Power distribution network multi-agent energy transaction method based on stackelberg-nash equilibrium and two-stage wdro reconstruction

Abstract

This invention provides a multi-entity energy trading method for distribution networks based on Stackelberg-Nash equilibrium and two-stage WDRO reconfiguration. It constructs a Stackelberg-GNE two-layer game model that simultaneously incorporates energy interactions between DSOs and microgrids, as well as among multiple microgrids. The objective function of the DSO and the uncertainties in the renewable energy output of each microgrid are transformed into a single-layer optimization problem and a two-stage robust model, respectively. The generalized Nash equilibrium model among the lower-level microgrids is equivalently transformed into a centralized optimization problem, and a distributed solution is performed using the alternating direction multiplier method combined with a column and constraint generation algorithm to obtain the energy interactions between multiple microgrids and between microgrids and DSOs. Through a fixed-point iteration method, the Stackelberg game equilibrium between the upper-level DSO and the lower-level microgrids is solved, yielding the market equilibrium solution for multi-entity energy trading in the distribution network. This provides a holistic characterization of the multi-entity energy interaction process, ensuring market equilibrium and effectively overcoming the problems of high computational complexity or insufficient robustness in existing WDRO methods.

Description

Technical Field

[0001] This invention relates to the field of technology, and in particular to a multi-entity energy trading method for distribution networks based on Stackelberg-Nash equilibrium and two-stage WDRO reconfiguration. Background Technology

[0002] Existing literature has extensively studied energy interaction models within distribution networks. These models can be mainly divided into two categories. The first category involves energy interaction between multi-agent microgrids (MMGs). Existing literature includes MMG collaborative optimization models based on the Nash-Stackelberg-Nash framework, employing Alternating Optimization Procedure (AOP) combined with Alternating Direction Method of Multipliers (ADMM) algorithms for efficient solutions. Some literature constructs collaborative models of multi-integrated energy systems considering electricity-hydrogen point-to-point (P2P) transactions, integrating traffic models into the hydrogen energy trading framework to enhance practicality. Other literature constructs energy interaction models for charging stations, battery swapping stations, and smart buildings within commercial microgrids, achieving fair revenue distribution based on asymmetric Nash negotiation theory. Some literature proposes MMG energy interaction models based on asymmetric Nash negotiation to reduce operating costs and carbon emissions. However, all of the above studies neglect the line flow constraints of the distribution network, thus affecting the feasibility and accuracy of the optimization results.

[0003] The second type of energy interaction focuses on the interaction between distribution network operators (DSOs) and microgrids. Existing literature has constructed non-cooperative game models between DSOs and multiple microgrids (MMGs) and solved them using the ADMM algorithm; some literature has proposed a two-level optimization model of "DSO-multiple microgrids" for power restoration scenarios and transformed it into a single-level problem through Karush-Kuhn-Tucker (KKT) conditions; some literature has proposed a "DSO-multiple microgrid" collaborative mechanism based on the distribution network node marginal price (DLMP) and obtained the equilibrium solution using an iterative method; and some literature has constructed an energy interaction model between DSOs and microgrids based on resource aggregation and projection domain computation.

[0004] Existing literature on the energy interaction among multiple entities in distribution networks still has certain limitations. Specifically, existing research focuses on energy interaction between "multi-microgrids" or "DSO-multi-microgrids", lacking a unified market framework that can simultaneously cover energy transactions of all entities. Under such a market framework, the interaction price and power between "DSO and multi-microgrids" and "within multi-microgrids" will change dynamically over time and jointly affect market equilibrium.

[0005] Furthermore, uncertainties such as upstream grid electricity prices and renewable energy output significantly impact the energy interaction outcomes among multiple stakeholders. Existing literature typically employs stochastic optimization and robust optimization to address these uncertainties. However, stochastic optimization relies on accurate probability distributions, which are often difficult to obtain in practice; while robust optimization usually optimizes based on the worst-case scenario of a pre-defined uncertainty set, potentially leading to overly conservative results. To address this issue, Distributed Robust Optimization (DRO) can be used to model uncertain stakeholders. DRO, as a compromise between stochasticity and robustness, has garnered widespread attention from researchers. Existing literature on DRO modeling primarily includes methods based on moment characteristics and distribution distance. Among these, Wasserstein distance-based DRO (WDRO) effectively utilizes historical data of uncertain stakeholders for modeling, thereby effectively reducing decision conservatism, and is therefore widely used in power system research. The key to solving the WDRO model lies in effectively reconstructing the expectation function of the worst-case distribution, transforming it into a problem solvable by existing algorithms or commercial solvers. Most existing literature uses a strong duality approach combined with worst-case enumeration to equivalently reconstruct the expectation function of WDRO. However, the number of constraints under this method grows exponentially with the sample size, which brings a huge computational burden in scenarios with large-scale samples. Some literature uses an improved column and constraint generation algorithm (C&CG) to reduce computational complexity, but the number of subproblems in its iteration process is still proportional to the number of samples, thus limiting the overall solution efficiency. Some literature uses a sample averaging strategy to approximate the expectation function, but such simplification fails to fully capture the potential worst-case scenarios of uncertain subjects, resulting in decisions that may lack sufficient robustness in practice.

[0006] In summary, existing research has the following shortcomings: First, regarding the multi-entity energy interaction problem in distribution networks, existing literature either focuses only on the energy interaction between DSOs and microgrids, or only analyzes the interaction mechanisms between multiple microgrids. However, when both "DSO-microgrid" and "microgrid-microgrid" interactions exist simultaneously, the coupling characteristics among multiple entities can significantly impact market equilibrium results. Currently, research considering both interaction mechanisms simultaneously is still relatively limited, making it difficult to support the construction of a stable and efficient market equilibrium mechanism. Second, when using the WDRO model to handle uncertain entities, existing methods often face problems of high computational complexity or overly simplified uncertainty sets, thus affecting the accuracy and engineering applicability of the solutions to some extent. Summary of the Invention

[0007] In view of this, the present invention proposes a multi-entity energy trading method for distribution networks based on Stackelberg-Nash equilibrium and two-stage WDRO reconfiguration, which can effectively characterize the energy interaction forms among multiple entities and obtain the corresponding market equilibrium solution, thereby realizing the coordinated operation of multiple entities.

[0008] The technical solution of this invention is implemented as follows: The multi-entity energy trading method for distribution networks based on Stackelberg-Nash equilibrium and two-stage WDRO reconfiguration includes the following steps: Step S1: Construct a Stackelberg-GNE two-layer game model that includes energy interactions between DSO and microgrids as well as among multiple microgrids. The upper layer of the two-layer game model is a Stackelberg game model between DSO and multiple microgrids, and the lower layer is a generalized Nash equilibrium game model among multiple microgrids. Step S2: Based on strong duality theory and boundary constraints of random variables, the electricity purchase cost of DSO under the worst case of the upper-level power grid electricity price distribution is equivalent, and the objective function of DSO is transformed into a single-layer optimization problem. Step S3: Perform a two-stage WDRO reconstruction on the uncertainties of renewable energy output for each microgrid, and transform the objective function of each microgrid into a two-stage robust model; Step S4: Based on the saddle point theorem, the generalized Nash equilibrium model between the lower-level microgrids is equivalently transformed into a centralized optimization problem. The alternating direction multiplier method combined with the column and constraint generation algorithm is used for distributed solution to obtain the energy interaction between the microgrids and between the microgrid and the DSO. Step S5: Using the fixed-point iteration method, solve the Stackelberg game equilibrium between the upper-level DSO and the lower-level multi-microgrid to obtain the market equilibrium solution for multi-entity energy trading in the distribution network.

[0009] Preferably, the objective function of the DSO in the two-layer game model includes the electricity purchase cost under the worst-case electricity price distribution at time t and the degradation cost of energy storage at time t, and the specific expression is as follows: ; in The cost of electricity is expressed as follows: , Let be the fuzzy set of the electricity price of the upper-level power grid at time t. Let t be the power purchased by DSO from the upstream grid. For the cost of degradation, and Let be the charging power and discharging power of the stored energy at time t, respectively, and sup denote the supremum. This is the expected operation.

[0010] Preferably, the objective function of the microgrid in the two-layer game model is: ; in Let be the dual multiplier of the power balance constraint of microgrid m at time t. The interaction power between microgrid m and DSO at time t, where M is the total number of lower-layer microgrids. Let be the interactive electricity price between microgrids n and m at time t. Let be the interaction power between microgrids n and m at time t, and let sup denote the supremum. For the expected operation, A fuzzy set that contributes to the new energy of microgrid m. Let t be the output of the gas turbine inside the microgrid m. Cost per unit output of a gas turbine.

[0011] Preferably, the expression for the electricity purchase cost in step S2 is obtained after equivalent transformation: ; in , , For Lagrange multipliers, The Wasserstein radius corresponding to the electricity price. The number of samples for electricity prices. Let be the I-th upper-level electricity price sample at time t. I This is an index of the upper-level electricity price samples. and This represents the lower and upper bounds of the electricity price range.

[0012] Preferably, the specific steps of step S3 are as follows: Based on the power constraints, fuzzy set constraints, and intraday cost function-related constraints of microgrid m, the objective function of the microgrid is transformed into a two-stage robust model. The power constraints are as follows:

[0013]

[0014]

[0015] in This represents the upper limit of the interaction power between the microgrid m and the DSO. This represents the upper limit of interaction between microgrid m and the other microgrids. Let be the interaction power between microgrids m and n at time t; The fuzzy set constraint is:

[0016]

[0017] in Let N be the sample index and the total number of samples of renewable energy in microgrid m, respectively. l L and L represent the index of new energy types and the total number of types, respectively. For the internal network m l New energy category The fluctuation value of a sample at time t. and These are the first m units within the microgrid. l The upper and lower boundaries of similar new energy sources at time t. The Wasserstein radius corresponding to the new energy source; The constraints related to the intraday cost function are:

[0018]

[0019] in For the gas turbine in the microgrid m, time t corresponds to the first Intraday variables for each sample, The renewable energy load at time t represents the size of the gas turbine in the microgrid m. The maximum intraday variable value of the gas turbine within the microgrid m; The two-stage robust model is as follows:

[0020] in, and The correlation coefficient matrix, For the current decision variable, For intraday decision variables, For the corresponding feasible region, For variables corresponding to uncertain subjects.

[0021] Preferably, the specific steps in step S4 of equivalently transforming the generalized Nash equilibrium model among the lower-level microgrids into a centralized optimization problem are as follows: Based on the saddle point theorem, the optimal solution of the two-stage robust model is the equilibrium solution of the generalized Nash equilibrium model between microgrids m and n. The optimal solution for the corresponding dual variable is the equilibrium electricity price. Thus, the generalized Nash equilibrium model is transformed into the following centralized optimization problem:

[0022] in These are the corresponding dual variables.

[0023] Preferably, the specific steps in step S4, which employ the alternating direction multiplier method combined with column and constraint generation algorithms for distributed solution to obtain the energy interaction quantities between multiple microgrids and between microgrids and DSOs, are as follows: An augmented Lagrangian function is constructed for the centralized optimization problem, and the augmented Lagrangian function is decomposed into sub-models corresponding to each microgrid based on the alternating direction multiplier method. The column and constraint generation algorithm is used to decompose the sub-model into the main problem and sub-problems, and iteratively solves them. When the column and constraint generation algorithm converges, the obtained interactive power is transferred to the corresponding sub-models of other micronets to continue iterating until the convergence condition of the alternating direction multiplier method is met. After solving the problem using the alternating direction multiplier method and the column AND constraint generation algorithm, the optimal solution is obtained. and ,Will The output is the interactive equilibrium solution between multiple micronets. The output is the amount of electricity each microgrid purchases from itself.

[0024] Preferably, the specific steps of step S5 are as follows: The upper-level DSO obtains the interactive equilibrium solution. Electricity Purchase Then, the dual optimal solution DLMP is obtained by solving the DSO objective function. This process is equivalent to the following mapping:

[0025] For DSO, in the interactive equilibrium solution Electricity Purchase Under the premise of very small changes, It is continuous; given DLMP, the microgrid obtains the interactive equilibrium solution by solving a centralized optimization problem. Electricity Purchase The entire process is defined as the following mapping:

[0026] in It is also continuous, transforming the energy interaction model between DSO and multiple microgrids into a solution for interaction equilibrium. Electricity Purchase Continuous self-mapping:

[0027] Output the fixed points in the above equation as the Stackelberg game equilibrium solutions for DSO and multi-micronet.

[0028] Compared with the prior art, the beneficial effects of the present invention are: The present invention provides a multi-entity energy trading method for distribution networks based on Stackelberg-Nash equilibrium and two-stage WDRO reconfiguration. It constructs a Stackelberg-GNE two-layer game model that simultaneously includes energy interaction between DSO and microgrids as well as between multiple microgrids, thereby achieving a holistic characterization of the multi-entity energy interaction process and ensuring market equilibrium. Simultaneously, a two-stage WDRO reconstruction is performed on the uncertainties of renewable energy output in each microgrid, thereby transforming the objective function of each microgrid into a two-stage robust model. Compared with the traditional WDRO reconstruction method, this invention achieves a better trade-off between computational efficiency and robustness preservation, and can effectively overcome the problems of high computational complexity or insufficient robustness of existing WDRO methods.

[0029] Compared with existing energy interaction models, this invention unifies the energy trading between the distribution network and multiple microgrids and between multiple microgrids into a Stackelberg-generalized Nash equilibrium problem, thereby achieving a holistic characterization of the energy interaction process among multiple entities and ensuring market equilibrium. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only preferred embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 The flowchart shows the multi-entity energy trading method for distribution networks based on Stackelberg-Nash equilibrium and two-stage WDRO reconfiguration of the present invention. Figure 2 This figure shows the intraday dispatch cost variation under different cases of microgrid 2 and Wasserstein radius in the implementation of the multi-entity energy trading method for distribution networks based on Stackelberg-Nash equilibrium and two-stage WDRO reconfiguration of the present invention. Detailed Implementation

[0032] To better understand the technical content of this invention, a specific embodiment is provided below, and the invention will be further described in conjunction with the accompanying drawings.

[0033] See Figure 1 The present invention provides a multi-entity energy trading method for distribution networks based on Stackelberg-Nash equilibrium and two-stage WDRO reconfiguration, comprising the following steps: Step S1: Construct a Stackelberg-GNE two-layer game model that includes energy interactions between DSO and microgrids as well as among multiple microgrids. The upper layer of the two-layer game model is a Stackelberg game model between DSO and multiple microgrids, and the lower layer is a generalized Nash equilibrium game model among multiple microgrids. The objective function of the DSO in the two-level game model includes the electricity purchase cost under the worst-case electricity price distribution at time t and the degradation cost of energy storage at time t. The specific expression is as follows: ; in The cost of electricity is expressed as follows: , Let be the fuzzy set of the electricity price of the upper-level power grid at time t. Let t be the power purchased by DSO from the upstream grid. For the cost of degradation, and Let be the charging power and discharging power of the stored energy at time t, respectively, and sup denote the supremum. This is the expected operation.

[0034] Preferably, the objective function of the microgrid in the two-layer game model is: ; In the objective function described above, the first term represents the electricity purchase cost of microgrid m from the DSO; the second part represents the electricity purchase cost of microgrid m from other microgrids, both of which are day-ahead scales; and the third part represents the expected intraday cost of the internal gas turbine of microgrid m under the worst-case scenario of renewable energy output distribution. In the above formula, Let be the dual multiplier of the power balance constraint of microgrid m at time t. The interaction power between microgrid m and DSO at time t is defined as follows: a value greater than 0 indicates that the microgrid m is purchasing electricity from the DSO, and a value less than 0 indicates that the microgrid m is selling electricity to the DSO. M represents the total number of lower-level microgrids. Let be the interactive electricity price between microgrids n and m at time t. Let be the interaction power between microgrids n and m at time t. A value greater than 0 indicates that microgrid n sells electricity to m, and a value less than 0 indicates that microgrid n buys electricity. sup denotes the supremum. For the expected operation, A fuzzy set that contributes to the new energy of microgrid m. Let t be the output of the gas turbine inside the microgrid m. Cost per unit output of a gas turbine.

[0035] As the upper-level decision-maker, the DSO, considering line power flow constraints and the worst-case distribution of electricity prices in the upper-level grid, performs day-ahead clearing with the goal of minimizing system operating costs. It sends the power balance multiplier as the nodal marginal price (DLMP) to each microgrid. After obtaining the DLMP, each microgrid decides on the interaction amount between itself and the energy interaction amount with the DSO with the goal of minimizing its own costs, and transmits the results to the DSO. Finally, the DSO and the multi-entity microgrids iteratively update their strategies until equilibrium is reached. This model corresponds to the day-ahead scheduling scale.

[0036] Based on the energy interaction mode among the lower-level multi-agent microgrids, a corresponding generalized Nash equilibrium (GNE) model was constructed. Specifically, after receiving the DLMP, each microgrid uses a two-stage WDRO model to model the objective function (minimizing operating costs). At this time, the energy interaction among the multi-agent microgrids is described by the generalized Nash equilibrium model. Specifically, with the DLMP fixed, if there exists an equilibrium price such that the energy exchange between microgrids m and n under their respective optimal strategies satisfies the supply and demand balance, then the two achieve equilibrium. This model can be regarded as a non-cooperative game model, which also corresponds to the day-ahead scheduling scale.

[0037] Step S2: Based on strong duality theory and boundary constraints of random variables, the electricity purchase cost of the DSO under the worst-case scenario of the upstream power grid price distribution is equivalently transformed into a single-level optimization problem. After equivalent transformation, the expression for the electricity purchase cost is obtained as follows: ; in , , For Lagrange multipliers, The Wasserstein radius corresponding to the electricity price. The number of samples for electricity prices. Let be the I-th upper-level electricity price sample at time t. I This is an index of the upper-level electricity price samples. and This represents the lower and upper bounds of the electricity price range.

[0038] Step S3: Perform a two-stage WDRO reconstruction on the uncertainties in the renewable energy output of each microgrid, transforming the objective function of each microgrid into a two-stage robust model. The specific steps are as follows: Based on the power constraints, fuzzy set constraints, and intraday cost function-related constraints of microgrid m, the objective function of the microgrid is transformed into a two-stage robust model. The power constraints are as follows:

[0039]

[0040]

[0041]

[0042]

[0043] in This represents the upper limit of the interaction power between the microgrid m and the DSO. This represents the upper limit of interaction between microgrid m and the other microgrids. Let be the interaction power between microgrids m and n at time t; Given the current dispatch decision, the expected cost function of microgrid m in the second stage is a convex function of renewable energy output. Therefore, similar to the equivalent transformation of the expression for electricity purchase cost, the fuzzy set and related constraints are equivalently reconstructed, where the fuzzy set constraints are:

[0044]

[0045] in Let N be the sample index and the total number of samples of renewable energy in microgrid m, respectively. l L and L represent the index of new energy types and the total number of types, respectively. For the internal network m l New energy category The fluctuation value of a sample at time t. and These are the first m units within the microgrid. l The upper and lower boundaries of similar new energy sources at time t. The Wasserstein radius corresponding to the new energy source; The constraints related to the intraday cost function are:

[0046]

[0047] in For the gas turbine in the microgrid m, time t corresponds to the first Intraday variables for each sample, The renewable energy load at time t represents the size of the gas turbine in the microgrid m. The maximum intraday variable value of the gas turbine within the microgrid m; The two-stage robust model is as follows:

[0048] in, and The correlation coefficient matrix, For the current decision variable, For intraday decision variables, For the corresponding feasible region, For variables corresponding to uncertain subjects, after the two-stage WDRO model of microgrid m is equivalently reconstructed and a two-stage robust model is obtained, it can be solved in a distributed manner by using the alternating direction multiplier method combined with column and constraint generation algorithm.

[0049] Given a fixed distribution network node marginal price (DLMP), the generalized Nash equilibrium (GNE) condition among multiple microgrids can be described as follows: If a certain interactive electricity price Substituting these values ​​into the two-stage robust models of microgrids m and n respectively, let the optimal price of microgrid m be... and The optimal solution for microgrid n is and If they satisfy the following definition:

[0050] Then the microgrids m and n form a corresponding generalized Nash equilibrium, and Then the corresponding equilibrium electricity price.

[0051] Step S4: Based on the saddle point theorem, the generalized Nash equilibrium model among the lower-level microgrids is equivalently transformed into a centralized optimization problem. The optimal solution of the two-stage robust model is the equilibrium solution of the generalized Nash equilibrium model between microgrids m and n. The optimal solution for the corresponding dual variable is the corresponding equilibrium electricity price. Thus, the generalized Nash equilibrium model is transformed into the following centralized optimization problem:

[0052] in Given the corresponding dual variables, the above equation represents a centralized optimization problem, which may lead to privacy leaks in each micronet. To simultaneously protect the privacy of each micronet and obtain an equilibrium solution, this invention employs the Alternating Direction Multiplier Method (ADMM) combined with the Column and Constraint Generation Algorithm (C&CG) for distributed solution, and transmits the obtained optimal solution to the DSO. The specific steps are as follows: Constructing the augmented Lagrangian function for a centralized optimization problem:

[0053] Where st(17-18) and (22-25) are constraint functions, 17-18 are the first two terms of the power constraint, and 22-25 are the fuzzy set constraints and... .

[0054] The augmented Lagrangian function is decomposed into sub-models corresponding to each microgrid based on the alternating direction multiplier method. Taking microgrid m as an example, its corresponding sub-model is as follows:

[0055] in This indicates the current iteration number of the ADMM algorithm. For the first The corresponding Lagrange multipliers for iteration, For microgrid n in the first The interactive power transmitted to microgrid m in the next iteration.

[0056] To solve the above sub-model, a column and constraint generation algorithm is used to decompose the sub-model into a main problem and sub-problems, and then iteratively solves them. The compact form of the main problem is as follows:

[0057] The compact form of the subproblem is:

[0058] Let the optimal solution to the main problem be... The optimal solution to the subproblem is ,make Then the convergence condition of the column and constraint generation algorithm is:

[0059] in To improve the convergence accuracy of the column and constraint generation algorithm, when the algorithm converges, the resulting interaction power is transferred to the corresponding sub-models of the remaining microgrids for continued iteration until the convergence condition of the alternating direction multiplier method is met:

[0060] in and These represent the convergence accuracy of the original residual and the dual residual of the ADMM algorithm, respectively.

[0061] After solving the problem using the alternating direction multiplier method and the column AND constraint generation algorithm, the optimal solution is obtained. and ,Will The output is the interactive equilibrium solution between multiple micronets. The output is the amount of electricity each microgrid purchases from itself.

[0062] Step S5: Using the fixed-point iteration method, solve the Stackelberg game equilibrium between the upper-level DSO and the lower-level multi-microgrid to obtain the market equilibrium solution for multi-entity energy trading in the distribution network. The specific steps are as follows: The upper-level DSO obtains the interactive equilibrium solution. Electricity Purchase Then, the dual optimal solution DLMP is obtained by solving the DSO objective function. This process is equivalent to the following mapping:

[0063] For DSO, in the interactive equilibrium solution Electricity Purchase Under the premise of very small changes, It is continuous; given DLMP, the microgrid obtains the interactive equilibrium solution by solving a centralized optimization problem. Electricity Purchase The entire process is defined as the following mapping:

[0064] in It is also continuous, transforming the energy interaction model between DSO and multiple microgrids into a solution for interaction equilibrium. Electricity Purchase Continuous self-mapping:

[0065] Output the fixed points in the above equation as the Stackelberg game equilibrium solutions for DSO and multi-micronet.

[0066] To verify the difference and effectiveness of the model proposed in this invention, this invention takes a 33-node system as an example. The system includes 3 microgrids and 1 energy storage system. The voltage range of each node is set between 0.94 pu and 1.06 pu. Microgrid 1, microgrid 2 and microgrid 3 are connected to nodes 8, 24 and 30 respectively, and the energy storage system is connected to node 12. Microgrid 1 uses photovoltaic (PV) as a renewable energy source, microgrid 2 uses wind power (WT), and microgrid 3 includes both types of renewable energy.

[0067] The electricity price of the upper-level grid and the renewable energy output of each microgrid were characterized using 20 samples. All models were solved in a Python 3.6.5 environment using the commercial solver Gurobi 9.1.2.

[0068] This invention sets up three sets of comparative examples for analysis: Case 1: The multi-micronet adopts a two-stage WDRO modeling method. The model reconstruction method and solution method adopt a strong duality combined with worst case enumeration to equivalently reconstruct the expectation function of WDRO, and solve it through an improved G&CG algorithm.

[0069] Case 2: The multi-agent micronetwork adopts two-stage WDRO modeling and the model is reconstructed according to the sample averaging strategy proposed in the literature.

[0070] Case 3: A multi-agent microgrid is modeled using a two-stage WDRO model and solved using the novel reconstruction method proposed in this invention.

[0071] The operating costs for the three cases are shown in Table 1. This represents the total electricity purchase cost from the microgrid m to the DSO. This represents the interaction cost between multiple micronetwork entities. The overall computational efficiency is shown in Table 2.

[0072] Table 1 Operation Cost of MMGs And DSO Under Different Case

[0073] Table 2 Calculation Behavior in Different Cases

[0074] A comparison of Case 1 and Case 3 shows that the results obtained by the two model reconstruction methods are generally consistent, indicating that the method proposed in this invention can maintain a solution accuracy comparable to traditional methods. However, as shown in Table 3, there is a significant difference in the total computation time: the total computation time of Case 1 is 1372.8 s, while the computation time of the proposed model is only 705.6 s, a reduction of approximately 48.6%. This performance improvement is mainly due to the model reconstruction method proposed in this invention, which effectively reduces the size of sub-problems and accelerates the solution process by integrating the fluctuations of all samples. Specifically, in Case 3, each microgrid only needs to solve one sub-problem during the C&CG iteration process; while in Case 1, the number of sub-problems is the same as the sample size N.

[0075] A comparison of Case 2 and Case 3 reveals that the intraday expected cost obtained by each microgrid under the model reconstruction proposed in this invention is higher than the results of the sample averaging strategy in traditional literature. The main reason for this difference lies in the different modeling methods used in the two examples. Specifically, Case 2 simplifies the fuzzy set of samples to its mean and optimizes the intraday cost function using the worst-case scenario of this mean, thus ignoring the worst-case scenarios corresponding to each sample. This process can be understood as directly applying the convex combination of samples to the intraday cost function. In contrast, Case 3 explicitly considers the possible worst-case scenarios for each sample and calculates the average intraday cost for all samples. This method is equivalent to taking a convex combination of the objective function values. According to Jason's inequality, the model reconstruction method proposed in this invention provides a tighter lower bound for the intraday cost function compared to Case 2.

[0076] In summary, Case 2 and Case 3 correspond to different worst-case scenarios for renewable energy output, leading to different day-ahead dispatch decisions. Based on this premise, this invention conducted a comparative experiment to evaluate the robustness of day-ahead dispatch decisions under a unified worst-case scenario. In this experiment, the day-ahead dispatch decisions obtained from the two calculation examples were fixed, and the worst-case scenario calculated from Case 3 was derived to evaluate the intraday power supply reliability under the two cases. Simultaneously, several sets of Wasserstein sphere radii were set for comparative analysis to explore their impact on cost. The five sets of Wasserstein radii are: 100 / 100 / 200, 200 / 200 / 400, 300 / 300 / 600, 400 / 400 / 800, and 500 / 500 / 1000, corresponding to microgrid 1, microgrid 2, and microgrid 3, respectively. In the simulation test, the intraday cost function used is defined as follows:

[0077] in This represents the potential load shedding power of microgrid m at time t during the day's scheduling. This represents the unit load shedding cost, which is set to 0.5 ($ / kW) in this invention. Represented by microgrid 2, Figure 2 The paper presents the changes in intraday costs under different examples and Wasserstein sphere radii. At the same radius, the intraday costs for each sample in Case 3 are relatively stable, while the costs for some samples in Case 2 show a significant increase. Furthermore, this difference becomes more pronounced as the radius increases. This phenomenon can be explained in two ways. First, when the radius is small, the Wasserstein fuzzy set contains fewer distributions, thus the intraday cost corresponding to the worst-case scenario is lower; as the radius increases, the uncertainty of renewable energy is further amplified, leading to increased costs. Second, Case 2 oversimplifies the sample space during model reconstruction, replacing the original sample set with the sample mean, thereby ignoring potential worst-case distributions. This simplification reduces the robustness of day-ahead scheduling decisions. Therefore, to maintain supply and demand balance under more unfavorable conditions, Case 2 requires additional load shedding, resulting in increased intraday costs.

[0078] Furthermore, the scalability and effectiveness of the proposed two-stage WDRO reconfiguration method are verified using an improved IEEE 69-node distribution system. This system comprises five microgrids and three energy storage systems. Microgrids 1-5 are connected to nodes 8, 25, 15, 18, and 50, respectively, while energy storage systems 1-3 are installed at nodes 21, 39, and 45, respectively. The parameters of the energy storage systems are set according to existing literature. Table 3 presents a comparison between the proposed reconfiguration method and existing reconfiguration methods. In addition, to compare the robustness of the three reconfiguration methods, the worst-case scenario obtained by the proposed method is applied to the intraday scheduling phase of each method to verify the feasibility of the obtained solutions.

[0079] Table 3 Result Comparison on the IEEE 69-Bus System

[0080] As shown in Table 3, the total operating cost of the multi-micronet obtained by the proposed reconstruction method is 7.7% higher than that of Scheme 2. However, the intraday scheduling scheme based on the proposed method remains feasible in all worst-case scenarios, while the feasibility rate of Case 2 only drops to 17%, fully demonstrating the robustness of the proposed method. Compared with the results of Case 1, the difference in the objective function values ​​of DSO and multi-micronet under the proposed reconstruction method is less than 0.1%, indicating that its solution accuracy is comparable to that of traditional methods. At the same time, the total computation time is reduced from 1233.69 s to 660.4 s, a reduction of approximately 46.5%. Overall, these results show that the proposed reconstruction method can meet the requirements of day-ahead scheduling in terms of solution time while maintaining robustness and solution accuracy.

[0081] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-entity energy trading method for distribution networks based on Stackelberg-Nash equilibrium and two-stage WDRO reconfiguration, characterized in that, Includes the following steps: Step S1: Construct a Stackelberg-GNE two-layer game model that includes energy interactions between DSO and microgrids as well as among multiple microgrids. The upper layer of the two-layer game model is a Stackelberg game model between DSO and multiple microgrids, and the lower layer is a generalized Nash equilibrium game model among multiple microgrids. Step S2: Based on strong duality theory and boundary constraints of random variables, the electricity purchase cost of DSO under the worst case of the upper-level power grid electricity price distribution is equivalent, and the objective function of DSO is transformed into a single-layer optimization problem. Step S3: Perform a two-stage WDRO reconstruction on the uncertainties of renewable energy output for each microgrid, and transform the objective function of each microgrid into a two-stage robust model; Step S4: Based on the saddle point theorem, the generalized Nash equilibrium model between the lower-level microgrids is equivalently transformed into a centralized optimization problem. The alternating direction multiplier method combined with the column and constraint generation algorithm is used for distributed solution to obtain the energy interaction between the microgrids and between the microgrid and the DSO. Step S5: Using the fixed-point iteration method, solve the Stackelberg game equilibrium between the upper-level DSO and the lower-level multi-microgrid to obtain the market equilibrium solution for multi-entity energy trading in the distribution network.

2. The method for multi-entity energy trading in distribution networks based on Stackelberg-Nash equilibrium and two-stage WDRO reconfiguration as described in claim 1, characterized in that, The objective function of the DSO in the two-level game model includes the electricity purchase cost under the worst-case electricity price distribution at time t and the degradation cost of energy storage at time t. The specific expression is as follows: ； in The cost of electricity is expressed as follows: , Let be the fuzzy set of the electricity price of the upper-level power grid at time t. Let t be the power purchased by DSO from the upstream grid. For the cost of degradation, and Let be the charging power and discharging power of the stored energy at time t, respectively, and sup denote the supremum. This is the expected operation.

3. The method for multi-entity energy trading in distribution networks based on Stackelberg-Nash equilibrium and two-stage WDRO reconfiguration as described in claim 2, is characterized in that... The objective function of the microgrid in the two-layer game model is: ； in Let be the dual multiplier of the power balance constraint of microgrid m at time t. The interaction power between microgrid m and DSO at time t, where M is the total number of lower-layer microgrids. Let be the interactive electricity price between microgrids n and m at time t. Let be the interaction power between microgrids n and m at time t, and let sup denote the supremum. For the expected operation, A fuzzy set that contributes to the new energy of microgrid m. Let t be the output of the gas turbine inside the microgrid m. Cost per unit output of a gas turbine.

4. The method for multi-entity energy trading in distribution networks based on Stackelberg-Nash equilibrium and two-stage WDRO reconfiguration as described in claim 3, is characterized in that... The expression for electricity purchase cost in step S2 is obtained after equivalent transformation: ； in , , For Lagrange multipliers, The Wasserstein radius corresponding to the electricity price. The number of samples for electricity prices. Let be the I-th upper-level electricity price sample at time t. I This is an index of the upper-level electricity price samples. and This represents the lower and upper bounds of the electricity price range.

5. The method for multi-entity energy trading in distribution networks based on Stackelberg-Nash equilibrium and two-stage WDRO reconfiguration as described in claim 4, characterized in that, The specific steps of step S3 are as follows: Based on the power constraints, fuzzy set constraints, and intraday cost function-related constraints of microgrid m, the objective function of the microgrid is transformed into a two-stage robust model. The power constraints are as follows: in This represents the upper limit of the interaction power between the microgrid m and the DSO. This represents the upper limit of interaction between microgrid m and the other microgrids. Let be the interaction power between microgrids m and n at time t; The fuzzy set constraint is: in Let N be the sample index and the total number of samples of renewable energy in microgrid m, respectively. l L and L represent the index of new energy types and the total number of types, respectively. For the internal network m l New energy category The fluctuation value of a sample at time t. and These are the first m units within the microgrid. l The upper and lower boundaries of similar new energy sources at time t. The Wasserstein radius corresponding to the new energy source; The constraints related to the intraday cost function are: in For the gas turbine in the microgrid m, time t corresponds to the first Intraday variables for each sample, The renewable energy load at time t represents the size of the gas turbine in the microgrid m. The maximum intraday variable value of the gas turbine within the microgrid m; The two-stage robust model is as follows: in, and The correlation coefficient matrix, For the current decision variable, For intraday decision variables, For the corresponding feasible region, For variables corresponding to uncertain subjects.

6. The method for multi-entity energy trading in distribution networks based on Stackelberg-Nash equilibrium and two-stage WDRO reconfiguration as described in claim 5, is characterized in that... The specific steps in step S4 of equivalently transforming the generalized Nash equilibrium model among the lower-level micronetworks into a centralized optimization problem are as follows: Based on the saddle point theorem, the optimal solution of the two-stage robust model is the equilibrium solution of the generalized Nash equilibrium model between microgrids m and n. The optimal solution for the corresponding dual variable is the equilibrium electricity price. Thus, the generalized Nash equilibrium model is transformed into the following centralized optimization problem: in These are the corresponding dual variables.

7. The method for multi-entity energy trading in distribution networks based on Stackelberg-Nash equilibrium and two-stage WDRO reconfiguration as described in claim 6, is characterized in that, The specific steps in step S4, which employs the alternating direction multiplier method combined with column and constraint generation algorithms for distributed solution to obtain the energy interaction quantities between multiple microgrids and between microgrids and DSOs, are as follows: An augmented Lagrangian function is constructed for the centralized optimization problem, and the augmented Lagrangian function is decomposed into sub-models corresponding to each microgrid based on the alternating direction multiplier method. The column and constraint generation algorithm is used to decompose the sub-model into the main problem and sub-problems, and iteratively solves them. When the column and constraint generation algorithm converges, the obtained interactive power is transferred to the corresponding sub-models of other micronets to continue iterating until the convergence condition of the alternating direction multiplier method is met. After solving using the alternating direction multiplier method and the column AND constraint generation algorithm, the optimal solution is obtained. and ,Will The output is the interactive equilibrium solution between multiple micronets. The output is the amount of electricity each microgrid purchases from itself.

8. The method for multi-entity energy trading in distribution networks based on Stackelberg-Nash equilibrium and two-stage WDRO reconfiguration as described in claim 1, characterized in that, The specific steps of step S5 are as follows: The upper-level DSO obtains the interactive equilibrium solution. Electricity Purchase Then, the dual optimal solution DLMP is obtained by solving the DSO objective function. This process is equivalent to the following mapping: For DSO, in the interactive equilibrium solution Electricity Purchase Under the premise of very small changes, It is continuous; given DLMP, the microgrid obtains the interactive equilibrium solution by solving a centralized optimization problem. Electricity Purchase The entire process is defined as the following mapping: in It is also continuous, transforming the energy interaction model between DSO and multiple microgrids into a solution for interaction equilibrium. Electricity Purchase Continuous self-mapping: Output the fixed points in the above equation as the Stackelberg game equilibrium solutions for DSO and multi-micronet.

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