Master-slave game collaborative operation optimization method for cross-border integrated energy system considering demand response

Abstract

The present application belongs to the research technical field of comprehensive energy system, and discloses a kind of master-slave game collaborative operation optimization method of cross-border comprehensive energy system considering demand response;The technical scheme used includes the following steps: S1) cross-border comprehensive energy system modeling, S2) the income model of each subject of cross-border comprehensive energy system considering demand response is established, S3) the master-slave game collaborative optimization model of cross-border comprehensive energy system considering demand response is established, S4) example analysis verification;By introducing the master-slave game model established by comprehensive energy system operator and user, the optimal solution of stager equilibrium is solved, by adjusting the price to guide each subject to adjust its output and energy demand, can effectively improve the source side income, reduce the cost of load side, introduce a variety of types of load demand response model, in reasonable range realizes the peak clipping and valley filling of user electricity, heat load, effectively suppresses load fluctuation, improves the economy of system.

Description

Technical Field

[0001] This invention, which considers demand response and employs a master-slave game-based collaborative operation optimization method for cross-border integrated energy systems, belongs to the research and technical field of integrated energy systems. Background Technology

[0002] With the deepening of cross-border energy trade in the future, the volume of cross-border transactions will show a rapid growth trend. However, the differences in energy market mechanisms, resource endowments, and energy trading policies among countries are becoming increasingly prominent. Energy interconnection has become an important part of China's foreign cooperation, and cross-border energy cooperation has become a crucial link in promoting rapid economic development. It plays a vital role in realizing the shared interests and destiny of energy cooperation and ensuring energy security for all countries. How to ensure the lowest system cost during long-distance cross-border energy transmission is a problem that needs further resolution. Existing research on integrated energy systems rarely considers heat load. As the degree of thermoelectric coupling continues to deepen, the demand response of heat load also has high research value. Currently, game theory models related to energy trading are mostly focused on the electricity market, lacking research on game theory methods for multiple energy trading aspects, and research on integrated energy trading involving electricity and heat interconnection is also limited. Summary of the Invention

[0003] This invention overcomes the shortcomings of existing technologies, and the technical problem it aims to solve is to provide a master-slave game-based collaborative operation optimization method for cross-border integrated energy systems that takes demand response into account.

[0004] To address the aforementioned technical problems, the present invention employs the following technical solution: a master-slave game-theoretic collaborative operation optimization method for cross-border integrated energy systems considering demand response, comprising the following steps:

[0005] S1) Cross-border integrated energy system modeling;

[0006] S2) Establish a benefit model for each entity in a cross-border integrated energy system that takes into account demand response;

[0007] S3) Establish a master-slave game collaborative optimization model for cross-border integrated energy systems that considers demand response;

[0008] S4) Case analysis and verification.

[0009] Compared with the prior art, the present invention has the following advantages:

[0010] 1. By introducing a master-slave game model between integrated energy system operators and users, the optimal solution of the Staberg equilibrium is found. By adjusting prices, the entities are guided to adjust their own output and energy demand, which can effectively improve the revenue on the source side and reduce the cost on the load side.

[0011] 2. By introducing various types of load demand response models, peak shaving and valley filling of user electricity and heat loads were achieved within a reasonable range, effectively smoothing load fluctuations and improving system economy;

[0012] 3. Considering that cross-border interaction between energy systems can regulate the imbalance of resource allocation between countries, it can effectively reduce the amount of electricity purchased by the grid, increase the proportion of natural gas used and the amount of renewable energy consumed, which is of great significance for reducing the carbon emissions of system units and achieving carbon neutrality. It is an important way to achieve coordinated operation of cross-border integrated energy systems. Attached Figure Description

[0013] The present invention will now be described in further detail with reference to the accompanying drawings;

[0014] Figure 1 This is a schematic diagram of the two-layer master-slave game framework of the cross-border integrated energy system in this invention;

[0015] Figure 2 This invention provides examples of IES load and wind and solar power output predictions for various countries.

[0016] Figure 3 The example analysis of this invention includes the revenue curves of integrated energy operators in various countries.

[0017] Figure 4 The example analysis of this invention includes user revenue curves in various countries.

[0018] Figure 5 The example analysis of the present invention focuses on the IER electricity price in country A.

[0019] Figure 6 The example analysis of the IER electricity price in country B in this invention;

[0020] Figure 7 The example analysis of the IER electricity price in country C in this invention;

[0021] Figure 8 The example analysis of the present invention is the IER heat price in country A;

[0022] Figure 9 The example analysis of the IER heat price in country B in this invention;

[0023] Figure 10 The example analysis of the IER heat price in country C in this invention;

[0024] Figure 11 The example analysis of this invention shows the electrical load curves of country A before and after the demand response;

[0025] Figure 12 The example analysis of this invention shows the electrical load curves of country B before and after the demand response.

[0026] Figure 13 The example analysis of this invention shows the electricity load curves of country C before and after the demand response;

[0027] Figure 14 The example analysis of this invention shows the heat load curves of country A before and after the demand response;

[0028] Figure 15 The example analysis of this invention shows the heat load curves of country B before and after the demand response;

[0029] Figure 16 The example analysis of this invention shows the heat load curves of country C before and after the demand response;

[0030] Figure 17 The example analysis of this invention shows the power dispatch results for country A.

[0031] Figure 18 The example analysis of this invention shows the power dispatch results for country B.

[0032] Figure 19 The results of power dispatching in country C are shown in the example analysis of this invention.

[0033] Figure 20 The results of thermal energy dispatching in country A are presented in the example analysis of this invention.

[0034] Figure 21 The results of thermal energy dispatching in country B are presented in the example analysis of this invention.

[0035] Figure 22 The results of thermal energy dispatching in country C are presented in the example analysis of this invention.

[0036] Figure 23 The example analysis of this invention includes the revenue curves of integrated energy operators in various countries.

[0037] Figure 24 The example analysis of this invention includes user revenue curves for various countries. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments; based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] A master-slave game-theoretic collaborative operation optimization method for cross-border integrated energy systems considering demand response includes the following steps:

[0040] S1) Cross-border integrated energy system modeling;

[0041] S2) Establish a benefit model for each entity in a cross-border integrated energy system that takes into account demand response;

[0042] S3) Establish a master-slave game collaborative optimization model for cross-border integrated energy systems that considers demand response;

[0043] S4) Case analysis and verification.

[0044] Step S1) Cross-border integrated energy system modeling includes:

[0045] S11) Gas Turbine

[0046] The mathematical model of a gas turbine can be expressed by the following formula:

[0047]

[0048] In the formula: This represents the output electrical power of the gas turbine in the integrated energy system of the i-th country at time t; L represents the output thermal power of the gas turbine in the integrated energy system of the i-th country at time t; NG This indicates the lower heating value of natural gas; η represents the amount of natural gas consumed by the gas turbine during time period t; GT N represents the power generation efficiency of a gas turbine. GT Indicates the waste heat recovery coefficient;

[0049] S12) Gas-fired boiler

[0050] The mathematical model of a gas-fired boiler is represented by the following formula:

[0051]

[0052] In the formula: L represents the output thermal power of the gas-fired boiler in the integrated energy system of the i-th country at time t; NG This indicates the lower heating value of natural gas; η represents the natural gas consumption of a gas-fired boiler during time period t; GB This indicates the heating efficiency of the gas-fired boiler;

[0053] S13) Renewable Energy

[0054] Renewable energy sources include wind power and solar power:

[0055] S131) ​​Wind power generation

[0056] Wind power output is limited by the incoming wind speed, but when the incoming wind speed is lower than the cut-in wind speed or higher than the cut-out wind speed, the wind farm does not generate electricity. The wind power output at time t in the i-th national integrated energy system... The relationship between the wind speed and the incoming wind speed is as follows:

[0057]

[0058] In the formula, ρ is the air density; A is the swept area of ​​the wind turbine blades; v is the wind speed; c wt The wind energy utilization coefficient is the ratio of the wind energy absorbed by the wind turbine per unit time to the total wind energy passing through the rotating surface of the wind turbine; λ wt The ratio of leaf tip speed;

[0059] S132) Photovoltaic power generation

[0060] The principle of photovoltaic power generation technology is to directly convert solar energy into electrical energy using the photovoltaic effect of semiconductor materials. The photovoltaic power generation capacity of the i-th country's integrated energy system at time t is... The mathematical model is as follows:

[0061]

[0062] In the formula, G is the illuminance (kW / m²). 2 );T s P represents the surface temperature of the photovoltaic cell (°C). stc G stc T stc These are the maximum output power (kW) and illuminance (kW / m²) under standard test conditions, respectively. 2 ), the surface temperature of the photovoltaic cell (25℃); ε is the temperature coefficient of the photovoltaic cell;

[0063] T s =T a +0.0138·(1+0.031T a In the formula )·(1-0.042v)·G(6), T a Ambient temperature (°C); v is wind speed (m / s); G is illuminance (kW / m²). 2 );

[0064] S14) Energy storage equipment

[0065] Energy storage systems can charge during off-peak hours at night and release energy during peak hours during the day, effectively reducing the peak-valley difference, achieving peak shaving and valley filling, and improving the stability of the power system. At the same time, in cross-border integrated energy systems, resources are unevenly distributed and energy situations vary greatly. Energy storage devices can smooth out power fluctuations caused by the access of a large number of renewable energy sources.

[0066] Energy storage devices include batteries and thermal storage tanks:

[0067] S141) Battery

[0068] When the battery discharges

[0069]

[0070] When the battery is charging

[0071]

[0072] In the formula, W t e,i Let be the amount of electricity (kWh) stored in the battery of the i-th national integrated energy system at time t; These represent the charging power and discharging power (kW) of the battery in the i-th national integrated energy system at time t. These are the battery's own discharge efficiency and charging efficiency, respectively. These are the battery's own discharge loss and charging loss, respectively.

[0073] S142) Heat storage tank

[0074] When the heat storage tank releases heat

[0075]

[0076] When the heat storage tank is heated

[0077]

[0078] In the formula, W t h,i Let be the thermal energy (kJ) stored in the thermal storage tank of the i-th national integrated energy system at time t; These are the heat release power and heat charging power (kW) of the thermal storage tank at time t in the i-th national integrated energy system; These are the heat release efficiency and heat charging efficiency of the heat storage tank itself, respectively. These are the heat release loss and heat charging loss of the heat storage tank itself, respectively.

[0079] S15) Electric Boiler

[0080] The mathematical model for an electric boiler is as follows:

[0081]

[0082] In the formula, Let be the heating capacity of the electric boiler in the integrated energy system of the i-th country at time t; η represents the electrical power required by the electric boiler in the integrated energy system of the i-th country at time t. EB The conversion efficiency of the electric boiler;

[0083] S16) Power Loss

[0084] Cross-border lines inevitably experience power losses due to their long lengths, and these losses vary over time, including both electrical and thermal power losses.

[0085] S161) Power Loss

[0086] By analyzing the changes in voltage, reactive power, and active power flowing through the line over a period of time, the power loss of the line can be calculated. The power loss model is as follows:

[0087]

[0088] In the formula, P k Q k U k The active and reactive power and voltage at a certain end of the line during each time period; R is the resistance of the line.

[0089] S162) Heat Power Loss

[0090] Given the user heat load, ambient temperature, and network structure, the outlet and return temperatures of the energy center during time period t are calculated using power flow analysis. Based on the outlet flow rate of the energy center, the total heat supply can be obtained, and the heat network loss during time period t can be calculated as follows:

[0091]

[0092] In the formula, C p This is the specific heat capacity of water; This refers to the outlet water flow rate of the heat source center. The outlet temperature of the heat source center; The temperature returned from the center of the heat source; To transfer heat power between the integrated energy systems of countries i and j.

[0093] Step S2) establishes a benefit model for each entity in a cross-border integrated energy system that considers demand response, including:

[0094] S21) Profit Model for Cross-border Integrated Energy System Operators

[0095] A two-tier game framework for cross-border integrated energy systems, such as Figure 1 As shown.

[0096] Integrated energy retailers (IERs) are leaders and coordinators in cross-border integrated energy systems. They are responsible for balancing the power output of market investors across energy sources, loads, and storage, acting as managers. Users can interact and trade with IERs by providing feedback on their energy demand. In any demand response period t, an IER formulates a pricing strategy based on its own energy supply equipment output plan and the energy demand on the consumer side. Its revenue function can be expressed as:

[0097]

[0098] in, This represents the revenue from energy sales to users by the integrated energy system of country i during time period t; Let $t$ represent the grid interaction cost of the integrated energy system of the i-th country during time period $t$. If $t$ is greater than 0, it means that the country is purchasing electricity from the grid; otherwise, it means that the country is selling electricity to the grid. This represents the fuel cost of the CCHP unit in the i-th integrated energy system country during time period t; This represents the equipment operation and maintenance cost of the integrated energy system of the i-th country during time period t; This represents the interaction costs between the integrated energy systems of various countries;

[0099]

[0100] In the formula, This represents the sum of electricity load energy prices for users in the i-th country's integrated energy system during time period t. Let $t$ be the sum of the heat load energy prices for users in the integrated energy system of country $i$ during time period $t$. and These represent the electrical load and heat load of users in the integrated energy system of the i-th country during time period t, respectively. and Let these represent the electricity and heat prices sold to users by the integrated energy system operator in the i-th country, respectively. and Let represent the electricity sales price and purchase price from the external power grid by the integrated energy system operator of the i-th country, respectively. and These represent the sales and purchase prices of heat to the external heating network by the integrated energy system operator of the i-th country, respectively. These represent the costs of purchasing electricity and heat between the integrated energy systems of different countries, respectively. This represents the power supply from the operator of the integrated energy system of the i-th country during time period t; c represents the heat supply of the integrated energy system operator in country i during time period t; GT c GB c EB c HS cES c PV c WT The unit power maintenance cost, in yuan, is for gas turbines, gas boilers, electric boilers, thermal storage tanks, batteries, photovoltaic systems, and wind turbines. and These represent the electrical output power of the gas turbine and the thermal output power of the gas boiler in the integrated energy system of the i-th country during time period t, respectively. Let be the heating capacity of the electric boiler in the integrated energy system of the i-th country at time t; Let be the thermal power of the thermal storage tank in the integrated energy system of the i-th country at time t; Let be the battery power of the integrated energy system of the i-th country at time t; Let be the photovoltaic power generation capacity of the integrated energy system of the i-th country at time t; Let a be the wind power output of the integrated energy system of the i-th country at time t; e b e c e a h b h c h These represent the fuel cost coefficients for gas turbines and gas-fired boilers, respectively. The electrical power transmitted between the integrated energy systems of countries i and j;

[0101] Furthermore, to avoid direct transactions between energy consumers and the grid, the price at which operators sell their energy should be slightly lower than the market price, and the following constraints must be met:

[0102]

[0103] In the formula, This represents the electricity price sold to users by the integrated energy system operator in the i-th country; and Let represent the electricity sales price and purchase price from the external power grid by the integrated energy system operator of the i-th country, respectively.

[0104] S22) User Benefit Model of Cross-border Integrated Energy System

[0105] In a comprehensive energy system, there are several electricity and heat users, each with different energy consumption tendencies. Based on the energy operator's set energy sales price, users optimize their electricity and heat loads according to incentive levels, reducing some non-critical loads and incurring response costs to earn response revenue. That is, demand-side electricity and heat users flexibly reduce their loads to respond to higher-level demand and obtain response revenue based on the amount of load reduction. The user's revenue function, which is the difference between their utility function and energy cost, can be expressed as follows for any demand response period t:

[0106]

[0107] In the formula, Let represent the utility function of a user in the integrated energy system of the i-th country, which represents the degree of satisfaction a user obtains from purchasing electricity and heat. It is usually non-decreasing and convex, and has various forms, including quadratic and logarithmic forms. and Let the electrical load and thermal load of the user in the i-th country at time t be represented by quadratic functions:

[0108]

[0109] In the formula, v e ,α e ,v h ,α h These represent preference coefficients for electricity and heat consumption, respectively, which reflect users' energy demand preferences and influence the magnitude of demand.

[0110] Step S3) establishes a master-slave game collaborative optimization model for a cross-border integrated energy system that considers demand response, including:

[0111] S31) Construction of Master-Slave Game Model

[0112] The master-slave game model established in this invention includes integrated energy retailers (IERs) and users, such as... Figure 1 As shown, where IER acts as the leader and users as followers, the Stackelberg game model for the cross-border integrated energy system established in this invention is as follows:

[0113] Participants: The main participants in the master-slave game include integrated energy operators and users from various countries. The set of participants is represented as follows:

[0114] N i ={ier i ,user i} (25)

[0115] In the formula, ier i user i Let them represent the integrated energy operator in country i and the user in country i, respectively.

[0116] Strategy sets: The strategy sets of integrated energy operators in various countries include the output of each unit and the electricity and heat sales prices in each country. The strategy sets of users in various countries include their own transferable electrical and heat loads. The strategy sets of integrated energy operators and users in various countries are represented by vectors as follows:

[0117]

[0118] In the formula, Let represent the strategy set of the integrated energy operator in the i-th country; Let represent the output power of the gas turbine, gas boiler, electric boiler, and storage battery in the integrated energy system of the i-th country, respectively. Let represent the unit price of electricity purchase and sale, and the unit price of electricity sale and heat sale, respectively, for the integrated energy system of country i.

[0119]

[0120] In the formula, This represents the policy set of users in the i-th country; Let i represent the transferable electrical load and transferable heat load of country i, respectively.

[0121] Payoff function: The payoff function of the master-slave game is the payoff function of the integrated energy operators of various countries and the payoff function of the users established in Section 4;

[0122] S311) Game Model Upper-Level Pricing Strategy

[0123] As the leader, the operator is at the top of the master-slave game model. Based on considerations such as demand response and power generation constraints, the operator sets subsidy prices with the aim of maximizing its revenue from demand response during any given demand response period. This can be expressed as:

[0124]

[0125] In the formula, This represents the revenue from energy sales to users by the integrated energy system of country i during time period t; Let $t$ represent the grid interaction cost of the integrated energy system of the i-th country during time period $t$. If $t$ is greater than 0, it means that the country is purchasing electricity from the grid; otherwise, it means that the country is selling electricity to the grid. This represents the fuel cost of the CCHP unit in the i-th integrated energy system country during time period t; This represents the equipment operation and maintenance cost of the integrated energy system of the i-th country during time period t;

[0126] S312) Lower-level response strategy in the game model

[0127] Users, as followers, are at the lower level of the master-slave game. Maximizing consumer surplus can be represented as:

[0128]

[0129] In the formula, Let represent the utility function of a user in the integrated energy system of the i-th country, which represents the degree of satisfaction a user obtains from purchasing electricity and heat. It is usually non-decreasing and convex, and has several forms such as quadratic and logarithmic. and Let the electrical load and thermal load of the user in the i-th country at time t be represented by quadratic functions:

[0130]

[0131] In the formula, v e ,α e ,v h ,α h These represent the preference coefficients for electricity and heat consumption, respectively, which can reflect users' energy demand preferences and affect the magnitude of demand.

[0132] S313) Constraints

[0133] To ensure the safe and reliable operation of the integrated energy system, in addition to defining the objective function, system constraints also need to be considered, including power balance constraints, unit output constraints, and unit ramp-up constraints.

[0134] S3131) Electrical balance constraint

[0135]

[0136] In the formula, These represent the power purchased from the grid and the power sold to the grid by the integrated energy system of the i-th country at time t, respectively. Let be the electrical power required by the electric boiler in the integrated energy system of the i-th country at time t; The electrical power transmitted between the integrated energy systems of countries i and j; The power loss transmitted between the integrated energy systems of countries i and j;

[0137] S3132) Thermal balance constraint

[0138]

[0139] In the formula, Let be the heat purchase power and heat sale power of the integrated energy system of the i-th country at time t, respectively, interacting with the heat network. For the heat power transferred between the integrated energy systems of countries i and j, The heat power loss in the heat network transmission between the integrated energy systems of countries i and j Let the heat load be that of the i-th country.

[0140] S3133) Comprehensive Demand Response Constraints

[0141] ① Electricity load demand response is divided into price-based demand response and incentive-based demand response:

[0142] Price-based demand response:

[0143] Price-based demand response incentivizes users to adjust their energy consumption strategies by introducing peak, off-peak, and flat time-of-use pricing, thereby achieving peak shaving and valley filling. The most commonly used modeling method is the price elasticity matrix method. Since residential load is included in the integrated energy systems of various countries, and residential load is highly sensitive to changes in electricity prices, price-based demand response is considered.

[0144]

[0145] In the formula: ξ is the elasticity coefficient; ΔP and P are the electricity consumption adjustment amount and electricity consumption, respectively; Δθ and θ are the electricity price adjustment amount and electricity price, respectively.

[0146] The electrical load power after demand response is expressed as:

[0147]

[0148] In the formula, P t i,0 Let ΔP be the electrical load before the demand response of the integrated energy system of the i-th country; t i Let $i$ be the amount of electricity load adjustment before and after the integrated energy system response of the $i$-th country.

[0149] Based on time-of-use pricing and fixed pricing, the following matrix is ​​established:

[0150]

[0151] Incentive-based demand response:

[0152] Industrial loads in the integrated energy systems of various countries are highly sensitive to direct economic incentives; therefore, incentive-based demand response is considered. Electrical load includes stationary electrical load and transferable electrical load, and can be expressed as:

[0153]

[0154] in, This represents the fixed electrical load of the integrated energy system of the i-th country at time t; This represents the transferable electrical load of the integrated energy system of the i-th country at time t;

[0155] Users can adjust their energy load reasonably based on the energy sales price offered by the operator, but the following constraints must be met:

[0156]

[0157] In the formula, W represents the upper limit of the electrical load that a user can transfer. selThis represents the total amount of transferable electrical load within T time periods, meaning that the total amount of transferable electrical load before and after demand response needs to remain unchanged.

[0158] ② Heat load demand response, including fixed heat load and transferable heat load, as shown below:

[0159]

[0160] In the formula, and Let represent the fixed heat load and the transferable heat load of the integrated energy system of the i-th country at time t, respectively. The transferable heat load can be transferred in a certain proportion according to the user's comfort and energy supply adequacy.

[0161]

[0162] In the formula, This represents the upper limit of the heat load that a user can transfer, W. sel This represents the total amount of transferable heat load within T time periods, meaning that the total amount of transferable heat load before and after the demand response needs to remain unchanged.

[0163] S3134) Power Constraints Between Integrated Energy Systems and Electricity / Heating Networks in Various Countries

[0164]

[0165] In the formula, Let be the maximum permissible power purchase capacity for the interaction between the integrated energy system and the power grid of the i-th country; The maximum permissible power sales capacity for the interaction between the integrated energy system and the power grid of the i-th country; This represents the flag bit indicating that the integrated energy system of the i-th country purchases electricity from the grid at time t, where 1 indicates the start of electricity purchase and 0 indicates the stop of electricity purchase; This represents the flag bit indicating that the integrated energy system of the i-th country sells electricity to the grid at time t, with 1 indicating the start of electricity sales and 0 indicating the stop of electricity sales;

[0166]

[0167] In the formula, The maximum permissible power purchase capacity for the interaction between the integrated energy system and the heating network of the i-th country; The maximum allowable power sales capacity for the interaction between the integrated energy system and the heating network of the i-th country; This represents the flag indicating that the integrated energy system of the i-th country purchases heat from the heat network at time t, with 1 indicating the start of heat purchase and 0 indicating the stop of heat purchase; This represents the flag indicating that the integrated energy system of the i-th country is selling heat to the heating network at time t, with 1 indicating the start of heat sales and 0 indicating the stop of heat sales;

[0168] S3135) Upper and lower limits of equipment output in national integrated energy systems

[0169]

[0170] In the formula, Let m be the electrical power of equipment m in the integrated energy system of the i-th country; Let m be the upper and lower limits of the electrical power of equipment m in the integrated energy system of the i-th country; Let m be the electrical power of device m; Let m be the upper and lower limits of the thermal power of equipment m in the integrated energy system of the i-th country.

[0171] S3136) Battery power constraint

[0172]

[0173] In the formula, Let be the battery capacity of the integrated energy system of the i-th country; Maximum charging rate; This is the maximum discharge rate; The state bit for charging at time t; The state bit for energy release at time t is a 0-1 variable, indicating that the charging and discharging state of the same device at the same time is unique. Let the maximum and minimum energy storage capacity of the battery in the integrated energy system of the i-th country be denoted by .

[0174] S3137) Power constraint of thermal storage tank

[0175]

[0176] In the formula, Let be the capacity of the thermal storage tank in the integrated energy system of the i-th country. This is the maximum heat charging rate; This represents the maximum heat release rate. Let be the maximum and minimum heat storage capacity of the thermal storage tank in the integrated energy system of the i-th country;

[0177] S3138) Inter-national power constraints on electricity and heat networks within integrated energy systems

[0178]

[0179] In the formula, This represents the maximum electrical power transmitted between the integrated energy systems of countries i and j. This represents the maximum heat transfer capacity between the integrated energy systems of countries i and j.

[0180] S3139) Constraints on power grid and heating network losses between national integrated energy systems

[0181]

[0182] In the formula, This represents the maximum power loss during power transmission between the integrated energy systems of countries i and j. The maximum heat power loss transmitted between the integrated energy systems of countries i and j is the maximum value of heat power loss in the heat network.

[0183] S32) Staberg equilibrium

[0184] When followers make the best response based on the leader's strategy, and the leader also obtains the best strategy, it indicates that the game has reached a Staberg equilibrium. If the condition of equation (54) is satisfied, then the equilibrium of the proposed Staberg game is reached:

[0185]

[0186] Once a game equilibrium is reached, none of the participants can unilaterally change their strategies to obtain higher returns.

[0187] Before finding the Staberg equilibrium solution, it is necessary to prove its existence and uniqueness.

[0188] The theorem used states that a unique Staberg equilibrium exists when the master-slave game model satisfies the following conditions:

[0189] 1) The strategy set of the leader and followers is a non-empty compact convex set;

[0190] 2) Once the leader's strategy is given, there is a unique optimal solution for all followers;

[0191] 3) Given the followers' strategies, there exists a unique optimal solution for the leader;

[0192] Proof: The following will prove that the master-slave game model of the cross-border integrated energy system satisfies the three conditions for the existence and uniqueness of the Staberg equilibrium mentioned above:

[0193] 1) According to the cross-border integrated energy system model, the leader's strategy needs to satisfy equation (30)-(53) and the user-side follower's strategy needs to satisfy equation (30)-(53). Therefore, the strategy set of each participant is non-empty and compact convex.

[0194] 2) Prove that given the leader's strategy, there exists a unique optimal solution for all followers:

[0195] Substitute equations (15)-(20) into equation (14), and then calculate the equations (14) with respect to the following conditions. The first-order partial derivative yields:

[0196]

[0197] In the formula, ηh =(1-η GT ) / η GT To establish the relationship between the output electrical power of the gas-fired boiler and the waste heat recovery power, setting the first-order partial derivative to zero, we can obtain:

[0198]

[0199] Then, find the equation (1) with respect to... The second-order partial derivative yields:

[0200]

[0201] Since the cost coefficient is positive, the second-order partial derivative is always less than 0. The extreme point is the maximum point of equation (23). However, due to the constraints of the upper and lower limits of the strategy interval, the extreme point may fall on the boundary of the interval when the energy price changes. Therefore, the value of the optimal strategy on the energy supply side can be expressed as:

[0202]

[0203] Therefore, regardless of the value, once the operator's purchase price is given, there exists a unique optimal solution for the integrated energy system operator.

[0204] Next, we calculate the objective function (24) of the user with respect to... and The first-order partial derivative yields:

[0205]

[0206] Setting the first-order partial derivative above to 0, we can obtain:

[0207]

[0208] Then find the equation (24) with respect to... and The second-order partial derivative yields:

[0209]

[0210] Since the energy preference coefficient is generally positive, the second-order partial derivatives here are all less than 0. and Given that this is the maximum point of equation (24), and considering the constraint on the interval of the optimization variables, the optimal solution can be expressed as:

[0211]

[0212] Therefore, once the operator's selling price is given, there is also a unique optimal solution for the user;

[0213] 3) Prove that once the follower's strategy is given, the leader has a unique optimal solution, and the operator's profit can be expressed as:

[0214]

[0215] The follower's set of optimization strategies are valued. Substituting into the above equation, and finding the leader's objective function (1) regarding... The first-order partial derivatives yield:

[0216]

[0217] In the formula, η h =(1-η GT ) / η GT At this point, the Hessian matrix of the leader's payoff function is expressed as:

[0218]

[0219] It can be observed that the Hessian matrix is ​​negative definite, thus indicating the existence of a maximum point. Similarly, when the follower takes other extreme points, it can be proven that the leader has a unique optimal solution, and the proof is similar to the above process. In summary, the master-follower game model proposed in this invention has a unique Staberg equilibrium.

[0220] S33) Model Solving Method

[0221] For the aforementioned master-slave game model, different solution algorithms are used to optimize the payoff functions of each agent in the upper and lower layers of the model. The solution for the leader (energy operator) is obtained using a differential evolution algorithm to reduce the difficulty, while the solution for the follower (user) is obtained using Yalmip modeling and the Cplex solution tool to accelerate the algorithm's solution speed and ensure the accuracy of the results. If each participant obtains the same optimal strategy in two consecutive rounds, i.e.:

[0222]

[0223] According to the definition of Staberg equilibrium, the country's strategy combination has converged to an equilibrium point, at which point no participant can change their strategy alone to gain more benefits.

[0224] The model solution process of the S33) model solution method is as follows:

[0225] The upper-level optimization algorithm includes the following steps:

[0226] ①: Input initial data and set parameters, including the user's typical daily and thermal power, wind turbine and photovoltaic predicted output, operating parameters of each device, and upper and lower limits of energy prices, etc.

[0227] ②: Initialize the population a and set the iteration count K = 0;

[0228] ③: The integrated energy operator sends the optimized energy selling price to the lower - layer user followers;

[0229] ④: The users call the lower - layer algorithm to calculate their own benefits;

[0230] ⑤: The integrated energy operator calculates its own objective function U1 according to Equation (14);

[0231] ⑥: Perform crossover and mutation operations on the population a to obtain a new population b;

[0232] ⑦: Call the lower - layer algorithm again to optimize and solve the follower's objective function, and send the optimization result to the upper - layer integrated energy operator. The integrated energy operator calculates its own objective function U2 according to Equations (15) - (25);

[0233] ⑧: Selection operation. If U2 > U1, then a = b and U1 = U2. If U2 < U1, then keep unchanged;

[0234] ⑨: Determine whether the iteration count is satisfied. If satisfied, output the optimal result. Otherwise, jump to ⑥;

[0235] The lower - layer algorithm includes the following steps:

[0236] ①: The users call the Cplex solving tool to calculate the user's electrical and thermal adjustable loads according to Equation (23);

[0237] ②: Send the optimization result to the upper - layer leader.

[0238] The result of the case analysis and verification in step S4) is as follows:

[0239] The iterative convergence results of integrated energy operators and users in various countries reach convergence at about 200 iterations. In the upper - layer game, the integrated energy operator's revenue shows a gradually increasing trend by continuously adjusting its energy selling price and equipment output. In the lower - layer game, the users' revenue function fluctuates by reasonably adjusting their energy - using strategies in combination with the upper - layer leader's energy selling price. There is an obvious game interaction between the two sides, and both finally reach convergence. Through the above game analysis, the game process between the two sides can be well reflected. When the game reaches the Stackelberg equilibrium, their strategies will no longer change.

[0240] The following is a detailed description of one of the case analysis and verification examples of the present invention.

[0241] Case analysis

[0242] To verify the economics and feasibility of the model built by the master-slave game collaborative operation optimization method of the cross-border integrated energy system considering demand response in this invention, this invention selects three regions—China, Laos, and Myanmar—for case analysis. In this case, the integrated energy system operators of each country can exchange thermal and electrical energy. Within each region, renewable energy generation and the power generation and heating of each unit prioritize meeting the load of users in the region. When there is a surplus, electricity and heat are sold to the power and heat network; when there is a shortage, electricity and heat are purchased from the power and heat network.

[0243] The simulation calculations for this invention were performed using MATLAB R2016a software combined with the YALMIMP plugin to call the CPLEX solver. The computer configuration was an Intel Core i7 processor with a clock speed of 1.8GHz and 16GB of memory. The particle swarm size was set to 10, and the number of evolutions was set to 30.

[0244] Example parameters

[0245] This example demonstrates the predicted renewable energy output and electricity and heat load forecasts for various countries' integrated energy systems. Figure 2 As shown, the peak electrical load occurs between 10:00-13:00 and 18:00-22:00, while the peak thermal load occurs between 4:00-8:00. Assuming that transferable electrical load accounts for 20% of the total electrical load, and transferable thermal load, due to its greater adjustment difficulty, accounts for 10% of the total thermal load, the upper limit of transferable electrical load power is 250kW, and the upper limit of transferable thermal load power is 200kW. The user's preference coefficient for electricity and heat energy is v. e v h a e a h The values ​​are 1.6, 1.2, 0.0011, and 0.0014 respectively, and the fuel cost coefficients a, b, and c of the IER are 0.0015, 0.16, and 0 respectively. The IES equipment capacity of each country is shown in Table 1, and the electricity and heat prices of each country are shown in Table 2. This system uses a 24-hour day as a cycle and adopts... Figure 1 The diagram shows the cross-border integrated energy system structure. Each country's IES includes residential users, commercial users, and industrial users.

[0246] Table 1 Equipment Capacity and Parameters

[0247]

[0248] Table 2 Electricity and Heat Prices in Various Countries

[0249]

[0250] Results Analysis

[0251] Independent operation of integrated energy systems in various countries

[0252] The simulation results show that the iterative convergence results for integrated energy operators and users in various countries are as follows: Figure 3 , 4 As shown, convergence was achieved after approximately 200 iterations. In the upper-level game, the integrated energy operator's revenue gradually increased by continuously adjusting its energy sales price and equipment output. In the lower-level game, users adjusted their energy consumption strategies based on the energy sales price of the upper-level leader, resulting in fluctuations in their revenue function. The graph clearly shows a significant game interaction between the two sides, ultimately leading to convergence. This game analysis effectively reflects the game process between the two parties. Once the Staberg equilibrium is reached, their strategies remain unchanged. Ultimately, the revenues of the leading integrated energy operators in countries A, B, and C are 16133.7, 16246.6, and 19016.6 yuan, respectively; the consumer surplus of the follower users in countries A, B, and C are 16807.7, 17593.5, and 18647.7 yuan, respectively.

[0253] The pricing strategies of top-level operators in various countries are as follows: Figure 5 , 6 As shown in Figure 7, the red and green dashed lines represent the time-of-use (TOU) price and the grid connection price, respectively, when interacting with the power grid. To prioritize the consumption of renewable energy within the system, operators' pricing strategies are always included within the pricing of the main grid, providing energy consumers with more favorable prices. The figure shows that the fluctuation trend of operators' electricity sales prices is consistent with the TOU price of the main grid, aiming to incentivize users to actively purchase electricity. Similarly, the analysis of heat prices is similar to that of electricity prices. Figure 8 , 9 As can be seen from point 10, the heating price strategy is always contained within the upper and lower limits of the heating network pricing, providing better prices for energy users. The purpose is to incentivize users to actively purchase heating, and the purchase price is related to the trend of user heat load.

[0254] Electricity and heat load curves before and after user-side demand response in various countries are as follows: Figure 11-16 As shown. By Figure 11-13 It can be seen that, driven by electricity price incentives, in order to reduce overall electricity costs, the electricity load curves of various countries exhibit a "peak shaving and valley filling" characteristic before and after demand response. The original peak load curves on the user side of various countries occurred between 10:00-13:00 and 18:00-22:00, when electricity prices were relatively high. After user-side optimization, the peak load significantly decreased, shifting to the valley load phases with lower electricity prices between 0:00-8:00 and 23:00-24:00, resulting in a significant reduction in the fluctuation of the electricity load curve. Figure 14-16 It can be seen that the trends of heat load and electrical load on the user side are roughly the same in various countries. However, since users are more sensitive to changes in heat, the amount of heat load transfer is relatively small in order to ensure user comfort.

[0255] This invention, based on the principle of low carbon emissions and considering the environmental friendliness of new energy sources, prioritizes the consumption of new energy power generation by integrated energy operators in various countries. Figure 17-19 According to power dispatch results, during the off-peak electricity consumption period from 23:00 to 7:00, electricity consumption is low in various countries, and electricity prices are at their lowest. The electricity load is mainly supplied by wind turbines, with the shortfall supplemented by gas turbines. During this time, the gas turbines operate at low pressure but produce a relatively high output; the excess power is transferred to the batteries in the IER (Integrated Electricity Recycling Unit) for charging and storage. Figure 20-22 The thermal energy dispatch results show that, to ensure heating supply, operators guide boiler output through price responses. The heat load is primarily borne by waste heat boilers and gas-fired boilers, with excess heat stored in IERs via thermal storage tanks. During periods of low demand, electricity demand gradually increases, wind and solar power output is fully absorbed, gas turbine output increases, and any shortfall is compensated for through interaction with the main power grid. The heat load is still provided by waste heat boilers and gas-fired boilers, with any shortfall supplemented by heat release through thermal storage tanks.

[0256] Comparison of the coordinated operation of integrated energy systems in various countries

[0257] The simulation results show that, considering coordinated operation, the iterative convergence results for integrated energy operators and users in various countries are as follows: Figure 23 , 24 As shown, once the Staberg equilibrium is reached, their strategies remain unchanged. Ultimately, the revenues of the leading integrated energy operators in countries A, B, and C are RMB 17,133.7, 17,246.6, and 19,816.6, respectively, while the surplus of the follower users in countries A, B, and C are RMB 17,807.7, 18,593.5, and 19,447.7, respectively. This demonstrates that by considering cross-border energy interactions within the integrated energy system, the interactions between countries are incorporated into the game strategy, improving the efficiency of resource optimization and allocation among countries, effectively reducing energy purchase costs for each country, and increasing the revenues of cross-border countries.

[0258] in conclusion

[0259] This invention proposes a master-slave game-theoretic collaborative operation optimization method for cross-border integrated energy systems that considers demand response. The game process is divided into two layers: the upper layer, the Integrated Energy Controller (IER), acts as the leader, disseminating the output of each unit and energy sales prices to the lower layer users. Users adjust their demand based on the output plan and energy sales prices provided by the upper-layer IER, achieving multi-entity collaborative optimization operation. Finally, numerical examples verify the effectiveness of the proposed model, leading to the following conclusions:

[0260] (1) This invention introduces a master-slave game model between integrated energy system vendors and users to solve the optimal solution of the Staberg equilibrium. By adjusting prices, it guides each entity to adjust its own output and energy demand, which can effectively improve the source-side revenue and reduce the load-side cost.

[0261] (2) By introducing various types of load demand response models, peak shaving and valley filling of user electricity and heat loads were achieved within a reasonable range, effectively smoothing load fluctuations and improving system economy;

[0262] (3) Considering that cross-border interaction between energy systems can regulate the imbalance of resource allocation between countries, it can effectively reduce the amount of electricity purchased by the grid, increase the proportion of natural gas used and the amount of renewable energy consumed, which is of great significance for reducing the carbon emissions of system units and achieving carbon neutrality. It is an important way to achieve coordinated operation of cross-border integrated energy systems.

[0263] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A master-slave game-theoretic collaborative operation optimization method for cross-border integrated energy systems considering demand response, characterized in that... Includes the following steps: S1) Cross-border integrated energy system modeling; Step S1) cross-border integrated energy system modeling includes: S11) Gas Turbine The mathematical model of a gas turbine can be expressed by the following formula: In the formula: This represents the output electrical power of the gas turbine in the integrated energy system of the i-th country at time t; L represents the output thermal power of the gas turbine in the integrated energy system of the i-th country at time t; NG Indicates the lower heating value of natural gas; η represents the amount of natural gas consumed by the gas turbine during time period t; GΤ N represents the power generation efficiency of a gas turbine. GT Indicates the waste heat recovery coefficient; S12) Gas-fired boiler The mathematical model of a gas-fired boiler is represented by the following formula: In the formula: L represents the output thermal power of the gas-fired boiler in the integrated energy system of the i-th country at time t; NG Indicates the lower heating value of natural gas; η represents the natural gas consumption of a gas-fired boiler during time period t; GB This indicates the heating efficiency of the gas-fired boiler; S13) Renewable Energy Renewable energy sources include wind power and solar power: S131) ​​Wind power generation Wind power output is limited by the incoming wind speed, but when the incoming wind speed is lower than the cut-in wind speed or higher than the cut-out wind speed, the wind farm does not generate electricity. The wind power output at time t in the i-th national integrated energy system... The relationship between the wind speed and the incoming wind speed is as follows: In the formula, ρ is the air density; A is the swept area of ​​the wind turbine blades; v is the wind speed; c wt The wind energy utilization coefficient is the ratio of the wind energy absorbed by the wind turbine per unit time to the total wind energy passing through the rotating surface of the wind turbine; λ wt The ratio of leaf tip speed; S132) Photovoltaic power generation Photovoltaic power generation of the i-th national integrated energy system at time t The mathematical model is as follows: In the formula, G is the light intensity, kW / m². 2 ;T s P represents the surface temperature of the photovoltaic cell, in °C. stc The maximum output power under standard test conditions is expressed in kW; G stc Light intensity under standard test conditions, kW / m² 2 ;T stc ε represents the surface temperature of the photovoltaic cell under standard test conditions, i.e., 25℃; ε is the temperature coefficient of the photovoltaic cell. T s =T a +0.0138·(1+0.031T a )·(1-0.042v)·G (6) In the formula, T a Ambient temperature (°C); wind speed (m / s); light intensity (kW / m²). 2 ; S14) Energy storage equipment Energy storage devices include batteries and thermal storage tanks: S141) Battery When the battery discharges When the battery is charging In the formula, W t e,i Let be the amount of electricity stored in the battery of the i-th national integrated energy system at time t, in kWh; Let be the charging power and discharging power of the battery in the i-th country's integrated energy system at time t, respectively, in kW; These are the battery's own discharge efficiency and charging efficiency, respectively. These are the battery's own discharge loss and charging loss, respectively. S142) Heat storage tank When the heat storage tank releases heat When the heat storage tank is heated In the formula, W t h,i The thermal energy stored in the thermal storage tank of the i-th national integrated energy system at time t is kJ. Let be the heat release power and heat charging power of the thermal storage tank at time t in the i-th national integrated energy system, respectively, in kW; These are the heat release efficiency and heat charging efficiency of the heat storage tank itself, respectively. These are the heat release loss and heat charging loss of the heat storage tank itself, respectively. S15) Electric Boiler The mathematical model for an electric boiler is as follows: In the formula, Let be the heating capacity of the electric boiler in the integrated energy system of the i-th country at time t; η represents the electrical power required by the electric boiler in the integrated energy system of the i-th country at time t. EB The conversion efficiency of the electric boiler; S16) Power Loss Power loss includes electrical power loss and thermal power loss: S161) Power Loss The power loss model is as follows: In the formula, P k Q k U k The active and reactive power and voltage at a certain end of the line during each time period; R is the resistance of the line. S162) Heat Power Loss Given the user heat load, ambient temperature, and network structure, the outlet and return temperatures of the energy center during time period t are calculated using power flow analysis. Based on the outlet flow rate of the energy center, the total heat supply can be obtained, and the heat network loss during time period t can be calculated as follows: In the formula, C p This is the specific heat capacity of water; This refers to the outlet water flow rate of the heat source center. The outlet temperature of the heat source center; The temperature returned from the center of the heat source; To transfer heat power between the integrated energy systems of countries i and j; S2) Establish a benefit model for each entity in a cross-border integrated energy system that takes into account demand response; Step S2) establishes a benefit model for each entity in a cross-border integrated energy system that considers demand response, including: S21) Profit Model for Cross-border Integrated Energy System Operators Based on the two-layer game framework of cross-border integrated energy systems, in any demand response period t, a pricing strategy is formulated considering both the output plan of its own energy supply equipment and the load demand on the energy consumption side. Its payoff function can be expressed as: in, This represents the revenue from energy sales to users by the integrated energy system of country i during time period t; Let $t$ represent the grid interaction cost of the integrated energy system of the i-th country during time period $t$. If $t$ is greater than 0, it means that the country is purchasing electricity from the grid; otherwise, it means that the country is selling electricity to the grid. This represents the fuel cost of the CCHP unit in the i-th integrated energy system country during time period t; This represents the equipment operation and maintenance cost of the integrated energy system of the i-th country during time period t; This represents the interaction costs between the integrated energy systems of various countries; In the formula, This represents the sum of electricity load energy prices for users in the i-th country's integrated energy system during time period t. Let $t$ be the sum of the heat load energy prices for users in the integrated energy system of country $i$ during time period $t$. and These represent the electrical load and heat load of users in the integrated energy system of the i-th country during time period t, respectively. and Let these represent the electricity and heat prices sold to users by the integrated energy system operator in the i-th country, respectively. and Let represent the electricity sales price and purchase price from the external power grid by the integrated energy system operator of the i-th country, respectively. and These represent the sales and purchase prices of heat to the external heating network by the integrated energy system operator of the i-th country, respectively. These represent the costs of purchasing electricity and heat between the integrated energy systems of different countries, respectively. This represents the power supply from the operator of the integrated energy system of the i-th country during time period t; c represents the heat supply of the integrated energy system operator in country i during time period t; GT c GB c EB c HS c ES c PV c WT The unit power maintenance cost, in yuan, is for gas turbines, gas boilers, electric boilers, thermal storage tanks, batteries, photovoltaic systems, and wind turbines. and These represent the electrical output power of the gas turbine and the thermal output power of the gas boiler in the integrated energy system of the i-th country during time period t, respectively. Let be the heating capacity of the electric boiler in the integrated energy system of the i-th country at time t; Let be the thermal power of the thermal storage tank in the integrated energy system of the i-th country at time t; Let be the battery power of the integrated energy system of the i-th country at time t; Let be the photovoltaic power generation capacity of the integrated energy system of the i-th country at time t; Let a be the wind power output of the integrated energy system of the i-th country at time t; e b e c e a h b h c h These represent the fuel cost coefficients for gas turbines and gas-fired boilers, respectively. The electrical power transmitted between the integrated energy systems of countries i and j; To avoid direct energy transactions between the consumer and the grid, the price at which operators sell their energy should be slightly lower than the market price, and the following constraints must be met: In the formula, This represents the electricity price sold to users by the integrated energy system operator in the i-th country. and Let represent the electricity sales price and purchase price from the external power grid by the integrated energy system operator of the i-th country, respectively. S22) User Benefit Model of Cross-border Integrated Energy System The difference between a user's utility function and energy cost, in any demand response period t, can be expressed as the revenue function: In the formula, Let represent the utility function of users in the integrated energy system of the i-th country, and let represent the degree of satisfaction obtained by users from purchasing electricity and heat. It is non-decreasing and convex, and has various forms, including quadratic and logarithmic forms. and Let the electrical load and thermal load of the user in the i-th country at time t be represented by quadratic functions: In the formula, v e ,α e ,v h ,α h These represent the preference coefficients for electricity and heat consumption, respectively, which can reflect users' energy demand preferences and affect the magnitude of demand. S3) Establish a master-slave game collaborative optimization model for cross-border integrated energy systems that considers demand response; Step S3) establishes a master-slave game collaborative optimization model for a cross-border integrated energy system that considers demand response, including: S31) Construction of Master-Slave Game Model The established master-slave game model includes integrated energy operators and users, with operators acting as leaders and users as followers. The established cross-border integrated energy system game model is as follows: Participants: The participants in the master-slave game include integrated energy operators from various countries and users from various countries. The set of participants is represented as follows: N i ={ier i ,user i } (25) In the formula, ier i user i Let them represent the integrated energy operator in country i and the user in country i, respectively. Strategy sets: The strategy sets of integrated energy operators in various countries include the output of each unit and the electricity and heat sales prices in each country. The strategy sets of users in various countries include their own transferable electrical and heat loads. The strategy sets of integrated energy operators and users in various countries are represented by vectors as follows: In the formula, Let represent the strategy set of the integrated energy operator in the i-th country; Let represent the output power of the gas turbine, gas boiler, electric boiler, and storage battery in the integrated energy system of the i-th country, respectively. Let represent the unit price of electricity purchase and sale, and the unit price of electricity sale and heat sale, respectively, for the integrated energy system of country i. In the formula, This represents the policy set of users in the i-th country; Let i represent the transferable electrical load and transferable heat load of country i, respectively. Payoff function: The payoff function of the master-slave game is the payoff function of the integrated energy operators of various countries and the payoff function of the users established in Section 4; S311) Game Model Upper-Level Pricing Strategy As the leader, the operator is at the top of the master-slave game model. Based on considerations of demand response and generation constraints, the operator sets subsidy prices with the aim of maximizing its revenue from demand response during any given demand response period. This can be expressed as: In the formula, This represents the revenue from energy sales to users by the integrated energy system of country i during time period t; Let $t$ represent the grid interaction cost of the integrated energy system of the i-th country during time period $t$. If $t$ is greater than 0, it means that the country is purchasing electricity from the grid; otherwise, it means that the country is selling electricity to the grid. This represents the fuel cost of the CCHP unit in the i-th integrated energy system country during time period t; This represents the equipment operation and maintenance cost of the integrated energy system of the i-th country during time period t; S312) Game Theory Model: Lower-Level Response Strategy Users, as followers, are at the lower level of the master-slave game. Maximizing consumer surplus can be represented as: In the formula, Let represent the utility function of users in the integrated energy system of the i-th country, and let represent the degree of satisfaction obtained by users from purchasing electricity and heat. It is non-decreasing and convex, and has several forms such as quadratic and logarithmic. and Let the electrical load and thermal load of the user in the i-th country at time t be represented by quadratic functions: In the formula, v e ,α e ,v h ,α h These represent the preference coefficients for electricity and heat consumption, respectively, which can reflect users' energy demand preferences and affect the magnitude of demand. S313) Constraints To ensure the safe and reliable operation of the integrated energy system, in addition to defining the objective function, system constraints also need to be considered: S3131) Electrical balance constraint In the formula, These represent the power purchased from the grid and the power sold to the grid by the integrated energy system of the i-th country at time t, respectively. Let be the electrical power required by the electric boiler in the integrated energy system of the i-th country at time t; The electrical power transmitted between the integrated energy systems of countries i and j; The power loss transmitted between the integrated energy systems of countries i and j; S3132) Thermal balance constraint In the formula, Let be the heat purchase power and heat sale power of the integrated energy system of the i-th country at time t, respectively, interacting with the heat network. For the heat power transferred between the integrated energy systems of countries i and j, The heat power loss in the heat network transmission between the integrated energy systems of countries i and j Let the heat load be that of the i-th country. S3133) Comprehensive Demand Response Constraints ① Electricity load demand response is divided into price-based demand response and incentive-based demand response: Price-based demand response: In the formula: ξ is the elasticity coefficient; ΔP and P are the electricity consumption adjustment amount and electricity consumption, respectively; Δθ and θ are the electricity price adjustment amount and electricity price, respectively. The electrical load power after demand response is expressed as: In the formula, P t i,0 Let ΔP be the electrical load before the demand response of the integrated energy system of the i-th country; t i Let $i$ be the amount of electricity load adjustment before and after the integrated energy system response of the $i$-th country. Based on time-of-use pricing and fixed pricing, the following matrix is ​​established: Incentive-based demand response: Electrical load includes stationary electrical load and transferable electrical load, and can be represented as: in, This represents the fixed electrical load of the integrated energy system of the i-th country at time t; This represents the transferable electrical load of the integrated energy system of the i-th country at time t; Users can adjust their energy load reasonably based on the energy sales price offered by the operator, but the following constraints must be met: In the formula, W represents the upper limit of the electrical load that a user can transfer. sel This represents the total amount of transferable electrical load within T time periods, meaning that the total amount of transferable electrical load before and after demand response needs to remain unchanged. ② Heat load demand response, including fixed heat load and transferable heat load, as shown below: In the formula, and Let represent the fixed heat load and the transferable heat load of the integrated energy system of the i-th country at time t, respectively. The transferable heat load can be transferred in a certain proportion according to the user's comfort and energy supply adequacy. In the formula, This indicates the upper limit of the heat load that a user can transfer, W. sel This represents the total amount of transferable heat load within T time periods, meaning that the total amount of transferable heat load before and after the demand response needs to remain unchanged. S3134) Power Constraints Between Integrated Energy Systems and Electricity / Heating Networks in Various Countries In the formula, Let be the maximum permissible power purchase capacity for the interaction between the integrated energy system and the power grid of the i-th country; The maximum permissible power sales capacity for the interaction between the integrated energy system and the power grid of the i-th country; This represents the flag bit indicating that the integrated energy system of the i-th country purchases electricity from the grid at time t, where 1 indicates the start of electricity purchase and 0 indicates the stop of electricity purchase; This represents the flag bit indicating that the integrated energy system of the i-th country sells electricity to the grid at time t, with 1 indicating the start of electricity sales and 0 indicating the stop of electricity sales; In the formula, The maximum permissible power purchase capacity for the interaction between the integrated energy system and the heating network of the i-th country; The maximum allowable power sales capacity for the interaction between the integrated energy system and the heating network of the i-th country; This represents the flag indicating that the integrated energy system of the i-th country purchases heat from the heat network at time t, with 1 indicating the start of heat purchase and 0 indicating the stop of heat purchase; This represents the flag indicating that the integrated energy system of the i-th country is selling heat to the heating network at time t, with 1 indicating the start of heat sales and 0 indicating the stop of heat sales; S3135) Upper and lower limits of equipment output in national integrated energy systems In the formula, Let m be the electrical power of equipment m in the integrated energy system of the i-th country; Let m be the upper and lower limits of the electrical power of equipment m in the integrated energy system of the i-th country; Let m be the electrical power of device m; Let m be the upper and lower limits of the thermal power of equipment m in the integrated energy system of the i-th country. S3136) Battery power constraint In the formula, Let be the battery capacity of the integrated energy system of the i-th country; Maximum charging rate; This is the maximum discharge rate; The state bit for charging at time t; The state bit for energy release at time t is a 0-1 variable, indicating that the charging and discharging state of the same device at the same time is unique. Let the maximum and minimum energy storage capacity of the battery in the integrated energy system of the i-th country be denoted by . S3137) Power constraint of thermal storage tank In the formula, Let be the capacity of the thermal storage tank in the integrated energy system of the i-th country. This is the maximum heat charging rate; This represents the maximum heat release rate. Let be the maximum and minimum heat storage capacity of the thermal storage tank in the integrated energy system of the i-th country; S3138) Inter-national power constraints on electricity and heat networks within integrated energy systems In the formula, This represents the maximum electrical power transmitted between the integrated energy systems of countries i and j. This represents the maximum heat transfer power between the integrated energy systems of countries i and j. S3139) Constraints on power grid and heating network losses between national integrated energy systems In the formula, This represents the maximum power loss during power transmission between the integrated energy systems of countries i and j. The maximum heat power loss transmitted between the integrated energy systems of countries i and j is the maximum value of heat power loss in the heat network. S32) Staberg equilibrium When followers make the best response based on the leader's strategy, and the leader also obtains the best strategy, it means that the game has reached a Staberg equilibrium. If the condition of equation (38) is satisfied, then the equilibrium of the proposed Staberg game is reached: Once a game equilibrium is reached, none of the participants can unilaterally change their strategies to obtain higher returns. S33) Model Solving Method For the aforementioned master-slave game model, different solution algorithms are used to optimize the payoff functions of each agent in the upper and lower layers of the model. The solution for the leader (energy operator) is obtained using a differential evolution algorithm to reduce the difficulty, while the solution for the follower (user) is obtained using Yalmip modeling and the Cplex solution tool to accelerate the algorithm's solution speed and ensure the accuracy of the results. If each participant obtains the same optimal strategy in two consecutive rounds, i.e.: According to the definition of Staberg equilibrium above, it is believed that the country's strategy combination has converged to an equilibrium point, at which point no participant can change their strategy alone to gain more benefits. S4) Case analysis and verification.

2. The optimization method for master-slave collaborative operation of a cross-border integrated energy system considering demand response, as described in claim 1, is characterized in that: In S32), before solving for the Staberg equilibrium solution, it is necessary to prove its existence and uniqueness. The theorem used states that a unique Staberg equilibrium exists when the master-slave game model satisfies the following conditions: 1) The strategy set of the leader and followers is a non-empty compact convex set; 2) Once the leader's strategy is given, there is a unique optimal solution for all followers; 3) When the strategies of the followers are given, there exists a unique optimal solution for the leader; Proof: The following will prove respectively that the master-slave game model of the cross-border integrated energy system satisfies the above three conditions for the existence and uniqueness of the Stackelberg equilibrium: 1) According to the cross-border integrated energy system model, the strategy of the leader needs to satisfy equation, and the strategy of the follower on the user side needs to satisfy equations (30)-(53). Therefore, the strategy set of each participant is non-empty and compact convex; 2) Prove that when the strategy of the leader is given, there exists a unique optimal solution for all followers: Substitute equations (15)-(20) into equation (14), and then calculate the equations (14) with respect to the following conditions. The first-order partial derivative yields: In the formula, η h =(1-η GT ) / η GT To establish the relationship between the output electrical power of the gas-fired boiler and the waste heat recovery power, setting the first-order partial derivative to zero, we can obtain: Then, find the equation (1) with respect to... The second-order partial derivative yields: Since the cost coefficient is positive, the second-order partial derivative is always less than 0. The extreme point is the maximum point of equation (23). However, due to the constraints of the upper and lower limits of the strategy interval, the extreme point may fall on the boundary of the interval when the energy price changes. Therefore, the value of the optimal strategy on the energy supply side can be expressed as: Therefore, regardless of the value, when the purchase price of the operator is given, there exists a unique optimal solution for the integrated energy system operator; Next, we calculate the objective function (24) of the user with respect to... and The first-order partial derivative yields: Let the above first-order partial derivatives be equal to 0, and we can get: Then find the equation (24) with respect to... and The second-order partial derivative yields: Since the energy preference coefficient is also positive, the second-order partial derivatives are all less than 0. and Given that this is the maximum point of equation (24), and considering the constraint on the interval of the optimization variables, the optimal solution can be expressed as: Therefore, when the selling price of the operator is given, there also exists a unique optimal solution for the user; 3) Prove that when the strategies of the followers are given, there exists a unique optimal solution for the leader. At this time, the revenue of the operator can be expressed as: The follower's set of optimization strategies are valued. Substituting into the above equation, and finding the leader's objective function (1) regarding... The first-order partial derivatives yield: In the formula, η h =(1-η GT ) / η GT At this point, the Hessian matrix of the leader's payoff function is expressed as: It can be found that the Hessian matrix is negative definite, so there exists a maximum point; when the followers take other extreme points, it can also be proved similarly that there exists a unique optimal solution for the leader, and the proof is similar to the above process; In summary, the proposed master-slave game model has a unique Stackelberg equilibrium.

3. The master-slave game-theoretic collaborative operation optimization method for cross-border integrated energy systems considering demand response as described in claim 1, characterized in that... The model solving process of the model solving method in S33) is as follows: The upper-layer optimization algorithm includes the following steps: ①: Input the initial data and set parameters, including the typical daily electricity and heat power of users, the predicted output of wind turbines and photovoltaic power, the operating parameters of each device, and the upper and lower limit constraints of energy prices; ②: Initialize the population a, and let the iteration number K = 0; ③: The integrated energy operator sends the optimized energy selling price to the lower-layer user followers; ④: The user calls the lower-layer algorithm to calculate its own revenue; ⑤: The integrated energy operator calculates its own objective function U1 according to equation (14); ⑥: Perform crossover and mutation operations on the population a to obtain a new population b; ⑦: Call the lower-layer algorithm again to optimize and solve the follower's objective function, and send the optimization result to the upper-layer integrated energy operator. The integrated energy operator calculates its own objective function U2 according to equations (15)-(25); ⑧: Selection operation. If U2 > U1, then a = b, U1 = U2. If U2 < U1, then keep it unchanged; ⑨: Judge whether the iteration number is satisfied. If it is satisfied, output the optimal result, otherwise jump to ⑥; The lower-layer algorithm includes the following steps: ①: The user calls the Cplex solving tool to calculate the adjustable electricity and heat loads of the user according to equation (23); ②: Send the optimization result to the upper-layer leader.

4. The master-slave game-theoretic collaborative operation optimization method for cross-border integrated energy systems considering demand response, as described in claim 1, is characterized in that... The result of the example analysis and verification in step S4) is as follows: In the upper-layer game, the integrated energy operator's revenue shows a gradually increasing trend by continuously adjusting its own energy selling price and device output; in the lower-layer game, the user's revenue function fluctuates by reasonably adjusting its own energy consumption strategy in combination with the energy selling price of the upper-layer leader. There is an obvious game interaction between the two sides, and both finally reach convergence. Through the above game analysis, the game process between the two sides can be well reflected. When the game reaches the Stackelberg equilibrium, their strategies will no longer change.

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