Park-factory-coordinative optimized scheduling method based on jacobi iteration method

Abstract

A park-factory-coordinative optimized scheduling method based on a Jacobi iteration method, which belongs to the technical field of energy scheduling optimization. A park-factory hierarchical game model is established, and by means of coordination and optimization between energy scheduling under a complex production constraint and production management and control that takes profit optimization as the goal, an optimal price regulating strategy and an optimal production scheduling strategy are obtained, such that a lower industrial park energy consumption and a higher factory production profit are achieved. A coordinative optimized scheduling model for a park control center and a factory management and control center is a multi-variable multi-constraint complex optimization issue; the solution of a high-order partial differential equation set involved in the model is calculated, and a cyclic iterative optimization algorithm is designed on the basis of a Jacobi iteration matrix, thereby greatly reducing the operation complexity; moreover, such a cyclic iterative algorithm requires a smaller storage capacity of a computer, and is thus suitable to be applied in practice by an engineer.

Description

Park-factory coordinated optimization scheduling method based on Jacobi iteration method Technical Field

[0001] The present invention belongs to the technical field of energy optimization scheduling, and relates to a park-factory coordinated optimization scheduling method based on the Jacobi iteration method. Background Art

[0002] Industrial production accounts for 42.6% of global electricity consumption. In recent years, the rapid development of smart grids and the rapid electrification of the market have put forward new requirements for the energy structure configuration, production scheduling, and energy efficiency reduction of industrial parks and their power users. In response to this, industrial microgrids integrating wind, solar, and energy storage have emerged. Their complex structures require energy consumption optimization to consider not only the effective control of industrial power loads but also the optimal scheduling of power generation and storage facilities within the industrial park. Industrial park energy consumption is closely related to production processes. Energy scheduling in industrial park microgrids must meet energy consumption demands under complex production constraints. Furthermore, the optimal scheduling of industrial park microgrid energy and the control of factory production loads are mutually constrained, resulting in a complex coupling relationship between the two. Furthermore, extensive research has demonstrated that market trading mechanisms can improve the interactivity of industrial park energy scheduling and reduce park operating costs. However, while the introduction of market trading mechanisms improves system interactivity, it also increases the coupling between industrial park energy scheduling and production control. To reduce industrial park energy costs and improve the economic benefits of factory production, it is necessary to design a coordinated operation strategy for energy scheduling and production control.

[0003] On the other hand, in the context of park energy scheduling and factory production control, game optimization scheduling requires a large number of machines to be scheduled and the variable dimension of the constraints is large. For game optimization problems with multi-dimensional complex constraints, designing an iterative optimization algorithm to obtain the optimal park pricing and factory production scheduling strategy is the key to achieving coordinated energy scheduling and production control. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to propose a park-factory coordinated optimization scheduling method based on the Jacobi iteration method, and use the Jacobi iteration method to design a cyclic iterative optimization algorithm for solving the hierarchical model. Through the coordinated optimization between energy scheduling under complex production constraints and production control with profit optimization as the goal, the optimal price control and production scheduling strategy is obtained.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] A park-factory coordinated optimization scheduling method based on Jacobi iteration method includes the following steps:

[0007] Step S1: Establish a coordinated optimization scheduling model for the park entity and individual factories. The park control center, with the goal of maximizing its own comprehensive benefits, is responsible for formulating scheduling strategies for energy storage devices and power generation equipment within the park. Based on the energy consumption data fed back by the factory control center, it also formulates electricity price strategies for external power purchases and sales to the factory. Factories within the park receive electricity prices published by the park control center, adjust the operating status of each machine within the factory, and formulate new energy consumption plans to feed back to the control center. Based on the above process, a coordinated optimization scheduling model between the "park-factory" is constructed. The model mainly includes a revenue maximization model for the park control center and a profit maximization model for the factory control center.

[0008] Step S2: Convert the constrained optimization problem to an unconstrained optimization problem. Based on the park revenue maximization model, the optimization variables include multiple unknown variables such as transaction price, external power purchase, and storage device charging and discharging. These are subject to constraints such as wind, solar, and storage characteristics and load power balance. Using the Lagrange multiplier method and KKT conditions, the constrained optimization problem of park revenue is converted to an unconstrained problem.

[0009] Step S3: Design a cyclic iterative algorithm based on the Jacobi iteration matrix. Use the Jacobi iteration method to solve the park revenue maximization model. Then, use the best response method to iteratively solve the hierarchical game model between the park control center and the factory control center to obtain the optimal park pricing mechanism, energy scheduling plan, and factory production scheduling strategy.

[0010] A further improvement of the technical solution of the present invention is that the specific steps of establishing the coordinated optimization scheduling model of the park entity and individual factories in step S1 are as follows:

[0011] Step S11: Acquire initial parameters of the park control center and the factory control center. The park control center initial parameters include wind power generation forecast value, photovoltaic power generation forecast value, power storage device capacity, wind turbine maintenance cost, photovoltaic panel maintenance cost, and power storage device maintenance cost; the factory control center initial parameters include upper and lower operating power limits of each machine in the factory;

[0012] Step S12: Based on the initial parameters of the park control center and the factory control center, a park revenue maximization model and a factory profit maximization model are constructed.

[0013] Step S13: By designing the pricing mechanism of the park, the interaction process between the park control center and the factory control center is established as a hierarchical game process, thereby constructing a hierarchical game problem between "park-factory".

[0014] A further improvement of the technical solution of the present invention is that the specific steps of converting the constrained problem into an unconstrained optimization problem in step S2 are as follows:

[0015] Step S21: Since the objective function and constraints of the park revenue maximization problem are both linear, it is considered that it can be solved equivalently using the KKT condition of the problem;

[0016] Step S22: Introduce Lagrange multipliers corresponding to the inequality constraints and equality constraints respectively, and write the Lagrange function of the park revenue maximization problem;

[0017] Step S23: Based on the constructed Lagrangian function, the equivalent KKT condition of the initial problem can be obtained.

[0018] A further improvement of the technical solution of the present invention is that the design of step S3 is based on the cyclic iteration algorithm of the Jacobi iteration matrix. The specific steps are as follows:

[0019] Step S31, using Jacobi iteration method to solve the linear equation system A consisting of KKT conditions s S p,s =b s , the iteration formula is:

[0020] in Any, G s is the Jacobi iteration matrix, and its expression is

[0021] Step S32: According to the post-inequality KKT conditions and the set parameters, the S optimal solutions are obtained. Screening is performed to finally obtain the park energy scheduling plan

[0022] Step S33: Use the best response method based on the Jacobi iteration method to iteratively solve the hierarchical game model of the park control center and the factory control center.

[0023] Due to the adoption of the above technical solution, the technical advancements achieved by the present invention are:

[0024] The coordinated optimization scheduling model of the park control center and the factory control center is a complex optimization problem with multiple variables and multiple constraints. For the numerical solution of the high-order partial differential equations involved in the model, a cyclic iterative optimization algorithm based on the Jacobi iteration matrix is ​​designed, which greatly reduces the complexity of the calculation. At the same time, such a cyclic iterative algorithm requires less computer storage and is suitable for practical application by engineers. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] FIG1 is a flow chart of a cyclic iteration algorithm based on the Jacobi iteration matrix. DETAILED DESCRIPTION

[0026] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments:

[0027] A park-factory coordinated optimization scheduling method based on Jacobi iteration method includes:

[0028] Step S1: Establish a coordinated optimization scheduling model for the park entity and individual factories. The park control center, with the goal of maximizing its own comprehensive benefits, is responsible for formulating scheduling strategies for energy storage devices and power generation equipment within the park. Based on the energy consumption data fed back by the factory control center, it also formulates electricity price strategies for external power purchases and sales to the factory. Factories within the park receive electricity prices published by the park control center, adjust the operating status of each machine within the factory, and formulate new energy consumption plans to feed back to the control center. Based on the above process, a coordinated optimization scheduling model between the "park-factory" is constructed. The model mainly includes a revenue maximization model for the park control center and a profit maximization model for the factory control center.

[0029] (1) Park control center profit maximization model: The park control center hopes to minimize the operation and maintenance costs and the cost of purchasing electricity from outside. Its goal can be expressed as maximizing the profit function, that is, maximizing the profit from selling electricity to factories minus the park operation and maintenance costs and the cost of purchasing electricity from outside. The profit function is as follows:

[0030] Among them, P fa (t) represents the power required by the factory during period t, P g (t) represents the amount of electricity purchased from the outside during period t, K p , K w and K e are the operation and maintenance cost coefficients of photovoltaic power generation, wind power generation and energy storage equipment, P p (t) and P w (t) are the predicted output values ​​of photovoltaic and wind power for the next day, P e (t) represents the charge / discharge power of the energy storage device during time period t.

[0031] The constraints of the park control center's revenue maximization model are as follows: P g (t)+P p (t)+P w (t)+P e (t) = P fa (t) (35) SOC(0)=SOC(T) (38) SOC min ≤SOC(t+1)≤SOC max (39)

[0032] Formula (34) indicates that the amount of electricity purchased from the park must meet the upper and lower limit constraints; Formula (35) represents the supply and demand balance constraint of the park microgrid, where P fa (t) represents the power required by the factory in time period t; Formula (36) represents the upper and lower limits of the charging and discharging power of the storage device, where P e (t)>0 means the storage device is charging, P e (t)<0 means discharge, P e (t) = 0 indicates that the device is not working; Formula (37) is the variable expression introduced to represent the state of charge of the energy storage device, where η(t) is the charging and discharging efficiency of the energy storage device, and E is the rated capacity of the energy storage system; in actual operation, in order to extend the service life of the energy storage device, it is necessary to constrain the state of charge, as shown in Formulas (38)-(39), where Formula (38) restricts the state of charge of the energy storage device in the initial period and the end period of the scheduling cycle to remain equal, and Formula (39) is the upper and lower limit constraints of the state of charge.

[0033] (2) Profit maximization model of factory control center: A profit model of factory control center based on discrete manufacturing assembly system model is established, where the whole group of assembly lines consists of M = {M1, M2…, M S-1 ,M S The nth workshop profit model in the factory control center aims to maximize product revenue minus the cost of purchasing electricity from the industrial park and the penalty cost for not meeting the expected processing target. The profit function is as follows:

[0034] Where: V represents the total revenue of processed products within the scheduling period; D represents the penalty cost for not reaching the expected production volume; P a and P b Respectively represent the rated power of the processing machine and the automatic guided vehicle; and They represent the operating status of the processing machine and the automatic guided vehicle in time period t respectively.

[0035] The constraints of the factory control center profit maximization model are as follows:

[0036] 1) Definition of the operating status and relationship between processing machines and automated guided vehicles:

[0037] The status of each automated guided vehicle should be consistent with the operating status of the processing machine behind it. The relationship expression is as follows:

[0038] 2) Constraints on the inventory capacity and storage capacity of each material buffer:

[0039] Formula (46) is the inventory capacity constraint of the material buffer on the first s-1 processing lines, and formulas (47)-(48) are the inventory capacity constraints of the material buffer on the s-th assembly line; Indicates the number of workpieces that can be processed by the processing machine within the time period t; the coefficient Indicates that the workpieces processed by the processing machines behind this material buffer must be provided by this material buffer;

[0040] 3) Daily processing income of the workshop:

[0041] Where δ is the profit of producing a single product; is the inventory of the jth material buffer on the i-th production line in time period t;

[0042] 4) Penalty costs for failing to meet expected production volume:

[0043] Where d represents the factory's expected daily production volume; β represents the penalty coefficient.

[0044] 5) Park-factory load coupling model: The coupling relationship in the park-factory collaborative optimization model is mainly manifested in that the load in the park microgrid comes from the power required for the operation of equipment in each workshop in the factory. The coupling relationship is expressed as:

[0045] Where, P fa (t) represents the total power required by the factory in time period t, which is equal to the sum of the power required for the operation of processing machines, automatic guided vehicles and other equipment in the factory during this period.

[0046] According to the park-factory coordinated optimization scheduling model constructed in step S1, the interaction process between the park control center and the factory control center is established as a hierarchical game process. The game model is as follows:

[0047] The meaning of each element in the model is as follows:

[0048] (1) The game involves two players: the park control center as the leader M and the factory control center as the follower N.

[0049] (2)S p ={Cp (t),P g (t),P e (t)} is the set of park strategies, including the price of electricity sold to factories and the amount of electricity purchased from outside; A set of factory strategies, including the operating status of processing machines and automated guided vehicles;

[0050] (3)S r is the revenue function of the park control center, is the profit function of the nth workshop in the factory.

[0051] Step S2: Convert the constrained optimization problem to an unconstrained optimization problem. Based on the park revenue maximization model, the optimization variables include multiple unknown variables such as transaction price, external power purchase, and storage device charging and discharging. These are subject to constraints such as wind, solar, and storage characteristics and load power balance. Using the Lagrange multiplier method and KKT conditions, the constrained optimization problem of park revenue is converted to an unconstrained problem. The conversion process is as follows:

[0052] First, since the objective function and constraints of the park revenue maximization problem are both linear, it can be solved equivalently using the KKT condition of the problem. The compact form of the park control center revenue maximization problem can be expressed as:

[0053] Where m represents m inequality constraints, and the corresponding Lagrange multiplier is λ = {λ i}; l means there are l equality constraints, and the corresponding Lagrange multiplier is μ={μ j}.

[0054] Then the Lagrangian function of the above problem can be written as:

[0055] Finally, the KKT conditions are used to convert the inequality constraints of the problem into equality constraints, and the extreme values ​​are obtained by the derivation method. The corresponding KKT conditions include: λ i ≥0,i=1,…,m (60)

[0056] Among them, formula (57) represents the necessary conditions for the Lagrangian function to obtain a feasible solution; formula (58) is the complementary relaxation condition, which gives the relationship between whether the Lagrangian multiplier is 0 and the tightness of the constraint corresponding to the multiplier under the optimal conditions; formulas (59) and (61) are the initial constraint conditions; formula (60) indicates that the Lagrangian multiplier of the inequality constraint must be greater than or equal to 0.

[0057] Step S3: Design a cyclic iterative algorithm based on the Jacobi iteration matrix. Use the Jacobi iteration method to solve the park revenue maximization model. Then, use the best response method to iteratively solve the hierarchical game model between the park control center and the factory control center to obtain the optimal park pricing mechanism, energy scheduling plan, and factory production scheduling strategy.

[0058] The designed cyclic iterative algorithm based on Jacobi iteration matrix includes the following processes:

[0059] 1) According to step S2, the Lagrange multiplier λ i Is it 0 classification discussion? Since it has m inequality constraints, a total of S=2 m Suppose the coefficient matrix of the first three rows of the equality conditions in the sth case (s∈[S]) is A s ,s∈[S], the constant matrix on the right is b s , then the coefficient matrix A can be s Decompose into A s =D s +L s +U s , where D s A s The diagonal matrix L is composed of the diagonal elements of s is a strictly lower triangular matrix, U s is a strictly lower triangular matrix. For the sth case, the first three rows of equations KKT conditions form a linear equation system A s S p,s =b s The Jacobi iteration method is used to find the optimal solution. The iteration formula is:

[0060] in Any, G s is the Jacobi iteration matrix, and its expression is

[0061] Then, according to the KKT conditions of the last two lines of inequalities and the set parameters, the S optimal solutions are obtained. Screening is performed to finally obtain the park energy scheduling plan

[0062] 2) Based on the above process, the best response method based on Jacobi iteration is used to iteratively solve the park-factory hierarchical game model. The flow chart of the cyclic iterative algorithm is shown in Figure 1. The specific steps of the algorithm are:

[0063] ① Parameter initialization, set the number of iterations k = 1, and randomly generate transaction electricity prices

[0064] ② Based on the constraints of the factory control center profit maximization model, CPLEX is used to solve the profit function of each workshop Get the operating status of each machine in the factory

[0065] ③Calculate the factory energy consumption value based on the park-factory load coupling model

[0066] ④Use the Jacobi iteration method given in step 1) to solve the energy scheduling plan of the park

[0067] ⑤ Determine whether the number of iterations k>k is satisfied at this time max or If yes, output the current park pricing mechanism, energy scheduling plan, and factory production scheduling strategy; otherwise, update the number of iterations k = k + 1 and return to step ②.

[0068] The present invention establishes a coordinated optimization scheduling model for the park entity and individual factories, and uses the Jacobi iteration method to design a cyclic iterative optimization algorithm for solving the hierarchical model. Through the coordinated optimization between energy scheduling under complex production constraints and production control with profit optimization as the goal, the optimal price control and production scheduling strategy is obtained to achieve lower energy consumption in the industrial park and higher production profits for the factory. Among them, the coordinated optimization scheduling model of the park control center and the factory control center is a complex optimization problem with multiple variables and multiple constraints. For the numerical solution of the high-order partial differential equations involved in the model, a cyclic iterative optimization algorithm is designed based on the Jacobi iteration matrix, which greatly reduces the complexity of the operation. At the same time, such a cyclic iterative algorithm requires a smaller computer storage capacity and is suitable for practical application by engineers.

Claims

1. A park-factory coordinated optimization scheduling method based on Jacobi iteration method, characterized by: The steps include: Step S1: Establish a coordinated optimization scheduling model for the park entity and individual factories, including a revenue maximization model for the park control center and a profit maximization model for the factory control center. The park control center is responsible for formulating scheduling strategies for energy storage devices and power generation equipment within the park, and formulating electricity price strategies for external power purchases and factory power sales based on energy consumption data fed back by the factory control center. Factories within the park receive electricity prices issued by the park control center, adjust the operating status of each machine within the factory, and formulate new energy consumption plans and feed them back to the park control center. Step S2: Convert the constrained optimization problem into an unconstrained optimization problem. Based on the park revenue maximization model, it can be seen that the optimization variables include multiple unknown variables such as transaction price, external power purchase, and storage device charging and discharging. Subject to conditions such as wind, solar, and storage characteristics and load power balance, the constrained optimization problem of park revenue is converted into an unconstrained problem using the Lagrange multiplier method and the KKT condition. Step S3: Design a cyclic iterative algorithm based on the Jacobi iterative matrix, use the Jacobi iterative method to solve the park profit maximization model, and then use the best response method to iteratively solve the hierarchical game model of the park control center and the factory control center to obtain the optimal park pricing mechanism, energy scheduling plan and factory production scheduling strategy.

2. The park-factory coordinated optimization scheduling method based on Jacobi iteration method according to claim 1 is characterized by: The specific steps of establishing the coordinated optimization scheduling model of the park entity and individual factories in step S1 are as follows: Step S11: Acquire initial parameters of the park control center and the factory control center. The park control center initial parameters include wind power generation forecast value, photovoltaic power generation forecast value, power storage device capacity, wind turbine maintenance cost, photovoltaic panel maintenance cost, and power storage device maintenance cost; the factory control center initial parameters include upper and lower operating power limits of each machine in the factory; Step S12: constructing a park revenue maximization model and a factory profit maximization model based on the initial parameters of the park control center and the factory control center; Step S13: By designing the pricing mechanism of the park, the interaction process between the park control center and the factory control center is established as a hierarchical game process, and a hierarchical game model between the park and the factory is constructed accordingly.

3. The park-factory coordinated optimization scheduling method based on Jacobi iteration method according to claim 1 is characterized by: The specific steps of converting the constrained problem into an unconstrained optimization problem in step S2 are as follows: Step S21: Since the objective function and constraints of the park revenue maximization problem are both linear, it is considered that it can be solved equivalently using the KKT condition of the problem; Step S22: Introduce Lagrange multipliers corresponding to the inequality constraints and equality constraints respectively, and write the Lagrange function of the park revenue maximization problem; Step S23: Based on the constructed Lagrangian function, the equivalent KKT condition of the initial problem can be obtained.

4. The park-factory coordinated optimization scheduling method based on Jacobi iteration method according to claim 2 is characterized by: The design of step S3 is based on the cyclic iteration algorithm of the Jacobi iteration matrix. The specific steps are as follows: Step S31, using Jacobi iteration method to solve the linear equation system A consisting of KKT conditions s S p,s =b s , the iteration formula is: in Any, G s is the Jacobi iteration matrix, and its expression is Step S32: According to the post-inequality KKT conditions and the set parameters, the S optimal solutions are obtained. Screening is performed to finally obtain the park energy scheduling plan Step S33: Use the best response method based on the Jacobi iteration method to iteratively solve the hierarchical game model of the park control center and the factory control center.

5. The park-factory coordinated optimization scheduling method based on Jacobi iteration method according to claim 2 is characterized by: Park control center profit maximization model: The profit function is as follows: Among them, P fa (t) represents the power required by the factory during period t, P g (t) represents the amount of electricity purchased from the outside during period t, K p , K w and K e are the operation and maintenance cost coefficients of photovoltaic power generation, wind power generation and energy storage equipment, P p (t) and P w (t) are the predicted output values of photovoltaic and wind power for the next day, P e (t) represents the charge / discharge power of the energy storage device during time period t; The constraints of the park control center's revenue maximization model are as follows: P g (t)+P p (t)+P w (t)+P e (t)=P fa (t) (4) SOC(0)=SOC(T) (7) SOC min ≤SOC(t+1)≤SOC max (8) Formula (3) indicates that the amount of electricity purchased from the park must meet the upper and lower limit constraints; Formula (4) indicates the supply and demand balance constraint of the park microgrid, where P fa (t) represents the power required by the factory in time period t; Formula (5) represents the upper and lower limits of the charging and discharging power of the storage device, where P e (t)>0 means the storage device is charging, P e (t)<0 means discharge, P e (t) = 0 means that the equipment is not working; Formula (6) is the variable expression introduced to represent the state of charge of the energy storage device, where η(t) is the charging and discharging efficiency of the energy storage device, and E is the rated capacity of the energy storage system; in actual operation, in order to extend the service life of the energy storage device, it is necessary to constrain the state of charge, as shown in Formulas (7)-(8), where Formula (7) restricts the state of charge of the energy storage device in the initial period and the end period of the scheduling cycle to remain equal, and Formula (8) is the upper and lower limit constraints of the state of charge.

6. The park-factory coordinated optimization scheduling method based on Jacobi iteration method according to claim 2, characterized in that: Profit maximization model of the factory control center: The profit function is as follows: Where: V represents the total revenue of processed products within the scheduling period; D represents the penalty cost for not reaching the expected production volume; P a and P b Respectively represent the rated power of the processing machine and the automatic guided vehicle; and They represent the operating status of the processing machine and the automatic guided vehicle in time period t respectively; The constraints of the factory control center profit maximization model are as follows: 1) Definition of the operating status and relationship between processing machines and automated guided vehicles: The status of each automated guided vehicle should be consistent with the operating status of the processing machine behind it. The relationship expression is as follows: 2) Constraints on the inventory capacity and storage capacity of each material buffer: Formula (15) is the inventory capacity constraint of the material buffer on the first s-1 processing lines, and formulas (16)-(17) are the inventory capacity constraints of the material buffer on the s-th assembly line; Indicates the number of workpieces that can be processed by the processing machine within the time period t; the coefficient Indicates that the workpieces processed by the processing machines behind this material buffer must be provided by this material buffer; 3) Daily processing income of the workshop: Where δ is the profit of producing a single product; is the inventory of the jth material buffer on the i-th production line in time period t; 4) Penalty costs for failing to meet expected production volume: Where d represents the factory's expected daily production volume; β represents the penalty coefficient. 5) Park-factory load coupling model: The coupling relationship in the park-factory collaborative optimization model is mainly manifested in that the load in the park microgrid comes from the power required for the operation of equipment in each workshop in the factory. The coupling relationship is expressed as: Where, P fa (t) represents the total power required by the factory in time period t, which is equal to the sum of the power required for the operation of processing machines, automatic guided vehicles and other equipment in the factory during this period.

7. The park-factory coordinated optimization scheduling method based on Jacobi iteration method according to claim 2 is characterized by: The interaction process between the park control center and the factory control center in step S13 is established as a hierarchical game process. The game model is as follows: The meaning of each element in the model is as follows: (1) The game involves two players: the park control center as the leader M and the factory control center as the follower N. (2)S p ={C p (t),P g (t),P e (t)} is the set of park strategies, including the price of electricity sold to factories and the amount of electricity purchased from outside; A set of factory strategies, including the operating status of processing machines and automated guided vehicles; (3)S r is the revenue function of the park control center, is the profit function of the nth workshop in the factory.

8. The park-factory coordinated optimization scheduling method based on Jacobi iteration method according to claim 3 is characterized by: The compact form of the park control center revenue maximization problem can be expressed as: Where m represents m inequality constraints, and the corresponding Lagrange multiplier is λ = {λ i }; l means there are l equality constraints, and the corresponding Lagrange multiplier is μ={μ j }; The Lagrangian function of the above problem is: Using the KKT conditions, the inequality constraints of the problem are converted into equality constraints, and the extreme values are found using the derivation method. The corresponding KKT conditions include: λ i ≥0,i=1,…,m (29) Among them, formula (26) represents the necessary conditions for the Lagrangian function to obtain a feasible solution; formula (27) is the complementary relaxation condition, which gives the relationship between whether the Lagrangian multiplier is 0 and the tightness of the constraint corresponding to the multiplier under the optimal conditions; formulas (28) and (30) are the initial constraint conditions; formula (29) indicates that the Lagrangian multiplier of the inequality constraint must be greater than or equal to 0.

9. The park-factory coordinated optimization scheduling method based on Jacobi iteration method according to claim 4, characterized in that: The best response method based on Jacobi iteration is used to iteratively solve the park-factory hierarchical game model. The specific process of the cyclic iterative algorithm is as follows: Process 1: According to the KKT condition of the park control center revenue maximization problem, the Lagrange multiplier λ is i Is it 0 classification discussion? Since it has m inequality constraints, a total of S=2 m Suppose in the sth case, s∈[S], the coefficient matrix of the first three rows of the equality conditions is A s ,s∈[S], the constant matrix on the right is b s , then the coefficient matrix A can be s Decompose into A s =D s +L s +U s , where D s A s The diagonal matrix L is composed of the diagonal elements of s is a strictly lower triangular matrix, U s For a strictly lower triangular matrix, the linear equation system A consisting of the KKT conditions of the first three rows of equations in the sth case is s S p,s =b s The Jacobi iteration method is used to find the optimal solution. The iteration formula is: in Any, G s is the Jacobi iteration matrix, and its expression is According to the KKT conditions of the last two lines of inequalities and the set parameters, the S optimal solutions are obtained Screening is performed to finally obtain the park energy scheduling plan Process 2: Based on process 1, the best response method based on Jacobi iteration method is used to iteratively solve the park-factory hierarchical game model. The specific steps of the algorithm are as follows: ① Parameter initialization, set the number of iterations k = 1, and randomly generate transaction electricity prices ② Based on the constraints of the factory control center profit maximization model, CPLEX is used to solve the profit function of each workshop Get the operating status of each machine in the factory ③Calculate the factory energy consumption value based on the park-factory load coupling model ④Use the Jacobi iteration method given in step 1 to solve the energy scheduling plan of the park ⑤ Determine whether the number of iterations k>k is satisfied at this time max or If yes, output the current park pricing mechanism, energy scheduling plan, and factory production scheduling strategy; otherwise, update the number of iterations k = k + 1 and return to step ②.

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