Abstract
A distributionally robust scheduling strategy is proposed to address the complex benefit allocation problem in regional integrated energy systems (RIESs) with multiple stakeholders. A two-level Stackelberg game model is established, with the RIES operator as the leader and the users as the followers. It considers the interests of the RIES operator and demand response users in energy trading. The leader optimizes time-of-use (TOU) energy prices to minimize costs while users formulate response plans based on prices. A two-stage distributionally robust game model with comprehensive norm constraints, which encompasses the two-level Stackelberg game model in the day-ahead scheduling stage, is constructed to manage wind power uncertainty. Karush-Kuhn-Tucker (KKT) conditions transform the two-level Stackelberg game model into a single-level robust optimization model, which is then solved using column and constraint generation (C&CG). Numerical results demonstrate the effectiveness of the proposed strategy in balancing stakeholders’ interests and mitigating wind power risks.
DRIVEN by the continuous advancement of Energy Internet policies, there has been a notable rise in integrated energy systems coupled with other networks, particularly the natural gas network, centered around the power grid, paving the way for a fresh development trend [
Numerous studies have been dedicated to optimizing the operation of RIESs. For instance, [
Given the significant impact of intermittent and stochastic renewable energy output on stable RIES operation, addressing uncertainty in RIES scheduling has become increasingly vital. Currently, robust optimization and stochastic programming are two commonly used methods for modeling uncertainties. On the one hand, Robust optimization aims to find optimal solutions by considering worst-case scenarios but often exhibits inherent conservatism [
This paper aims to address the limitations of previous studies by proposing a novel strategy that combines distributionally robust optimization and Stackelberg game theory for optimal scheduling in RIESs. First, a two-level leader-follower game model is established, in which RIES operators and CDR users are viewed as the leaders and followers, with time-of-use (TOU) energy pricing serving as the linkage between them. The objective of the leader is to minimize operational costs by determining optimal time-varying electricity prices, while the users formulate demand response plans based on these prices and their aggregated utility functions. Secondly, decision-making models for each gaming entity are constructed, incorporating a two-stage distributionally robust game model (TSDRGM) to address the uncertainty inherent in wind energy. Furthermore, a comprehensive norm constraint is introduced to mitigate the shortcomings of conservative robust optimization and the poor resistance of stochastic optimization. The follower model is treated as an equilibrium constraint to simplify the resolution process and is incorporated into the decision-making model of the leader using the Karush-Kuhn-Tucker (KKT) condition. This modification transforms the original two-level Stackelberg game model into a single-level sub-Brue-bar optimization model, which can be solved iteratively using the column and constraint generation (C&CG) algorithm. Finally, the effectiveness of the two-level Stackelberg game model is validated through simulation examples, providing evidence of its efficacy in addressing the challenges of optimal scheduling in RIESs.
RIES serves as a pivotal enabler for implementing concepts like multi-energy complementarity and optimizing energy efficiency. In the RIES framework described within this study, the electricity demand of the load is met by the main grid, wind turbines (WTs), and gas turbines (GTs). Gas boilers (GBs) and GTs also cater to the heat demand. A portion of the gas supplied by the gas network is directed towards the GT, while another portion is allocated to the GB. Cloud energy storage systems (CESSs) are utilized as energy buffers to augment the stability and flexibility of the system, encompassing both the cloud electrical storage (CES) and cloud thermal storage (CTS). These systems play a critical role in balancing and managing energy resources dynamically, enhancing the system stability and flexibility. On the load side, CDR is considered, allowing for load time-shifting and interruption capabilities. The specific energy coupling configuration is visually represented in

Fig. 1 Specific energy coupling configuration.
1) GT generates both electricity and heat through the combustion of natural gas. The constraints and outputs associated with GTs are as follows:
(1) |
where and are the power generation and heating power of GT at time t, respectively; is the gas consumption of GT at time t; and are the power generation efficiency and heating efficiency of GT, respectively; and are the maximum and minimum power generation values of GT at time t, respectively; and are the maximum and minimum heating power values of GT at time t, respectively; and is a binary variable of GT indicating the on/off state.
2) The GB produces heat by burning natural gas. The heating power output and constraints associated with the GB are as follows:
(2) |
where is the heating power of GB at time t; is the gas consumption of GB at time t; is the heating efficiency of GB; and and are the upper and lower limits of the heating power of GB, respectively.
The CESS leverages energy storage resources from numerous small- and medium-sized users. It employs a “shared energy storage” approach, which maximizes the complementary nature and economies of scale in energy storage behavior. This approach helps avoid charging and discharging disorderliness while reducing costs for users. The CESS described in this study primarily comprises two types of energy storage: CES and CHS. The pertinent constraints for CESS can be outlined as follows:
(3) |
where is the capacity of CESS at time t; is the rented energy storage capacity of CESS; and are the upper and lower limits of the charging state of CESS, respectively; is the maximum capacity of CESS that can be rented; and are the charging and discharging power of CESS at time t, respectively; and are the charging and discharging power limits for rented CESS, respectively; and are the binary variables indicating the charging or discharging state of CESS, respectively; and are the upper limits of charging and discharging power for rented CESS, respectively; and are the charging and discharging efficiencies of CESS, respectively; and is the self-loss coefficient of CESS.
In this study, the electricity load is categorized into two main types: fixed load and flexible load. The flexible load is further subdivided into two distinct types based on their demand response characteristics: shiftable load (SL) and interruptible load (IL).
SL: it refers to a type of electricity consumption where the total amount of electricity remains constant, but the timing of consumption can be flexibly adjusted [
(4) |
where is the time-shifted electricity load of RIES at time t; and are the maximum and minimum limits of the time-shifted electricity load of RIES at time t, respectively; and , , and are the allocated Lagrange multipliers.
IL: it is a form of electricity consumption where users can interrupt a portion of their load during periods of inadequate power supply or high electricity prices to alleviate pressure on the power grid [
(5) |
where and are the maximum and minimum limits of interruptible electricity load for RIES at time t, respectively; and and are the allocated Lagrange multipliers.
The motivation for demand response for heating is the fact that users have a certain degree of tolerance or fuzziness in their perception of temperature. Furthermore, minor temperature adjustments within a specific range do not significantly impact the user’s comfort experience [
(6) |
where is the shiftable load at time t; is the maximum value of shiftable load at time t; and and are the allocated Lagrange multipliers.
RIES incorporates various types of electricity and heat loads. To comprehensively evaluate the impact of CDR implementation in the RIES on user experience, we introduce as the user utility function, representing the overall satisfaction derived from purchasing electricity and heat. Additionally, when users deviate from the most suitable baseline load during each time period, their satisfaction is reduced to a certain extent, which is expressed as a function .
(7) |
where en represents the energy type; E is the set of energy types for user consumption; is the actual load of energy en in the MG at time t; and are the preference coefficients for RIES users’ energy consumption, which are related to the energy type; and and are the satisfaction loss parameters for energy en.
The specific representation of the actual response quantity for the user can be expressed as:
(8) |
where and are the initial values of electricity and heat load, respectively; and are the magnitudes of electricity and heat loads after CDR, respectively; and and are the allocated Lagrange multipliers.
In conclusion, the benefit demands of RIES on the load side can be expressed by the maximization of a comprehensive utility function, which is denoted as:
(9) |
where is the comprehensive utility function of the user; and is the electricity price set by the RIES.
A TSDRGM is proposed for the daily and real-time operation of RIES operators. The first stage involves day-ahead scheduling, implemented as a Stackelberg game. The upper-level MG serves as the leader, while the lower-level users act as the followers. Using day-ahead forecasted wind power information, the upper-level MG determines energy prices and unit schedule plans, which are then communicated to the lower-level users. The lower-level users adjust their load demands through CDR, considering the upper-level information and providing feedback to the upper level. The day-ahead decision-making process is independent of wind power uncertainty. The second stage is the real-time rescheduling, which builds upon the decisions made in the day-ahead scheduling stage x. In this stage, flexible adjustments are made to the unit output to achieve optimal rescheduling costs under different scheduling decisions. To facilitate explanation, the entire process is simplified and represented in matrix form, described by (10)-(12).
(10) |
(11) |
(12) |
where is the vector of decision variables in the day-ahead stage; is the vector of decision variables in the real-time stage; is the revenue from energy sale of RIES operator in the day-ahead stage; is the system operating cost of RIES after adjustments in the real-time stage, which is influenced by uncertain parameter d; K is the total number of clustering scenarios; is the probability of an individual clustering scenario; , , , , and are the matrices corresponding to relevant parameters; and are the column vectors of parameters in the objective function; and , , , and are the column vectors of parameters under constraint conditions.
(13) |
where and are the capacities of CES and CTS at time t, respectively; and are the rented energy storage capacities of CES and CTS, respectively; and are the maximum rented energy capacities of CES and CTS, respectively; and are the charging and discharging power limits for rented CES, respectively; and are the charging and discharging power limits for rented CTS, respectively; and are the binary variables indicating the charging or discharging state of CES, respectively; and are the binary variables indicating the charging or discharging state of CTS, respectively; and are the power adjustments for purchasing and selling electricity from/to the main grid at time t, respectively; and are the upward and downward adjustments of electric power for GT at time t, respectively; and are the upward and downward adjustments of heating power for GB at time t, respectively; and are the power adjustments for charging and discharging of CES at time t, respectively; and and are the power adjustments for charging and discharging of CHS at time t, respectively.
Moreover, given the challenge of acquiring the probability density function of actual wind power scenarios, this study utilizes historical wind power data. It implements the K-means clustering algorithm to identify representative discrete scenarios. The information of the initial scenario probability density is obtained, aiming to maximize the expected operating cost for the worst-case distribution among these typical scenarios. The values of is chosen regarding the benchmark fluctuations of . According to [
(14) |
where and are the allowable deviation values for the 1-norm and ∞-norm probabilities, respectively; and V is the historical data sample. Additionally, we set the right-hand side of (14) to a given confidence level, denoted as and .
In the day-ahead stage, it is necessary to ensure the reliable supply of wind power consumption and load safety. The objective function of the day-ahead scheduling includes the objective function, gas purchasing cost of RIES , operating cost of WT , operating cost of CESS , carbon trading cost , and cost of interaction power with the main grid .
(15) |
where is the gas purchasing price at time t; is the quantity of gas purchased at time t; is the actual power output of WT at time t; and are the power interactions between the MG and the main grid at time t; and are the prices of power interaction between the MG and the main grid at time t; is the carbon tax price; and are the carbon emission coefficients corresponding to the unit power output of GT and GB, respectively; is the carbon emission coefficient for electricity generation from the grid; is the electric power output of GT at time t; is the heating power output of GB at time t; is the collection of CESSs; is the capacity of CSEE i at time t; and are the charging and discharging power of CSEE, respectively; and are the leasing costs per unit capacity and per unit power for CESS, respectively; and is a coefficient representing operating and maintenance costs for charging/discharging operations of CESS.
Real-time adjustments are implemented in the day-ahead schedule to manage wind power forecasting errors effectively. Methods such as rescheduling and wind curtailment are employed to address these errors. It is important to highlight that in RIES, load demand response is guided in the preceding stage by establishing peak/off-peak TOU energy prices, which helps form rational load plans. However, CDR from the load side necessitates pre-signed contracts. As a result, the load side determines its response plan in the prior stage, and this response remains unchanged in the real-time stage. The objective function of the rescheduling includes the main grid interaction rescheduling cost , wind curtailment penalty cost , and generator power adjustment cost .
(16) |
where and are the real-time prices at which the MG purchases or sells electricity from/to the main grid, respectively; is the wind curtailment penalty coefficient; is the wind power adjustment in the MG at time t; and are the upward and downward penalty coefficients for the power adjustment of GT in the MG, respectively; and and are the upward and downward penalty coefficients for the power adjustment of GB in the MG, respectively.
To ensure the coordination of user interests, the average value of TOU energy prices set by the operator should not surpass the initial selling price of energy. This constraint can be expressed as (taking electricity price as an example):
(17) |
where T is the scheduling period; is the energy price; and are the maximum and minimum values of the set electricity price, respectively; and is the initially set electricity price. The process of setting heat prices follows a similar approach and will not be further detailed in this context.
(18) |
where and are the maximum values of electricity purchasing from and selling to the main grid by the MG, respectively; and is the status that represents the electricity purchasing from or selling to the main grid by the MG at time t.
(19) |
where is the maximum value of the gas purchased for the MG.
(21) |
where and are the charging and discharging power of CES at time t, respectively; and and are the charging and discharging power of CTS at time t, respectively.
In addition to the above-mentioned constraints (17)-(21), the day-ahead scheduling stage also includes additional constraints related to the thermal-coupled supply system, CESS, and CDR constraints. These constraints are described in (1)-(6), which will not be reiterated here.
Based on the day-ahead scheduling, RIES undergoes real-time rescheduling to make adjustments. It is important to ensure that the adjusted output of each device satisfies its respective operational constraints and system power balance constraints. Specifically, the real-time rescheduling constraints are modified by altering the day-ahead scheduling decision variables in (1)-(3), (18), and (21). As an example, the constraint for GB in (2) can be modified as:
(22) |
where and are the minimum and maximum up adjustable power of GB at time t, respectively; and and are the minimum and maximum downward adjustable power of GB at time t, respectively.
In the Stackelberg game, the RIES operator serves as the leader, while the users on the RIES side act as followers. When the game between the RIES operator and its users reaches a Nash equilibrium (NE), which maximizes their respective interests, no party can unilaterally change the NE to obtain greater benefits. The Stackelberg game model exhibits a unique NE when the following conditions are met: the objective functions of all participants are non-empty and continuous functions with respect to their respective strategy sets. The objective function of each follower is a continuous convex or concave function with respect to their own strategy set.
Proof: in the game, the leader is the RIES operator, and its objective function is given by (15), which is non-empty and continuous. The followers are the users on the RIES side, and their objective function is the time-dependent power consumption, represented by (17), which has a non-empty and continuous decision set. The utility function of the game-following user is differentiated to obtain the second-order partial derivatives concerning its decision variables in the game. The value of this derivative is , where and are the positive real numbers, and . Therefore, the is a continuous convex function concerning its strategy set. Based on these observations, it can be concluded that the described Stackelberg game model has a unique NE.
The TSDRGM constructed in this study encompasses a two-level Stackelberg game model in the day-ahead scheduling stage. The coupling between the upper-level and lower-level models poses difficulties in direct solution. The Lagrangian function of the lower-level model is formulated to address this challenge, and the KKT complementary relaxation conditions [
Upon applying the KKT equivalent transformation, (10) is transformed into a three-level optimization problem in the form of min-max-min. The optimization variables in the day-ahead and real-time stages are interconnected, making direct solutions unattainable. To overcome this challenge, the C&CG algorithm decomposes the model into a master problem (MP) and sub-problems (SPs). The solution process using C&CG algorithm is shown in

Fig. 2 Diagram of solution process using C&CG algorithm.
This decomposition efficiently converts the three-level optimization model into a more manageable structure. For detailed solution procedures, please refer to [
To evaluate the effectiveness of the proposed strategy for RIES, an actual RIES in north China was chosen for simulation analysis. The optimization problem was solved using MATLAB R2018b software with the YALMIP plugin and the Cplex solver. The computer configuration comprised an Intel Core i7 processor with a clock frequency of 1.8 GHz and 16 GB of memory. For the case study, typical daily data from a specific region in north China were chosen as the background. The initial load curve and wind power forecasting curve are presented in

Fig. 3 Initial load curve and wind power forecast curve.
Parameter | Value | Parameter | Value |
---|---|---|---|
2000 kW | 150 kW | ||
2000 kW | 150 kW | ||
500 kW | 2 | ||
500 kW | 0.008 | ||
110 CNY/kW | 3 | ||
37 CNY/kW | 0.015 | ||
0.01 CNY/kW | 1000 kW | ||
30 CNY/kW | 5000 kW | ||
10 CNY/kW | 200 kW | ||
0.005 CNY/kW | 200 kW | ||
150 kW | 500 kW | ||
150 kW | 500 kW |

Fig. 4 Interactive electricity prices between RIES and main grid.
In order to validate the feasibility of the proposed strategy, this subsection conducts an analysis using ten sets of typical scenarios from various historical data. The relationship among the total operating cost of the RIES, the computational time of the program, and the number of scenarios is examined. The results of this analysis are visually presented in

Fig. 5 Relationship among total operating cost, computational time, and number of scenarios.
It can be observed from
Moreover, although the computational time of the model fluctuates and increases with an increasing number of scenarios, it remains within acceptable limits for day-ahead scheduling, considering the computing hardware conditions mentioned in this study.
Additionally, as computing hardware conditions improve, computational speed is likely to increase significantly, meeting the requirement for computational efficiency. Considering the relationship among the total operating cost, computational time, and number of scenarios, this study selects 5000 historical data samples and ten discrete scenarios to solve the TSDRGM. The determined energy selling prices of RIES, as shown in

Fig. 6 Energy selling prices of RIES.
This analysis aims to assess how the comprehensive norm constraints enforced by the 1-norm and ∞-norm sets in the TSDRGM affect the total operating cost of RIES. In this part, 5000 historical data samples are selected to examine variations in scheduling costs within the TSDRGM at varying confidence levels.
Total operating cost (CNY) | ||||
---|---|---|---|---|
0.50 | 136600.92 | 136909.02 | 137345.91 | 137388.62 |
0.70 | 137025.63 | 137114.97 | 137480.23 | 137500.09 |
0.85 | 137203.20 | 137316.51 | 137527.74 | 137592.13 |
0.99 | 137321.79 | 137514.22 | 137656.22 | 137682.27 |
Based on
The above analysis indicates that by adjusting the combined value of confidence levels and , the robustness and economic efficiency of the adaptive balancing scheduling scheme can be effectively balanced. In the following examples, unless otherwise specified, is set to be 0.50, and is set to be 0.99.
To assess the superiority of the proposed strategy, this study conducted a comparison with deterministic optimization (strategy 1), two-stage stochastic optimization (strategy 2), and two-stage robust optimization (strategy 3).
The impact of different optimization scheduling strategies on the costs of RIES is shown in
Strategy | Total operating cost (CNY) | Day-ahead scheduling cost (CNY) | Real-time scheduling cost (CNY) | Computational efficiency (s) |
---|---|---|---|---|
1 | 92915.01 | 92915.01 | 63.50 | |
2 | 105780.17 | 102888.67 | 2891.50 | 66.50 |
3 | 240649.88 | 210289.13 | 30360.75 | 84.20 |
Proposed | 137514.22 | 128839.69 | 8674.50 | 90.05 |
In uncertainty optimization, strategy 2 yields the lowest day-ahead and real-time scheduling costs. This is because strategy 2 models the day-ahead scheduling scenarios of wind power based on accurate information about the probability density function of uncertain input parameters, thus enhancing economic efficiency and overall performance. Indeed, relying solely on precise probability distributions in strategy 2 may lead to overly optimistic expectations of real-time risks, making the system less robust to extreme wind power output scenarios and potentially leading to failure.
Strategy 3 has the highest day-ahead and real-time scheduling costs. This is because it relies on predetermined ranges for variable fluctuations during day-ahead scheduling, aiming to ensure results applicable in “worst-case” scenarios with a low probability of occurrence. In real-time decision-making, it prioritizes robustness by primarily increasing energy reserves to mitigate risks in real-time scheduling, often at the expense of economic efficiency. However, strategy 3 balances stochastic and robust optimization, yielding a total operating cost that falls between the two. This strategy utilizes the worst-case probability distribution of forecast errors for day-ahead scheduling while incorporating probabilistic information from historical data. It achieves a trade-off between economic efficiency and robustness, making it a promising solution for RIES optimization.
In this part, the effectiveness of the proposed model in the strategies for mitigating wind power uncertainty risk is validated by comparing it with the deterministic game model (model 1). The initial scenario probabilities are identical for both models. An error range of 0-40% is considered to explore the impact of wind power forecast errors, with a 10% increment for each scenario. Simulations are conducted for both models, and the results are presented in
Model | ρ (%) | Total operating cost (CNY) | Wind power curtailment rate (%) | System carbon emission cost (CNY) | Energy sale revenue (CNY) | Computational efficiency (s) |
---|---|---|---|---|---|---|
1 | 0 | 137416.17 | 2.62 | -4698.89 | 38289.42 | 62.60 |
10 | 137488.19 | 4.89 | -4476.27 | 38252.39 | 63.50 | |
20 | 137782.41 | 5.32 | -4394.71 | 38231.27 | 64.30 | |
30 | 137910.98 | 5.84 | -4236.45 | 38198.76 | 66.20 | |
40 | 138245.13 | 6.27 | -4175.33 | 38183.81 | 69.50 | |
Proposed | 0 | 137416.17 | 2.62 | -4698.89 | 38289.42 | 83.52 |
10 | 137514.22 | 4.91 | -4482.84 | 38123.91 | 90.05 | |
20 | 137634.16 | 4.96 | -4479.69 | 38021.76 | 98.23 | |
30 | 137758.08 | 5.25 | -4475.24 | 37848.59 | 105.20 | |
40 | 137865.12 | 5.78 | -4473.52 | 37684.35 | 120.20 |
When the wind power forecast error is 0, both model 1 and the proposed model produce the same results. This is because the wind power output consistently aligns with the initial scenario probability distribution, leaving no room for deviations in either model. As the wind power forecast error gradually increases, the overall energy sales revenue of model 1 surpasses that of the proposed model. This discrepancy arises from the ability of model 1 to accurately predict wind power generation during day-ahead scheduling, allowing the operator to effectively optimize energy sale revenue while ensuring that the load demand is adequately met. The proposed model, on the other hand, incorporates a conservative approach to handle uncertainties, which may lead to slightly lower energy sales revenue as a precautionary measure against potential deviations in wind power output. During the real-time scheduling stage, the proposed model adjusts equipment power and energy sales revenue values based on real-time wind power scenarios, effectively compensating for wind power uncertainty. To mitigate risks, the operator adopts a more cautious energy sales strategy, often resorting to purchasing electricity from the main grid to ensure an adequate energy supply.
Consequently, the proposed model reduces the energy sales revenue compared with a more aggressive strategy. Upon analyzing
Consequently, during situations involving substantial changes in wind power forecast errors, model 1 exhibits higher curtailment rates and carbon emission costs compared with the proposed model. In summary, the proposed model fully accounts for forecast errors in wind power generation during decision-making, offering enhanced uncertainty-handling capabilities. It effectively optimizes the power interaction between the RIES and the main grid, especially in the case of significant forecast errors. This optimization reduces curtailment rates and carbon emissions, thereby improving the operational efficiency and sustainability.
The loads with demand response capability mentioned in this paper include electricity loads and heat loads, which respond to their own demand based on the energy trading prices set by RIES operators.
Figures

Fig. 7 Operation plans of electricity load before and after demand response.

Fig. 8 Operation plans of heat load before and after demand response.
To further illustrate the rationality and feasibility of the proposed CDR scheme in this paper, a comparison is made between this scheme and a scheme that does not consider users’ CDR behavior (without a master-slave game relationship), which is denoted as scheme 1.
A comparison of the energy cost and comprehensive benefits of RIES users under different schemes is shown in
Scheme | Energy cost (CNY) | Comprehensive benefit (CNY) |
---|---|---|
1 | 41892.48 | 32674.21 |
Proposed | 38123.91 | 51883.26 |
This subsection utilizes a sample of 5000 historical wind power generation scenarios from a specific location in China.
The scenarios are further divided into ten discrete cases for analysis. The results of the optimal scheduling from the proposed model are displayed in

Fig. 9 Optimal electricity supply plan for RIES.

Fig. 10 Optimal heating supply plan for RIES.
In the context of optimizing electricity supply, as illustrated in
Additionally, during these periods, operators actively charge the GTs. The stored energy is later discharged and utilized during high-demand periods. This load-shifting strategy effectively manages peaks in electricity consumption, thereby contributing to a more balanced and efficient electricity supply system.
Concerning the optimization of heating supply, the heating model in this study incorporates GT and GB. The electricity generated by the GT and WT is used to meet the demand response for electricity loads, while the heat produced simultaneously maintains the heat balance of the system. As depicted in
This study focuses on the integration of multiple stakeholders in the RIES. A TSDRGM based on Stackelberg game theory involving RIES operators and CDR users is proposed. The efficient C&CG algorithm is employed to iteratively solve the master problem and subproblems. The validation of the proposed model leads to the following conclusions.
1) The optimal scheduling strategy presented in this study significantly improves the economic efficiency of system operation through the Stackelberg game process between RIES operators and CDR users, effectively handling different levels of wind power forecast errors. The strategy demonstrates its capability to effectively mitigate uncertainties and risks associated with wind power forecast.
2) The distributionally robust optimization allows for well-balanced trade-offs between the economic performance and the robustness of scheduling plans. It achieves this by flexibly adjusting confidence levels, combining the advantages of stochastic optimization, which reflects expected risks based on historical forecast error data, and strong robustness in robust optimization.
3) The CDR scheme proposed in this paper realizes the demand response of electricity and heat loads within a reasonable range, reducing the user’s energy cost by 8.99% and significantly increasing the user’s energy satisfaction by 58.79%. This not only alleviates the energy supply pressure of RIES operators during peak periods but also benefits users by providing economically comfortable energy use.
4) The proposed model and strategy hold promise for achieving optimal scheduling in RIESs considering the interests of various stakeholders, and effectively handling uncertainties in energy generation and demand response.
This paper examines energy pricing through a master-slave game without addressing the actual pricing mechanism for optimal energy pricing. Future research should explore more comprehensive optimization configuration schemes to promote the coordinated development of RIESs.
References
J. Wang, H. Zhong, Z. Yang et al., “Exploring the trade-offs between electric heating policy and carbon mitigation in China,” Nature Communications, vol. 11, p. 6054, Nov. 2020. [Baidu Scholar]
Q. Meng, J. Xu, F. Luo et al., “Collaborative and effective scheduling of integrated energy systems with consideration of carbon restrictions,” IET Generation, Transmission & Distribution, vol. 17, no. 18, pp. 4134-4145, Sept. 2023. [Baidu Scholar]
X. Jin, H. Jia, Y. Mu et al., “A stackelberg game based optimization method for heterogeneous building aggregations in local energy markets,” IEEE Transactions on Energy Markets, Policy and Regulation, vol. 1, no. 4, pp. 360-372, Dec. 2023. [Baidu Scholar]
P. Li, F. Zhang, X. Ma et al., “Operation cost optimization method of regional integrated energy system in electricity market environment considering uncertainty,” Journal of Modern Power Systems and Clean Energy, vol. 11, no. 1, pp. 368-380, Jan. 2023. [Baidu Scholar]
Q. Meng, J. Xu, L. Ge et al., “Economic optimization operation approach of integrated energy system considering wind power consumption and flexible load regulation,” Journal of Electrical Engineering & Technology, vol. 19, no. 1, pp. 209-221, Jan. 2024. [Baidu Scholar]
L. Ge, Y. Li, J. Yan et al., “Short-term load prediction of integrated energy system with wavelet neural network model based on improved particle swarm optimization and chaos optimization algorithm,” Journal of Modern Power Systems and Clean Energy, vol. 9, no. 6, pp. 1490-1499, Nov. 2021. [Baidu Scholar]
Q. Xu, L. Li, X. Chen et al., “Optimal economic dispatch of combined cooling, heating and power-type multi-microgrids considering interaction power among microgrids,” IET Smart Grid, vol. 2, no. 3, pp. 391-398, Sept. 2019. [Baidu Scholar]
X. Wang, C. Yang, M. Huang et al., “Multi-objective optimization of a gas turbine-based CCHP combined with solar and compressed air energy storage system,” Energy Conversion and Management, vol. 164, pp. 93-101, May 2018. [Baidu Scholar]
S. Bahrami and A. Sheikhi, “From demand response in smart grid toward integrated demand response in smart energy hub,” IEEE Transactions on Smart Grid, vol. 7, no. 2, pp. 650-658, Aug. 2016. [Baidu Scholar]
N. Liu, L. He, X. Yu et al., “Multiparty energy management for grid-connected microgrids with heat- and electricity-coupled demand response,” IEEE Transactions on Industrial Informatics, vol. 14, no. 5, pp. 1887-1897, May 2018. [Baidu Scholar]
N. Liu, L. Zhou, C. Wang et al., “Heat-electricity coupled peak load shifting for multi-energy industrial parks: a stackelberg game approach,” IEEE Transactions on Sustainable Energy, vol. 11, no. 3, pp. 1858-1869, Jul. 2020. [Baidu Scholar]
J. Chen, B. Qi, Z. Rong et al., “Multi-energy coordinated microgrid scheduling with integrated demand response for flexibility improvement,” Energy, vol. 217, p. 119387, Feb. 2021. [Baidu Scholar]
X. Jin, Q. Wu, H. Jia et al., “Optimal integration of building heating loads in integrated heating/electricity community energy systems: a bi-level MPC approach,” IEEE Transactions on Sustainable Energy, vol. 12, no. 3, pp. 1741-1754, Jul. 2021. [Baidu Scholar]
M. Sim, D. Bertsimas, and M. Zhang, “Adaptive distributionally robust optimization,” Manage Science, vol. 65, no. 2, pp. 604-618, Feb. 2019. [Baidu Scholar]
Q. Meng, G. Zu, L. Ge et al., “Dispatching strategy for low-carbon flexible operation of park-level integrated energy system,” Applied Sciences, vol. 12, no. 23, p. 12309, Dec. 2022. [Baidu Scholar]
Y. Li, F. Bu, J. Gao et al., “Optimal dispatch of low-carbon integrated energy system considering nuclear heating and carbon trading,” Journal of Cleaner Production, vol. 378, p. 134540, Dec. 2022. [Baidu Scholar]
J. Wang, L. Chen, Z. Tan et al., “Inherent spatiotemporal uncertainty of renewable power in China,” Nature Communications, vol. 14, no. 1, p. 5379, Sept. 2023. [Baidu Scholar]
T. Ding, Q. Yang, Y. Yang et al., “A data-driven stochastic reactive power optimization considering uncertainties in active distribution networks and decomposition method,” IEEE Transactions on Smart Grid, vol. 9, no. 5, pp. 4994-5004, Sept. 2018. [Baidu Scholar]
Y. Cao, W. Wei, L. Chen et al., “Supply inadequacy risk evaluation of stand-alone renewable powered heat-electricity energy systems: a data-driven robust approach,” IEEE Transactions on Industrial Informatics, vol. 17, no. 3, pp. 1937-1947, Mar. 2021. [Baidu Scholar]
W. Fan, L. Ju, Z. Tan et al., “Two-stage distributionally robust optimization model of integrated energy system group considering energy sharing and carbon transfer,” Applied Energy, vol. 331, p. 120426, Feb. 2023. [Baidu Scholar]
W. Wang, S. Huang, G. Zhang et al., “Optimal operation of an integrated electricity-heat energy system considering flexible resources dispatch for renewable integration,” Journal of Modern Power Systems and Clean Energy, vol. 9, no. 4, pp. 699-710, Aug. 2021. [Baidu Scholar]
H. Zhao, B. Wang, X. Wang et al., “Active dynamic aggregation model for distributed integrated energy system as virtual power plant,” vol. 8, no. 5, pp. 831-840, Sept. 2020. [Baidu Scholar]
W. Zheng and D. Hill, “Distributed real-time dispatch of integrated electricity and heat systems with guaranteed feasibility,” IEEE Transactions on Industrial Informatics, vol. 18, no. 2, pp. 1175-1185, Feb. 2022. [Baidu Scholar]
Y. Li, M. Han, M. Shahidehpour et al., “Data-driven distributionally robust scheduling of community integrated energy systems with uncertain renewable generations considering integrated demand response,” Applied Energy, vol. 335, p. 120749, Apr. 2023. [Baidu Scholar]
F. T. Hamzehkolaei, N. Amjady, and B. Bagheri, “A two-stage adaptive robust model for residential micro-CHP expansion planning,” Journal of Modern Power Systems and Clean Energy, vol. 9, no. 4, pp. 826-836, Aug. 2021. [Baidu Scholar]
S. He, H. Gao, H. Tian et al., “A two-stage robust optimal allocation model of distributed generation considering capacity curve and real-time price based demand response,” Journal of Modern Power Systems and Clean Energy, vol. 9, no. 1, pp. 114-127, Jan. 2021. [Baidu Scholar]
J. Zhang, M. Cui, Y. He et al., “Multi-period two-stage robust optimization of radial distribution system with cables considering time-of-use price,” Journal of Modern Power Systems and Clean Energy, vol. 11, no. 1, pp. 312-323, Jan. 2023. [Baidu Scholar]