A hybrid game-based proactive power distribution network photovoltaic load carrying capacity stochastic-robust evaluation method

Abstract

The present application relates to the field of photovoltaic carrying capacity evaluation, in particular to a kind of active distribution network photovoltaic carrying capacity stochastic-robust evaluation method based on mixed game.The method constructs the three-layer model of photovoltaic carrying capacity based on multi-agent evolution-master-slave mixed game, the upper model carries out optimization decision to photovoltaic capacity configuration and purchase and sale price strategy;Middle layer model and lower layer model are based on purchase and sale price and photovoltaic capacity system production simulation;Considering the source and load uncertainty of distribution network distributed photovoltaic and load, the stochastic-robust evaluation model of distribution network photovoltaic carrying capacity is established;When model is solved, middle layer model feeds back the power purchase and sale of distribution network operator to producer and consumer to upper layer model, and lower layer model feeds back the actual output of each producer and consumer to upper layer model.The present application considers the game behavior of distribution network operator, producer and consumer and electric vehicle cluster multi-agent, so that photovoltaic carrying capacity evaluation result is more in line with actual.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of photovoltaic carrying capacity evaluation, in particular to a kind of active distribution network photovoltaic carrying capacity stochastic-robust evaluation method based on mixed game. BACKGROUND

[0002] As the core technology of low-carbon transformation of energy structure, the installed capacity of photovoltaic is growing rapidly. However, the large-scale access of distributed photovoltaic leads to multiple technical challenges for distribution network. Distribution network operators urgently need to establish an accurate photovoltaic carrying capacity evaluation system to balance the contradiction between renewable energy consumption demand and system safety operation constraints. Existing researches form two technical routes around photovoltaic carrying capacity evaluation. One is the safety constraint analysis method based on global unified modeling, which solves the maximum photovoltaic access capacity that meets the static safety boundary by constructing an optimization model containing multiple constraint conditions such as thermal stability, short-circuit current capacity, voltage deviation and harmonic distortion rate. The other is the photovoltaic carrying capacity evaluation considering improvement measures, in which the demand response adjustment potential of the load side is a key research content.

[0003] However, the above technical routes have significant limitations. The deepening of power market reform is reshaping the operation paradigm of distribution network. Traditional load-side users evolve into producers and consumers with bidirectional energy interaction capability. The global modeling method regards the distribution network as a single decision-making subject, ignoring the game behavior of multiple subjects such as distribution network operators, producers and consumers, and electric vehicle clusters in the power market environment, leading to mismatch between the evaluation results and the real decision-making scenario. The game strategies of emerging market subjects such as producers and consumers, and electric vehicle clusters may cause systematic bias in carrying capacity evaluation results by changing the temporal and spatial distribution of load.

[0004] In the power market, the behavior of producers and consumers trading electricity with distribution network operators constitutes a typical master-slave game process. At the same time, electric vehicle clusters dynamically adjust their charging demand based on the price signal, and their temporal and spatial flexibility provides a new dimension for load regulation. The access of these emerging market subjects significantly increases the complexity of market game. Although existing researches have focused on the game relationship between distribution network operators and a single subject, the dynamic game mechanism in the multi-level coordinated scheduling of distribution network operators-producers and consumers-electric vehicle clusters is still lacking in systematic modeling. On the one hand, distribution network operators need to guide the response behavior of producers and consumers through node prices. On the other hand, the dynamic pricing strategy of producers and consumers will also guide the charging decisions of electric vehicle clusters. Such multi-scale game interaction will significantly change the power flow distribution of the distribution network, and thus affect the evaluation boundary of photovoltaic carrying capacity evaluation.

[0005] For the uncertainty of distribution network, the existing research mainly adopts stochastic optimization, robust optimization and its derivative methods. Stochastic optimization generates expected cost through probability scenario, but it depends on accurate probability distribution and is prone to optimistic bias; robust optimization seeks the worst-case solution based on the preset uncertainty set, but it reduces the practicability due to excessive conservatism. Hybrid stochastic robustness improves system flexibility by processing different uncertainty sources in different scenarios, but this method is still a simple superposition of stochastic optimization and robust optimization, and still has double limitations: stochastic optimization needs to assume accurate distribution, and the robust optimization part still has a conservative tendency, and fails to achieve organic integration at the methodological level. SUMMARY

[0006] The present application proposes a hybrid game-based active distribution network photovoltaic carrying capacity stochastic-robust evaluation method to solve the problem that the current research method ignores the game behavior of multiple subjects such as distribution network operators, producers and consumers, and electric vehicle clusters, resulting in mismatch between evaluation results and real decision-making scenarios. The method proposes a three-layer photovoltaic carrying capacity model based on multi-agent evolution-master-slave hybrid game. This model innovatively combines multi-agent game behavior with system safety constraints, quantitatively analyzes the dynamic influence of emerging agent game strategy on photovoltaic consumption space, and provides a new method for photovoltaic carrying capacity evaluation. In addition, a data-driven stochastic weighted robust method is proposed to handle the source-load uncertainty of the system. A large number of scenarios with similar statistical characteristics and distribution characteristics to the actual scenario are generated based on the generative adversarial network, which better describes the correlation and volatility of new energy output, and is used to construct the uncertainty scenarios required for stochastic weighted robustness, improving the accuracy and robustness of photovoltaic carrying capacity evaluation.

[0007] The technical scheme adopted by the present application is as follows: a hybrid game-based active distribution network photovoltaic carrying capacity stochastic-robust evaluation method, comprising the following steps:

[0008] Step 1: Construct a three-layer photovoltaic carrying capacity model based on multi-agent evolution-master-slave hybrid game. The model adopts a three-layer evaluation architecture: the upper layer model optimizes the photovoltaic capacity configuration and the purchase and sale price strategy from the perspective of the distribution network operator; the middle layer model and the lower layer model simulate the system production based on the purchase and sale price and the photovoltaic capacity decided by the upper layer model, wherein the middle layer model solves the power transaction problem between the distribution network operator and the producer and consumer, and the lower layer model checks the safety constraint conditions of the distribution network operation through the second-order cone programming optimal power flow model;

[0009] Step 2: Considering the source-load bilateral uncertainty of distributed photovoltaic and load in the distribution network, establish a photovoltaic carrying capacity stochastic-robust evaluation model for the distribution network based on the three-layer photovoltaic carrying capacity model in step 1;

[0010] Step 3: Model solution: In the middle layer model, the electric vehicle cluster selects the charging station with the highest charging station utility evaluation value to charge, and each producer and consumer maximizes its own profit based on the purchase and sale price of electricity and the photovoltaic capacity, and feeds back to the upper layer model the purchase and sale of electricity by the distribution network operator to the producer and consumer, and the lower layer model checks the safety constraint conditions of the distribution network operation and feeds back to the upper layer model the actual output of each producer and consumer connected to the grid.

[0011] The above-mentioned active distribution network photovoltaic carrying capacity random-robust evaluation method based on mixed game, the objective function of the upper layer model involves photovoltaic carrying capacity, distribution network operator operation cost and light rejection rate;

[0012] The photovoltaic carrying capacity evaluation considers maximizing the total installed capacity of distributed photovoltaics in the distribution network: , wherein: is the total installed capacity of distributed photovoltaics, is the photovoltaic capacity at the distribution network node ; and is the photovoltaic grid-connected node.

[0013] The distribution network operator operation cost is considered in the photovoltaic carrying capacity evaluation process, and the distribution network operator operation cost is the difference between the purchase cost of electricity from the upper grid , the purchase cost of electricity from the producer and consumer , the energy storage operation cost , the user voltage satisfaction cost , the active management invocation cost and the producer and consumer electricity sales revenue : , , , , , , ,

[0014] , wherein: is the distribution network operator operation cost, is the number of time nodes; and respectively represent the purchase price and purchase quantity of electricity by the distribution network operator and the upper grid; and are respectively the purchase and sale of electricity by the distribution network operator to the producer and consumer; and are respectively the purchase and sale prices of electricity by the distribution network operator to the producer and consumer; is the unit power output cost of energy storage; and are respectively the charging power and discharging power of the energy storage; is the cost of a shunt capacitor bank emitting a unit of reactive power. The cost of sending or absorbing unit reactive power for the shunt capacitor bank; The cost of sending or absorbing unit reactive power for the static var compensator; The reactive power sent or absorbed by the static var compensator; The cost of unit action considering on-load voltage regulation; The number of actions considering on-load voltage regulation; The set of all load nodes in the distribution system; The set of nodes with shunt capacitor bank; The set of nodes with static var compensator; The set of nodes in the distribution system, The set of nodes with energy storage; The set of nodes with each producer and consumer; The loss to the user due to voltage deviation not meeting the requirements, , wherein: The voltage satisfaction cost coefficient; The on-grid power of each node in the distribution network; The voltage satisfaction value of the user, The node voltage;

[0015] The abandoned light rate is considered to be minimized, , wherein: The abandoned light rate, The actual output of each producer and consumer calculated by the lower model.

[0016] The above-mentioned active distribution network photovoltaic carrying capacity random-robust evaluation method based on mixed game, the upper model constraint conditions include the photovoltaic installation capacity constraint and the electricity price constraint of each node,

[0017] The photovoltaic installation capacity constraint of each node: , wherein: The upper limit of the photovoltaic installation capacity at the distribution network node ;

[0018] The purchase price and the selling price of the distribution network operator to the producer and consumer are constrained: , , , , wherein: And The lower limit and the upper limit of the purchase price of the distribution network operator to the producer and consumer respectively; The average value of the purchase price; And The lower limit and the upper limit of the selling price of the distribution network operator to the producer and consumer respectively; The average value of the selling price.

[0019] The above-mentioned active power distribution network photovoltaic carrying capacity random-robust evaluation method based on mixed game, the middle layer model constructs an electric vehicle cluster-charging station selection evolutionary game model based on service fee adjustment strategy, which is used to simulate the interactive decision-making process between the electric vehicle cluster and the charging station; An optimization scheduling model considering the uncertainty of producer and consumer internal source and load is also constructed, and finally the transaction results are fed back to the upper layer model;

[0020] The construction process of the electric vehicle cluster-charging station selection evolutionary game model is as follows: first, a dynamic charging service fee adjustment strategy based on user occupancy rate is proposed, and the dynamic charging service fee adjustment strategy is as follows: , wherein: is the charging service fee adjustment round; is the charging station charging service fee change amount for the electric vehicle cluster; 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 time ; then the charging service fee of the charging station in the round is calculated as follows: , wherein: , are the upper and lower limits of the charging service fee, respectively; is the charging service fee of the charging station in the round;

[0021] When selecting a charging station, the electric vehicle cluster selects charging price, user occupancy rate, and traffic convenience as evaluation indexes, wherein the charging price of the electric vehicle is calculated as follows: , wherein, is the charging service fee of the charging station; based on the above three factors, the utility model of the electric vehicle cluster selecting the charging station is established, , wherein: is the utility evaluation value, is the weight of the index of the electric vehicle cluster; is the ​​​The first charging station The evaluation value of each indicator; the electric vehicle cluster selects the charging station with the highest utility evaluation value for charging.

[0022] The process of constructing the optimized scheduling model is as follows: Each producer-consumer aims to maximize its own revenue, and constructs the internal optimized scheduling model for the producer-consumer as follows: , , , , The following constraints are satisfied: , , , , In the formula: For the benefit of the producers and consumers themselves, For producer-consumer demand response costs, For the revenue of producers and consumers from selling electricity to distribution network operators, The cost of electricity purchased by producers and consumers from distribution network operators, Revenue from charging electric vehicle clusters; The unit scheduling cost for demand response load; for The actual dispatch power of the demand response load at any given moment; for The expected power consumption of the load at any given time. Charging load for electric vehicle clusters; For photovoltaics Contributing effort at all times; For photovoltaics Predicted equivalent power output coefficient at time step; Contribute to photovoltaic power; The total electricity demand of the demand response load during the dispatch cycle; and For demand response load in Maximum and minimum electricity demand at any given time; for The load power within the consumer at all times; and These are the upper limits for electricity purchases and electricity sales, respectively. and It is a 0-1 variable.

[0023] The aforementioned stochastic-robust evaluation method for the active distribution network photovoltaic carrying capacity based on hybrid game theory constructs a second-order cone programming optimal power flow model for the distribution network, aiming to optimize the following formula for the distribution network operator. The constraints include energy storage system constraints, reactive power compensation device constraints, power flow constraints, producer and consumer output constraints, and distribution network gateway power constraints, wherein the producer and consumer output constraints are as follows: .

[0024] The process of step 2 of the above-mentioned active distribution network photovoltaic carrying capacity stochastic-robust evaluation method for establishing a distribution network photovoltaic carrying capacity stochastic-robust evaluation model is as follows: first, the optimization scheduling model and the lower model are converted into a deterministic compact form: , , wherein: is the feasible region of ; 、 is a coefficient column vector corresponding to the optimization scheduling model and the lower model; 、 、 、 、 、 、 and are coefficient matrices corresponding to variables under constraints; 、 、 、 is a constant column vector; is a source and load power prediction value; the vector 、 and 、 are binary and continuous variables, respectively: , wherein, and respectively represent the charge state and discharge state of the energy storage system, and are the active power and reactive power of each branch of the distribution network, respectively; is a node voltage; is a branch current;

[0025] It is assumed that the fluctuation range of photovoltaic and load power is constrained by a box-type uncertainty set: , wherein: is a box-type uncertainty set constructed; 、 is a different typical day source and load power prediction value; 、 is a source and load variable after introducing uncertainty; 、 is the maximum value of source and load fluctuation;

[0026] The deterministic compact form is re-expressed as: , wherein: To generate the discrete probability distribution extracted after clustering the scene based on the generative adversarial network; The first half of the formula represents the optimal power flow problem of the distribution network, and the second half corresponds to the internal optimization problem of the producer and consumer, and the minimization of the outer layer of the second half is the first stage problem, and the optimization variable is ; The inner layer maximization minimization is the second stage problem, and the optimization variable is and , ℑ k = [ ℑ k PV , ℑ k L ] T ; The feasible region of , The probability of the clustered scenario , , The corresponding continuous variable of the scene .

[0027] The above-mentioned active distribution network photovoltaic carrying capacity random-robust evaluation method based on mixed game, the upper model adopts NSGA III algorithm for solving, in the process of each iteration calculation, the upper model and the lower model are converted into multi-stage random robust optimization problem, and C&CG algorithm is used for solving.

[0028] Compared with the prior art, the beneficial effects of the present application are:

[0029] The application provides a distributed robust joint opportunity constraint photovoltaic carrying capacity evaluation model based on deep learning. Firstly, the model can realize the Pareto optimality of the maximum photovoltaic carrying capacity, economy and technology, and consider different photovoltaic carrying capacity improvement measures. Through reasonable scheduling and active management measures and energy storage, the operation cost and light rejection rate are reduced, and the carrying capacity of the photovoltaic access distribution network is greatly improved. Secondly, the model constructs a multi-agent distribution network system architecture and transaction framework of distribution network operators, producers and consumers and electric vehicle clusters, and combines master-slave game and evolutionary game in the photovoltaic carrying capacity evaluation process. Through the joint action of distribution network operation and market mechanism, the photovoltaic carrying capacity of the distribution network can be more accurately described. Finally, the model adopts a data-driven random weighted robust method to process the source and load uncertainty of the system, which can effectively avoid the optimism of the traditional stochastic optimization model and the conservatism of the traditional robust optimization model, so that the photovoltaic carrying capacity evaluation result is more in line with the actual situation. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 It is a three-layer model framework diagram of photovoltaic carrying capacity based on multi-agent evolution-master-slave mixed game.

[0031] Figure 2 It is a user voltage satisfaction function diagram.

[0032] Figure 3 The overall solution flowchart.

[0033] Figure 4 The IEEE33 node system diagram.

[0034] Figure 5 The photovoltaic carrying capacity evaluation result pareto frontier diagram. DETAILED DESCRIPTION

[0035] A hybrid game-based active distribution network photovoltaic carrying capacity stochastic-robust evaluation method, comprising the following steps:

[0036] Step 1: Construct a three-layer model of photovoltaic carrying capacity based on multi-agent evolution-master-slave hybrid game.

[0037] The model adopts a three-layer evaluation architecture: the upper layer model optimizes the photovoltaic capacity configuration and the purchase and sale price strategy from the perspective of the distribution network operator agent; the middle layer model and the lower layer model simulate the system production based on the purchase and sale price and the photovoltaic capacity decided by the upper layer model. Among them, the middle layer model mainly solves the power transaction problem between the distribution network operator and the producer and consumer, and the lower layer model checks the safety constraint conditions of the distribution network operation through the second-order cone programming optimal power flow model.

[0038] 1.1 Upper layer model

[0039] 1.1.1 Objective function

[0040] 1) Photovoltaic carrying capacity

[0041] The photovoltaic carrying capacity evaluation first considers maximizing the total installed capacity of the distributed photovoltaic in the distribution network:

[0042] (1)

[0043] In the formula: is the total installed capacity of the distributed photovoltaic, is the photovoltaic capacity at the node of the distribution network; is the photovoltaic grid-connected node.

[0044] 2) Distribution network operator operation cost

[0045] In the photovoltaic carrying capacity evaluation process, the distribution network operator operation cost is considered, which requires the upper-level power grid purchase cost , the producer and consumer purchase cost , the energy storage operation cost , the user voltage satisfaction cost , and the active management (AM) invocation cost The difference between the electricity selling revenue to the prosumers and the electricity purchasing cost from the superior grid is minimized:

[0046] (2)

[0047] (3)

[0048] (4)

[0049] (5)

[0050] (6)

[0051] (7)

[0052] (8)

[0053] In the formula: is the operation cost of the distribution network operator, is the number of time nodes; and respectively represent the electricity purchasing price and the electricity purchasing quantity of the distribution network operator from the superior grid; and are respectively the electricity purchasing quantity and the electricity selling quantity of the distribution network operator to the prosumers; and are respectively the electricity purchasing price and the electricity selling price of the distribution network operator to the prosumers; is the unit power output cost of the energy storage; and are the charging power and the discharging power of the energy storage; is the cost of the capacitor banks (CB) for emitting unit reactive power; is the reactive power emitted by the capacitor banks (CB); is the cost of the static VAR compensation (SVC) for emitting or absorbing unit reactive power; is the reactive power emitted or absorbed by the static VAR compensation (SVC); is the unit action cost of the on-load tap changer (OLTC); is the action number of the on-load tap changer (OLTC); is the set of all load nodes in the distribution network system;​ The set of nodes for CB; A set of nodes equipped with SVC; As a balancing node in the distribution network system, A collection of energy storage grid-connected nodes; For the collection of grid-connected nodes of various producers and consumers; Losses incurred by users due to voltage deviation not meeting requirements:

[0054] (9)

[0055] In the formula: The voltage satisfaction cost coefficient; This refers to the grid-connected power of each node in the distribution network; This represents the user's voltage satisfaction value. For node voltage, such as Figure 2 As shown, the smaller the voltage deviation, the higher the satisfaction level.

[0056] 3) Discard rate

[0057] (10)

[0058] In the formula: For light rejection rate, The actual grid-connected power output of each producer and consumer is calculated from the lower-level model.

[0059] 1.1.2 Constraints

[0060] 1) Photovoltaic installation capacity constraints at each node

[0061] (11)

[0062] In the formula: This represents the upper limit of the photovoltaic capacity that can be installed at node i of the distribution network.

[0063] 2) Electricity price constraints

[0064] To protect the fairness of the game process 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 should be placed on the electricity purchase price and electricity sales price of the power distribution network operator to producers and consumers.

[0065] (12)

[0066] (13)

[0067] (14)

[0068] (15)

[0069] are the lower and upper bounds of the electricity purchase price of the distribution network operator to the prosumers, respectively; 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, respectively; is the average value of the electricity sale price.

[0070] 1.2 Middle-layer model

[0071] The middle-layer model contains two core models: 1) an electric vehicle cluster-charging station selection evolutionary game model based on a dynamic charging service fee adjustment strategy is constructed to simulate the interactive decision-making process between electric vehicle users and charging stations; 2) an optimization scheduling model considering the internal source-load uncertainty of the prosumers is constructed, and finally the transaction results are fed back to the upper-layer model. The two models cooperate with each other to realize the optimization decision-making function of electricity trading.

[0072] 1.2.1 Electric vehicle cluster-charging station selection evolutionary game model

[0073] 1) Dynamic charging service fee adjustment strategy

[0074] To ensure a reasonable investment return period, a dynamic charging service fee adjustment strategy based on user occupancy rate is proposed. When the actual user occupancy rate is lower than the expected one, the dynamic charging service fee adjustment strategy is started to attract users; on the contrary, when the actual user occupancy rate exceeds the expected one and the internal operation pressure of the prosumers is large, the charging service fee is increased to limit the charging of some users. The dynamic charging service fee adjustment strategy is as follows:

[0075] (16)

[0076] is the adjustment round of the charging service fee; is the charging station in the th adjustment round; is the charging service fee change amount for the electric vehicle cluster of the th type; is the expected user occupancy rate set by the charging station , which is positively correlated with the internal photovoltaic capacity of the prosumers, i.e., the expected user occupancy rate is equal to the proportion of the internal photovoltaic capacity of the prosumers to the total photovoltaic capacity of the distribution network; is the actual user occupancy rate of the charging station , is the adjustment step of the charging service fee; is the number of charging stations; is the ​​​​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.

[0077] Charging service fee for the nth round of charging stations The calculation is as follows:

[0078] (17)

[0079] In the formula: , These are the upper and lower limits for charging service fees, respectively.

[0080] 2) Evolutionary game model

[0081] When selecting charging stations, electric vehicle clusters typically conduct multi-faceted evaluations, using charging price, user occupancy rate, and accessibility as key performance indicators. The charging price for electric vehicles is calculated as follows:

[0082] (18)

[0083] In the formula, Charging service fee for charging stations.

[0084] Taking into account the above three factors, establish Electric vehicle cluster selection number The utility model of a charging station is shown below:

[0085] (19)

[0086] In the formula: For utility assessment, 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.

[0087] 1.2.2 Optimize the scheduling model

[0088] Each prosumer aims to maximize its own profits, and the internal optimization scheduling model for prosumers is constructed as follows:

[0089] (20)

[0090] (twenty one)

[0091] (twenty two)

[0092] (twenty three)

[0093] (twenty four)

[0094] The following constraints must be met:

[0095] (25)

[0096] (26)

[0097] (27)

[0098] (28)

[0099] (29)

[0100] In the formula: For the benefit of the producers and consumers themselves, For producer-consumer demand response costs, The revenue generated by producers from selling electricity to distribution network operators. The cost of electricity purchased by producers and consumers from distribution network operators. Revenue from charging electric vehicle clusters; The unit scheduling cost for demand response load; for The actual dispatch power of the load demand response at any given moment; for The expected power consumption of the load at any given time. To provide charging load for electric vehicle clusters.

[0101] Equation (25) is the photovoltaic power constraint; Equations (26)-(27) are the demand response constraints; Equation (28) is the power balance constraint; Equation (29) is the power purchase and sale constraint. For photovoltaics Contributing effort at all times; For photovoltaics The predicted equivalent power output coefficient at time 10:00. Contribute to photovoltaic power; The total electricity demand of the demand response load during the dispatch cycle; and For demand response load in The maximum and minimum power demand at any given time are related to the user's requirements for comfort. for The load power generated and consumed at any given time. and respectively, are the upper limits of the purchased and sold power. and is a 0-1 variable to avoid simultaneous purchase and sale of electricity. The absolute value term in equation (21) is used to represent the deviation between the actual scheduled power and the expected power consumption, which is introduced by the auxiliary variable 、 and constraints (31), (32), which can be converted into the linear form shown in equation (30):

[0102] (30)

[0103] (31)

[0104] (32)

[0105] 1.3 Lower Model

[0106] 1.3.1 Objective Function

[0107] The lower model constructs a power distribution network second-order cone programming optimal power flow model, which optimizes the following equation for the power distribution network.

[0108] (33)

[0109] 1.3.2 Constraint Conditions

[0110] The constraint conditions include energy storage system constraints, reactive power compensation device constraints, power flow constraints, producer and consumer output constraints, and power distribution network gateway power constraints.

[0111] Among them, the producer and consumer output constraints are as follows: (34)

[0112] When the producer and consumer sell electricity to the power distribution network, if the power distribution network regulation capacity cannot meet the system safety demand, the producer and consumer output can be reduced at the necessary moment to ensure the safe and stable operation of the system.

[0113] 1.4 Deterministic Compact Expression

[0114] The second objective function in the upper model is calculated through the middle model and the lower model. In order to facilitate subsequent discussion, the optimization scheduling model of PCU and the lower model are first converted into the following deterministic compact form:

[0115] (35)

[0116] (36)

[0117] In the formula: is the feasible region of ; 、 is the coefficient vector corresponding to the objective function (20), (33); 、 、 、 、 、 、 and is the coefficient matrix corresponding to the variables under constraints; 、 、 、 is the constant vector; is the source load power prediction value; vector 、 and 、 are binary and continuous variables, respectively:

[0118] (37)

[0119] wherein, 、 denote the state of charge and the state of discharge of the energy storage system, respectively, and are the active and reactive power of each branch of the distribution network; is the node voltage; is the branch current.

[0120] Step 2: Construction of a multi-objective multi-stage stochastic-robust evaluation model of photovoltaic carrying capacity of distribution network considering uncertainty

[0121] The photovoltaic carrying capacity evaluation model proposed in step 1 is deterministic and can be solved by using conventional deterministic optimization methods. However, new energy and load have strong uncertainty. In step 2, the source-load double-sided uncertainty of distributed photovoltaic and load of the distribution network is considered, and a stochastic-robust evaluation model of photovoltaic carrying capacity of the distribution network is established.

[0122] In the middle and lower layer models, in order to cope with multiple uncertainties in the system, a two-stage stochastic-robust evaluation model is constructed to reduce the conservatism of the solution and reduce the dependence on complete uncertainty information. First, it is assumed that the fluctuation range of photovoltaic and load power is constrained by a box-type uncertainty set:

[0123] (38)

[0124] wherein: is the box-type uncertainty set constructed; 、 are the source load power prediction values of different typical days; 、 to introduce the source-load variable after uncertainty; 、 is the maximum value of source-load fluctuation. Equation (35) can be re-expressed as:

[0125] (39)

[0126] where: is the discrete probability distribution extracted from the clustered scenarios based on the generative adversarial network (GAN); the first half of the formula represents the optimal power flow problem of the distribution network, and the latter half corresponds to the internal optimization problem of the producer and consumer. The minimization of the outer layer of the latter half is the first-stage problem, and the optimization variable is ; the maximization-minimization of the inner layer is the second-stage problem, and the optimization variable is and , ; is the feasible region of , is the probability of the clustered scenario , appears, 、 is the corresponding continuous variable of the scenario .

[0127] Step 3: Model solution

[0128] The complex multi-objective multi-stage photovoltaic carrying capacity evaluation model with a multi-layer nested structure constructed by the present application involves multi-objective optimization and contains significant nonlinear characteristics. Therefore, the NSGA III-C&CG algorithm is used to solve the model, the upper model uses the NSGA III algorithm for solution, and the layer model and the lower model can be converted into a multi-stage stochastic robust optimization problem in the process of each iteration calculation, and the C&CG algorithm is used for solution.

[0129] Embodiment

[0130] To verify the effectiveness of the method proposed by the present application, the model effectiveness is verified by using the IEEE33 node system as shown in Figure 4 . The IEEE33 node system contains 4 regions, and the four producer and consumer PCUs are located in different regions. The source-load uncertainty adjustment parameter is set to 6, For 12. The development environment of Python 3.9 is used to train the GAN on the open source platform Pytorch. The system environment is Intel(R) Core(TM) i9-13900k CPU@3.00GHz, NVIDIA GeForce RTX 3060 (12GB) and 32G memory, MATLAB 2023b and GUROBI solver are used to solve the optimization problem. The population size of NSGA-III is set to 100, and the maximum number of iterations is 100.

[0131] Analysis of photovoltaic hosting capacity (PVHC) evaluation results

[0132] Figure 5 The pareto front diagram for photovoltaic hosting capacity evaluation. The membership function is used to classify the pareto solution set, and the hierarchical analysis method is used to calculate the comprehensive membership, and the solution with the highest comprehensive membership is selected as the optimal solution. The cost of each subject and its corresponding photovoltaic capacity under the optimal solution are shown in Table 1. In addition to the operating cost, each producer and consumer PCU needs to consider the investment and construction cost of photovoltaic, and the cost of unit capacity photovoltaic is set to 3 million yuan / MW in the present application, and it is calculated into daily cost based on the equivalent coefficient. From the table, it can be seen that the operating cost of each interest subject decreases to different degrees after the photovoltaic is connected to the distribution network. The active distribution system operator (ADSO) reduces the external power purchase cost by integrating the photovoltaic output of each producer and consumer PCU, and the overall cost decreases by 8.84%. After connecting photovoltaic, each producer and consumer PCU reduces its dependence on ADSO for power supply through self-generation and self-use and surplus electricity on the network, and enhances its bargaining power, so the cost reduction of each producer and consumer PCU is much higher than that of ADSO. The photovoltaic (PV) capacity of PCU1 and PCU4 is higher because the load level in this area is relatively high, and the energy storage and AM measures can effectively improve the photovoltaic consumption capacity of the distribution network.

[0133] Table 1 Photovoltaic hosting capacity evaluation results

[0134]

[0135] To analyze the influence of energy storage and AM measures on the PVHC evaluation results, the present application quantitatively compares and analyzes the four scenarios (combination of energy storage and AM measures) shown in Table 2. The cost composition of ADSO under different scenarios is shown in Table 3, and the pareto optimal solution of each scenario is shown in Table 4.

[0136] Table 2 Comparison of different scenarios

[0137]

[0138] Table 3 ADSO cost of different scenarios

[0139]

[0140] Table 4 Evaluation results of different scenarios

[0141]

[0142] Scenario 1 does not consider any carrying capacity improvement measures, so its PVHC evaluation result is low, and the light rejection rate is high.

[0143] Scenario 2 only considers energy storage for evaluation. Compared with scenario 1, the application of energy storage reduces the operation cost by 3.41%, the light rejection rate decreases by 9.88%, and the PVHC evaluation result increases by 8.82%. This shows that energy storage effectively improves the system economy and energy utilization by smoothing the photovoltaic output fluctuation. However, the voltage satisfaction cost of scenario 2 reaches the highest value of the fourth scenario, indicating that the voltage quality of the distribution network is poor at this time. Therefore, although the application of energy storage alone improves the economy and consumption capacity compared with scenario 1, it still has limited improvement on the light rejection rate without the support of AM.

[0144] Scenario 3 only considers AM for evaluation. AM measures can improve the stability of the power grid voltage, and the light rejection rate decreases by 9.36% compared with scenario 1. However, due to the lack of energy storage for power fluctuation smoothing, the PVHC evaluation result only increases by 1.1%, and the operation cost increases by 0.56%. This shows that AM measures can reduce the light rejection rate through voltage management, but its improvement of carrying capacity is still limited by the system's ability to consume short-term photovoltaic output fluctuations.

[0145] Scenario 4 (the model proposed in the present application) considers both energy storage and AM. Compared with scenario 1, the operation cost decreases by 4.24%, the PVHC evaluation result increases by 10.2%, and the light rejection rate decreases by 23.05%. This result shows that the power buffering capacity of energy storage effectively amplifies the voltage regulation benefit of AM, and the two work together to significantly improve the performance boundary of single carrying capacity improvement strategy. Compared with scenario 2, scenario 4 has a 0.86% decrease in cost, a 1.4% increase in PVHC, and a 23.05% decrease in light rejection rate. This is because the AM measures optimize the energy storage output curve, reduce line losses, and reduce the voltage satisfaction cost. Therefore, the model proposed in the present application can reduce the operation cost and light rejection rate while maximizing the carrying capacity of distributed photovoltaic access to the distribution network.

Claims

1. A stochastic-robust evaluation method for the photovoltaic carrying capacity of an active distribution network based on hybrid game theory, characterized in that: Includes the following steps: Step 1: Construct a three-layer photovoltaic carrying capacity model based on multi-agent evolution and master-slave hybrid game theory. This model adopts a three-layer evaluation architecture: the upper-layer model starts from the perspective of the distribution network operator and makes optimization decisions on photovoltaic capacity allocation and power purchase and sale pricing strategies; the middle-layer model and the lower-layer model simulate system production based on the power purchase and sale pricing and photovoltaic capacity decided by the upper-layer model. Among them, the middle-layer model solves the power trading problem between the distribution network operator and the producers and consumers, while the lower-layer model verifies the safety constraints of the distribution network operation through a second-order cone programming optimal power flow model. Step 2: Considering the source-load uncertainties of distributed photovoltaic and load in the distribution network, establish a stochastic-robust evaluation model of photovoltaic carrying capacity of the distribution network based on the three-layer photovoltaic carrying capacity model in Step 1; Step 3: Model Solving: In the middle-level model, the electric vehicle cluster selects the charging station with the highest utility evaluation value for charging. Each producer-consumer aims to maximize its own benefits based on the purchase and sale price of electricity and the photovoltaic capacity, and feeds back the electricity purchased and sold by the distribution network operator to the producer-consumer to the upper-level model. The lower-level model verifies the safety constraints of the distribution network operation and feeds back the actual grid-connected output of each producer-consumer to the upper-level model. The objective function of the upper-level model involves photovoltaic carrying capacity, distribution network operator operating costs, and curtailment rate; The photovoltaic carrying capacity assessment considers maximizing the total installed capacity of distributed photovoltaic power in the distribution network: In the formula: This represents the total installed capacity of distributed photovoltaic power. Let be the photovoltaic capacity at node i in the distribution network; For photovoltaic grid connection nodes; The photovoltaic carrying capacity assessment process considers the operating costs of distribution network operators, which are equivalent to the electricity purchase costs from the upstream power grid. Electricity purchase costs from producers and consumers Energy storage operating costs User voltage satisfaction cost Active management of call costs Electricity sales revenue from producers and consumers Difference: , , , , , , In the formula: For the operating costs of distribution network operators, This represents the number of time nodes; and These represent the electricity purchase price and the amount of electricity purchased by the distribution network operator and the upstream power grid, respectively. and These refer to the electricity purchased and sold by the power distribution network operator from producers and consumers, respectively. and These refer to the electricity purchase price and the electricity sales price from producers to consumers by the power distribution network operator; Cost per unit power output for energy storage; and 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; To take into account the unit operating cost of on-load tap changers; To account for the number of on-load tap changer operations; It is the set of all load nodes in the distribution network system; For a parallel capacitor bank, the set of nodes is provided. The set of nodes equipped with static var compensators; As a balancing node in the distribution network system, A collection of energy storage grid-connected nodes; For the collection of grid-connected nodes of various producers and consumers; To compensate users for losses caused by voltage deviations not meeting requirements, In the formula: The voltage satisfaction cost coefficient; This refers to the grid-connected power of each node in the distribution network; This represents the user's voltage satisfaction value. Node voltage; To minimize the light rejection rate, In the formula: For light rejection rate, The actual grid-connected power output of each producer and consumer is calculated from the lower-level model; The middle-layer model constructs an evolutionary game model for the selection of electric vehicle clusters and charging stations based on a service fee adjustment strategy to simulate the interactive decision-making process between electric vehicle clusters and charging stations; it also constructs an optimized scheduling model that considers the uncertainty of source load within the producer-consumer group, and finally feeds the transaction results back to the upper-layer model. The construction process of the electric vehicle cluster-charging station selection evolutionary game model is as follows: First, a dynamic charging service fee adjustment strategy based on user occupancy is proposed. The dynamic charging service fee adjustment strategy is as follows: In the formula: Adjustment rounds for charging service fees; For the first Charging stations on wheels Regarding the first Changes in charging service fees for electric vehicle clusters; 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; then the... Charging service fee at electric vehicle charging stations The calculation is as follows: In the formula: , These are the upper and lower limits for charging service fees, respectively. For the first Charging service fee at electric vehicle charging stations; When selecting charging stations, electric vehicle clusters use three factors as user evaluation indicators: charging price, user occupancy rate, and transportation convenience. The charging price for electric vehicles is calculated as follows: In the formula, Charging service fees for charging stations; taking into account the above three factors, establish Electric vehicle cluster selection number A utility model for a charging station. In the formula: For utility assessment, 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 value of each indicator; the electric vehicle cluster selects the charging station with the highest utility evaluation value for charging. The process of constructing the optimized scheduling model is as follows: Each producer-consumer aims to maximize its own revenue, and constructs the internal optimized scheduling model for the producer-consumer as follows: , , , , The following constraints are satisfied: , , , , In the formula: For the benefit of the producers and consumers themselves, For producer-consumer demand response costs, For the revenue of producers and consumers from selling electricity to distribution network operators, The cost of electricity purchased by producers and consumers from distribution network operators, Revenue from charging electric vehicle clusters; The unit scheduling cost for demand response load; for The actual dispatch power of the load demand response at any given moment; for The expected power consumption of the load at any given time. Charging load for electric vehicle clusters; For photovoltaics Contributing effort at all times; For photovoltaics Predicted equivalent power output coefficient at time step; Contribute to photovoltaic power; The total electricity demand of the demand response load during the dispatch cycle; and For demand response load in Maximum and minimum electricity demand at any given time; for The load power within the consumer at all times; and These are the upper limits for electricity purchases and electricity sales, respectively. and 0-1 variables; The lower-level model constructs a second-order cone programming optimal power flow model for the distribution network, and optimizes it for distribution network operators with the following formula as the objective. The constraints include energy storage system constraints, reactive power compensation equipment constraints, power flow constraints, producer-consumer output constraints, and distribution gateway power constraints. Among them, the producer-consumer output constraints are as follows: ; The upper-level model constraints include photovoltaic installation capacity constraints and electricity price constraints at each node. Photovoltaic installation capacity constraints at each node: In the formula: For distribution network nodes The upper limit of the installed photovoltaic capacity; Constraints should be placed on the electricity purchase and sales prices charged by power distribution network operators to producers and consumers. , , , In the formula: and These represent 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. and These represent the lower and upper limits of the electricity price that distribution network operators sell to producers and consumers, respectively. This represents the average electricity price.

2. The stochastic-robust evaluation method for photovoltaic carrying capacity of active distribution networks based on hybrid game theory as described in claim 1, characterized in that: Step 2, establishing a stochastic-robust evaluation model for the photovoltaic carrying capacity of the distribution network, involves first transforming the optimal scheduling model and the lower-level model into a deterministic compact form: , In the formula: for The feasible domain; , To optimize the scheduling model, the coefficient column vector corresponding to the lower-level model; , , , , , , and This is the coefficient matrix of the variables under the corresponding constraints; , , , A constant column vector; The source load power prediction value; vector , and , They are binary and continuous variables, respectively: In the formula, and These represent the charging and discharging states of the energy storage system, respectively. and These are the active and reactive power of each branch of the distribution network, respectively. Node voltage; Branch current; Assume that the fluctuation range of photovoltaic and load power is constrained by a box-shaped uncertainty set: In the formula: For constructing a box-shaped uncertain set; , For different typical daily source load power prediction values; , To introduce source load variables with added uncertainty; , This represents the maximum value of the source load fluctuation. The deterministic compact form is restated as follows: In the formula: This is the discrete probability distribution extracted after scene clustering based on generative adversarial networks; the first part of the formula represents the optimal power flow problem of the distribution network, while the second part corresponds to the internal optimization problem of the prosumers. The minimization of the outer layer of the second part is the first-stage problem, and the optimization variables are... The inner-layer maximum / minimum problem is a second-stage problem, with the optimization variables being... and , ; for feasible domain, Post-clustering scenario The probability of occurrence , For the scene The corresponding continuous variables.

3. The stochastic-robust evaluation method for photovoltaic carrying capacity of active distribution networks based on hybrid game theory as described in claim 2, characterized in that: The upper-level model is solved using the NSGAⅢ algorithm. In each iteration, the upper-level and lower-level models are transformed into multi-stage stochastic robust optimization problems and solved using the C&CG algorithm.

Images