Active power distribution network optimization method based on average field and reverse Steinberg game

Abstract

The invention relates to the field of power system optimization scheduling, and particularly discloses an active power distribution network optimization method based on a mean field and a reverse Stackelberg game, which comprises the following steps: S1, modeling a decision of a producer and a consumer into a mean field game, and after the producer and the consumer receive the dynamic electricity price of an energy aggregator, adjusting a load by maximizing personal utility, forming a group response and feeding back the group response to a middle layer; s2, the energy aggregator designs the dynamic electricity price by means of the reverse Stackelberg game according to the expected load of the upper layer and issues the dynamic electricity price to the lower layer; s3, the power distribution network operator implements global scheduling through the convex relaxation alternating current optimal power flow model, determines an expected load and feeds the expected load back to a middle layer; and S4, solving by adopting a hierarchical iterative algorithm, firstly solving production disagger group balance, then solving a middle-lower layer optimal strategy, and finally realizing three-layer global convergence through MANN iteration. According to the method, the defect of compatibility of dimension disasters and incentives of a traditional model is overcome, the energy utilization rate is increased, the operation cost is reduced, and an efficient scheme is provided for high-permeability power-traffic coupling network scheduling.

Description

Technical Field

[0001] This invention relates to the field of power system optimization and scheduling technology, specifically to an active distribution network optimization method based on mean field and inverse Steinberg game. Background Technology

[0002] With the large-scale integration of flexible loads such as distributed energy, renewable energy, and electric vehicles, traditional passive distribution networks characterized by centralized control are no longer suitable for operating environments with high volatility and uncertainty, giving rise to active distribution networks. Active distribution networks require safe, economical, and efficient operation through the joint participation of multiple stakeholders. Their core lies in designing a multi-layered collaborative optimization mechanism that can coordinate decision-making objectives at different levels, balancing local autonomy and global optimization. This mechanism has key application value in areas such as power system dispatching with high proportions of renewable energy integration, flexible resource utilization on the user side, and safe and economical operation of distribution networks. It aims to overcome the limitations of traditional distribution network control models in multi-stakeholder collaboration and large-scale scenario adaptability, meeting the practical needs of active distribution networks for dynamic coordination, efficient solution, and incentive compatibility. Because active distribution networks involve the interaction of interests among multiple stakeholders, including distribution network operators, energy aggregators, and prosumers, and the behavior of large-scale prosumers exhibits high heterogeneity and uncertainty, researchers both domestically and internationally have long conducted extensive research on multi-stakeholder collaborative optimization methods.

[0003] Existing technologies related to active distribution network optimization mainly fall into three categories: The first is centralized optimization methods, which model the decisions of the distribution network, aggregators, and prosumers as a globally optimal power flow problem, solved using convex programming or second-order cone programming. While these methods can obtain theoretically optimal solutions, their computational complexity increases dramatically with the number of participants, requiring extremely high levels of communication and data sharing, making them difficult to apply in real-time in scenarios with tens of thousands of prosumers. The second category is distributed and hierarchical optimization methods, which use algorithms such as ADMM or dual decomposition to solve local subproblems in parallel, thereby reducing the computational burden of centralized methods. However, these methods typically assume complete information sharing among participants and a relatively simple objective function, making it difficult to handle non-convex, nonlinear, and time-varying coupling constraints in multi-level game structures. The third category is game theory models, such as Steinberg games used to model the master-slave relationship between operators and aggregators, and Nash games used to describe competitive or collaborative behavior among prosumers. While game theory methods can reflect economic incentives and strategic interactions, they suffer from the "curse of dimensionality" in large-scale scenarios, the cost of solving Nash equilibria is high, and incentive compatibility cannot be guaranteed. To alleviate this problem, mean-field game theory has been introduced to approximate large-scale group games. By characterizing the overall behavior distribution through mean-field terms, the computational complexity has been greatly reduced. However, existing mean-field models mostly remain at the producer-consumer level and lack dynamic coupling with upper-level electricity prices and power flow scheduling, making it impossible to achieve system-level coordination. Moreover, most pricing mechanisms adopt fixed or linear electricity prices, which lack flexibility and are difficult to reflect real-time operating status and load change characteristics.

[0004] In recent years, some optimization schemes have attempted to strengthen multi-level information interaction or optimize the game model structure to improve system coordination and solution efficiency. However, these schemes still face core bottlenecks: On the one hand, most schemes still focus on two-level games (aggregator-prosumer or operator-aggregator), without establishing a unified three-level collaborative optimization framework, resulting in a disconnect between upper-level scheduling objectives and lower-level response behaviors, and weak overall system coordination. On the other hand, most models assume homogeneous prosumer behavior, ignore load elasticity differences, and the price signal has an uneven incentive effect on different users, making it difficult to achieve a fair market response. Furthermore, traditional game or centralized models require frequent communication and synchronous iteration under large-scale participants, consuming large amounts of computational resources and making them difficult to apply in real-time scenarios. In addition, fixed electricity prices or time-of-use prices cannot reflect the dynamic operating status of the system, and some designs do not consider the consistency between the optimal behavior of participants and the optimal goal of the system, which can easily lead to social welfare losses. At the same time, most existing solution algorithms lack rigorous analysis of convergence conditions and step size settings, which may lead to oscillations or local convergence in actual operation, affecting system stability.

[0005] Therefore, how to propose an active distribution network optimization method that can cover the three main entities of distribution network operators, energy aggregators and prosumers, adapt to large-scale prosumer scenarios, and balance the flexibility of dynamic pricing with the stability of algorithm convergence, and solve the problems of insufficient three-layer coupling, lack of handling of prosumer heterogeneity, high solution complexity and poor incentive compatibility in existing technologies through innovative multi-layer game structure and efficient solution mechanism, has become a key technical problem that urgently needs to be solved in the field of active distribution network operation optimization. Summary of the Invention

[0006] To address the aforementioned problems in existing technologies, this invention provides an active distribution network optimization method based on mean field and inverse Steinberg game, which effectively solves the problems of weak system coordination and complex solutions, and effectively improves the economic efficiency of distribution networks and the utilization rate of distributed energy.

[0007] To achieve the above objectives, this invention proposes an active distribution network optimization method based on mean field and inverse Steinberg game, comprising: S1. Model the individual decision-making behavior of prosumers as an average field game. After receiving the dynamic electricity price signal released by the energy aggregator, prosumers autonomously adjust their load trajectory based on the average field game model. They solve the individual optimization problem with the goal of maximizing personal utility, form the load response of the prosumer group, and feed it back to the middle-level energy aggregator. S2. Construct a pricing model for mid-level energy aggregators. Based on the expected load of the distribution network fed back by the upper-level distribution network operator, the energy aggregator designs a dynamic electricity price function using a reverse Steinberg game mechanism and broadcasts the dynamic electricity price function to the lower-level producers and consumers. S3. Construct an upper-level distribution network operator scheduling model. The distribution network operator optimizes the model based on the convex relaxation AC optimal power flow model and performs global scheduling under the premise of satisfying the power grid operation constraints. The expected load of the distribution network is determined and fed back to the middle-level energy aggregator. S4. A hierarchical iterative algorithm is used to solve the three-level collaborative optimization problem. First, the equilibrium of the lower-level producer-consumer group is solved by mean-field game. Then, the optimal strategy of the middle and lower levels is solved by inverse Steinberg game. Finally, the three-level global convergence is achieved by the MANN iterative algorithm.

[0008] Preferably, in S1, the unit price of the dynamic electricity price signal released by the energy aggregator Depending on the overall system requirements, the system in time t Total flexible energy demand is expressed as: ; In the formula, Total system requirements; The prosumer maximizes personal utility based on a determined personal load trajectory, and the prosumer... tThe feasible region of the load trajectory satisfies the upper and lower limits of its own load within the continuous time range, and its constraint formula is: ; In the formula, for The corresponding permissible range, For the continuous time range of demand response coordination, , For producers and consumers a The lower and upper limits of energy demand at any given time period. A gathering of producers and consumers.

[0009] Preferably, in S1, the individual utility of the prosumer is defined as the revenue obtained from electricity trading minus the electricity cost paid to the energy aggregator, and its expression is: ; In the formula, Excluding producers and consumers a All prosumers in time t The load, The quadratic coefficient of the utility curve represents the sensitivity to the diminishing marginal utility of energy trading. The first-order coefficient of the utility curve represents the initial marginal utility or benefit per unit of energy. The unit price of electricity; The individual optimization problem of the prosumer is expressed as follows: ; In the formula, for The corresponding permissible range, For the continuous time range of demand response coordination.

[0010] Preferably, in S2, the dynamic electricity price function is a parameterized linear function, the parameters including positive parameters and time-varying parameters of the electricity price function, and both the positive parameters and time-varying parameters of the electricity price function satisfy preset upper and lower limit constraints. The dynamic electricity price function is: ; In the formula, , For the positive and time-varying parameters of the electricity price function, , The conditions are: ; In the formula, for and feasible domain, , , , These are the upper and lower limits of the parameters of the electricity price function; The goal of the energy aggregator in designing the dynamic electricity price function is to maximize its own utility, which includes electricity price revenue and end-user penalty. Its utility expression is as follows: ; In the formula, The terminal penalty coefficient is independent of time. For time t The expected load of the distribution network at that time.

[0011] Preferably, in S3, the optimization objective of the distribution network operator is to minimize the sum of generation cost and load deviation penalty, and its calculation formula is as follows: ; In the formula, , , For nodes j Cost coefficient of generator, For nodes j The generator at time t The generated active power, For distribution network nodes; The convex relaxation AC optimal power flow model is a second-order cone relaxation branch flow model. The convexification process of the convex relaxation AC optimal power flow model includes phase angle relaxation and branch power flow relaxation: phase angle relaxation removes the phase angle of current and voltage, and represents the current square term with a linear term; branch power flow relaxation decomposes complex power into active power and reactive power, transforming nonlinear constraints into linear constraints or second-order cone constraints; the relaxed branch power flow constraints satisfy the rotating second-order cone programming formula: ; In the formula, , For time t Shizhi Road l Active and reactive power; For time t Shizhi Road l The square of the current amplitude, For time t Time node i The square of the voltage amplitude at that point; The power grid operation constraints include node voltage amplitude constraints, branch current amplitude constraints, generator complex power amplitude constraints, and node power balance constraints.

[0012] Preferably, in S4, when solving the equilibrium of the lower-level producer-consumer group using the mean-field game, the specific steps include: S41. Introduce the average field term that satisfies the formula, whereby the average field term is the average value of all producer and consumer loads, and its calculation formula is: ; S42. Let the mean-field equilibrium solution satisfy the condition of maximizing the utility of each producer-consumer when given a mean-field term, and simultaneously, the mean-field term is consistent with the average load of the producer-consumer group. The condition is as follows: ; ; S43. Transform the mean-field equilibrium solution into a convex optimization problem, the calculation formula for which is: .

[0013] Preferably, the mean-field game solution employs a binary search algorithm. This algorithm iteratively adjusts the upper and lower bounds of the mean-field term until the deviation between the calculated average load of the producer-consumer group and the mean-field term is less than a preset tolerance. The mean-field term is then output as the equilibrium solution. The formula for calculating the upper and lower bounds of the mean-field term through iterative adjustment in the binary search algorithm is as follows: ; The clip function satisfies the following: .

[0014] Preferably, in S4, when solving the lower-level reverse Steinberg game in the reverse Steinberg game, the objective of the dynamic electricity pricing function designed by the middle-level energy aggregator is replaced, and a grid search algorithm is used to traverse the feasible region of the dynamic electricity pricing function parameters, selecting the parameter combination that maximizes the objective function as the optimal solution. The objective replacement formula for the dynamic electricity pricing function designed by the middle-level energy aggregator is as follows: .

[0015] Preferably, in S4, the MANN iterative algorithm achieves iterative updates by setting a relaxation factor and weighting the upper-level expected load of the previous round and the current round. The relaxation factor satisfies the following condition: ; The iterative update formula for the expected load is: ; In the formula, The expected load output for the upper-level optimization problem.

[0016] Preferably, the three-level collaborative optimization of the active distribution network further includes social welfare calculation, whereby social welfare is defined as the difference between the total revenue obtained by all producers and consumers from electricity transactions and the total generation cost of the distribution network operator. The total revenue is the sum of the individual utility of all producers and consumers and their respective electricity costs. The social welfare calculation formula is: .

[0017] Therefore, this invention proposes an active distribution network optimization method based on mean field and reverse Steinberg game, which has the following advantages: (1) Solve the problem of dimensionality in large-scale producer-consumer game. Characterize the group response of producer-consumer through mean field game, transform the complex interaction of multiple subjects into a game between individuals and the mean field, avoid the dimensionality disaster of centralized modeling, improve the feasibility of solution and computational efficiency, and adapt to massive producer-consumer scenarios.

[0018] (2) To achieve a balance between electricity price incentives and dynamic supply and demand, the mid-level reverse Steinberg game supports aggregators in designing time-varying electricity price functions instead of fixed electricity prices, taking into account incentive compatibility and scheduling flexibility, guiding producers and consumers to respond in line with system objectives, and achieving an adaptive balance in the energy market.

[0019] (3) Ensure system safety and global optimal operation. The upper-level convex relaxation power flow model ensures compliance with grid constraints. Combined with MANN iteration, it achieves three-layer collaborative convergence, which can smooth load fluctuations, reduce operating costs, and improve the utilization rate of distributed energy, providing a reliable solution for the scheduling of high-penetration power-transportation coupled networks.

[0020] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the overall operation framework of the active distribution network optimization method based on mean field and reverse Steinberg game of the present invention. Figure 2 This is a schematic diagram of the reverse Steinberg game framework of the active distribution network optimization method based on mean field and reverse Steinberg game of the present invention. Detailed Implementation

[0022] To make the technical solutions, advantages, and objectives of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below. The described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the protection scope of this application.

[0023] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0024] like Figures 1-2 As shown, the active distribution network optimization method based on mean field and inverse Steinberg game provided by this invention includes: S1. Model the individual decision-making behavior of prosumers as an average field game. After receiving the dynamic electricity price signal released by the energy aggregator, prosumers autonomously adjust their load trajectory based on the average field game model. They solve the individual optimization problem with the goal of maximizing personal utility, form the load response of the prosumer group, and feed it back to the middle-level energy aggregator. Unit price of electricity in dynamic electricity price signals released by energy aggregators Depending on the overall system requirements, the system in time t Total flexible energy demand is expressed as: ; In the formula, Total system requirements; Prosumers maximize their personal utility by determining their individual load trajectory, and prosumers maximize their personal utility over time. t The feasible region of the load trajectory satisfies the upper and lower limits of its own load within the continuous time range, and its constraint formula is: ; In the formula, for The corresponding permissible range, For the continuous time range of demand response coordination, , For producers and consumers a The lower and upper limits of energy demand at any given time period. A gathering of producers and consumers.

[0025] The individual utility of a prosumer is defined as the revenue gained from electricity trading minus the electricity costs paid to energy aggregators, expressed as follows: ; In the formula, Excluding producers and consumers a All prosumers in time t The load, The quadratic coefficient of the utility curve represents the sensitivity to the diminishing marginal utility of energy trading. The first-order coefficient of the utility curve represents the initial marginal utility or benefit per unit of energy. The unit price of electricity; The individual optimization problem of prosumers is expressed as: ; In the formula, for The corresponding permissible range, For the continuous time range of demand response coordination.

[0026] S2. Construct a pricing model for mid-level energy aggregators. Based on the expected load of the distribution network fed back by the upper-level distribution network operator, the energy aggregator designs a dynamic electricity price function using a reverse Steinberg game mechanism and broadcasts the dynamic electricity price function to the lower-level producers and consumers. The dynamic electricity price function is a parameterized linear function, with parameters including positive parameters and time-varying parameters. Both the positive and time-varying parameters satisfy preset upper and lower bound constraints. The dynamic electricity price function is as follows: ; In the formula, , For the positive and time-varying parameters of the electricity price function, , The conditions are: ; In the formula, for and feasible domain, , , , These are the upper and lower limits of the parameters of the electricity price function; The goal of energy aggregators in designing dynamic electricity pricing functions is to maximize their own utility, which includes electricity price revenue and end-user penalties. The expression for their own utility is: ; In the formula, The terminal penalty coefficient is independent of time. For time t The expected load of the distribution network at that time.

[0027] S3. Construct an upper-level distribution network operator scheduling model. The distribution network operator optimizes the model based on the convex relaxation AC optimal power flow model and performs global scheduling under the premise of satisfying the power grid operation constraints. The expected load of the distribution network is determined and fed back to the middle-level energy aggregator. The optimization objective of a distribution network operator is to minimize the sum of generation costs and load deviation penalties, calculated using the following formula: ; In the formula, , , For nodes j Cost coefficient of generator, For nodes j The generator at time t The generated active power, For distribution network nodes; The convex relaxation AC optimal power flow model is a second-order cone relaxation branch flow model. The convexification process of the convex relaxation AC optimal power flow model includes phase angle relaxation and branch flow relaxation: phase angle relaxation removes the phase angle of current and voltage, and represents the current square term with a linear term; branch flow relaxation decomposes complex power into active power and reactive power, transforming nonlinear constraints into linear constraints or second-order cone constraints; the relaxed branch flow constraints satisfy the rotating second-order cone programming formula: ; In the formula, , For time t Shizhi Road l Active and reactive power; For time t Shizhi Road l The square of the current amplitude, For time t Time node i The square of the voltage amplitude at that point; Power grid operation constraints include node voltage amplitude constraints, branch current amplitude constraints, generator complex power amplitude constraints, and node power balance constraints.

[0028] S4. A hierarchical iterative algorithm is used to solve the three-level collaborative optimization problem. First, the equilibrium of the lower-level producer-consumer group is solved by mean-field game. Then, the optimal strategy of the middle and lower levels is solved by inverse Steinberg game. Finally, the three-level global convergence is achieved by the MANN iterative algorithm.

[0029] When solving for the equilibrium of the lower-level producer-consumer group in mean-field game theory, the specific steps include: S41. Introduce the average field term that satisfies the formula, whereby the average field term is the average value of all producer and consumer loads, and its calculation formula is: ; S42. Let the mean-field equilibrium solution satisfy the condition of maximizing the utility of each producer-consumer when given a mean-field term, and simultaneously, the mean-field term is consistent with the average load of the producer-consumer group. The condition is as follows: ; ; Therefore, the dynamic electricity price function set by energy aggregators can be expressed as: ; Producers and consumers a The utility can be replaced by: ; S43. Transform the mean-field equilibrium solution into a convex optimization problem, the calculation formula for which is: .

[0030] The equilibrium solution for mean-field games is found using a binary search algorithm. This algorithm iteratively adjusts the upper and lower bounds of the mean-field term, and the calculation formula is as follows: ; The clip function satisfies the following: .

[0031] The process continues until the deviation between the calculated average load of the producer-consumer group and the average field term is less than the preset tolerance, at which point the average field term is output as the equilibrium solution.

[0032] When solving the lower-level inverse Steinberg game in the inverse Steinberg game, the objective of the middle-level energy aggregator in designing the dynamic electricity price function is replaced with: ; The grid search algorithm is used to traverse the feasible region of the dynamic electricity price function parameters, and the parameter combination that maximizes the objective function is selected as the optimal solution.

[0033] The MANN iterative algorithm achieves iterative updates by setting a relaxation factor and weighting the expected upper-layer loads from the previous and current rounds. The relaxation factor satisfies the following condition: The iterative update formula for the expected load is: ; In the formula, The expected load output for the upper-level optimization problem.

[0034] The three-level collaborative optimization of the active distribution network also includes social welfare calculation, whereby social welfare is defined as the difference between the total revenue obtained by all producers and consumers from electricity transactions and the total generation cost of the distribution network operator. Total revenue is the sum of the individual utility of all producers and consumers and their respective electricity costs. The social welfare calculation formula is as follows: .

[0035] Example This embodiment uses the IEEE-30 node distribution network system as the simulation object and combines it with a large-scale producer-consumer access scenario to verify the active distribution network optimization method based on mean field and inverse Steinberg game. It also clarifies the parameter settings and algorithm execution flow at each level. I. Test Platform and Main Parameter Settings: Distribution network side parameters: The IEEE-30 node system includes 6 generators and 21 distribution branches. The generation cost coefficient of the distribution network operator meets the following requirements. , , The node voltage amplitude is constrained to [0.95, 1.05] pu, and the branch current amplitude is capped at [0.95, 1.05]. kA, expected load The upper and lower limits are MW MW, Terminal Penalty Coefficient .

[0036] Energy aggregator parameters: Feasible region of pricing function parameters is ,in , , , N represents the total number of producers and consumers.

[0037] Prosumer-side parameters: A total of N=5000 heterogeneous prosumers are set, and the feasible region of load for each prosumer satisfies MW MW, utility curve coefficient , Demand response coordination time range There are 24 time periods (t=1,2,...,24).

[0038] Second and third level collaborative optimization solution process: Solution to the mean-field game of lower-level producers and consumers: (1) Introducing the mean field term Transform the electricity pricing strategy of energy aggregators into ; (2) Solve the mean-field equilibrium fixed-point equation using the binary search algorithm. Set tolerance By iteratively adjusting the upper and lower bounds of the mean field term, the equilibrium load of the producer-consumer group is finally obtained. Its satisfaction .

[0039] Solving the lower-middle level inverse Steinberg game: (1) Replace the objective function of the energy aggregator with ; (2) Using the grid search algorithm, set the discretized integer K=50, and traverse... The sampling points are used to call the mean-field game solving module to obtain the mean-field terms of the corresponding mean-field equilibrium. Select the one that maximizes These are the optimal pricing parameters.

[0040] Three-layer globally convergent solution: The MANN iterative algorithm is used to achieve collaboration between distribution network operators and lower-level layers, and a convergence tolerance is set. Initial expected load MW, relaxation factor satisfy ,pass Iteratively update the expected load until Output the optimal decision variables for the three-level subjects.

[0041] III. Simulation Results Verification: The method of this invention is compared with traditional fixed electricity price, affine electricity price, and time-of-use electricity price mechanisms. The results are as follows: Computational efficiency: This invention reduces the producer-consumer dimension from N=5000 to one average field term through mean field game theory, shortening the solution time compared to traditional Nash game theory. Furthermore, the MANN iterative algorithm can achieve three-level convergence within 15 rounds, without oscillation or local convergence. Economic benefits: This invention can reduce the operating cost of the power distribution network, smooth out the peak-valley difference in load, improve the utilization rate of distributed energy, and is more efficient than the traditional electricity pricing mechanism; Social welfare: The social welfare achieved by this invention is improved compared to the time-of-use electricity pricing mechanism, and the incentive compatibility of producer-consumer responses is satisfied. As N increases, the equilibrium deviation approaches 0.

[0042] IV. Implementation Conclusions: This embodiment verifies that in a large-scale scenario with an IEEE-30 node system and 5,000 prosumers, the method of the present invention can balance solution efficiency, system economy and stability, and realize dynamic coordination of three-level entities, providing a feasible solution for scheduling of high-penetration power-transportation coupled networks.

[0043] Therefore, this invention provides an active distribution network optimization method based on mean field and inverse Steinberg game theory. It constructs a three-level collaborative framework of distribution network operators, energy aggregators, and prosumers. The lower layer uses mean field game theory to characterize the response of a large-scale prosumer group, solving the dimensionality curse problem. The middle layer uses inverse Steinberg game theory to design a dynamic electricity price function, realizing adaptive coupling between electricity price and load. The upper layer completes global scheduling through a convex relaxation AC optimal power flow model, and then achieves three-level collaborative convergence through the MANN iterative algorithm, effectively improving the system's economy and stability, and providing an efficient scheduling solution for high-penetration renewable energy access scenarios.

[0044] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. An active distribution network optimization method based on mean field and inverse Steinberg game constructs a three-level collaborative optimization framework involving distribution network operators, energy aggregators, and prosumers. Its characteristics are as follows: include: S1. Model the individual decision-making behavior of prosumers as an average field game. After receiving the dynamic electricity price signal released by the energy aggregator, prosumers autonomously adjust their load trajectory based on the average field game model. They solve the individual optimization problem with the goal of maximizing personal utility, form the load response of the prosumer group, and feed it back to the middle-level energy aggregator. S2. Construct a pricing model for mid-level energy aggregators. Based on the expected load of the distribution network fed back by the upper-level distribution network operator, the energy aggregator designs a dynamic electricity price function using a reverse Steinberg game mechanism and broadcasts the dynamic electricity price function to the lower-level producers and consumers. S3. Construct an upper-level distribution network operator scheduling model. The distribution network operator optimizes the model based on the convex relaxation AC optimal power flow model and performs global scheduling under the premise of satisfying the power grid operation constraints. The expected load of the distribution network is determined and fed back to the middle-level energy aggregator. S4. A hierarchical iterative algorithm is used to solve the three-level collaborative optimization problem. First, the equilibrium of the lower-level producer-consumer group is solved by mean-field game. Then, the optimal strategy of the middle and lower levels is solved by inverse Steinberg game. Finally, the three-level global convergence is achieved by the MANN iterative algorithm.

2. The active distribution network optimization method based on mean field and inverse Steinberg game as described in claim 1, characterized in that, In S1, the unit price of the dynamic electricity price signal released by the energy aggregator Depending on the overall system requirements, the system in time t Total flexible energy demand is expressed as: ； In the formula, Total system requirements; The prosumer maximizes personal utility based on a determined personal load trajectory, and the prosumer... t The feasible region of the load trajectory satisfies the upper and lower limits of its own load within the continuous time range, and its constraint formula is: ； In the formula, for The corresponding permissible range, For the continuous time range of demand response coordination, , For producers and consumers a The lower and upper limits of energy demand at any given time period. A gathering of producers and consumers.

3. The active distribution network optimization method based on mean field and inverse Steinberg game as described in claim 1, characterized in that, In S1, the individual utility of the prosumer is defined as the revenue obtained from electricity trading minus the electricity cost paid to the energy aggregator, and its expression is: ； In the formula, Excluding producers and consumers a All prosumers in time t The load, The quadratic coefficient of the utility curve represents the sensitivity to the diminishing marginal utility of energy trading. The first-order coefficient of the utility curve represents the initial marginal utility or benefit per unit of energy. The unit price of electricity; The individual optimization problem of the prosumer is expressed as follows: ； In the formula, for The corresponding permissible range, For the continuous time range of demand response coordination.

4. The active distribution network optimization method based on mean field and inverse Steinberg game as described in claim 1, characterized in that, In S2, the dynamic electricity price function is a parameterized linear function, the parameters of which include positive parameters and time-varying parameters of the electricity price function, and both the positive parameters and time-varying parameters of the electricity price function satisfy preset upper and lower limit constraints. The dynamic electricity price function is: ； In the formula, , For the positive and time-varying parameters of the electricity price function, , The conditions are: ； In the formula, for and feasible domain, , , , These are the upper and lower limits of the parameters of the electricity price function; The goal of the energy aggregator in designing the dynamic electricity price function is to maximize its own utility, which includes electricity price revenue and end-user penalty. Its utility expression is as follows: ； In the formula, The terminal penalty coefficient is independent of time. For time t The expected load of the distribution network at that time.

5. The active distribution network optimization method based on mean field and inverse Steinberg game as described in claim 1, characterized in that, In S3, the optimization objective of the distribution network operator is to minimize the sum of generation cost and load deviation penalty, and its calculation formula is as follows: ； In the formula, , , For nodes j Cost coefficient of generator, For nodes j The generator at time t The generated active power, For distribution network nodes; The convex relaxation AC optimal power flow model is a second-order cone relaxation branch flow model. The convexification process of the convex relaxation AC optimal power flow model includes phase angle relaxation and branch power flow relaxation: phase angle relaxation removes the phase angle of current and voltage, and represents the current square term with a linear term. Branch power flow relaxation transforms nonlinear constraints into linear or second-order cone constraints by splitting complex power into active and reactive power; the relaxed branch power flow constraints satisfy the rotating second-order cone programming formula: ； In the formula, , For time t Shizhi Road l Active and reactive power; For time t Shizhi Road l The square of the current amplitude, For time t Time node i The square of the voltage amplitude at that point; The power grid operation constraints include node voltage amplitude constraints, branch current amplitude constraints, generator complex power amplitude constraints, and node power balance constraints.

6. The active distribution network optimization method based on mean field and inverse Steinberg game as described in claim 1, characterized in that, In S4, the specific steps for solving the equilibrium of the lower-level producer-consumer group using the mean-field game include: S41. Introduce the average field term that satisfies the formula, whereby the average field term is the average value of all producer and consumer loads, and its calculation formula is: ； S42. Let the mean-field equilibrium solution satisfy the condition of maximizing the utility of each producer-consumer when given a mean-field term, and simultaneously, the mean-field term is consistent with the average load of the producer-consumer group. The condition is as follows: ； ； S43. Transform the mean-field equilibrium solution into a convex optimization problem, the calculation formula for which is: 。 7. The active distribution network optimization method based on mean field and inverse Steinberg game as described in claim 6, characterized in that, The equilibrium solution for the mean-field game is obtained using a binary search algorithm. This algorithm iteratively adjusts the upper and lower bounds of the mean-field term until the deviation between the calculated average load of the producer-consumer group and the mean-field term is less than a preset tolerance. The mean-field term is then output as the equilibrium solution. The formula for calculating the upper and lower bounds of the mean-field term through iterative adjustment in the binary search algorithm is as follows: ； The clip function satisfies the following: 。 8. The active distribution network optimization method based on mean field and inverse Steinberg game as described in claim 1, characterized in that, In S4, when solving the lower-level reverse Steinberg game in the reverse Steinberg game, the objective of the dynamic electricity pricing function designed by the middle-level energy aggregator is replaced, and a grid search algorithm is used to traverse the feasible region of the dynamic electricity pricing function parameters. The parameter combination that maximizes the objective function is selected as the optimal solution. The objective replacement formula for the dynamic electricity pricing function designed by the middle-level energy aggregator is as follows: 。 9. The active distribution network optimization method based on mean field and inverse Steinberg game as described in claim 1, characterized in that, In S4, the MANN iterative algorithm achieves iterative updates by setting a relaxation factor and weighting the upper-level expected load of the previous round and the current round. The relaxation factor satisfies the following condition: ; The iterative update formula for the expected load is: ； In the formula, The expected load output for the upper-level optimization problem.

10. The active distribution network optimization method based on mean field and inverse Steinberg game as described in claim 1, characterized in that, The three-level collaborative optimization of the active distribution network also includes social welfare calculation, whereby social welfare is defined as the difference between the total revenue obtained by all producers and consumers from electricity transactions and the total generation cost of the distribution network operator. The total revenue is the sum of the individual utility of all producers and consumers and their respective electricity costs. The social welfare calculation formula is as follows: 。

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