, C. Wang, G. Li, C. Chen, "Optimal Scheduling of Integrated Demand Response-Enabled Integrated Energy Systems With Uncertain Renewable Generations: A Stackelberg Game Approach," Energy Conversion and Management, vol. 235,DOI: 10.1016/j.enconman.2021.113996, 2021.

[21] J. He, Y. Li, H. Q. Li, "Application of Game Theory in Integrated Energy System Systems: A Review," IEEE Access, vol. 8, pp. 93380-93397, DOI: 10.1109/ACCESS.2020.2994133, 2020.

[22] L. Ma, N. Liu, J. Zhang, W. Tushar, C. Yuen, "Energy Management for Joint Operation of CHP and PV Prosumers Inside a Grid-Connected Microgrid: A Game Theoretic Approach," IEEE Transactions on Industrial Informatics, vol. 12 no. 5, pp. 1930-1942, DOI: 10.1109/TII.2016.2578184, 2016.

[23] F. F. Chen, H. F. Liang, Y. J. Gao, Y. C. Yang, Y. X. Chen, "Research on Double-Layer Optimal Scheduling Model of Integrated Energy Park Based on Non-Cooperative Game," Energies, vol. 12 no. 16,DOI: 10.3390/en12163164, 2019.

[24] L. Sun, F. You, "Machine Learning and Data-Driven Techniques for the Control of Smart Power Generation Systems: An Uncertainty Handling Perspective," Engineering, vol. 7 no. 9, pp. 1239-1247, 2021.

[25] L. Z. Zhang, J. Y. Kuang, B. Sun, F. Li, C. H. Zhang, "A Two-Stage Operation Optimization Method of Integrated Energy Systems With Demand Response and Energy Storage," Energy, vol. 208, 2020.

[26] Z. Li, Y. Xu, "Optimal Coordinated Energy Dispatch of a Multi-Energy Microgrid in Grid-Connected and Islanded Modes," Applied Energy, vol. 210 no. 15, pp. 974-986, DOI: 10.1016/j.apenergy.2017.08.197, 2018.

[27] L. W. Zheng, X. Q. Zhou, Q. Qiu, L. Yang, "Day-Ahead Optimal Dispatch of an Integrated Energy System Considering Time-Frequency Characteristics of Renewable Energy Source Output," Energy, vol. 209 no. 15, 2020.

[28] Y. Li, M. Han, Z. Yang, G. Q. Li, "Coordinating Flexible Demand Response and Renewable Uncertainties for Scheduling of Community Integrated Energy Systems With an Electric Vehicle Charging Station: A Bi-Level Approach," vol. 12, pp. 2321-2331, .

[29] W. Q. Guo, X. Y. Xu, "Comprehensive Energy Demand Response Optimization Dispatch Method Based on Carbon Trading," Energies, vol. 15 no. 9,DOI: 10.3390/en15093128, 2022.

[30] R. B. Wu, Z. G. Pan, L. Tang, "Smart Dispatch System for Integrated Energy Systems With Demand Response," .

[31] L. Zhang, Z. T. Xiang, J. Ye, "Centralized Dispatch Method of Heat and Electricity Integrated System Based on Network Simplification of Large-Scale Heating Networks," pp. 1246-1252, .

[32] X. H. Liu, X. Li, C. Geng, "Day-Ahead Economic Dispatch of Integrated Energy System Including Power to Gas," pp. 1889-1894, .

[33] Z. S. Liu, M. Yang, W. H. Jia, T. Ding, "Low-Carbon Economic Dispatch of Integrated Electricity-Heat-Hydrogen Systems Considering Integrated Demand Response," pp. 1173-1177, .

[34] L. Song, H. T. Wu, D. P. Ke, "Stochastic Optimal Dispatching of Electrothermal Integrated Energy System Considering Uncertainty of Heat Load, 2022," pp. 997-1001, .

[35] Y. Zhang, Y. Han, D. Liu, X. Dong, "Low-Carbon Economic Dispatch of Electricity-Heat-Gas Integrated Energy Systems Based on Deep Reinforcement Learning," Journal of Modern Power Systems and Clean Energy, vol. 11 no. 4, pp. 1827-1841, DOI: 10.35833/MPCE.2022.000671, 2023.

[36] L. M. Hajagos, M. J. Basler, "IEEE Recommended Practice for Excitation System Models for Power System Stability Studies," vol. l, 2016. IEEE Std 421.5-2016 (Revision of IEEE Std 421.5-2005)

[37] "Test Data for Combined Heat and Power Dispatch[EB/OL]," . http://motor.ece.iit.edu/data

[38] Y. Zhang, Y. Hu, J. Ma, Z. Bie, "A Mixed-Integer Linear Programming Approach to Security-Constrained Co-Optimization Expansion Planning of Natural Gas and Electricity Transmission Systems," IEEE Transactions on Power Systems, vol. 33 no. 6, pp. 6368-6378, DOI: 10.1109/TPWRS.2018.2832192, 2018.