A multi-agent electric-thermal coupled system optimal scheduling method considering benefit balance game

Abstract

The application discloses a multi-agent electric-thermal coupling system optimal scheduling method considering benefit balance game, which comprises the following steps: establishing a multi-agent electric-thermal coupling system game framework based on the benefit composition and related influence components in each agent; analyzing the interaction relationship between each game agent and game subject and the benefit balance mechanism between electric and thermal agents in the game process based on the established multi-agent electric-thermal coupling system game framework, and establishing a multi-agent electric-thermal coupling system game model; and obtaining the output and electricity price strategy of each agent in the Stackelberg equilibrium state by using a differential evolution algorithm based on the established multi-agent electric-thermal coupling system game model. The multi-agent electric-thermal coupling system optimal scheduling method considering benefit balance game aims at analyzing the interaction relationship between each game agent and game subject and the benefit balance mechanism between electric and thermal agents in the game process, so as to improve the benefit distribution balance degree of the multi-agent electric-thermal coupling system and realize the optimal scheduling of the multi-agent electric-thermal coupling system.

Description

Technical Field

[0001] This invention relates to the field of integrated energy system operation and control technology, specifically to an optimal scheduling method for a multi-entity electrothermal coupling system that takes into account the balance of interests in a game-theory approach. Background Technology

[0002] Based on energy type, integrated energy systems include electro-thermal integrated energy systems, electro-thermal integrated energy systems, and electro-thermal and transportation integrated energy systems. Among these, the electro-thermal integrated energy system is representative of the "Three Norths" region of my country. On the one hand, combined heat and power (CHP) units are the main components of electro-thermal coupling systems. During operation, these units convert energy into electrical energy and use the steam that has done work as heat energy. This energy supply method greatly reduces primary energy consumption and improves energy utilization efficiency. On the other hand, electrical and thermal energy have strong physical complementarity. Energy in the power system is relatively easy to transmit but difficult to store, while thermal systems are easy to store but difficult to transmit. The power system has a natural advantage in transmitting energy over a large spatial range, while the energy storage advantage of the thermal system has a certain smoothing function for short-term fluctuations in the power system. The combination of the two helps to absorb new energy sources.

[0003] With the development of district heating systems, electrothermal systems are gradually taking on a "one-electricity-multiple-heating" form. Within a city, a single electrical entity and multiple heat entities are directly interconnected and coupled, transmitting electrical energy over long distances. This multi-entity electrothermal coupling system exhibits a distributed structure in physical space. As the number of heat entities increases, the scale of energy data in the electrothermal coupling system gradually expands, and the constraints between the electrical and heat entities also gradually strengthen, ultimately leading to energy mutual assistance and collaborative optimization among the entities in large-scale scenarios.

[0004] On the other hand, with the further opening of the electricity market, energy suppliers have gained greater decision-making power in dispatching output, and their bargaining power has correspondingly increased. Currently, the relationship between the power grid and energy suppliers is no longer a fixed, one-way decision-making relationship, but rather a market structure with grid operators as leaders and energy suppliers as followers. Traditional dispatching strategies only consider the overall electricity price and output requirements of multiple energy suppliers, ignoring the differences in the power supply performance of each energy supplier and failing to simultaneously consider the dispatching decision-making needs of both energy suppliers and grid operators. This makes it impossible for multiple stakeholders to achieve a balance of interests under dispatching decisions. Therefore, to ensure the efficient and fair operation of multi-stakeholder systems under autonomous dispatching, it is urgent to propose optimized dispatching methods that can effectively guarantee the balance of interests in multi-stakeholder electro-thermal coupling systems, thereby enhancing the dispatching enthusiasm of each participating stakeholder and promoting efficient and fair operation. Summary of the Invention

[0005] To enable multi-agent systems to operate efficiently and fairly under autonomous scheduling, this invention provides an optimal scheduling method for multi-agent electrothermal coupling systems that considers the game of interest equilibrium. The method aims to fully analyze the interaction relationships between the various game agents and their followers and the interest equilibrium mechanism among the electrothermal agents during the game process, so as to improve the balance of interest distribution in the multi-agent electrothermal coupling system and realize the optimal scheduling of the multi-agent electrothermal coupling system.

[0006] The technical solution adopted in this invention is as follows:

[0007] A method for optimal scheduling of a multi-agent electrothermal coupling system that considers the equilibrium game of interests includes the following steps:

[0008] Step 1: Based on the interests and related influencing factors of each subject, establish a game framework for a multi-subject electrothermal coupling system;

[0009] Step 2: Based on the game framework of the multi-agent electrothermal coupling system established in Step 1, analyze the interaction between the players and their followers and the interest balance mechanism among the electrothermal players during the game process, and establish a game model of the multi-agent electrothermal coupling system.

[0010] Step 3: Based on the game model of the multi-agent electrothermal coupling system established in Step 2, the power output and electricity price strategy of each agent under the Stackelberg equilibrium state are obtained by using the differential evolution algorithm.

[0011] Through the above steps, the optimized scheduling of a multi-entity electrothermal coupling system can be achieved.

[0012] In step 1, the game framework of the multi-entity electrothermal coupling system is: a game framework in which the power grid operator is the leader and one electrical entity and multiple thermal entities are the followers.

[0013] In the game between the main players, the grid operator exchanges information with each energy supplier and coordinates with them to minimize its own operating costs while meeting user electricity demand. In the game between the secondary players, the grid-connected electricity price guides the output decisions of each energy supplier, leading to varying dispatch motives based on the price offered by the grid operator, while also satisfying their own output constraints, in order to maximize their power generation revenue. Therefore, the electricity price information set by the leader and the output decisions fed back by the followers can be iteratively optimized within a non-cooperative game framework until all participating players reach an equilibrium state.

[0014] In step 2, the game model of the multi-agent electrothermal coupling system includes a participant model, a strategy model, and a benefit model, wherein:

[0015] The set of participants is shown in the following formula:

[0016] N={E,ELE,HEAT1,HEAT2,...,HEAT j} (1);

[0017] In formula (1): E represents the power grid operator, ELE represents the electrical body, HEAT represents the thermal body, and the subscripts 1 to j represent the numbers of different thermal bodies respectively;

[0018] The strategy model includes principal strategies and subordinate strategies:

[0019] In this game, the power grid operator aims to minimize its own operating costs. Under the premise of maintaining a balance between power supply and demand, it sets electricity purchase prices for different energy suppliers based on historical data of output decisions. S represents the electricity price information distributed to each supplier within 24 hours, and its set form can be expressed as:

[0020]

[0021] In equation (2): s ele,t This represents the overall on-grid electricity price for both coal-fired power units and wind power units within the power plant at time t. Then, these represent the on-grid electricity prices of the combined heat and power units in heat body 1 to j at time t.

[0022] In the game theory scenario, one electrical entity and multiple thermal entities act as followers. Each energy supplier will make its own output decision based on the different electricity prices set by the leader, while satisfying its own output characteristics and aiming to maximize its own benefit, as shown in the following equation:

[0023] D = {P} t G +P t W} (3);

[0024]

[0025] Where: P t G This represents the electrical output of the coal-fired power unit within the main electrical system at time t, in MW; P. t W This represents the electrical output of the wind turbine unit within the electrical system at time t.

[0026] These represent the electrical output of the combined heat and power (CHP) units 1 to j in the heat body at time t, in MW.

[0027] D represents the set of electrical output decisions for the electrical agent, H1, H2, ..., H jIt is represented as the decision set of electrical output from different thermal subjects.

[0028] The slaves in the game feed back the contribution decisions of each follower to the main player. The main player then readjusts its electricity pricing arrangements and transmits the updated electricity pricing information back to the slaves. This cycle continues until an optimal result that satisfies the Stackelberg equilibrium is found.

[0029] The benefit model includes the benefit model of the electricity entity, the benefit model of the heat entity, and the cost model of the grid operator;

[0030] The interest model of the electric subject is based on interest S ELE Maximization is the optimization objective, with units of yuan, and its objective function is expressed as follows:

[0031] S ELE =max[S e-sell -(C PG(E) +C ST(E) +C e-m +C wind(fall) (5);

[0032] In equation (5): S e-sell Revenue from electricity sales by the main power company, unit: yuan; C PG(E) Operating costs for each coal-fired power unit, unit: yuan; C ST(E) Start-up and shutdown costs of coal-fired power units, unit: yuan; C e-m Operating and maintenance costs, unit: yuan; C wind(fall) The penalty for wind curtailment is expressed in yuan.

[0033]

[0034] In equation (6): s ele,t This represents the overall on-grid electricity price of coal-fired power units and wind power units within the main power generation system during time period t. T is the total number of dispatching times, in hours; t represents different time periods; and i represents the unit number.

[0035] U represents the electrical output of the i-th coal-fired power unit during time period t, in MW; G A collection of coal-fired power units; U W Represents a collection of wind turbine units; The actual power generation of the wind turbine during time period t, in MW;

[0036]

[0037] In equation (7): a 2i a 1i and a 0iThe coefficients of the secondary power generation cost function of the i-th coal-fired power unit are represented.

[0038]

[0039] In equation (8): This represents the start-up and shutdown status of the i-th coal-fired power unit at time t. A value of 0 indicates that the machine is stopped. A value of 1 indicates that the device is powered on; c i This represents the startup cost of the i-th unit, in yuan.

[0040]

[0041] In equation (9): δ is the cost coefficient for wind curtailment penalty; Let t be the maximum predicted wind power output at time t, in MW;

[0042] Constraints of the electricity subject interest model:

[0043] Power constraints of coal-fired power units:

[0044]

[0045] In equation (10), and These are the upper and lower limits of the electrical output of the i-th coal-fired power unit, respectively, in MW.

[0046] Climbing constraints for coal-fired power units:

[0047]

[0048] In equation (11), P i,t P represents the electrical output of the i-th coal-fired power unit during time period t. i,t-1 This represents the electrical output of the i-th coal-fired power unit during time period t-1, in MW.

[0049] R Ui and R Di These are the ramp rate and landslide rate of the i-th coal-fired power unit, respectively, in MW.

[0050] Wind turbine output constraints:

[0051]

[0052] In equation (12), The maximum predicted wind power output at time t is expressed in MW.

[0053] Power flow constraints on the line:

[0054] Pl,min ≤P l,t ≤P l,max (13)

[0055] In equation (13), P l,t P represents the power of branch l at time t, in MW. l,min P l,max These are the minimum and maximum power values ​​for line l, respectively, in MW.

[0056] The interest model of the hot subject is based on interests Maximization is the optimization objective, with units of yuan, and its objective function is expressed as follows:

[0057]

[0058] In equation (14), S h-j-sell C is the revenue from the sale of electricity by combined heat and power (CHP) units. CHP,j-i Cost of energy supply for combined heat and power units; C h-m For operation and maintenance costs;

[0059]

[0060] In equation (15), This represents the set of CHP units within the district heating system j; This represents the electrical output of the j-th CHP unit in the district heating system during time period t, in MW. This represents the on-grid electricity price of the CHP unit in the thermal body j at time t.

[0061] Constraints of the hot subject interest model:

[0062] Operating constraints of combined heat and power units:

[0063]

[0064] Equation (16) represents the "heat-driven power" coupling operation constraint that the electrical output and thermal output of the CHP unit under back pressure conditions. This represents the electrical output of the i-th CHP unit within the j-th district heating system during time period t, in MW; L j-i The elastic coefficients of electrical output and thermal output of the j-th CHP unit under back pressure in the district heating system; This represents the heat output of the i-th CHP unit within the j-th district heating system during time period t, in MW.

[0065]

[0066] Equation (17) indicates that the unit output must meet the requirement of a certain fuel quantity range, F min and Fmax These represent the minimum and maximum fuel quantities, respectively, in kg; η P,CHP η Q,CHP These represent fuel consumption per unit of electrical output and fuel consumption per unit of thermal output, respectively, in kg / MW.

[0067]

[0068] Equation (18) indicates that the thermal output of the CHP unit must meet certain conditions, where, This represents the upper limit of the heat output of the i-th CHP unit within the j-th district heating system.

[0069] Combined heat and power (CHP) unit ramp-up constraints:

[0070]

[0071] In equation (19), Let be the electrical output of the i-th combined heat and power unit during time period t; These are the ramp rate and landslide rate of the i-th cogeneration unit, respectively, in MW.

[0072] Heat balance constraints between heat source and heat load:

[0073]

[0074] In equation (20), This represents the heat output of the i-th CHP unit in the district heating system 1 during time period t; This represents the heat load of district heating system 1 during time period t; This refers to the set of CHP units within the district heating system 1.

[0075] T represents the scheduling period, in hours; t represents the scheduling time, in hours.

[0076]

[0077] In equation (21), This represents the heat output of the i-th CHP unit within the district heating system 2; This indicates the heat load during time period t within region 2; This refers to the collection of CHP units within the district heating system 2.

[0078] ...

[0079]

[0080] In equation (22), This represents the heat output of the i-th CHP unit within the district heating system j during time period t. This represents the heat load within region j during time period t, in MW.

[0081]

[0082] In equation (23), c h This indicates the specific heat capacity of water; This represents the mass flow rate of pipe l in the i-th CHP unit within region j, in m³ / s. 3 / h; These represent the supply water temperature and return water temperature of the CHP unit's supply pipeline nodes, respectively, in °C; n represents the equivalent output node of the CHP unit; x p This refers to the heating network pipeline.

[0083] l indicates the pipe number connected to the CHP unit; This represents the set of pipes connected to the i-th CHP unit within region j; This represents the set of CHP unit nodes within region j.

[0084] I pipe Represents the set of heating network pipelines; s represents the supply pipeline node; r represents the return pipeline node; This represents a pipe node. The above formula indicates that the heat supply among j district heating systems remains balanced within a fixed time period.

[0085] Heat source temperature constraint:

[0086]

[0087]

[0088] In equations (24) and (25), This represents the lower temperature limit of the supply pipeline node for the i-th CHP unit within region j; This represents the temperature of the supply pipeline node for the i-th CHP unit within region j; This represents the upper temperature limit of the supply pipeline node for the i-th CHP unit within region j, in °C.

[0089] This represents the lower temperature limit of the return pipeline node of the i-th CHP unit within region j; This represents the temperature of the i-th CHP unit returning to the pipeline node within region j. This represents the upper limit of the return pipeline node of the i-th CHP unit within region j, in °C.

[0090] Heat exchanger balance constraints:

[0091]

[0092] In equation (26), This represents the mass flow rate of the v-th exchange station in region j, in m³ / s. 3 / h; This represents the heat load of the vth heat exchange station in the regional heating network at time t, in MW.

[0093] These represent the supply and return pipe temperatures of the equivalent node u of the heat exchange station at time t, respectively, in °C.

[0094] Let represent the set of equivalent nodes for the v-th heat exchange station in the regional heating network j. Let u represent an equivalent node.

[0095] Temperature constraints of heat exchange station:

[0096]

[0097] In equation (27), and These represent the lower and upper temperature limits of the equivalent node of the heat exchange station, respectively.

[0098] This indicates the temperature at the equivalent node of the heat exchange station. Unit: °C.

[0099] Pipeline node mixing temperature:

[0100]

[0101] In equation (28), The mass flow temperature of pipe l at time t, taking heat loss into account, is expressed in °C. The mass flow outlet temperature of pipe l at time t, taking heat loss into account, in °C;

[0102] m l This represents the mass flow rate of pipe l, in meters (m³). 3 / h; Represents a node Temperature at time t, in °C;

[0103] Indicates outflow node A collection of pipes, Indicates the inflow node A collection of pipes; N node Represents the set of pipeline nodes;

[0104] Operational constraints of water supply and return pipelines:

[0105]

[0106]

[0107]

[0108] In equations (29) to (31),

[0109] The values ​​represent the mass flow outlet temperatures of pipe l at time t, with and without heat loss, respectively, in °C.

[0110] The values ​​represent the mass flow inlet temperatures of pipe l at time t, with and without heat loss, respectively, in °C.

[0111] The superscripts "out" and "in" indicate the inflow and outflow sections of the pipe, respectively.

[0112] τ G,t The ambient temperature at time t, in °C; m l This represents the mass flow rate of pipe l, in meters (m³). 3 / h;ρ h The density of water in the pipe, kg / m³ 3 ;

[0113] μ l R represents the time delay parameter indicating the temperature change in pipe l. l μ l The total mass flowing into pipe l during the time period; k l The coefficient variable representing the outlet temperature of pipe l; α l This represents the cooling coefficient of pipe l.

[0114] A l ,L l ,λ l Let represent the cross-sectional area of ​​pipe l, pipe length, and transmission coefficient, respectively.

[0115] △t represents the time resolution of the nodal method, in hours (h). This represents the set of heating network pipes in region j.

[0116] Cost model for power grid operators:

[0117] The cost model of a power grid operator is based on cost C. E Minimization is the optimization objective, and its objective function is expressed as follows:

[0118]

[0119]

[0120] In equations (32) to (33):

[0121] Se-sell This indicates the cost of purchasing electricity from the power source, in yuan; S h-j-sell This indicates the cost of purchasing electricity from the heat source, in yuan; C env This indicates the environmental operating cost, in yuan.

[0122] This represents the pollutant emission coefficient of thermal power unit i. ρ represents the pollutant coefficient emitted by the i-th cogeneration unit within the heat source j. c This indicates the penalty fees for emissions from each unit.

[0123] Constraints:

[0124] Electric power balance constraints:

[0125]

[0126] In equation (34), N DHN Represents a collection of thermal entities. U represents the set of CHP units. G Represents a set of coal-fired power units; U W Represents a collection of wind turbine units; P represents the power output (MW) of the i-th CHP unit in region j at time t, which is determined by the district heating system. L,t This represents the power demand of the electrical load at time t, in MW.

[0127] In summary, the master-slave game model of a multi-entity electrothermal coupling system can be expressed as:

[0128]

[0129] In equation (35), E represents the power grid operator, ELE represents the electrical body, HEAT represents the thermal body, and subscripts 1 to j represent the numbers of different thermal bodies; {ELE,HEAT1,HEAT2,...,HEAT j} represents the set of electrical and thermal entities as participants; S represents the electricity price information issued to each entity within 24 hours; D represents the set of electrical output decisions of the electrical entities, H1, H2, ..., H... j Represented as the decision set of electrical output from different thermal subjects; {D,H1,H2,...,H j} indicates that the output of the electrical and thermal components are considered as the same game entity; C E S represents the cost of the power grid operator; ELE Representing the interests of the electrical subject; Representing the interests of the thermal subject; This indicates that the interests of the electrical body and the thermal body are considered as the same interest group.

[0130] In step 3, the Stackelberg equilibrium state is: when all participants cannot obtain greater benefits by changing their own strategies, it indicates that the game has reached Stackelberg equilibrium.

[0131] At this point, the equilibrium solution of the master-slave game model of the multi-entity electrothermal coupling system can be expressed as:

[0132]

[0133] In the above formula, This represents the equilibrium solution of the overall on-grid electricity price for the coal-fired power units and wind power units within the power plant at time t. This represents the equilibrium solution of the grid-connected electricity price for the combined heat and power units in heat body 1 to j at time t; This represents the equilibrium solution of the electrical output of coal-fired power unit i within the main electrical system at time t. This represents the equilibrium solution of the electric output of wind turbine i within the main body of the electrical system at time t; This represents the equilibrium solution of electrical output of the combined heat and power units in the thermal body 1 to j at time t.

[0134] And it satisfies the condition of equation (36):

[0135]

[0136] In equation (36), This represents the grid operator cost under the equilibrium solution; This represents the grid operator's cost when the electrical output of both the electrical and thermal components is in equilibrium, but the grid-connected electricity price of the electrical and thermal components is not in equilibrium. This represents the interests of the electrical entity under the equilibrium solution; This represents the benefits of the electricity subject when the grid-connected electricity price and the thermal output of the thermal subject are both in equilibrium, but the electricity output of the electricity subject is not in equilibrium. This represents the interests of the thermal entity under the equilibrium solution; This represents the benefits of the electricity subject when the grid-connected electricity price and the electricity output of the electricity subject are both in equilibrium, the electricity output of the heat subject 2 to j is also in equilibrium at time t, but the electricity output of the heat subject 1 is not in equilibrium. This represents the interests of the thermal entity under the equilibrium solution; This represents the benefits of the electricity subject when the grid-connected electricity price and the electricity output of both the electricity subject and the heat subject are in equilibrium, the electricity output of heat subjects 1 and 3~j are also in equilibrium at time t, but the electricity output of heat subject 2 is not in equilibrium. This represents the interests of the thermal entity under the equilibrium solution; It represents the benefit of the electrical entity when the on-grid electricity prices of the electrical entity and the thermal entity and the electrical output of the electrical entity are all equilibrium solutions, and the electrical outputs of the thermal entities 1 to j - 1 at time t are also equilibrium solutions, but the electrical output of the thermal entity j is not an equilibrium solution.

[0137] In step 3, the steps for solving the output and electricity price strategies of each entity in the Stackelberg equilibrium state are as follows:

[0138] Step (1): Input information such as load demand, unit parameters and related constraints, and electricity price change range into the system.

[0139] Step (2): Set the initial population x of the upper-layer electricity price, and the initial iteration number k = 0.

[0140] Step (3): The power grid operator transmits the initial electricity purchase price to the lower-layer entities, enabling the lower-layer entities to optimize their outputs according to the upper-layer information.

[0141] Step (4): Each lower-layer entity receives the electricity price information, sets the electricity price in its independent optimization target as a fixed value, takes the maximization of its own benefit as the goal, uses the Cplex toolbox to plan and solve the unit output values within the entity, obtains the final output values, and transmits the results to the upper layer.

[0142] Step (5): The upper layer receives the specific output information of each lower-layer entity's unit, and calculates the cost U1 of the power grid operator based on the original electricity price information.

[0143] Step (6): The original population x undergoes crossover and mutation to obtain a new population y, that is, the upper-layer entity obtains new electricity price information.

[0144] Step (7): The upper-layer entity calculates the cost U2 of the power grid operator based on the new electricity price information and the current output values of the units.

[0145] Step (8): Compare the magnitudes of U1 and U2. If U1 > U2, then x = y; if U1 = U2 or U1 < U2, then keep the original result unchanged.

[0146] Step (9): Determine whether the iteration number requirement is met at this time. If it is met, output the result; if not, return to step (3) for the next round of iteration.

[0147] For the multi-agent electro-thermal coupling system optimal scheduling method considering benefit equilibrium game in this invention, the technical effects are as follows:

[0148] 1) The optimized scheduling method of this invention considers the information interaction relationship between the main players and the secondary players in the game process, regards the power system and the thermal system as the same interest entity, fully considers the autonomous decision-making rights of each thermal entity, truly realizes the balance of interests among multiple entities under the "one power, multiple heat" structure, improves the enthusiasm of each entity to participate in scheduling, and realizes the optimized scheduling of multi-entity electric-thermal coupling system.

[0149] 2) This invention analyzes the interaction relationships between various stakeholders and their followers during the game process, and uncovers the interest equilibrium mechanism among the electrothermal entities. Based on this, a multi-stakeholder electrothermal coupling system interest model is constructed; compared with traditional economic scheduling, the interest coordination method among electrothermal entities based on master-slave game theory is more balanced in interest distribution.

[0150] 3) This invention proposes to use the difference improvement method to solve the Stackelberg equilibrium solution, which requires fewer iterations to obtain the equilibrium solution. The selected algorithm has a fast solution speed and good convergence. Attached Figure Description

[0151] Figure 1 Game theory framework diagram of a multi-entity electrothermal coupling system.

[0152] Figure 2 Flowchart of master-slave game algorithm for multi-entity electrothermal coupling system.

[0153] Figure 3 It is a diagram showing the electric heating load and the maximum predicted output of wind power.

[0154] Figure 4 This is a diagram showing the convergence of the equilibrium solution in a multi-entity electrothermal coupling system.

[0155] Figure 5 It is a diagram showing the electric heating load and the maximum predicted output of wind power.

[0156] Figure 6 This is a diagram showing the thermal output results of each component.

[0157] Figure 7 This is a chart showing the on-grid electricity prices for different entities at different times.

[0158] Figure 8 This is a comparison chart showing the balance of interests among various stakeholders in different scenarios. Detailed Implementation

[0159] A multi-agent electrothermal coupling system optimization scheduling method considering the interest equilibrium game is proposed. The method aims at the balanced distribution of interests within the multi-agent electrothermal coupling system, fully considering the information interaction between the main players and their followers during the game process, and establishing a game framework for the multi-agent electrothermal coupling system. Simultaneously, a multi-agent electrothermal coupling system game model is established, with the goal of minimizing grid operator costs, satisfying power balance constraints, maximizing the interests of both the electricity and heat-generating entities, and unit output constraints, using grid connection, grid electricity prices, and grid output instructions as the overall game strategy. Then, the optimal result of the multi-agent electrothermal coupling system optimization scheduling method considering the interest equilibrium game is obtained through a differential evolution algorithm combined with the Cplex toolbox. Finally, the interest equilibrium degree is used as an evaluation index to quantitatively analyze the interest distribution of each entity during the game process. The specific steps include the following:

[0160] Step 1: Based on the interests and related influencing factors of each subject, establish a game framework for a multi-subject electrothermal coupling system;

[0161] Step 2: Based on the game framework of the multi-agent electrothermal coupling system established in Step 1, analyze the interaction between the players and their followers and the interest balance mechanism among the electrothermal players during the game process, and establish a game model of the multi-agent electrothermal coupling system.

[0162] Step 3: Based on the game model of the multi-agent electrothermal coupling system established in Step 2, the differential evolution algorithm is used to obtain the output and electricity price strategy of each agent under the Stackelberg equilibrium state.

[0163] In step 1, the interest framework of the multi-agent electrothermal coupling system is a game framework with the grid operator as the leader and one electrical entity and multiple thermal entities as followers, such as... Figure 1 As shown in the diagram, in the game between the main players, the grid operator exchanges information with each energy supplier and coordinates with them to achieve the lowest possible operating cost while meeting user electricity demand. In the secondary players, the grid-connected electricity price guides the output decisions of each energy supplier, leading to varying dispatch motives based on the price offered by the grid operator, while simultaneously satisfying their own output constraints, in order to maximize their power generation revenue. Therefore, the electricity price information set by the leader and the output decisions fed back by the followers can be iteratively optimized within a non-cooperative game framework until all participating players reach an equilibrium state.

[0164] In step 2, the multi-agent electrothermal coupling system game model includes a participant model, a strategy model, and a benefit model. The set of participants is shown in the following equation:

[0165] N={E,ELE,HEAT1,HEAT2,...,HEAT j} (1);

[0166] E represents the power grid operator, ELE represents the electrical entity, HEAT represents the thermal entity, and the subscripts 1 to j represent the numbers of different thermal entities.

[0167] The strategy model is divided into principal strategy and subordinate strategy:

[0168] In this game, the grid operator aims to minimize its own operating costs. Under the premise of maintaining a balance between power supply and demand, it sets electricity purchase prices for different energy suppliers based on historical data of output decisions. S represents the electricity price information distributed to each supplier within 24 hours, which can be represented as a set:

[0169]

[0170] s ele,t This represents the overall on-grid electricity price for both coal-fired power units and wind power units within the power plant at time t. Then, these represent the on-grid electricity prices of the combined heat and power units in heat body 1 to j at time t.

[0171] In the game theory scenario, one electrical entity and multiple thermal entities act as followers. Each energy supplier will make its own output decision based on the different electricity prices set by the leader, while satisfying its own output characteristics and aiming to maximize its own benefit, as shown in the following equation:

[0172] D = {P} t G +P t W} (3);

[0173]

[0174] P t G This represents the electrical output of the coal-fired power unit within the main electrical system at time t, in MW; P. t W This represents the electrical output of the wind turbine unit within the electrical system at time t. H1, H2, ..., Hj represent the electrical output of the combined heat and power (CHP) units 1 to j in the heat body at time t, in MW; D represents the electrical output decision set of the heat body, H1, H2, ..., Hjj. jThis is represented as a set of power output decisions from different thermal entities. The slave entities feed back the power output decisions of each follower to the main entity, which then readjusts its own electricity pricing arrangements and transmits the updated electricity price information back to the slave entities. This process continues until an optimal result satisfying the Stackelberg equilibrium is found.

[0175] The benefit model includes the benefit model of the electricity entity, the benefit model of the heat entity, and the cost model of the grid operator:

[0176] The interest model of the electric subject is based on interest S ELE Maximizing is the optimization objective, expressed in units of yuan. Its objective function is as follows:

[0177] S ELE =max[S e-sell -(C PG(E) +C ST(E) +C e-m +C wind(fall) (5);

[0178]

[0179]

[0180]

[0181]

[0182] Among them, C PG(E) Operating costs for each coal-fired power unit, unit: yuan; S e-sell Revenue from electricity sales by the main power company, unit: yuan; C ST(E) Start-up and shutdown costs of coal-fired power units, unit: yuan; C e-m Operating and maintenance costs, unit: yuan. wind(fall) The penalty for wind curtailment is expressed in yuan. T represents the total number of scheduling time slots, expressed in hours. a represents the electrical output of the i-th coal-fired power unit during time period t, in MW; 2i a 1i and a 0i U represents the coefficient of the secondary power generation cost function of the i-th coal-fired power unit. G It is a collection of coal-fired power units. This represents the start-up and shutdown status of the i-th coal-fired power unit at time t. A value of 0 indicates that the machine is stopped. A value of 1 indicates that the device is powered on. i Let represent the startup cost of the i-th generating unit, in yuan. δ is the wind curtailment penalty cost coefficient. Let t be the maximum predicted wind power output at time t, in MW; The actual power generation of the wind turbine during time period t, in MW; U W This refers to a collection of wind turbine units.

[0183] Constraints of the electricity subject interest model:

[0184] Power constraints of coal-fired power units:

[0185]

[0186] In the formula, and These represent the upper and lower limits of the electrical output of the i-th coal-fired power unit, in MW.

[0187] Climbing constraints for coal-fired power units:

[0188]

[0189] In the formula, P i,t R represents the electrical output of the i-th coal-fired power unit during time period t. Ui and R Di These are the ramp rate and landslide rate of the i-th coal-fired power unit, respectively, in MW.

[0190] Wind turbine output constraints:

[0191]

[0192] Power flow constraints:

[0193] P l,min ≤P l,t ≤P l,max (13);

[0194] In the formula, P l,t P represents the power of branch l at time t, in MW. l,min and P l,max These are the minimum and maximum power values ​​for line l, respectively, in MW.

[0195] The interest model of the hot subject is based on interests Maximizing is the optimization objective, denoted by element . Its objective function is expressed as follows:

[0196]

[0197]

[0198] Among them, S h-j-sell C is the revenue from the sale of electricity by combined heat and power (CHP) units. CHP,j-i Cost of energy supply for combined heat and power units; C h-m For operation and maintenance costs; This represents the set of CHP units within the district heating system j; This represents the electrical output of the th CHP unit within the district heating system during time period t, in MW.

[0199] Constraints of the hot subject interest model:

[0200] Operating constraints of combined heat and power units:

[0201]

[0202]

[0203]

[0204] Equation (16) represents the "heat-driven power" coupling operation constraint followed by the electrical output and thermal output of the CHP unit under back pressure conditions. j-i Let the elastic coefficients of electrical and thermal output of the i-th CHP unit in the district heating system under back pressure be given. The electrical output (MW) of the i-th CHP unit in the district heating system j during time period t; This represents the heat output of the i-th CHP unit within the j-th district heating system during time period t, in MW.

[0205] Equation (17) indicates that the unit output must meet the requirement of a certain fuel quantity range, F min and F max These represent the minimum and maximum fuel quantities, respectively, in kg; η P,CHP and η Q,CHP These represent fuel consumption per unit of electrical output and fuel consumption per unit of thermal output, respectively, in kg / MW.

[0206] Equation (18) indicates that the thermal output of the CHP unit must meet certain conditions, where, This represents the upper limit of the heat output of the i-th CHP unit within the district heating system.

[0207] Combined heat and power (CHP) unit ramp-up constraints:

[0208]

[0209] In the formula, Let be the electrical output of the i-th combined heat and power unit during time period t; and These are the ramp rate and landslide rate of the i-th cogeneration unit, respectively, in MW.

[0210] Heat balance constraints between heat source and heat load:

[0211]

[0212]

[0213] ...

[0214]

[0215]

[0216] In equations (20) to (22), The unit represents the heat load within region j during time period t, in MW; T represents the scheduling period, in hours; t represents the scheduling time, in hours; I pipe This represents a collection of heating network pipes.

[0217] In equation (23), c h This indicates the specific heat capacity of water. This represents the mass flow rate of pipe l in the i-th CHP unit within region j, in m³ / s. 3 / h;

[0218] and These represent the supply water temperature and return water temperature of the supply pipeline nodes of the CHP unit, respectively, in °C;

[0219] n represents the equivalent output node of the CHP unit. This represents the set of pipes connected to the i-th CHP unit within region j. Let T represent the set of CHP unit nodes within region j, and let T represent the time set of the scheduling cycle.

[0220] The above formula indicates that the heat supply among the j district heating systems remains balanced within a fixed time period.

[0221] Heat source temperature constraint:

[0222]

[0223]

[0224] In the formula, and This represents the upper and lower temperature limits of the supply pipeline node for the i-th CHP unit within region j, in °C. and This represents the upper and lower limits of the temperature returned to the pipeline node of the i-th CHP unit within region j, in °C.

[0225] Heat exchanger balance constraints:

[0226]

[0227] In the formula, This represents the mass flow rate of the v-th exchange station in region j, in m³ / s. 3 / h; This represents the heat load of the vth heat exchange station in the regional heating network at time t, in MW.

[0228] and The supply and return pipe temperatures at the equivalent node u of the heat exchange station at time t are respectively expressed in °C.

[0229] Let represent the set of equivalent nodes of the v-th heat exchange station in the regional heating network j.

[0230] Temperature constraints of heat exchange station:

[0231]

[0232] In the formula, and These represent the lower and upper temperature limits of the equivalent node of the heat exchange station, respectively, in °C.

[0233] Pipeline node mixing temperature:

[0234]

[0235] In the formula, The mass flow outlet temperature of pipe l at time t, taking heat loss into account, in °C; The mass flow temperature of pipe l at time t, taking heat loss into account, is expressed in °C.

[0236] m l This represents the mass flow rate of pipe l, in meters (m³). 3 / h;N node Represents the set of pipeline nodes. Indicates outflow node A collection of pipes, Indicates the inflow node A collection of pipes, Represents a node Temperature at time t, in °C.

[0237] Operational constraints of water supply and return pipelines:

[0238]

[0239]

[0240]

[0241] In the formula, and The values ​​represent the mass flow outlet temperatures of pipe l at time t, with and without heat loss, respectively, in °C.

[0242] and The numbers represent the mass flow inlet temperatures at time t for pipe l with and without heat loss, respectively, in °C; the superscripts out and in represent the inlet and outlet sections of the pipe, respectively.

[0243] τ G,t This represents the ambient temperature at time t, in °C.

[0244] m l This represents the mass flow rate of pipe l, in meters (m³). 3 / h;

[0245] ρ h The density of water inside the pipe, unit: kg / m³ 3 ;

[0246] μ l ,R l ,k l ,α l This indicates parameters related to heat loss and time delay in pipe l;

[0247] A l ,L l ,λ l This represents the cross-sectional area, length, and transmission coefficient of pipe l;

[0248] △t represents the time resolution of the nodal method, in hours (h). This represents the set of heating network pipes in region j.

[0249] Cost model for power grid operators:

[0250] The cost model of a power grid operator is based on cost C. E Minimize the cost as the optimization objective, taking into account the market and environmental responsibilities that grid operators should bear, and the cost is determined by the electricity purchase price S from the power source. e-sell Unit: Yuan, Cost of purchasing electricity from the heat source (S) h-j-sell Yuan, environmental operating costs C env Unit: yuan, composition. Its objective function is expressed as follows:

[0251]

[0252]

[0253] In the formula, S e-sell This indicates the cost of purchasing electricity from the power source, in yuan; S h-j-sellThis indicates the cost of purchasing electricity from the heat source, in yuan; C env This indicates the environmental operating cost, in yuan.

[0254] This represents the pollutant emission coefficient of thermal power unit i. ρ represents the pollutant coefficient emitted by the i-th cogeneration unit within the heat source j. c This indicates the penalty fees for emissions from each unit.

[0255] Constraints:

[0256] Electric power balance constraints:

[0257]

[0258] In the formula, N DHN Represents a collection of thermal entities. U represents the set of CHP units. G U represents a set of coal-fired power units; W Represents a collection of wind turbine units; This represents the power output of the i-th CHP unit in region j at time t, in MW; this value is determined by the district heating system. L,t This represents the power demand of the electrical load at time t, in MW.

[0259] In summary, the master-slave game model of a multi-entity electrothermal coupling system can be expressed as:

[0260]

[0261] In step 3, the Stackelberg equilibrium state is: during the game, when none of the participants can gain a greater benefit by changing their own strategies, it indicates that the game has reached Stackelberg equilibrium. At this point, the equilibrium solution of the master-slave game model of the multi-agent electrothermal coupling system can be expressed as:

[0262] And it satisfies the conditions of equation (36);

[0263]

[0264] In step 3, the steps for solving the power output and electricity pricing strategies of each entity under the Stackelberg equilibrium state are as follows:

[0265] (1) Input information such as load demand, unit parameters and related constraints, and electricity price change range into the system.

[0266] (2) Set the upper-level electricity price to initialize the population x, and the initial iteration number k = 0.

[0267] (3) The grid operator transmits the initialized power purchase price to the lower-level entities, enabling the lower-level entities to optimize their output according to the upper-level information.

[0268] (4) Each lower-level entity receives the electricity price information, sets the electricity price in its autonomous optimization target as a fixed value, aims to maximize its own interests, uses the Cplex toolbox to plan and solve the output values of the units within the entity, obtains the final output values, and transmits the results to the upper level.

[0269] (5) The upper level receives the specific output information of the units of each lower-level entity and calculates the cost U1 of the grid operator based on the original electricity price information.

[0270] (6) The original population x undergoes crossover and mutation to obtain a new population y, that is, the upper-level entity obtains new electricity price information.

[0271] (7) The upper-level entity calculates the cost U2 of the grid operator based on the new electricity price information and the current output values of the units.

[0272] (8) Compare the magnitudes of U1 and U2. If U1 > U2, then x = y; if U1 = U2 or U1 < U2, then keep the original result unchanged.

[0273] (9) Determine whether the iteration count requirement is met at this time. If it is met, output the result; if not, return to step (3) for the next round of iteration. The algorithm solving process is as Figure 2 shown.

[0274] Example:

[0275] Taking a multi-agent electric-thermal coupling system as the research object, which includes a grid operator, one electric entity, and two thermal entities. The curves of electric-thermal load variation and wind power prediction are as Figure 3 shown. Set the economic dispatch period as 1 day, with a total of 24 time periods. The original on-grid electricity prices of the electric entity and the thermal entities are taken as 450 yuan / MW·h and 500 yuan / MW·h respectively.

[0276] Establish a corresponding mathematical simulation model in the commercial software Matlab, and through simulation verification, demonstrate the effectiveness and superiority of considering the interest equilibrium game in improving the system interest equilibrium distribution in the multi-agent electric-thermal coupling system.

[0277] (1) Equilibrium solution analysis:

[0278] The game iteration results of the grid operator and each energy supply entity are as Figure 4 shown. The master-slave game of the multi-agent electric-thermal coupling system will converge at the 23rd iteration, and the number of iterations required to obtain the equilibrium solution is less. It can be seen that the selected algorithm has a fast solving speed and good convergence. From Figure 4It is evident that during this iterative process, the grid operator, as the leader, possesses the dominant power in electricity price regulation. It continuously seeks optimization towards minimizing its own costs during the interaction process, and by the 14th iteration, it had found a stable convergence direction, with the trend gradually stabilizing and no longer experiencing large-scale reverse fluctuations. The output changes of other power supply entities showed no obvious pattern, all gradually stabilizing after a period of time.

[0279] (2) Analysis of power scheduling results for each entity:

[0280] Figure 5 The results of power output optimization for each main body are as follows: Figure 6 For the thermal output results of each entity, Figure 7 This section describes the grid-connected electricity prices for each entity at different times. Looking at the power output of the power generation units, since each power generation unit includes both wind turbines and thermal power units, during periods of wind power surplus, such as 01:00-07:00 and 22:00-24:00, wind turbines output more power, resulting in lower thermal power output. As wind power output decreases, thermal power output gradually increases, peaking at 15:00. The two thermal power units should prioritize meeting their own heat load demands, while simultaneously considering grid power balance and the constraints of unit output adjustment ranges to provide the final electrical output. Figure 5 It can be seen that the electrical power output trend of the heat body is similar to that of the electrical load. During the period of low electrical load, such as 01:00-08:00, the electrical output power of the heat body is relatively low, while as the electrical load increases, its electrical output power also shows an upward trend.

[0281] Figure 7 This represents the optimized electricity pricing results for grid operators and lower-level stakeholders. Figure 7 It can be seen that the changing patterns of the on-grid electricity prices of each entity show a certain similarity to the trends of the corresponding power output dispatch curves. During the periods of 0:00-08:00 and 21:00-24:00, grid operators, in order to minimize their own costs, set the overall electricity price at a relatively low level. During the 0:00-08:00 period, the average electricity price for the main power source was 508.89 yuan / MW·h, the average electricity price for heat source 1 was 510.36 yuan / MW·h, and the average electricity price for heat source 2 was 509.81 yuan / MW·h. During the 21:00-24:00 period, the average electricity price for the main power source was 556.55 yuan / MW·h, the average electricity price for heat source 1 was 564.67 yuan / MW·h, and the average electricity price for heat source 2 was 566.92 yuan / MW·h. Figure 5The dispatch results show that the aforementioned periods coincide with peak demand for wind power and thermal power. To prioritize the grid connection of wind power and cogeneration units, it is necessary to suppress the output of thermal power units to a certain extent. Therefore, the electricity price set by the grid operator for thermal power should be higher than that for electricity. During the 8:00-21:00 period, to meet the energy demand during peak hours, the grid operator maintains a higher electricity price to encourage participation from various entities in dispatch. During this period, the average electricity price for electricity entities is 611.21 yuan / MW·h, for thermal power entity 1 it is 599.17 yuan / MW·h, and for thermal power entity 2 it is 599.01 yuan / MW·h. However, even when the wind turbines within the electricity entities and the cogeneration units within the thermal entities reach their optimal output, the electricity load demand is still not met. Therefore, the grid operator needs to set a higher electricity price for electricity entities to increase the output willingness of thermal power units. To explore the effect of this master-slave game theory method on the equilibrium distribution of interests, a comparison is made between the autonomous economic scheduling model and the interest game model. The results of the interest equilibrium of each subject at different time periods are obtained. The comparison results of the two equilibrium degrees are as follows: Figure 8 As shown.

[0282] The specific calculation method for the balance of interests is as follows:

[0283]

[0284]

[0285]

[0286] ...

[0287]

[0288] In the formula, u δ1 (t),u δ2 (t),......,u δ(j+1) (t) represent the return coefficients of each subject at time t, where u δ1 (t) represents the return coefficient of the electric agent, u δ2 (t),......,u δj (t),u δ(j+1) (t) then correspond to the return coefficients of heat bodies 1 to j, respectively; IC ele IC h1 ,…,IC h(j+1) U(u) represents the total installed capacity of the units within each main body. δ1 (t),u δ2 (t),......,u δ(j+1) (t) represents the balance of interest distribution. The closer this value is to 1, the more balanced the interest distribution among the various entities.

[0289] Depend on Figure 8 It is evident that the balance of interests in the multi-entity electrothermal coupling system game model and the traditional scheduling model exhibit largely consistent changes across different time periods. The balance of interests among the entities is relatively high between 0:00-08:00 and 21:00-24:00, while it fluctuates slightly within a lower range between 08:00-21:00. Between 0:00-5:00, the demand for electricity decreases continuously, while the demand for heat remains high. During this time, both cogeneration units within the heat entities and wind turbines within the electricity entities have a strong desire to connect to the grid. The grid operator will try to absorb wind power while considering the grid connection demands of multiple entities, resulting in a slight decrease in the balance of interests, but it remains at a relatively high level. Between 05:00-08:00, the amount of wind power connected to the grid gradually decreases, while the electricity load gradually increases. The various entities will compete for grid connection within areas with a larger market share. At this time, thermal power units begin to connect to the grid, and all entities are operating at full capacity, leading to a slight increase in the balance of interests. From 8:00 AM to 9:00 PM is the peak electricity consumption period, during which heat load demand is relatively low. During this time, wind power output decreases significantly, while thermal power units operate at a high proportion, widening the profit gap between the power generation entity and the various heat-generating entities, severely reducing the balance of profit distribution. From 9:00 PM to midnight, electricity load demand decreases, and the conflict between wind and heat power becomes more apparent. The willingness of combined heat and power (CHP) units and wind turbines to connect to the grid gradually increases. At this time, power generation entities absorb wind power under low electricity prices, and the balance of profit increases as all entities cooperate in power generation.

[0290] Overall, the equilibrium degree of the multi-agent electrothermal coupling system game model is significantly higher than that of the traditional economic scheduling model. The equilibrium degree of the traditional economic scheduling model ranges from 0.91 to 0.97, with an average equilibrium degree of 0.9335. The equilibrium degree of the proposed model ranges from 0.91 to 0.98, with an average equilibrium degree of 0.9429, representing a 1.01% improvement compared to the traditional model. This demonstrates superior equilibrium distribution characteristics. Its equilibrium degree is only slightly lower than that of the economic scheduling model during the 23:00-24:00 period, but its overall equilibrium degree remains higher. In conclusion, the multi-agent electrothermal coupling system game model can better balance the equilibrium degree of interests among the agents, exhibiting greater overall stability and superior interest balancing effect.

Claims

1. A method for optimal scheduling of a multi-agent electrothermal coupling system considering the equilibrium game of interests, characterized in that... Includes the following steps: Step 1: Based on the interests and related influencing factors of each subject, establish a game framework for a multi-subject electrothermal coupling system; Step 2: Based on the game framework of the multi-agent electrothermal coupling system established in Step 1, analyze the interaction between the players and their followers and the interest balance mechanism among the electrothermal players during the game process, and establish a game model of the multi-agent electrothermal coupling system. Step 3: Based on the game model of the multi-agent electrothermal coupling system established in Step 2, the power output and electricity price strategy of each agent under the Stackelberg equilibrium state are obtained by using the differential evolution algorithm. Through the above steps, the optimized scheduling of the multi-entity electrothermal coupling system can be achieved; In step 2, the game model of the multi-agent electrothermal coupling system includes a participant model, a strategy model, and a benefit model. The benefit model includes the benefit model of the electricity entity, the benefit model of the heat entity, and the cost model of the grid operator; The interest model of the electric subject is based on interests Maximization is the optimization objective, with units of yuan, and its objective function is expressed as follows: （5）； In equation (5): Revenue from electricity sales by the electricity entity, unit: yuan; Operating costs for each coal-fired power unit, unit: yuan; Cost of starting and stopping coal-fired power units, unit: yuan; Operating and maintenance costs, unit: yuan; The penalty for wind curtailment is expressed in yuan. （6）； In formula (6): Indicates in The overall on-grid electricity price for coal-fired power units and wind power units within the main power generation system during the specified time period. Total number of scheduling times, in hours (h). Indicates different time periods, Indicates the unit number; Indicates the first Taiwan coal-fired power units Electric output during a given time period, in MW; A collection of coal-fired power units; Represents a collection of wind turbine units; For wind turbine units Actual power generation during the period, in MW; （7）； In equation (7): , and Indicates the first The coefficients of the secondary power generation cost function of a coal-fired power unit; （8）； In equation (8): Indicates the first Taiwan coal-fired power units The start / stop status at any given time. A value of 0 indicates that the machine is stopped. A value of 1 indicates that the device is powered on; Indicates the first Start-up cost of the unit, unit: yuan; （9）； In equation (9): This represents the cost coefficient for wind curtailment penalties. for The maximum predicted wind power output at the current moment, in MW; Constraints of the electricity subject interest model: Power constraints of coal-fired power units: （10）； In equation (10), and The first Upper and lower limits of electrical output of coal-fired power units in Taiwan, in MW; Climbing constraints for coal-fired power units: （11）； In equation (11), Indicates the first Taiwan coal-fired power units Electrical output during a given time period Indicates the first Taiwan coal-fired power units Electric output during a given time period, in MW; and The first The ramp rate and landslide rate of a coal-fired power unit, in MW; Wind turbine output constraints: （12） In equation (12), for The maximum predicted wind power output at the current moment, in MW; Power flow constraints on the line: （13） In equation (13), for Time Branch Power, unit: MW; , The lines are respectively Minimum and maximum power, in MW; The interest model of the hot subject is based on interests Maximization is the optimization objective, with units of yuan, and its objective function is expressed as follows: （14）； In equation (14), Revenue from electricity sales by combined heat and power (CHP) units; Energy supply costs for combined heat and power (CHP) units; For operation and maintenance costs; （15）； In equation (15), Indicates district heating system Internal CHP unit assembly; Indicates the first in the district heating system Taiwan CHP unit in Electricity output per time period, in MW; Indicates in Current hot body On-grid electricity price for the CHP unit; Constraints of the hot subject interest model: Operating constraints of combined heat and power units: （16）； Equation (16) represents the "heat-driven power" coupling operation constraint that the electrical output and thermal output of the CHP unit under back pressure conditions. Indicates district heating system Inner Taiwan CHP unit in Electricity output per time period, in MW; For district heating systems No. The elastic coefficients of electrical and thermal output of the CHP unit under back pressure; Indicates district heating system Inner Taiwan CHP unit in Thermal output per time period, unit: MW; （17）； Equation (17) indicates that the unit output must be within a certain range of fuel quantity. and These represent the minimum and maximum fuel quantities, respectively, in kg. , These represent fuel consumption per unit of electrical output and fuel consumption per unit of thermal output, respectively, in kg / MW. （18）； Equation (18) indicates that the thermal output of the CHP unit must meet certain conditions, where, Indicates district heating system Inner Upper limit of thermal output of CHP units; Combined heat and power (CHP) unit ramp-up constraints: （19） In equation (19), For the first Taiwan cogeneration units Electrical output during a given time period; , The first Taiwan cogeneration unit ramp rate and landslide rate, unit: MW; Heat balance constraints between heat source and heat load: （23）； In equation (23), This indicates the specific heat capacity of water; Indicates the region Inner Piping in Taiwan CHP unit Mass flow rate, unit: ; , These represent the supply water temperature and return water temperature of the supply pipeline nodes of the CHP unit, respectively, in °C. Indicates the equivalent output node of the CHP unit; Indicates heating network pipelines; Indicates the pipe number connected to the CHP unit; Indicates the region Inner The collection of pipes connected to the CHP unit; Indicates the region Internal CHP unit node set, Represents a collection of heating network pipes; Indicates a node in the supply pipeline; This indicates a return to the pipeline node; Indicates a pipe node; Heat source temperature constraint: （24）； （25）； In equations (24) and (25), Indicates the region Inner Temperature limit of the pipeline nodes supplying the CHP unit; Indicates the region Inner Temperature of the pipeline nodes supplied by the CHP unit; Indicates the region Inner Upper temperature limit of the pipeline nodes supplying the CHP unit, in °C; Indicates the region Inner The lower limit of the temperature of the return pipeline node of the CHP unit; Indicates the region Inner Temperature of the CHP unit returning to the pipeline node; Indicates the region Inner Upper temperature limit of the return pipeline node for each CHP unit, in °C; Heat exchanger balance constraints: （26）； In equation (26), Indicates the area No. Mass flow rate of a single exchange station, unit: ; Indicates regional heating network No. A heat exchange station Heat load at any given time, in MW; , These represent the equivalent nodes of the heat exchange station. exist Temperature of the supply and return pipelines at any given time, in °C; Indicates regional heating network No. The equivalent node set of a heat exchange station; Indicates the equivalent node; Temperature constraints of heat exchange station: （27）； In equation (27), and These represent the lower and upper temperature limits of the equivalent node of the heat exchange station, respectively. This indicates the temperature at the equivalent node of the heat exchange station; unit: °C. Pipeline node mixing temperature: （28） In equation (28), Indicates the pipes that take heat loss into account. exist The mass flow temperature at any given moment, in °C; Indicates the pipes that take heat loss into account. exist Mass flow outflow temperature at any given moment, in °C; Indicates pipeline Mass flow rate, unit: ; Represents a node exist Temperature at any given time, in °C; Indicates outflow node A collection of pipes, Indicates the inflow node A collection of pipes; Represents the set of pipeline nodes; Operational constraints of water supply and return pipelines: （29）； （30）； （31）； In equations (29) to (31), , These represent pipes with and without heat loss, respectively. exist Mass flow outflow temperature at any given moment, in °C; , These represent pipes with and without heat loss, respectively. exist The mass flow temperature at any given moment, in °C; superscript These represent the inflow section and outflow section of the pipeline, respectively. Indicates in Ambient temperature at any given time, in °C; Indicates pipeline Mass flow rate, unit: ; The density of the water inside the pipe, ; Indicates pipeline The time delay parameter for temperature change; express Inflow into the pipeline during the period Total mass; Indicates pipeline The coefficient variable of the outlet temperature; Indicates pipeline The cooling coefficient; They represent pipes The cross-sectional area, pipe length, and transmission coefficient; The time resolution of the nodal method is expressed in hours (h). Indicates the region The collection of heating network pipelines; Cost model for power grid operators: The cost model of grid operators is based on cost Minimization is the optimization objective, and its objective function is expressed as follows: （32）； （33）； In equations (32) to (33): This indicates the cost of purchasing electricity from the power supplier, in yuan. This indicates the cost of purchasing electricity from the heat source, in yuan. This represents the environmental operating cost, in yuan. Indicates thermal power unit The pollutant coefficients emitted, Indicates the thermal body Inner The pollutant emission coefficient of Taiwan's combined heat and power units. This indicates the penalty fees for emissions from each generating unit; Constraints: Electric power balance constraints: （34）； In equation (34), Represents a collection of thermal entities. This represents the collection of CHP units. This represents a collection of coal-fired power generating units; Represents a collection of wind turbine units; Indicates the region No. The CHP unit was in the first The power supply at any given time, in MW, is determined by the district heating system. Indicates in The power demand of electrical load at any given time, in MW; In summary, the master-slave game model of a multi-entity electrothermal coupling system can be expressed as: （35）； In equation (35), Indicates grid operator, Indicates the electrical body, Indicates the thermal body, subscript These represent the numbers of different thermal bodies; This represents the collection of electrical and thermal entities as participants. This indicates the electricity price information distributed to various entities within 24 hours; This represents the set of electrical output decisions for an electrical entity. Represented as a set of electrical output decisions for different thermal entities; This indicates that the output of the electrical and thermal components are considered as the same entity in a game; This represents the costs incurred by the power grid operator; Representing the interests of the electrical subject; Representing the interests of the thermal subject; This indicates that the interests of the electrical body and the thermal body are considered as the same interest group.

2. The optimal scheduling method for a multi-agent electrothermal coupling system considering interest equilibrium game theory as described in claim 1, characterized in that: In step 1, the game framework of the multi-agent electrothermal coupling system is a game framework in which the grid operator is the leader and one electrical agent and multiple thermal agents are the followers.

3. The method for optimal scheduling of a multi-agent electrothermal coupling system considering interest equilibrium game theory as described in claim 1, characterized in that: In the participant model, the participant set is shown in the following equation: （1）； In formula (1): Indicates grid operator, Indicates the electrical body, Indicates the thermal body, subscript These represent the numbers of different thermal bodies.

4. The optimal scheduling method for a multi-agent electrothermal coupling system considering interest equilibrium game theory as described in claim 1, characterized in that: The strategy model includes principal strategies and subordinate strategies: In this game, grid operators aim to minimize their own operating costs and, while ensuring a balance between power supply and demand, formulate electricity purchase prices for different energy suppliers based on historical data of power output decisions. The electricity price information distributed to various entities within 24 hours can be represented in aggregate form as follows: （2）； In formula (2): Indicates in The overall on-grid electricity price for coal-fired power units and wind power units within the main power plant at the current time. Then they respectively represent in Current hot body On-grid electricity price for combined heat and power (CHP) units; In the game theory scenario, one electrical entity and multiple thermal entities act as followers. Each energy supplier will make its own output decision based on the different electricity prices set by the leader, while satisfying its own output characteristics and aiming to maximize its own benefit, as shown in the following equation: （3）； ， ，…， （4）； in: express Electric output of coal-fired power units within the main electrical unit at any given time, in MW; express The electrical output of the wind turbine unit within the main electrical unit at all times; They represent in Current hot body Electricity output of a combined heat and power (CHP) unit, in MW; This represents the set of electrical output decisions for the electrical entity. Represented as a set of electrical output decisions for different thermal entities; The slaves in the game feed back the contribution decisions of each follower to the main player. The main player then readjusts its electricity pricing arrangements and transmits the updated electricity pricing information back to the slaves. This cycle continues until an optimal result that satisfies the Stackelberg equilibrium is found.

5. The optimal scheduling method for a multi-agent electrothermal coupling system considering interest equilibrium game theory as described in claim 1, characterized in that: In step 3, the Stackelberg equilibrium state is: when all participants cannot obtain greater benefits by changing their own strategies, it indicates that the game has reached Stackelberg equilibrium. At this point, the equilibrium solution of the master-slave game model of the multi-entity electrothermal coupling system can be expressed as: ； In the above formula, Indicates in The equilibrium solution of the overall on-grid electricity price for coal-fired power units and wind power units within the main power generation unit at the current moment; Indicates in Current hot body Equilibrium solution of grid-connected electricity price for combined heat and power (CHP) units; express The main body of the power plant is a coal-fired power unit. The equilibrium solution of the electrical output; express Wind turbine unit inside the main body of the power station The equilibrium solution of the electrical output; Indicates in Current hot body Equilibrium solution of electrical output of a combined heat and power unit; And it satisfies the condition of equation (36): （36） In equation (36), This represents the grid operator cost under the equilibrium solution; This represents the grid operator's cost when the electrical output of both the electrical and thermal components is in equilibrium, but the grid-connected electricity price of the electrical and thermal components is not in equilibrium. This represents the interests of the electrical entity under the equilibrium solution; This represents the benefits of the electricity subject when the grid-connected electricity price and the thermal output of the thermal subject are both in equilibrium, but the electricity output of the electricity subject is not in equilibrium. This represents the interests of the thermal entity under the equilibrium solution; This indicates that the grid connection price of both the electrical and thermal components, as well as the electrical output of the electrical component, are equilibrium solutions. Current hot body The electrical output is also an equilibrium solution, but the electrical output of thermal body 1 is not an equilibrium solution, which is the benefit of the electrical body. This represents the interests of the thermal entity under the equilibrium solution; This indicates that the grid connection price of both the electrical and thermal components, as well as the electrical output of the electrical component, are equilibrium solutions. At any given moment, the hot body 1 and The electrical output is also an equilibrium solution, but the electrical output of the thermal body 2 is not an equilibrium solution, which is the benefit of the electrical body. This represents the interests of the thermal entity under the equilibrium solution; This indicates that the grid connection price of both the electrical and thermal components, as well as the electrical output of the electrical component, are equilibrium solutions. Current hot body The electrical output is also an equilibrium solution, but the thermal body... The interests of the electric subject when the electric output is not in equilibrium.

6. The method for optimal scheduling of a multi-agent electrothermal coupling system considering interest equilibrium game theory as described in claim 1, characterized in that: In step 3, the steps for solving the power output and electricity pricing strategies of each entity under the Stackelberg equilibrium state are as follows: Step (1): Input information such as load demand, unit parameters and related constraints, and electricity price variation range into the system; Step (2): Set upper-level electricity price to initialize the population x Initial iteration count k =0; Step (3): The grid operator transmits the initial electricity purchase price to the lower-level entity, so that the lower-level entity can optimize its output based on the information from the upper level; Step (4): Each entity at the lower level receives the electricity price information, sets the electricity price in the self-optimization target to a fixed value, takes the maximization of its own interests as the goal, uses the Cplex toolbox to plan and solve the output value of the unit within the entity, obtains the final output value, and transmits the result to the upper level. Step (5): The upper layer receives the specific output information of each main unit at the lower layer and calculates the grid operator's cost based on the original electricity price information. U 1; Step (6): Original population x A new population was obtained after crossover and mutation. y That is, the upper-level entity obtains new electricity price information; Step (7): The upper-level main body calculates the grid operator's cost based on the new electricity price information and the current output value of the generating units. U 2; Step (8): Comparison U 1 and U The size of 2, if U 1> U 2, then x = y ; like U 1= U 2, or U 1< U 2. Then keep the original result unchanged; Step (9): Determine whether the required number of iterations has been reached. If it has, output the result. If not, return to step (3) for the next iteration.

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