A Method for Assessing the Photovoltaic Carrying Capacity of Distribution Networks Based on Distributed Bar Joint Opportunity Constraints and Hybrid Game Theory

Abstract

This invention relates to the field of photovoltaic (PV) carrying capacity assessment, specifically a method for assessing the PV carrying capacity of distribution networks based on distributed robust joint opportunity constraints and hybrid game theory. This method constructs a multi-agent hybrid game architecture involving distribution network operators, prosumers, and electric vehicle clusters, thereby building a two-layer PV carrying capacity assessment model that integrates master-slave game theory and evolutionary game theory. The upper-layer master-slave game model deeply integrates distributed robust joint opportunity constraints with master-slave game theory, constructing a directly solvable framework; the lower-layer evolutionary game model establishes the evolutionary game process of the electric vehicle cluster. The dynamic interaction between the master-slave game of distribution network operators and prosumers and the evolutionary game of the electric vehicle cluster achieves joint convergence of evolutionary stability and master-slave game equilibrium. The maximum carrying capacity assessment results obtained by the proposed method not only conform to the system safety boundary but also fully reflect the interactive effects among market participants, possessing not only mathematical rigor but also practical engineering value.

Description

Technical Field

[0001] This invention relates to the field of photovoltaic carrying capacity assessment, specifically a method for assessing the photovoltaic carrying capacity of distribution networks based on distributed bar joint opportunity constraints and hybrid game theory. Background Technology

[0002] With the increasing penetration rate of photovoltaics, its inherent uncertainties have significantly impacted the safe and economical operation of power distribution networks. Traditionally, stochastic optimization and robust optimization are classic methods for handling uncertainty. However, stochastic optimization assumes that uncertain variables follow a certain distribution, which is often unrealistic and may lead to overly optimistic optimization results. Robust optimization, on the other hand, focuses primarily on worst-case scenarios and is therefore quite conservative. Distributed robust optimization combines the advantages of both stochastic and robust optimization and has become a new approach to addressing uncertainty. However, current distributed robust optimization models mainly focus on individual chance constraints. Compared to individual chance constraints, distributed robust joint chance constraints can simultaneously enforce the satisfaction of multiple security constraints, providing a stronger guarantee for the security of the entire power system.

[0003] Furthermore, against the backdrop of profound changes in the electricity market mechanism, the operating paradigm of distribution networks is undergoing a fundamental restructuring. Existing photovoltaic carrying capacity assessment models, employing a global modeling approach based on a single decision-making entity, neglect the market game process involving multiple stakeholders such as distribution operators, producers / consumers, and electric vehicle clusters. This leads to a fundamental misalignment between the model's decision-making logic and the multi-stakeholder interaction scenarios in the real market environment. The bidding strategies and game behaviors of producers / consumers and electric vehicle clusters can create implicit disturbances in network power flow by altering the spatiotemporal distribution characteristics of load. However, existing methods have not yet established a two-way coupled analysis framework of "technical constraints - market game," and this singular physical modeling approach will cause systematic distortion in the carrying capacity assessment results.

[0004] However, while decompositional bar optimization and bilevel programming, represented by market game theory, have become research hotspots in their respective fields due to their complexity, combining decompositional bar optimization with market game theory presents even greater complexity and challenges. Therefore, few studies currently integrate decompositional bar optimization with market game theory to assess photovoltaic carrying capacity. Summary of the Invention

[0005] To address the problem of systematic distortion in photovoltaic (PV) carrying capacity assessment results caused by existing single-physical modeling methods, this invention proposes a distribution network PV carrying capacity assessment method based on distributed robust joint opportunity constraints and hybrid game theory. This invention constructs a multi-agent hybrid game architecture involving distribution network operators, prosumers, and electric vehicle clusters, thereby building a two-layer PV carrying capacity assessment model that integrates master-slave game theory and evolutionary game theory. The upper-layer master-slave game model deeply integrates distributed robust joint opportunity constraints based on Wasserstein metric with master-slave game theory through reconstruction techniques, constructing a directly solvable framework; the lower-layer evolutionary game model establishes the evolutionary game process of the electric vehicle cluster. The dynamic interaction between the master-slave game of distribution network operators and prosumers and the evolutionary game of the electric vehicle cluster achieves joint convergence of evolutionary stability and master-slave game equilibrium.

[0006] This invention is achieved using the following technical solution: a method for assessing the photovoltaic carrying capacity of distribution networks based on split-bar joint opportunity constraints and hybrid game theory, comprising the following steps:

[0007] Step 1: Construct a photovoltaic carrying capacity assessment model for distribution networks based on a multi-entity master-slave-evolutionary hybrid game: This model adopts a two-layer model. The upper-layer master-slave game model has the distribution network operator as the leader and each producer-consumer as a follower in the master-slave game. Each producer-consumer reports the amount of electricity purchased and sold. Under the premise of ensuring the safe operation of the system, the distribution network operator aims to minimize the operating cost of the distribution network and sets different prices according to the energy consumption characteristics of each producer-consumer to determine the photovoltaic capacity that each producer-consumer can access and the purchase and sale price. Each producer-consumer adjusts the amount of electricity purchased and sold according to the purchase and sale price issued by the distribution network operator and then feeds it back to the distribution network operator. This process continues until a settlement is reached and the transaction is completed through multiple games between the distribution network operator and each producer-consumer, thus determining the purchase and sale price and the amount of electricity purchased and sold as a result of the master-slave game. The lower-layer evolutionary game model conducts an evolutionary game of electric vehicle clusters based on the electricity sales price decided by the upper-layer master-slave game model. The result of the evolutionary game, the charging power of electric vehicles, will in turn affect the result of the master-slave game.

[0008] Step 2: Solution method for photovoltaic carrying capacity assessment model of distribution network: KKT conditions are used to solve the upper master-slave game model, and distributed robust joint chance constraints are used to handle source load uncertainty; Logit dynamic evolution equations are used to solve the game process for the lower evolution game model.

[0009] The aforementioned method for assessing the photovoltaic carrying capacity of distribution networks based on the combined opportunity constraint and hybrid game theory of distributed grids includes an upper-level master-slave game model comprising the objective function of the leader and the objective function of the follower.

[0010] The objective function of the leader in a master-slave game is ,Right now The cost of purchasing electricity from the upper-level power grid at all times Electricity purchase costs from producers and consumers Shared energy storage operating costs Producer-consumer response subsidy costs Reactive power compensation call cost Revenue from electricity sales The difference is the smallest, among which, , , , , , , In the formula: For the operating costs of distribution network operators, This represents the number of time nodes; , These represent the electricity purchase price and the amount of electricity purchased by the distribution network operator and the upstream power grid, respectively. , These refer to the electricity purchased and sold by the power distribution network operator from producers and consumers, respectively. , These refer to the electricity purchase price and the electricity sales price from producers and consumers by the power distribution network operator; Cost per unit power output for energy storage; , These are the energy storage charging power and the discharging power, respectively. The cost of generating a unit of reactive power for a parallel capacitor bank; This refers to the reactive power generated by the parallel capacitor bank. The cost of generating or absorbing unit reactive power by a static var compensator; The reactive power generated or absorbed by the static var compensator; For a parallel capacitor bank, the set of nodes is provided. The set of nodes equipped with static var compensators; A collection of energy storage grid-connected nodes; For the collection of grid-connected nodes of various producers and consumers; Power to respond to producer and consumer demand; , These refer to the ability of producers and consumers to reduce or transfer electrical load; For the utility function of electric comfort loss for producers and consumers; , All are electrical comfort loss coefficients; , These are the subsidy coefficients for producers and consumers reducing or transferring electricity load, respectively.

[0011] The objective function of the follower in a master-slave game is: Each producer-consumer aims to maximize their own benefits, including producer-consumer response subsidies. Revenue from electricity sales to distribution network operators Electricity purchase cost from distribution network operators Revenue from selling electricity to electric vehicles and photovoltaic investment costs ,in, , , , In the formula: For the benefit of the producers and consumers themselves, The electricity price for electric vehicles, Charging power for electric vehicles, The lifespan of the photovoltaic system; The discount rate; Cost per unit of photovoltaic power capacity.

[0012] The aforementioned method for assessing the photovoltaic carrying capacity of distribution networks based on distributed bar joint opportunity constraints and hybrid game theory includes the following leader constraints in the master-slave game:

[0013] Photovoltaic installation capacity constraints at each node: In the formula: For distribution network Node installed photovoltaic capacity, For distribution network The upper limit of the photovoltaic capacity installed at each node;

[0014] Electricity price constraints: , , , In the formula: and These are the lower and upper limits of the electricity purchase price that distribution network operators charge producers and consumers; This represents the average electricity purchase price. , These are the lower and upper limits of the electricity price that distribution network operators sell to producers and consumers; This represents the average electricity price.

[0015] Constraints of energy storage systems: In the formula, and These represent the charging and discharging states of energy storage, respectively. For energy storage The state of electrical energy at any given moment. For energy storage The state of electrical energy, and These are the charging efficiency and discharging efficiency of energy storage, respectively. and These represent the minimum and maximum states of charge for energy storage, respectively. For energy storage capacity, This represents the maximum value of the energy storage discharge power. This represents the maximum charging power of the energy storage system.

[0016] Constraints of reactive power compensation equipment: , In the formula: and These are the upper and lower limits of the power of the static var compensator, respectively. The reactive power compensation power of a unit parallel capacitor bank; The number of parallel capacitor banks connected for grid connection; This represents the total number of parallel capacitor banks. and The variable is 0-1, representing the connection and disconnection of the parallel capacitor bank; The initial number of parallel capacitor banks to be connected to the grid; In order to be in The maximum number of times a parallel capacitor bank can operate within a given time period;

[0017] Photovoltaic output constraints: , In the formula: , Photovoltaics Every moment involves contributing effort, whether it's effective or not; For photovoltaics The equivalent power output coefficient at any given time; , These are the maximum and minimum power factor angles for photovoltaic power, respectively. This represents the maximum light rejection rate.

[0018] Current constraints: In the formula: and These represent the active power and reactive power of each node at each time point; and These represent the active load power and reactive load power of each node at each time point; The reactive power generated by the upstream power grid; and These are the resistance matrix and the reactance matrix, respectively. and It is a block matrix of the admittance matrix of the distribution network nodes. It is the voltage at the balancing node; For the voltage of the distribution network, For the current in the distribution network; The system's nominal voltage;

[0019] Joint opportunity constraint: In the formula: the joint opportunity constraint includes voltage constraint and current constraint; and These are the upper and lower limits of the voltage, respectively. The risk coefficient for exceeding the limit of inequality constraints. and These are the upper and lower limits of the current, respectively; Represents a probability distribution. It is a fuzzy set of probability distributions.

[0020] The aforementioned method for assessing the photovoltaic carrying capacity of distribution networks based on the joint opportunity constraint of distributed rods and hybrid game theory includes the following follower constraints in the master-slave game:

[0021] Prosumer response constraints: In the formula: for Consumers are constantly reducing their electricity load; for The transfer of burden between producers and consumers at all times; , These are the load reduction ratio and the load transfer ratio, respectively. Forecast power for load;

[0022] Electric power balance constraints: ;

[0023] Electricity purchase and sale constraints: In the formula: , These are the upper limits for electricity purchases and sales, respectively; to avoid simultaneous electricity purchases and sales, [the following settings are provided]. and It is a 0-1 variable.

[0024] The aforementioned method for assessing the photovoltaic carrying capacity of distribution networks based on the joint chance constraint of distributed rods and hybrid game theory involves the following process for constructing the lower-level evolutionary game model: firstly, a service fee adjustment strategy is proposed. In the formula: Adjustment rounds for charging service fees; For the first Charging stations on wheels Changes in charging service fees; For charging stations The set expected user share; For charging stations Actual user share Adjust the step size for charging service fees; The number of charging stations; for The difference between the maximum and minimum charging service fees at each charging station at any given time is then... Charging service fee at electric vehicle charging stations The calculation is as follows: In the formula: For the first Charging service fee at charging stations , These are the upper and lower limits for charging service fees, respectively.

[0025] When selecting charging stations, electric vehicle clusters use three factors as user evaluation indicators: charging price, user occupancy rate, and transportation convenience. The electric vehicle charging price is calculated as follows: In the formula: The final iterative electricity price in the evolutionary game. Considering the above three factors, a system is established... Electric vehicle cluster selection number A utility model for a charging station. In the formula: for Electric vehicle cluster selection number The utility evaluation value of a charging station. For the first electric vehicle cluster Weight of each indicator; For the first electric vehicle clusters for the first The first charging station The evaluation values ​​of each indicator; the electric vehicle cluster selects the charging station with the highest utility evaluation value for charging.

[0026] The aforementioned method for assessing the photovoltaic carrying capacity of distribution networks based on joint chance constraints and hybrid game theory in the upper-level master-slave game model uses the KKT conditions for solution as follows: the McCormick envelope method is used to linearize the objective function, and the two upper-level objective functions are equivalently transformed into a mixed-integer linear programming problem using the KKT conditions for solution. The solution is then obtained directly through a commercial solver. Node installed photovoltaic capacity Electricity purchases between distribution network operators and their upstream power grids The electricity purchase price from producers and consumers by distribution network operators Electricity purchased by power grid operators from producers and consumers Electricity prices sold by distribution network operators to producers and consumers Electricity sold by power distribution network operators to producers and consumers Producer-consumer demand response power Photovoltaics Contributing merit at all times Voltage of the distribution network Current in the distribution network .

[0027] The above-mentioned method for assessing the photovoltaic carrying capacity of distribution networks based on distributed robust joint opportunity constraints and hybrid game theory involves the following process for handling distributed robust joint opportunity constraints during the solution of the upper-level master-slave game model:

[0028] 1) The compact form of the joint opportunity constraint is expressed as follows: In the formula: It is a vector composed of decision variables in the distribution network. and yes A linear function, It is the number of individual opportunity constraints in the joint opportunity constraint;

[0029] 2) Use the Bonferroni inequality to transform the joint opportunity constraint into a single opportunity constraint: In the formula: The middle represents the risk coefficient under individual opportunity constraints. and ;

[0030] 3) Use the worst-case conditional risk value (CVaR) constraint to approximate a single worst-case opportunity constraint: In the formula: As an auxiliary variable; , Represents the mathematical expectation;

[0031] Further transformation yields: In the formula: , , These are the dual variables generated during the transformation process. It is an infinite norm. Represents the radius of the Wasserstein sphere. Let the boundary vector of the uncertain set be... The constraint coefficient matrix is ​​used. By utilizing the Bonferroni equation and the CVaR approximation, the distributed robust joint chance constraint equation based on the Wasserstein distance is transformed into a linear constraint equation, and the original distributed robust joint constraint problem is transformed into a mixed integer linear programming problem for solution.

[0032] The above-mentioned method for assessing the photovoltaic carrying capacity of distribution networks based on the joint chance constraint of distributed rods and hybrid game theory has the following solution process for the lower-level evolutionary game model:

[0033] The Logit model is used as the decision-making mechanism in the evolutionary game, and the evolutionary game process is described by a system of differential equations: , , In the formula: Indicates in Within a certain time period Electric vehicle cluster selection number The ratio of charging stations express The derivative with respect to time is used to describe Dynamic evolution over time; For the first electric vehicle clusters from charging stations Converted into a charging station The probability of; For the first electric vehicle clusters from charging stations Converted into a charging station The probability, for Electric vehicle cluster selection number The utility evaluation value of a charging station. for Electric vehicle cluster selection number The utility evaluation value of each charging station; the dynamic evolution equation of the electric vehicle cluster is obtained as follows: When the number of users at each charging station stabilizes, the system reaches an equilibrium state in the evolutionary game; the dynamic evolution process of the user group is as follows: In the formula: For iteration rounds, The iteration step size is used to calculate the electric vehicle charging power of charging stations within different consumer groups. In the formula: For the first Total charging power of electric vehicle clusters.

[0034] In summary, compared with the prior art, the beneficial effects of the present invention are:

[0035] This invention proposes a method for assessing the photovoltaic carrying capacity of distribution networks based on distributed robust joint opportunity constraints and hybrid game theory. First, the proposed model constructs a multi-agent hybrid game architecture involving distribution network operators, prosumers, and electric vehicle clusters. This architecture forms a two-layer photovoltaic carrying capacity assessment model integrating master-slave game theory and evolutionary game theory. The upper layer combines the master-slave game process with distributed robust joint opportunity constraints through reconstruction techniques, forming a directly solvable framework. The lower layer establishes the evolutionary game process of the electric vehicle cluster, with the master-slave game and the electric vehicle cluster evolutionary game iterating between the two layers to achieve joint convergence of evolutionary stability and master-slave game equilibrium. The maximum carrying capacity assessment results obtained by the proposed method not only conform to the system safety boundary but also fully reflect the interactive effects among market participants, possessing both mathematical rigor and practical engineering value. Attached Figure Description

[0036] Figure 1 This is a framework diagram of a photovoltaic carrying capacity assessment model for distribution networks based on a combination of randomized block joint opportunity constraints and hybrid game theory.

[0037] Figure 2 This is a flowchart of the overall solution process. Detailed Implementation

[0038] A method for assessing the photovoltaic carrying capacity of distribution networks based on distributed bar joint opportunity constraints and hybrid game theory includes the following steps:

[0039] Step 1: Construct a photovoltaic carrying capacity assessment model for distribution networks based on a multi-agent master-slave-evolutionary hybrid game.

[0040] The model employs a two-layer approach: the upper-layer master-slave game model, where the distribution network operator acts as the leader and each producer-consumer acts as a follower, engages in master-slave competition. Each producer-consumer reports their electricity purchase and sale volume. Under the premise of ensuring the safe operation of the system, the distribution network operator aims to minimize the operating cost of the distribution network and sets differentiated prices based on the energy consumption characteristics of each producer-consumer, determining the photovoltaic capacity that each producer-consumer can access and the purchase and sale price. Each producer-consumer adjusts their purchase and sale volume according to the purchase and sale price issued by the distribution network operator and then feeds it back to the distribution network operator. This process continues until a settlement is reached and the transaction is completed through multiple rounds of competition between the distribution network operator and each producer-consumer, determining the purchase and sale price and the purchase and sale volume as the master-slave game outcome. The lower-layer evolutionary game model then conducts an evolutionary game of electric vehicle clusters based on the electricity sales price determined by the upper-layer master-slave game model. The result of the evolutionary game, the electric vehicle charging power, in turn affects the master-slave game outcome.

[0041] 1.1 Upper-level master-slave game model

[0042] 1.1.1 Leader Objective Function in Master-Slave Game

[0043] The operating costs of distribution network operators are optimized during the carrying capacity assessment process, namely... The cost of purchasing electricity from the upper-level power grid at all times Electricity purchase costs from producers and consumers Shared energy storage operating costs Producer-consumer response subsidy costs Reactive power compensation call cost Revenue from electricity sales Minimum difference:

[0044] (1)

[0045] (2)

[0046] (3)

[0047] (4)

[0048] (5)

[0049] (6)

[0050] (7)

[0051] (8)

[0052] In the formula: For the operating costs of distribution network operators, This represents the number of time nodes; , These represent the electricity purchase price and the amount of electricity purchased by the distribution network operator and the upstream power grid, respectively. , These refer to the electricity purchased and sold by the power distribution network operator from producers and consumers, respectively. , These are the electricity purchase price and electricity sales price charged by the power distribution network operator to producers and consumers, respectively. Cost per unit power output for energy storage; , These are the energy storage charging power and the discharging power, respectively. The cost of generating one unit of reactive power for parallel capacitor banks (CB); This refers to the reactive power generated by the parallel capacitor bank. The cost of generating or absorbing a unit of reactive power by a static var compensator (SVC); The reactive power generated or absorbed by the static var compensator; For a parallel capacitor bank, the set of nodes is provided. The set of nodes equipped with static var compensators; A collection of energy storage grid-connected nodes; It is a collection of grid-connected nodes for each producer and consumer. Power to respond to producer and consumer demand; , These refer to the ability of producers and consumers to reduce or transfer electrical load; For the utility function of electric comfort loss for producers and consumers; , All are electrical comfort loss coefficients, and , The higher the value, the better the energy comfort for both producers and consumers. , These are the subsidy coefficients for producers and consumers reducing or transferring their electricity load, respectively.

[0053] 1.1.2 Leader Constraints in Master-Slave Game

[0054] 1) Photovoltaic installation capacity constraints at each node

[0055] (9)

[0056] In the formula: For distribution network Node installed photovoltaic capacity, For distribution network The upper limit of the photovoltaic capacity that can be installed at a node.

[0057] 2) Electricity price constraints

[0058] To protect the fairness of the game and prevent the power distribution network operator, as the leader of the game, from maliciously inflating the electricity purchase price for producers and consumers in order to maximize profits, constraints are imposed on the electricity purchase price and sales price of the power distribution network operator to producers and consumers.

[0059] (10)

[0060] (11)

[0061] (12)

[0062] (13)

[0063] In the formula: and These are the lower and upper limits of the electricity purchase price that distribution network operators charge producers and consumers; This represents the average electricity purchase price. , These are the lower and upper limits of the electricity price that distribution network operators sell to producers and consumers; This represents the average electricity price.

[0064] 3) Constraints of energy storage systems

[0065] Energy storage is a typical multi-time-coupling device and must meet the following constraints:

[0066] (14)

[0067] In the formula, , and These represent the charging and discharging states of energy storage, respectively, and are 0-1 variables. For energy storage The state of electrical energy at any given moment. For energy storage The state of electrical energy, and These refer to the charging efficiency and discharging efficiency of energy storage, respectively. Furthermore, to extend the lifespan of energy storage and reduce investment costs, fully charging and discharging the energy storage is not permitted. and These represent the minimum and maximum states of charge for energy storage, respectively. For energy storage capacity, This represents the maximum value of the energy storage discharge power. This represents the maximum charging power of the energy storage system.

[0068] 4) Constraints of reactive power compensation equipment

[0069] The equivalent model of a static var compensator is: (15)

[0070] In the formula: and These are the upper and lower limits of the power of the static var compensator, respectively.

[0071] The equivalent model of a parallel capacitor bank is:

[0072] (16)

[0073] In the formula: The reactive power compensation power of a unit parallel capacitor bank; The number of parallel capacitor banks connected for grid connection; This represents the total number of parallel capacitor banks. and The variable is 0-1, representing the connection and disconnection of the parallel capacitor bank; The initial number of parallel capacitor banks to be connected to the grid; In order to be in The maximum number of times a parallel capacitor bank can operate within a given time period.

[0074] 5) Photovoltaic output constraints

[0075] (17)

[0076] (18)

[0077] In the formula: , Photovoltaics (PV) Every moment involves contributing effort, whether it's effective or not; For photovoltaics The equivalent power output coefficient at any given time; , These are the maximum and minimum power factor angles for photovoltaic power, respectively. This represents the maximum light rejection rate.

[0078] 6) Current constraints:

[0079] (19)

[0080] In the formula: and These represent the active power and reactive power of each node at each time point; and These represent the active load power and reactive load power of each node at each time point; The reactive power generated by the upstream power grid; and These are the resistance matrix and the reactance matrix, respectively. and It is a block matrix of the admittance matrix of the distribution network nodes. It is the voltage at the balancing node; For the voltage of the distribution network, For the current in the distribution network; This is the system's nominal voltage.

[0081] 7) Joint Opportunity Constraint

[0082] (20)

[0083] In the formula: the joint opportunity constraint includes voltage constraint and current constraint; and These are the upper and lower limits of the voltage, respectively. The risk coefficient for exceeding the limit of inequality constraints. and These are the upper and lower limits of the current, respectively; Represents a probability distribution. It is a fuzzy set of probability distributions.

[0084] 1.1.3 Follower Objective Function in Master-Slave Game

[0085] Each producer-consumer aims to maximize its own benefits, including producer-consumer response subsidies. Revenue from electricity sales to distribution network operators Electricity purchase cost from distribution network operators Revenue from selling electricity to electric vehicles and photovoltaic investment costs .

[0086] (twenty one)

[0087] (twenty two)

[0088] (twenty three)

[0089] (twenty four)

[0090] (25)

[0091] (26)

[0092] In the formula: For the benefit of the producers and consumers themselves, The electricity price for electric vehicles, Charging power for electric vehicles, d represents the lifespan of the photovoltaic system; d represents the discount rate. Cost per unit of photovoltaic power capacity.

[0093] 1.1.4 Follower Constraints in Master-Slave Game

[0094] 1) Prosumer Response Constraints

[0095] (27)

[0096] In the formula: for Consumers are constantly reducing their electricity load; for The transfer of burden between producers and consumers at all times; , These are the load reduction ratio and the load transfer ratio, respectively. Predicted power for load.

[0097] 2) Power balance constraints

[0098] The power balance constraint can be transformed into the following opportunity constraint form:

[0099] (28)

[0100] 3) Constraints on electricity purchase and sale

[0101] (29)

[0102] In the formula: , These are the upper limits for electricity purchases and sales, respectively; to avoid simultaneous electricity purchases and sales, [the following settings are provided]. and It is a 0-1 variable.

[0103] 1.2 Lower-level evolutionary game model

[0104] 1) Service Fee Adjustment Strategy

[0105] The cost of electricity for charging stations is the electricity price paid by producers and consumers. Charging stations can guide user charging behavior by adjusting charging service fees. The service fee adjustment strategy is as follows:

[0106] (30)

[0107] In the formula: Adjustment rounds for charging service fees; For the first Charging stations on wheels Changes in charging service fees; For charging stations The set expected user occupancy rate is positively correlated with the photovoltaic capacity within the producer-consumer network, that is, the expected user occupancy rate is equal to the proportion of photovoltaic capacity within the producer-consumer network to the total photovoltaic capacity of the distribution network. For charging stations Actual user share Adjust the step size for charging service fees; The number of charging stations; for The difference between the maximum and minimum charging service fees at each charging station at any given time. To ensure the basic revenue of charging stations and prevent malicious price gouging, the service fee should meet upper and lower limit constraints. When the charging service fee reaches the upper or lower limit, the service fee will no longer change.

[0108] Charging service fee for the nth round of charging stations The calculation is as follows:

[0109] (31)

[0110] In the formula: , These are the upper and lower limits for charging service fees, respectively.

[0111] 2) Lower-level evolutionary game model

[0112] When selecting charging stations, electric vehicle clusters primarily consider three factors as evaluation indicators: charging price, user occupancy rate, and transportation convenience. The electric vehicle charging price is calculated as follows:

[0113] (32)

[0114] In the formula: The final iterative electricity price in the evolutionary game.

[0115] Taking into account the above three factors, establish Electric vehicle cluster selection number The utility model of a charging station is shown below:

[0116] (33)

[0117] In the formula: for Electric vehicle cluster selection number The utility evaluation value of a charging station. For the first electric vehicle cluster Weight of each indicator; For the first electric vehicle clusters for the first The first charging station Evaluation value of each indicator.

[0118] Step 2: Solution Method for the Two-Layer Assessment Model of Photovoltaic Carrying Capacity of Distribution Network

[0119] The multi-stage photovoltaic carrying capacity assessment model with a double-layer nested structure constructed in this invention contains significant nonlinear characteristics. Therefore, the upper-layer master-slave game model is solved using KKT conditions, and distributed robust joint chance constraints are employed to handle source-load uncertainties. The lower-layer evolutionary game model is solved using Logit dynamic evolution equations to solve the game process.

[0120] 2.1 Solving the Master-Slave Game Model Based on KKT Conditions

[0121] In the upper-level master-slave game model, the complex trading strategies and coupled iterative processes between the leader (distribution network operator) and the followers (prosumers) result in a model exhibiting strong nonlinearity and nonconvexity, making it impossible to directly obtain the global optimum. To enable commercial solvers to directly solve this model, the McCormick envelope method is used to linearize the objective function, and the KKT conditions are used to equate the biobjective problem to a mixed-integer linear programming problem for solution. The solution is then obtained directly by a commercial solver: [The following text appears to be a separate, unrelated section:] In the distribution network... Node installed photovoltaic capacity Electricity purchases between distribution network operators and their upstream power grids The electricity purchase price from producers and consumers by distribution network operators Electricity purchased by power grid operators from producers and consumers Electricity prices sold by distribution network operators to producers and consumers Electricity sold by power distribution network operators to producers and consumers Producer-consumer demand response power Photovoltaics Contributing merit at all times Voltage of the distribution network Current in the distribution network .

[0122] 2.2 Distributed Robust Joint Chance Constraint Solution

[0123] 1) The compact form of the joint opportunity constraint is expressed as follows:

[0124] (34)

[0125] In the formula: It is a vector composed of decision variables in the distribution network. and yes A linear function, It is the number of individual opportunity constraints in the joint opportunity constraint;

[0126] 2) Use the Bonferroni inequality to transform the joint opportunity constraint into a single opportunity constraint:

[0127] (35)

[0128] In the formula: The middle represents the risk coefficient under individual opportunity constraints. and ;

[0129] 3) Use the worst-case conditional risk value (CVaR) constraint to approximate a single worst-case opportunity constraint:

[0130] (36)

[0131] In the formula: As an auxiliary variable; , Expressing the mathematical expectation; further transformation yields:

[0132] (37)

[0133] In the formula: , , These are the dual variables generated during the transformation process. It is an infinite norm. Represents the radius of the Wasserstein sphere. Let the boundary vector of the uncertain set be... The constraint coefficient matrix is ​​used. By utilizing the Bonferroni equation and the CVaR approximation, the distributed robust joint chance constraint equation based on the Wasserstein distance is transformed into a linear constraint equation, and the original distributed robust joint constraint problem is transformed into a mixed integer linear programming problem for solution.

[0134] 2.3 Solving the Evolutionary Game Model

[0135] The Logit model is used as the decision-making mechanism in evolutionary game theory. The evolutionary game process can be described by a system of differential equations:

[0136] (38)

[0137] (39)

[0138] (40)

[0139] In the formula: Indicates in Within a certain time period Electric vehicle cluster selection number The proportion of charging stations; express The derivative with respect to time is used to describe Dynamic evolution over time; For the first electric vehicle clusters from charging stations The probability of converting it to charging station i; For the first electric vehicle clusters from charging stations Converted into a charging station The probability, for Electric vehicle cluster selection number The utility evaluation value of a charging station. for Electric vehicle cluster selection number The utility evaluation value of each charging station. The dynamic evolution equation of the user group can be obtained as follows:

[0140] (41)

[0141] When the number of users at each charging station stabilizes, the system reaches an evolutionary game equilibrium. The dynamic evolution of the user group is as follows:

[0142] (42)

[0143] In the formula: n is the iteration round, Let be the iteration step size. From this, the electric vehicle charging power of charging stations within different consumer groups can be calculated as follows:

[0144] (43)

[0145] In the formula: For the first Total charging power of electric vehicle user clusters.

Claims

1. A distribution network photovoltaic carrying capacity evaluation method based on distribution robust joint opportunity constraint and mixed game, characterized by: Comprising the following steps: Step 1: Constructing a power distribution network photovoltaic carrying capacity evaluation model based on multi-agent master-slave-evolution hybrid game: The model adopts a double-layer model, the upper layer master-slave game model takes the power distribution network operator as the leader and each producer and consumer as the follower to carry out master-slave game, each producer and consumer reports the power purchase and sale, the power distribution network operator minimizes the power distribution network operation cost as the target under the premise of ensuring the safe operation of the system, determines the accessible photovoltaic capacity and the purchase and sale price of each producer and consumer according to the energy use characteristic difference of each producer and consumer, each producer and consumer adjusts the power purchase and sale according to the purchase and sale price issued by the power distribution network operator and feeds back to the power distribution network operator, and so on, through multiple games between the power distribution network operator and each producer and consumer until the settlement is reached to complete the transaction, and the master-slave game result of the purchase and sale price and the power purchase and sale is determined; the lower layer evolutionary game model carries out the evolutionary game of the electric vehicle cluster based on the sale price decided by the upper layer master-slave game model, and the evolutionary game result of the electric vehicle charging power will in turn affect the master-slave game result; Step 2: Solution method of power distribution network photovoltaic carrying capacity evaluation model: the KKT condition is used to solve the upper layer master-slave game model, and the distributed robust joint opportunity constraint is used to deal with the source and load uncertainty; the Logit dynamic evolution equation is used to solve the game process for the lower layer evolutionary game model.

2. The method of claim 1, wherein the method is characterized by: The upper layer master-slave game model comprises a master-slave game leader target function and a master-slave game follower target function; The leader objective function of the master-slave game is That is The purchase cost of electricity from the upper grid at time t The purchase cost of electricity from the producer-consumer The operation cost of shared energy storage The subsidy cost of the producer-consumer response The cost of calling reactive power compensation And the difference between the electricity selling revenue Is minimum, wherein , , , , , , , wherein: The operation cost of the distribution network operator, The number of time nodes; , The purchase price and purchase quantity of electricity of the distribution network operator and the upper grid respectively; , The purchase quantity and selling quantity of electricity of the distribution network operator to the producer-consumer; , The purchase price and selling price of electricity of the distribution network operator to the producer-consumer; The unit power output cost of energy storage; , The charging power and discharging power of energy storage respectively; The cost of emitting unit reactive power of shunt capacitor bank; The reactive power emitted by the shunt capacitor bank; The cost of emitting or absorbing unit reactive power of static reactive power compensator; The reactive power emitted or absorbed by the static reactive power compensator; The node set of the shunt capacitor bank; The node set equipped with the static reactive power compensator; The energy storage grid-connected node set; The grid-connected node set of each producer-consumer; The demand response power of the producer-consumer; , The reducible electric load and the transferable electric load of the producer-consumer respectively; The electric comfort loss utility function of the producer-consumer; , Both are electric comfort loss coefficients; , The subsidy coefficients of the producer-consumer to reduce electric load and transfer electric load respectively; The follower objective function of the master-slave game is Each producer and consumer aims to maximize its own profit, including the producer and consumer response subsidy , the electricity sale revenue to the distribution network operator , the electricity purchase cost from the distribution network operator , the electricity sale revenue to the electric vehicle , and the photovoltaic investment cost , wherein , , , In the formula: is the producer and consumer's own profit, is the electricity sale price to the electric vehicle, is the electric vehicle charging power, is the service life of the photovoltaic; is the discount rate; is the unit photovoltaic power capacity cost.

3. The method of claim 2, wherein the method is characterized by: The master-slave game leader constraint condition comprises: Node photovoltaic installation capacity constraint: wherein: is the installed photovoltaic capacity at node in the distribution network, is the installed photovoltaic capacity at node in the distribution network; Electricity price constraints: , , , , where: and are the lower and upper bounds of the electricity purchase price of the distribution network operator from the prosumers; is the average value of the electricity purchase price; , are the lower and upper bounds of the electricity sale price of the distribution network operator to the prosumers; is the average value of the electricity sale price; Energy storage system constraints: , where and denote the charge state and discharge state of the energy storage, respectively, is the energy state of the energy storage at time , is the energy state of the energy storage at time , and are the charge efficiency and discharge efficiency of the energy storage, respectively, and are the minimum and maximum state of charge of the energy storage, respectively, is the energy capacity of the energy storage, is the maximum discharge power of the energy storage, is the maximum charge power of the energy storage; Reactive power compensation equipment constraints: , , where: and are the upper and lower limits of the static reactive power compensator power, is the reactive power compensation power of the unit shunt capacitor bank; is the number of shunt capacitor banks put into the grid; is the total number of shunt capacitor banks; and are 0-1 variables, indicating the shunt capacitor bank put into operation, cut-off operation; is the initial number of shunt capacitor banks put into the grid; is the upper limit of the number of shunt capacitor bank actions within the time period; photovoltaic power output constraint: , , where: , are the active power and the reactive power of the photovoltaic at the time instant ; is the equivalent power output coefficient of the photovoltaic at the time instant ; , are the maximum power factor angle and the minimum power factor angle of the photovoltaic, respectively; is the maximum light rejection rate; Current constraints: In the formula: and These represent the active power and reactive power of each node at each time point; and These represent the active load power and reactive load power of each node at each time point; The reactive power generated by the upstream power grid; and These are the resistance matrix and the reactance matrix, respectively. and It is a block matrix of the admittance matrix of the distribution network nodes. It is the voltage at the balancing node; For the voltage of the distribution network, For the current in the distribution network; The system's nominal voltage; Joint chance constraint: , where: the joint chance constraint contains voltage constraints, current constraints; and are upper and lower limits of voltage, respectively, is a risk factor for inequality constraint out-of-limit, and are upper and lower limits of current, respectively; represents a probability distribution, is a fuzzy set of the probability distribution.

4. The method of claim 3, wherein the method is characterized by: The master-slave game follower constraint condition comprises: Producer-consumer response constraints: wherein: is the curtailed electric load of the producer-consumer at the moment; is the transferred load of the producer-consumer at the moment; , are respectively the curtailed load proportionality coefficient and the transferred load proportionality coefficient, is the predicted power of the load; An electrical power balance constraint: ; The purchase and sale power constraints are as follows: , wherein: , are the upper limit of the purchase power and the upper limit of the sale power, respectively; to avoid simultaneous purchase and sale of power, and are 0-1 variables.

5. The method of claim 4, wherein the method is characterized by: The construction process of the lower evolutionary game model is as follows: first, a service fee adjustment strategy is proposed , wherein: is the charging service fee adjustment round; is the charging service fee change amount of the charging station in the th round; is the expected user occupancy rate set by the charging station ; is the actual user occupancy rate of the charging station , is the charging service fee adjustment step; is the number of charging stations; is the difference between the maximum and minimum charging service fees of each charging station at the moment , then the charging service fee of the charging station in the th round is calculated as follows: , wherein: is the charging service fee of the charging station in the th round, , are the upper and lower limits of the charging service fee respectively; When selecting charging stations, electric vehicle clusters use three factors as user evaluation indicators: charging price, user occupancy rate, and transportation convenience. The electric vehicle charging price is calculated as follows: In the formula: To determine the final iterative electricity price in the evolutionary game, considering the above three factors, a system is established. Electric vehicle cluster selection number A utility model for a charging station. In the formula: for Electric vehicle cluster selection number The utility evaluation value of a charging station. For the first electric vehicle cluster Weight of each indicator; For the first electric vehicle clusters for the first The first charging station The evaluation values ​​of each indicator; the electric vehicle cluster selects the charging station with the highest utility evaluation value for charging.

6. The method of claim 5, wherein the method is characterized by: The process of solving the upper master-slave game model by using KKT condition is as follows: the objective function is linearized by using McCormick envelope method, and the two objective functions of the upper layer are equivalent to a mixed integer linear programming problem by using KKT condition for solving, and the following is obtained by directly solving by using a commercial solver: in the distribution network Node installation photovoltaic capacity , the power purchase of the distribution network operator and the superior power grid , the power purchase price of the distribution network operator to the producer and consumer , the power purchase of the distribution network operator to the producer and consumer , the power selling price of the distribution network operator to the producer and consumer , the power selling of the distribution network operator to the producer and consumer , the demand response power of the producer and consumer , the active power output of photovoltaic at moment , the voltage of the distribution network , the current of the distribution network .

7. The method of claim 6, wherein the method is characterized by: The processing process of the distributed robust joint opportunity constraint in the solution process of the upper layer master-slave game model is as follows: 1) The compact form of the joint opportunity constraint is expressed as follows: In the formula: It is a vector composed of decision variables in the distribution network. and yes A linear function, It is the number of individual opportunity constraints in the joint opportunity constraint; 2) transform the joint chance constraint into a single chance constraint using Bonferroni's inequality: where: is the risk coefficient of the individual chance constraint, and ; 3) Approximating individual worst-case chance constraints with worst-case conditionally value-at-risk CVaR constraints: where: is an auxiliary variable; , denotes the mathematical expectation; Further transformation gives: , where: , , is the dual variable generated by the transformation process, is the infinity norm, denotes the Wasserstein ball radius, is the boundary vector of the uncertainty set, is the constraint coefficient matrix; thus, by using the Bonferroni inequality and CVaR approximation, the distributionally robust joint chance-constrained equation based on the Wasserstein distance is transformed into a linear constraint equation, and the original distributionally robust joint constraint problem is transformed into a mixed integer linear programming problem for solving.

8. The method of claim 6 or 7, wherein the method is characterized by: The solution process of the lower layer evolutionary game model is as follows: The Logit model is used as the decision-making mechanism in the evolutionary game, and the evolutionary game process is described by a system of differential equations: , , In the formula: Indicates in Within a certain time Electric vehicle cluster selection number The ratio of charging stations express The derivative with respect to time is used to describe Dynamic evolution over time; For the first User type from charging station Converted into a charging station The probability of; For the first User type from charging station Converted into a charging station The probability, for Electric vehicle cluster selection number The utility evaluation value of a charging station. for Electric vehicle cluster selection number The utility evaluation value of each charging station; the dynamic evolution equation of the electric vehicle cluster is obtained as follows: When the number of users at each charging station stabilizes, the system reaches an equilibrium state in the evolutionary game; the dynamic evolution process of the user group is as follows: In the formula: For iteration rounds, The iteration step size is used to calculate the electric vehicle charging power of charging stations within different consumer groups. In the formula: For the first Total charging power of electric vehicle clusters.

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