Multi-user heating system optimization operation method based on master-slave game

Abstract

A multi-user heating system optimization operation method based on a master-slave game comprises the steps that a double-layer master-slave game architecture is established, a load aggregator LA serves as a game leader, the internal electricity purchasing and selling price of a heating system is formulated, and the target is to maximize the income of the system; a heating user serves as a game follower, photovoltaic output, an energy storage charging and discharging strategy and electric heating power are optimized, and the target is to minimize comprehensive cost including electricity purchasing cost, light abandoning punishment and comfort deviation cost; setting an electric energy transaction process; establishing an electric heating model and a heating user energy storage model; a double-layer master-slave game optimization model is established, wherein the double-layer optimization model comprises an upper-layer load aggregator LA income model and a response model with the lowest heating cost, the maximum photovoltaic consumption and the optimal comfort of a lower-layer heating user as targets; and performing linearization processing and solving on the double-layer master-slave game optimization model. According to the method, on the premise that the comfort of the heating users is guaranteed, the economical efficiency of operation of the multi-user heating system is achieved.

Description

Technical Field

[0001] This invention relates to the field of energy optimization and scheduling technology, specifically to a method for optimizing the operation of a multi-user heating system based on master-slave game theory. Background Technology

[0002] Among various clean heating equipment, electric heating stands out due to its advantages such as good controllability, cleanliness, and environmental friendliness. Currently, electric heating equipment has gradually achieved large-scale and high-proportion adoption. However, problems remain prominent in townships and rural areas, including imperfect dispatching methods, low utilization rate of electric heating resources, crude management of electric heating, and insufficient exploration of the potential for synergistic regulation between photovoltaics and energy storage. Furthermore, users have evolved from simply consuming electricity to becoming both generators and consumers. Therefore, how to utilize rooftop photovoltaic power generation for self-consumption to supply electricity for electric heating, achieving synergistic and optimized operation of "photovoltaics + energy storage + electric heating," is an urgent problem to be solved in townships and rural areas. Summary of the Invention

[0003] This invention proposes an optimization method for multi-user heating systems based on a master-slave game theory approach. This method employs a two-tiered master-slave game theory optimization, with the load aggregator (LA) as the leader and heating users as followers. First, based on thermodynamics and the working principles of electric heating equipment, a second-order thermodynamic model and an energy storage model are established for electric heating. Second, the upper-level load aggregator (LA) sets its internal time-of-use electricity price according to its own revenue model. Lower-level heating users respond to the upper-level electricity price by formulating their own heating plans based on the objectives of minimizing heating costs, maximizing photovoltaic absorption, and achieving optimal comfort, thus establishing a two-tiered master-slave game model. Finally, the Big-M method is used to linearize the nonlinear constraints of energy storage, and a genetic algorithm is used in MATLAB 2022b to solve the upper-level model, while the Gurobi and Yalmip solvers are used to solve the lower-level model. The proposed method achieves economic efficiency in the operation of multi-user heating systems while ensuring the comfort of heating users.

[0004] The technical solution adopted in this invention is as follows: The method for optimizing the operation of a multi-user heating system based on master-slave game theory includes the following steps: Step 1: Establish a two-layer master-slave game architecture: A multi-user heating system includes a load aggregator (LA) and heating users; Leader Level: Load aggregator LA, as the game leader, sets the internal electricity purchase and sale price for the heating system. , The goal is to maximize one's own profits; Follower layer: Heating users, as game followers, respond to the electricity price signals set by load aggregator LA and optimize photovoltaic output. Energy storage charging and discharging strategies and electric heating power The objective is to minimize overall costs, including electricity purchase costs. Discarding light punishment Comfort deviates from cost ; Step 2: Set up the electricity trading process: The electricity trading process includes two stages: pricing decision-making and quantitative decision-making. These two stages are sequential and influence each other. Pricing decision stage: The upper-level load aggregator (LA) sets the electricity purchase and sale price based on the electricity supply and demand relationship and market information. , In order to maximize their own benefits; Quantitative decision-making stage: Lower-level heating users determine the optimal output for electric heating based on the price signal from the upper-level load aggregator LA. Therefore, the optimal decision at the lower level can be viewed as a function of the decision variables at the upper level; Step 3: Establish electric heating model and heating user energy storage model; Step 4: Establish a two-layer master-slave game optimization model: The two-layer optimization model includes an upper-layer load aggregator LA revenue model and a lower-layer heating user response model that aims to minimize their own heating costs, maximize photovoltaic absorption, and achieve optimal comfort. Step 5: Linearize the two-layer master-slave game optimization model and solve it.

[0005] In step 1, the load aggregator LA acts as an intermediary connecting the distribution network and heating users, exchanging energy and information with both parties to form a two-layer optimization model between the distribution network and heating users. Its decision variables include the electricity purchase and sale price within the heating system. , ; Heating users, as followers, formulate heating plans based on heating comfort and the electricity prices set by the load aggregator LA (Local Energy Provider) to minimize their heating costs; the decision variables for heating users include solar power output. Energy storage charging and discharging strategy Electric heating power .

[0006] In step 3, the temperature change process in the building rooms mainly includes thermal equilibrium and heat transfer processes. The thermal equilibrium process of the building can be approximated as the temperature change of the walls and indoor air with their heat capacity gain and dissipation, while the heat transfer process can be approximated as the heat transfer process of the walls and indoor air thermal resistance. Therefore, by using electric heating power to correspond to RC current, and using the heat capacity and thermal resistance of the walls and indoor air to correspond to capacitance and resistance, a relationship is established between electric heating power, the building room thermodynamic model, and indoor temperature, thus constructing a second-order distributed parametric thermodynamic model of the building. As shown in the following equation: ; In the formula: express The indoor temperature at any given time; express The wall temperature at any given time; express The indoor temperature at any given time; express The wall temperature at any given time; express The outdoor temperature at any given time; This represents the electric heating power at time t; This represents the simulation step size; e is a natural number; , These are the equivalent heat capacity of indoor air and the equivalent heat capacity of the wall, respectively. , These are the equivalent thermal resistances of indoor air and the inner side of the wall, and the equivalent thermal resistances of the outer side of the wall and outdoor air, respectively.

[0007] In step 3, the energy storage model for heating users is established based on the functional relationship between the charging power and discharging power of the energy storage system at any given time and the SOC of the energy storage system. The numerical expression for SOC is: ; In the formula, Indicates the state of charge of the energy storage system at the next moment; This indicates the current state of charge of the energy storage system. Let be the charging and discharging power of the energy storage system at time t; The capacity of the energy storage system; To control the time interval. To ensure the safe and stable operation of the energy storage system, energy storage... It must be within the range of the highest and lowest values.

[0008] In step 4: 4.1: The upper-level load aggregator LA revenue model mainly includes the upper-level objective function and constraints; (1) Objective function: The upper-level load aggregator (LA) uses maximizing profits as its objective function in the game: ; In the formula: for Total revenue; For the revenue generated from transactions between LA and the distribution network; for Revenue from transactions with users; The total number of time periods in a day refers to 24 hours in a day, with each time period consisting of 15 minutes, for a total of 96 time periods. This represents the t-th time period.

[0009] (2) Constraints: The constraints on the upper load aggregator (LA) include: power balance constraints, tie-line power constraints, and electricity price constraints. a: Power balance constraint: because There are no power sources or energy storage devices, therefore it is necessary to ensure... The power purchased and sold by the distribution network and the power purchased and sold by users must be kept in balance at all times. ; In the formula: for For the distribution network Electricity sales capacity at any given time; for For the distribution network The amount of electricity purchased at any given time; For time step, For users exist Always towards The power consumption of electricity purchased; For users exist Always towards The electricity sales capacity is N; N is the number of users.

[0010] b: Tie line power constraint: When interacting with the distribution network for energy, it is necessary to ensure The interaction power on the tie line to the distribution network satisfies the following constraints; ; In the formula: and They are respectively The power limit of the power distribution network interconnection line.

[0011] c: Electricity price constraints: To ensure While gaining benefits within the master-slave game framework, electricity prices will not fluctuate significantly to ensure that users also benefit from electricity consumption within this framework. Furthermore, to prevent problem degradation and avoid direct transactions between users and the distribution network, it should be ensured that… The purchase price is slightly higher than the power distribution network's electricity purchase and sale price. The selling price is slightly lower than the power distribution network's purchase and sale price; ; In the formula: , For the distribution network at Time-of-use electricity pricing and grid connection pricing at specific times; The electricity purchase and sale price set for load aggregators; This represents the average electricity price for purchase and sale within the heating system.

[0012] 4.2: The lower-level heating user response model mainly includes the objective function and constraints of the upper level; (1) Objective function: Heating users, as followers, formulate heating plans based on their own actual conditions and actively respond. The electricity price set, while ensuring user comfort, can effectively reduce their heating costs. Heating users use minimizing heating costs as their objective function in this game: ; In the formula: The comprehensive heating cost function for users; For users The cost of purchasing electricity; For users The cost of penalties for abandoning light; For user comfort functions; , , These are the weighting coefficients.

[0013] (2) Constraints: The constraints for lower-level heating users include: power balance constraints, photovoltaic output constraints, energy storage constraints, electric heating power constraints, and indoor temperature constraints. a. Power balance constraint: To ensure the safe and reliable operation of the heating system, it is necessary to maintain the power balance of users at all times.

[0014] ; In the formula: For users and The interaction power; For users The actual output of photovoltaic power; For users Electric heating power; For users The energy storage charging and discharging power; For users Energy storage charging power; For users Energy storage discharge power; For users The base load; Indicates user The power purchased at time t; Indicates user Electricity sales power at time t; b. Photovoltaic output constraints: ; In the formula: The actual output of photovoltaic power; For users The maximum output of photovoltaic power.

[0015] c. Energy storage constraints: To ensure the safe and sustainable operation of energy storage, it is necessary to constrain the state of charge and charging / discharging power of the energy storage, and to restrict simultaneous charging and discharging. ; In the formula: For users State of charge during time period t; The self-discharge rate of the stored energy; For users State of charge during time period t-1; and These are the charging efficiency and discharging efficiency of energy storage, respectively. and users respectively The charging power and discharging power during time period t; and These represent the lower and upper limits of the actual achievable capacity of energy storage, respectively.

[0016] ; In the formula: and users respectively The flags indicating the charging and discharging of the energy storage during time period t; For users Maximum charging and discharging power of energy storage.

[0017] d. Electric heating power constraints: ; In the formula: For users Rated power of electric heating.

[0018] e. Indoor temperature constraints: To ensure the comfort of users' heating, the temperature needs to be controlled within a certain range.

[0019] ; In the formula: Indicates user The indoor temperature at time t; The lower limit of indoor temperature; This is the lower limit of indoor temperature.

[0020] In step 5, the constraints of energy storage include nonlinear constraints. To improve the solution efficiency, the Big-M method is used to linearize the energy storage charging and discharging power constraints, equivalently transforming the original nonlinear constraints into mixed integer linear constraints. The transformed constraints are shown in the following equation: .

[0021] In the formula: It is a sufficiently large constant.

[0022] In step 5, the model is solved: After linearizing the charging and discharging power constraints of energy storage, the optimization operation model of a multi-user heating system based on master-slave game is transformed into a mixed integer linear programming problem. The upper-level LA revenue model is solved using a genetic algorithm in MATLAB 2022b, and the lower-level heating user response model is solved using the solver Gurobi and Yalmip toolbox.

[0023] This invention proposes an optimized operation method for multi-user heating systems based on master-slave game theory, achieving efficient scheduling of "photovoltaic + energy storage + electric heating" in rural areas and effectively reducing users' heating costs. Its advantages are: 1) Achieve closed-loop optimization of "electricity price signal - user response". LA is the leader and users are the followers. LA uses internal electricity price as guidance. Different heating users respond to internal electricity price and formulate their own heating plans to maximize the interests of both parties in the game.

[0024] 2) Achieve multi-energy collaborative decision-making: The user's photovoltaic, energy storage, electric heating and base load are optimized in a coordinated manner to ensure the reliability of the user's heating. Photovoltaic and energy storage provide power for electric heating, which can effectively reduce the user's heating costs.

[0025] 3) LA guides users to optimize operation, enabling users to respond to internal electricity prices. When electricity prices are high, users' heating power is appropriately reduced; when electricity prices are low, users' heating power is appropriately increased. While ensuring users' heating comfort, it effectively reduces heating costs for all types of users.

[0026] 4) Achieve efficient model solution: The non-convex problem is transformed into a mixed-integer linear programming problem by linearizing it using the Big-M method. Combined with genetic algorithm and Gurobi hierarchical solution, the scheduling complexity problem of large-scale rural users is solved. Attached Figure Description

[0027] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a flowchart of the operation method of the present invention.

[0028] Figure 2 This is a flowchart of the model solution process for this invention.

[0029] Figure 3 A structural diagram of a multi-user heating system.

[0030] Figure 4 This is a schematic diagram of a second-order distributed parametric thermodynamic model of a room.

[0031] Figure 5 This is a schematic diagram of a second-order lumped-parameter thermodynamic model of a room.

[0032] Figure 6 This is the internal optimal electricity price map.

[0033] Figure 7 This is a schematic diagram of a Class I room heating plan.

[0034] Figure 8 This is a schematic diagram of a heating plan for Class II rooms.

[0035] Figure 9 This is a schematic diagram of a heating plan for Class III rooms.

[0036] Figure 10 This is a graph showing the relationship between electric heating power and indoor temperature in Class I rooms.

[0037] Figure 11 This is a graph showing the relationship between electric heating power and indoor temperature in Class II rooms.

[0038] Figure 12 This is a graph showing the relationship between electric heating power and indoor temperature in Class III rooms. Detailed Implementation

[0039] This invention proposes a two-level master-slave game optimization method with a load aggregator (LA) as the leader and heating users as followers. In this two-level master-slave game optimization model, the upper-level load aggregator (LA) sets its internal time-of-use electricity price based on its own revenue model, while the lower-level heating users respond to the upper-level electricity price based on their minimum heating costs, and formulate their own heating plans, fully exploring the synergistic control potential of the "photovoltaic + energy storage + electric heating" system. Case studies show that the proposed method achieves economic efficiency in the operation of the user's heating system while ensuring user comfort.

[0040] 1. Multi-user heating system framework: (1) System Introduction: Multi-user heating systems primarily consist of load aggregators (LAs) and heating users. The LA acts as a bridge connecting the distribution network and heating users, exchanging energy and information with both sides to form a two-tiered optimization model. User optimization resources mainly include rooftop photovoltaics, energy storage, electric heating, and base load. The LA, as the leader, aggregates multiple users based on the thermodynamic model of their rooms, considering the differences in upper and lower limits of control capacity caused by the varying electric heating load characteristics of different user groups. The revenue of the LA is closely related to fluctuations in the electricity price for heating users. Before setting electricity prices for heating users, it is essential to consider the users' electricity consumption response to different prices to determine the optimal pricing that maximizes the LA's revenue. Heating users, as followers, respond based on their own heating comfort and cost considerations. Set electricity prices and develop heating plans to minimize your heating costs.

[0041] The decision variables for load aggregator LA include the electricity purchase and sale price within the heating system; the decision variables for users include photovoltaic output, energy storage-to-wind power strategy, and electric heating power. The structure of a multi-user heating system is as follows: Figure 3 As shown: (2) Electricity trading process Energy trading in a multi-user heating system involves two stages: pricing decision-making and quantitative decision-making. These two stages are sequential and influence each other.

[0042] Pricing stage: Upper level Electricity purchase and sales prices are set based on the supply and demand relationship of electricity and market information in order to maximize their own profits.

[0043] Quantitative stage: Lower-level heating users are respectively based on The price signal determines the optimal output of electric heating, so the optimal decision at the lower level can be regarded as a function of the decision variables at the upper level.

[0044] 2. Electric heating model and energy storage model: (1) Electric heating model: The temperature change process in a building's rooms mainly involves thermal equilibrium and heat transfer. Indoor temperature changes are related to the building's thermal equilibrium, i.e., the building's heat production and heat dissipation. When heat production exceeds heat dissipation, the building as a whole stores heat, causing the indoor temperature to rise; conversely, the indoor temperature decreases. When the heat production and heat dissipation reach a dynamic equilibrium, the indoor temperature remains constant. Heat transfer occurs between media at different temperatures. The strength of this heat transfer can be characterized by the heat transfer coefficient; a weaker heat transfer process results in a smaller heat transfer coefficient, and vice versa.

[0045] The thermal equilibrium process of a building can be approximated as the change in temperature of the walls and indoor air with respect to their heat capacity, specifically the heat gain and dissipation. The heat transfer process can be approximated as the heat transfer process due to the thermal resistance of the walls and indoor air. The heat generation in building rooms mainly includes the heat generated by electric heating equipment. The heat generated by the sun radiating through windows and walls Heat generated by other indoor cooking appliances Therefore, by using electric heating power to correspond to RC current, and using the heat capacity and thermal resistance of walls and indoor air to correspond to capacitance and resistance, a relationship is established between electric heating power, room thermodynamics model, and indoor temperature, thus constructing a second-order distributed parametric thermodynamic model of the building, such as... Figure 4 As shown. Because the distributed parameter thermodynamic model of the room has a relatively high order and is computationally complex, it can be simplified to obtain the lumped parameter thermodynamic model of the room, as shown. Figure 5 As shown.

[0046] Due to the heat generated by other electrical appliances indoors and heat generated by solar radiation The heat output is far lower than that of electric heating. Therefore, it can be ignored. and We can obtain the second-order differential equations describing the indoor temperature and the electric heating power: (1); In the formula: , These are the equivalent heat capacity of indoor air and the equivalent heat capacity of the wall, respectively. , These are the equivalent thermal resistances of indoor air and the inner side of the wall, and the equivalent thermal resistances of the outer side of the wall and outdoor air, respectively. , and These are, respectively, indoor temperature, wall temperature, and outdoor temperature; This refers to the heating capacity of the electric heating equipment.

[0047] Solve the two differential equations simultaneously, and approximate them as follows: Much larger wall heat capacity air heat capacity Simplifying the differential equation, we get: (2); If the outdoor temperature at a certain moment is known Indoor temperature and wall temperature Then the indoor temperature at the next moment can be calculated. and wall temperature .

[0048] (2) Energy storage model: The mathematical model of the energy storage system is established based on the functional relationship between the charging power and discharging power of the energy storage system at any given time and the SOC of the energy storage system. The numerical expression for SOC is: (3); In the formula, This indicates the current state of charge of the energy storage system. Indicates the state of charge of the energy storage system at the next moment; The charging and discharging power of the energy storage system; The capacity of the energy storage system; To control the time interval. To ensure the safe and stable operation of the energy storage system, energy storage... It must be within the range of the highest and lowest values.

[0049] 3. Two-layer optimization model for multi-user heating systems: (1) Upper-level LA model: 1) Objective function: LA uses maximizing profit as the objective function for participating in the game: (4); In the formula: for Total revenue; For the revenue generated from transactions between LA and the distribution network; for Revenue from transactions with users; This refers to the total number of time periods in a day. In this article, we mean a 24-hour day, with each time period consisting of 15 minutes, for a total of 96 time periods.

[0050] ①. LA and distribution network transaction revenue: (5); In the formula: , For the distribution network at Time-of-use electricity pricing and grid connection pricing at specific times; for For the distribution network Electricity sales capacity at any given time; for For the distribution network The amount of electricity purchased at any given time; The time step for this article is 15 minutes.

[0051] Revenue from transactions with users: (6); In the formula: for Internal electricity purchase and sale price, For users exist Always towards The power consumption of electricity purchased; For users exist Always towards The electricity sales capacity is N; N is the number of users.

[0052] 2) Constraints: ① Power balance constraints: because There are no power sources or energy storage devices, therefore it is necessary to ensure... The power purchased and sold by the distribution network and the power purchased and sold by users must be kept in balance at all times.

[0053] (7); ② Tie line power constraints: When interacting with the distribution network for energy, it is necessary to ensure The interaction power on the tie line to the distribution network satisfies the following constraints: (8); In the formula: and for The maximum power limit of the connection line with the distribution network.

[0054] ③ Electricity price constraints To ensure While gaining benefits within the master-slave game framework, electricity prices will not fluctuate significantly to ensure that users also benefit from electricity consumption within this framework. Furthermore, to prevent problem degradation and avoid direct transactions between users and the distribution network, it should be ensured that… The purchase (sell) price is slightly higher (lower) than the power distribution network purchase and sale price.

[0055] (9); In the formula: This represents the average electricity price for purchase and sale within the heating system.

[0056] (2) Lower-level user model: 1) Objective function: Users, as followers, formulate heating plans based on their own actual situations and actively respond. The electricity price set can effectively reduce users' heating costs while ensuring user comfort. Users use minimizing heating costs as their objective function in participating in the game: (10); In the formula: The comprehensive heating cost function for users; For users The cost of purchasing electricity; For users The cost of penalties for abandoning light; This is a function for user comfort. , , These are the weighting coefficients.

[0057] ① User electricity purchase cost: (11); In the formula: For users exist The amount of electricity purchased from LA at all times; For users exist Always towards Electricity sales capacity.

[0058] ② Cost of user abandonment penalty: (12); In the formula: This is the penalty coefficient for discarded light; For users The projected output of photovoltaic power; For users The actual output of photovoltaic power.

[0059] ③ User comfort function: (13); In the formula: Indoor temperature; The lower limit of indoor temperature; This is the upper limit of indoor temperature; 2) Constraints: ① Power balance constraints: To ensure the safe and reliable operation of the heating system, it is necessary to maintain the power balance of users at all times. (14); In the formula: For users and The interaction power; For users The actual output of photovoltaic power; For users Electric heating power; For users The energy storage charging and discharging power; For users Energy storage charging power; For users Energy storage discharge power; For users The basic load.

[0060] ② Photovoltaic output constraints: (15); In the formula: For users The maximum output of photovoltaic power.

[0061] ③ Energy storage constraints: To ensure the safe and sustainable operation of energy storage, it is necessary to constrain the state of charge and charging / discharging power of the energy storage, and to restrict simultaneous charging and discharging. (16); In the formula: For users State of charge during time period t; The self-discharge rate of the stored energy; and These are the charging efficiency and discharging efficiency of energy storage, respectively. and users respectively The charging power and discharging power during time period t; and These represent the lower and upper limits of the actual achievable capacity of energy storage, respectively.

[0062] (17); In the formula: and users respectively The flags indicating the charging and discharging of the energy storage during time period t; For users Maximum charging and discharging power of energy storage.

[0063] ④ Electric heating power constraints: (18); In the formula: For users Rated power of electric heating.

[0064] ⑤ Indoor temperature constraints: To ensure the comfort of users' heating, the temperature needs to be controlled within a certain range.

[0065] (19); In the formula: The lower limit of indoor temperature; This is the lower limit of indoor temperature.

[0066] (3) Model solution: The decision variables in the optimized operation model proposed in this invention are: the electricity price of the upper-level model and the actual photovoltaic output of each user, the charging and discharging power and charging and discharging flag of energy storage, the heating power of electric heating, and the power purchase and sale constraints between users and the distribution network. Among them, the constraint of energy storage, formula (17) is obviously a nonlinear constraint. The Big-M method is used to linearize the energy storage charging and discharging power constraint into formula (20), which can equivalently transform the original nonlinear constraint into a mixed integer linear constraint. The transformed constraint condition is shown in the following formula: (20); Where M is a sufficiently large constant. After linearizing the charging and discharging power constraints of energy storage, the optimization operation model of the multi-user heating system based on master-slave game is transformed into a mixed integer linear programming problem. The upper-level model is solved using a genetic algorithm in MATLAB 2022b, and the lower-level model is solved using the solver Gurobi and Yalmip toolboxes.

[0067] 4. Case Analysis: (1) Simulation settings: The key parameters of the example in this invention are as follows: 220 users were selected. Considering the influence of room thermodynamic models on the actual operation of electric heating equipment, the rooms were classified into categories I to III based on these models. Category I consisted of 100 households, Category II of 50 households, and Category III of 70 households. The photovoltaic installed capacity was 5 kW per household, and the energy storage capacity was 20 kWh per household. The thermodynamic models and equipment power parameters for each type of room are shown in Table 1.

[0068] To verify the effectiveness of the proposed game theory model for time-of-use pricing and heating load optimization, the following two simulation scenarios are set up for analysis: 1) Example 1: LA provides heating control services to users, but users do not participate in the master-slave game.

[0069] 2) Example 2: LA provides heating control services to users, and users participate in master-slave game.

[0070] (2) Optimal electricity price for upper-level LA: The optimized electricity price in Example 2 is as follows: Figure 6 As shown, since Example 1 does not participate in the master-slave game, the LA electricity price in Example 1 is the average price. Figure 6 It is known that the electricity price set by LA falls between the time-of-use price of the distribution network and the grid connection price. Peak electricity prices occur between 12:30 and 15:00 and between 20:00 and 23:00, while off-peak prices occur between 0:00 and 8:00. By ensuring user comfort, and by better guiding users to reduce heating power during peak hours and appropriately increase heating power during off-peak hours, heating costs can be effectively reduced.

[0071] (3) Analysis of scheduling results in Example 2: Depend on Figure 7 , Figure 8 , Figure 9 The heating plan reveals that LA's electricity pricing can fully leverage the synergistic control capabilities of the "photovoltaic + energy storage + electric heating" system. During off-peak hours (0:00-8:00), users respond to LA's pricing guidance by increasing their heating power. During peak hours (12:30-15:00), due to the presence of user-generated photovoltaic power, users still employ higher heating power to maximize photovoltaic absorption. However, as outdoor temperatures rise, electric heating power gradually decreases, with excess electricity used to charge energy storage. During peak hours (20:00-23:00), without user-generated photovoltaic power, users reduce their heating power to ensure economic efficiency. However, as outdoor temperatures decrease, electric heating power gradually increases.

[0072] Depend on Figure 10 , Figure 11 , Figure 12 It can be observed that during off-peak hours (0:00-8:00), the indoor temperature is generally maintained at 22 degrees Celsius to ensure user comfort. During peak hours (12:30-15:00), due to the presence of user-owned solar panels, users still use higher heating power to maximize solar energy utilization and maintain an indoor temperature of 22 degrees Celsius. However, as the outdoor temperature rises, the electric heating power continuously decreases. During peak hours (20:00-23:00), the indoor temperature is maintained at 18 degrees Celsius to ensure economical heating.

[0073] (4) Comparative analysis of numerical examples: To verify the effectiveness of the proposed game theory model for time-of-use pricing and heating load optimization, a comparative analysis of user heating power consumption and user heating costs in Example 1 and Example 2 is conducted, as shown in Table 2:

[0074] Table 2 shows that: In Example 1, the heating electricity consumption per household for Class I rooms is 42.321 kWh / day, with a heating cost of 21.2 yuan / day; for Class II rooms, the heating electricity consumption per household is 42.178 kWh / day, with a heating cost of 21.11 yuan / day; and for Class III rooms, the heating electricity consumption per household is 45.24 kWh / day, with a heating cost of 23.37 yuan / day. In Example 2, the heating electricity consumption per household for Class I rooms is 44.75 kWh / day, with a heating cost of 17.64 yuan / day; for Class II rooms, the heating electricity consumption per household is 42.66 kWh / day, with a heating cost of 15.48 yuan / day; and for Class III rooms, the heating electricity consumption per household is 50.12 kWh / day, with a heating cost of 20.41 yuan / day. Compared to Example 1, the heating cost of Class I rooms in Example 2 was reduced by 16.69%, and the heating cost of Class II rooms was reduced by 12.67%.

Claims

1. A method for optimizing the operation of a multi-user heating system based on master-slave game theory, characterized in that... Includes the following steps: Step 1: Establish a two-layer master-slave game architecture: A multi-user heating system includes a load aggregator (LA) and heating users; Leader Level: Load aggregator LA, as the game leader, sets the internal electricity purchase and sale price for the heating system. , The goal is to maximize one's own profits; Follower layer: Heating users, as game followers, respond to the electricity price signals set by load aggregator LA and optimize photovoltaic output. Energy storage charging and discharging strategies and electric heating power The objective is to minimize overall costs, including electricity purchase costs. Discarding light punishment Comfort deviates from cost ; Step 2: Set up the electricity trading process: The electricity trading process includes two stages: pricing decision-making and quantitative decision-making. Pricing decision stage: The upper-level load aggregator (LA) sets the electricity purchase and sale price based on the electricity supply and demand relationship and market information. , In order to maximize their own benefits; Quantitative decision-making stage: Lower-level heating users determine the optimal output for electric heating based on price signals from the upper-level load aggregator LA. , Step 3: Establish electric heating model and heating user energy storage model; Step 4: Establish a two-layer master-slave game optimization model: The two-layer optimization model includes an upper-layer load aggregator LA revenue model and a lower-layer heating user response model that aims to minimize their own heating costs, maximize photovoltaic absorption, and achieve optimal comfort. Step 5: Linearize the two-layer master-slave game optimization model and solve it.

2. The method for optimizing the operation of a multi-user heating system based on master-slave game theory as described in claim 1, characterized in that: In step 1, the load aggregator LA acts as an intermediary connecting the distribution network and heating users, exchanging energy and information with both parties to form a two-layer optimization model between the distribution network and heating users. Its decision variables include the electricity purchase and sale price within the heating system. , ; Heating users, as followers, formulate heating plans based on heating comfort and the electricity prices set by the load aggregator LA (Local Energy Provider) to minimize their heating costs; the decision variables for heating users include solar power output. Energy storage charging and discharging strategy Electric heating power .

3. The method for optimizing the operation of a multi-user heating system based on master-slave game theory as described in claim 2, characterized in that: In step 3, a relationship is established between the electric heating power, the building's room thermodynamic model, and the indoor temperature to construct a second-order distributed parametric thermodynamic model, as shown in the following equation: ； In the formula: express The indoor temperature at any given time; express The wall temperature at any given time; express The indoor temperature at any given time; express The wall temperature at any given time; express The outdoor temperature at any given time; This represents the electric heating power at time t; This represents the simulation step size; e is a natural number; , These are the equivalent heat capacity of indoor air and the equivalent heat capacity of the wall, respectively. , These are the equivalent thermal resistances of indoor air and the inner side of the wall, and the equivalent thermal resistances of the outer side of the wall and outdoor air, respectively.

4. The method for optimizing the operation of a multi-user heating system based on master-slave game theory as described in claim 3, characterized in that: In step 3, the energy storage model for heating users is established based on the functional relationship between the charging power and discharging power of the energy storage system at any given time and the SOC of the energy storage system. The numerical expression for SOC is: ； In the formula, Indicates the state of charge of the energy storage system at the next moment; This indicates the current state of charge of the energy storage system. Let be the charging and discharging power of the energy storage system at time t; The capacity of the energy storage system; To control the time interval; to ensure the safe and stable operation of the energy storage system, energy storage... It must be within the range of the highest and lowest values.

5. The method for optimizing the operation of a multi-user heating system based on master-slave game theory according to claim 4, characterized in that: In step 4, the upper-level load aggregator (LA) revenue model mainly includes the upper-level objective function: The upper-level load aggregator (LA) uses maximizing profits as its objective function in the game: ； In the formula: for Total revenue; For the revenue generated from transactions between LA and the distribution network; for Revenue from transactions with users; This represents the total number of time periods within a day. This represents the t-th time period.

6. The method for optimizing the operation of a multi-user heating system based on master-slave game theory as described in claim 5, characterized in that: The constraints on the upper load aggregator (LA) include: power balance constraints, tie-line power constraints, and electricity price constraints. a: Power balance constraint: ； In the formula: for For the distribution network Electricity sales capacity at any given time; for For the distribution network The amount of electricity purchased at any given time; For time step, For users exist Always towards The power consumption of electricity purchased; For users exist Always towards The electricity sales capacity is N; N is the number of users. b: Tie line power constraint: ； In the formula: and They are respectively Power limits for distribution network interconnections; c: Electricity price constraints: The purchase price is higher than the power purchase and sale price on the distribution network. The selling price is lower than the power purchase and sale price on the distribution network; ； In the formula: , For the distribution network at Time-of-use electricity pricing and grid connection pricing at specific times; The electricity purchase and sale price set for load aggregators; This represents the average electricity price for purchase and sale within the heating system.

7. The method for optimizing the operation of a multi-user heating system based on master-slave game theory as described in claim 6, characterized in that: The lower-level heating user response model includes the objective function of the upper level: As followers, heating users take minimizing heating costs as their objective function in participating in the game. ； In the formula: The comprehensive heating cost function for users; For users The cost of purchasing electricity; For users The cost of penalties for abandoning light; For user comfort functions; , , These are the weighting coefficients.

8. The method for optimizing the operation of a multi-user heating system based on master-slave game theory according to claim 7, characterized in that: The constraints for lower-level heating users include: power balance constraints, photovoltaic output constraints, energy storage constraints, electric heating power constraints, and indoor temperature constraints. a. Power balance constraint: To ensure the safe and reliable operation of the heating system, it is necessary to maintain the power balance of users at all times; ； In the formula: For users and The interaction power; For users The actual output of photovoltaic power; For users Electric heating power; For users The energy storage charging and discharging power; For users Energy storage charging power; For users Energy storage discharge power; For users The base load; Indicates user The power purchased at time t; Indicates user Electricity sales power at time t; b. Photovoltaic output constraints: ； In the formula: The actual output of photovoltaic power; For users Maximum output of photovoltaic power; c. Energy storage constraints: To ensure the safe and sustainable operation of energy storage, it is necessary to constrain the state of charge and charging / discharging power of the energy storage, and to restrict simultaneous charging and discharging. ； In the formula: For users State of charge during time period t; The self-discharge rate of the stored energy; For users State of charge during time period t-1; and These are the charging efficiency and discharging efficiency of energy storage, respectively. and users respectively The charging power and discharging power during time period t; and These represent the lower and upper limits of the actual achievable capacity of energy storage, respectively. ； In the formula: and users respectively The flags indicating the charging and discharging of the energy storage during time period t; For users Maximum charge and discharge power of energy storage; d. Electric heating power constraints: ； In the formula: For users Rated power of electric heating; e. Indoor temperature constraints: To ensure the comfort of users' heating, the temperature needs to be restricted to a certain range; ； In the formula: Indicates user The indoor temperature at time t; The lower limit of indoor temperature; This is the lower limit of indoor temperature.

9. The method for optimizing the operation of a multi-user heating system based on master-slave game theory as described in claim 8, characterized in that: In step 5, the constraints of energy storage include nonlinear constraints. To improve the solution efficiency, the Big-M method is used to linearize the energy storage charging and discharging power constraints, equivalently transforming the original nonlinear constraints into mixed integer linear constraints. The transformed constraints are shown in the following equation: ； In the formula: It is a sufficiently large constant.

10. The method for optimizing the operation of a multi-user heating system based on master-slave game theory according to claim 9, characterized in that: Step 5, the model solution includes: After linearizing the charging and discharging power constraints of energy storage, the optimization operation model of a multi-user heating system based on master-slave game is transformed into a mixed integer linear programming problem. The upper-level LA revenue model is solved using a genetic algorithm in MATLAB 2022b, and the lower-level heating user response model is solved using the solver Gurobi and Yalmip toolbox.

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