Electric vehicle charging station double-layer pricing method based on multi-agent master-slave game

Abstract

The invention discloses an electric vehicle charging station double-layer pricing method based on a multi-agent master-slave game. The method comprises the following steps: constructing a road network model; according to the EV appearance time period information, the SOC information and the charging probability selection, analyzing EV charging behavior influence factors; evaluating the response capability of the EV; the schedulable capability of the charging station is predicted, and basic data is provided for a pricing strategy; establishing a charging station double-layer pricing model based on a stackelberg game, wherein the charging station double-layer pricing model comprises an outer-layer DSO optimization model and an inner-layer EVCS-EV optimization model; and solving the established double-layer pricing model of the charging station based on the stackelberg game through a double-layer iteration method. The pricing method can reduce the cost of the EV user and the power distribution network while improving the profit of the charging station, and gives consideration to the benefits of all subjects.

Description

Technical Field

[0001] The present invention relates to the field of pricing strategies for electric vehicle charging stations, and in particular to a double-layer pricing method for electric vehicle charging stations based on multi-agent master-slave game. Background Art

[0002] Electric vehicles (EVs) have developed rapidly due to their low carbon emission characteristics. As a bridge connecting EVs and power grids, electric vehicle charging stations (EVCSs) can guide the charging and discharging of large-scale EVs by formulating reasonable pricing strategies, thereby improving the economic benefits of EVCSs and the safety and stability of power grids while reducing the costs of EV users, thus achieving a win-win situation for multiple entities. EV driving behavior simulation and charging demand prediction are the primary tasks for formulating pricing strategies and orderly EV charging and discharging scheduling.

[0003] Among them, literature [1]: Wang Haolin, Zhang Yongjun, Mao Haipeng. Electric vehicle charging load prediction method based on moment-to-moment charging probability [J]. Electric Power Automation Equipment, 2019, 39(3): 207-213. Through the study of EV travel and charging habits, a probabilistic model of charging load influencing factors was established, but the impact of traffic factors on EV travel was not considered.

[0004] Reference [2]: Shao Yinchi, Mu Yunfei, Yu Xiaodan, et al. Spatiotemporal prediction of electric vehicle charging load under the “vehicle-road-network” model and its impact on distribution network flow [J]. Proceedings of the CSEE, 2017, 37(18): 5207-5219+5519. Reference [3]: Zhang Meixia, Zhang An, Yang Xiu, et al. Electric vehicle charging load prediction based on traffic equilibrium theory [J / OL]. China Southern Power Grid Technology, 1-12 [2024-08-08]. http: / / kns.cnki.net / kcms / detail / 44.1643.TK.20240711.1735.014.html. Considering the impact of dynamic road network on driving behavior, a method for predicting EV charging load is proposed by combining traffic network topology characteristics and speed-flow model. However, the above literature only considers the impact of travel habits and traffic factors on EV charging demand, ignoring the ability and willingness of EV users to participate in demand response (DR), making it difficult to accurately characterize the actual dispatchable potential of EV.

[0005] Reference [4]: ​​Zhu Yongsheng, Chang Wen, Wu Dongya, et al. Master-slave game optimization scheduling strategy considering the interaction between charging and discharging integrated station and electric vehicles [J]. Power System Protection and Control, 2024, 52(7): 157-167. Based on consumer psychology, the mechanism of EV users' response to charging prices is studied, and an EV charging price responsiveness model is established. On this basis, Reference [5]: Dong X, Wei X, Zu G, et al. The charge-discharge compensation pricing strategy of electric vehicle aggregator considering users response willingness from the perspective of Stackelberg game [J / OL]. IET Smart Grid, 2024, 7(3): 277-293. https: / / doi.org / 10.1049 / stg2.12148. The discharge price responsiveness is modeled, and EVs are guided to discharge to the grid through price incentives, which fully taps the dispatchable potential of EVs, but the impact of the traffic side on charging behavior is not discussed.

[0006] In recent years, there have been many papers that have studied the pricing strategies of EVCS.

[0007] Reference [6]: Ou Mingyong, Chen Zhongwei, Tan Yudong, et al. Optimization of electric vehicle charging load based on peak-valley time-of-use electricity prices [J]. Journal of Electric Power Science and Technology, 2020, 35(5): 54-59. Based on the charging needs of EV users, a peak-valley time-of-use electricity price strategy is proposed to guide EV orderly charging.

[0008] Reference [7]: Yang Shuai, Dai Zhaohua, Guo Ai, et al. Fast charging pricing mechanism considering load spatial balance and charging station cooperation game [J]. Automation of Electric Power Systems, 2024, 48(7): 190-200. Considering the subjective willingness of users, combined with the road network model and speed-flow model, a dynamic pricing strategy for charging stations is proposed.

[0009] Reference [8]: Moradipari A, Alizadeh M. Pricing and Routing Mechanisms for Differentiated Services in an Electric Vehicle Public Charging Station Network [J]. IEEE Transactions on Smart Grid, 2020, 11(2): 1489-1499. From the perspective of EVCS, differentiated services and incentives are formulated to maximize the profits of charging stations. However, the above literature only considers the interaction between EV users and EVCS, and does not consider the impact on the distribution network. While charging, EVs will cause load fluctuations in the distribution network, increasing the operating costs of the distribution system operator (DSO).

[0010] Reference [9]: Luo C, Huang YF, Gupta V. Stochastic Dynamic Pricing for EV Charging Stations With Renewable Integration and Energy Storage [J]. IEEE Transactions on Smart Grid, 2018, 9(2): 1494-1505. Taking into account the fluctuation of charging demand and the consumption of new energy, the charging station price is formulated by using stochastic dynamic programming and greedy algorithm, which reduces the impact of charging load on the power grid.

[0011] Reference

[10] : Xia Xin, Zhong Hao, Zhang Lei, et al. Two-layer optimization strategy for electric vehicles participating in microgrid dispatch considering dynamic electricity prices [J]. Electric Power Engineering Technology, 2024, 43(3): 140-150. Using dynamic electricity prices to guide EV charging demand, shift net load fluctuations, and reduce the economic impact on microgrid operation. The above charging station dynamic pricing strategies are mostly limited to a single or two entities, lacking consideration of the interests of multiple entities.

[0012] Reference

[11] : Li K, Shao C, Zhang H, et al. Strategic Pricing of Electric Vehicle Charging Service Providers in Coupled Power-Transportation Networks[J]. IEEE Transactions on Smart Grid, 2023, 14(3): 2189-2201. Taking into account the interests of EV, EVCS and DSO, a charging station pricing model is established by combining user equilibrium theory and node marginal price (distribution locational marginal price, DLMP) theory, but the formulation of discharge price is not discussed. Summary of the invention

[0013] To solve the above problems, the present invention proposes a two-tier pricing method for electric vehicle charging stations based on multi-agent master-slave game. This pricing method can increase the profits of charging stations while reducing the costs of EV users and distribution networks, taking into account the interests of all entities.

[0014] The technical solution adopted by the present invention is:

[0015] The two-tier pricing method for electric vehicle charging stations based on multi-agent master-slave game includes the following steps:

[0016] Step 1: Build a road network model;

[0017] Step 2: Analyze the factors affecting EV charging behavior based on EV appearance time information, SOC information, and charging probability selection;

[0018] Step 3: Evaluate EV responsiveness;

[0019] Step 4: Predict the dispatchable capacity of the charging station;

[0020] Step 5: Establish a two-layer pricing model for charging stations based on Stackelberg game, including an outer DSO optimization model and an inner EVCS-EV optimization model;

[0021] Step 6: Solve the two-layer pricing model of charging stations based on Stackelberg game established in step 5 through a two-layer iterative method.

[0022] In step 1, the road network model is a dynamic road network model, which is expressed as:

[0023]

[0024] In formula (1), G represents the road network set; V represents the road network node set, with a total of u nodes; E represents the road segment set in the road network; H represents the time period set, dividing the whole day into T time periods; W represents the road segment weight set; v i represents the i-th road network node; u represents the number of nodes v ij represents the road section connecting the road network nodes i and j; t represents the tth time period among T time periods; T represents the division of the whole day into T time periods w ij (t) represents the road section v during time period t ij The weight of

[0025] The connection relationship between nodes in the road network set G is described by the adjacency matrix D. The element d of the adjacency matrix D is ij The expression of (t) is:

[0026]

[0027] In formula (2): v j represents the jth road network node;

[0028] The travel time is selected as the road resistance for modeling, and the speed-flow model is introduced; the EV driving speed v ij The expression of (t) is:

[0029]

[0030] In formula (3): v ij,max is the zero flow velocity of road ij; C ij is the traffic capacity of road ij; Q ij (t) is the traffic volume of road ij in time period t; k1, k2, k3 are road grade adaptive coefficients; ω represents the road saturation coefficient

[0031] Section v during period t ij The weight w ij The expression of (t) is:

[0032]

[0033] In formula (4): L ij is the length of road ij; R i is the waiting time for the traffic light at intersection i.

[0034] In the step 2,

[0035] 2.1: EV appearance period information, as follows:

[0036] The Gaussian mixture model is used to describe the distribution of EV travel time periods:

[0037]

[0038] In the above formula, t represents the travel time, f(t) represents the travel time distribution function; K represents the number of Gaussian distribution; χ i , μ i and σ i Respectively represent the weight, mean and standard deviation of the i-th Gaussian distribution; i represents the i-th Gaussian distribution;

[0039] is the probability density function of Gaussian distribution;

[0040] 2.2: SOC information, i.e. the initial state of charge of EV, is a random variable with Gaussian distribution, and its probability density function is:

[0041]

[0042] In formula (7), s represents the initial SOC of EV, f(s) represents the probability density function of the initial SOC of EV; μ s and σ s denote the mean and standard deviation respectively; is the probability density function of Gaussian distribution;

[0043] The power consumption of EV increases linearly with the driving distance. The SOC of EV at time t is:

[0044] S t =S t-1 -△l△S (8);

[0045] In formula (8): S t represents the SOC of EV at time t; S t-1 It represents the remaining power of EV at time t-1; Δl represents the driving distance of EV in the period [t-1, t]; ΔS represents the power consumption per kilometer.

[0046] 2.3: EV user charging behavior is mainly affected by the SOC value. The lower the SOC, the greater the probability that the user will choose to charge. The charging probability selection function is:

[0047]

[0048] In formula (9): S up and S down They represent the upper and lower SOC thresholds that trigger charging selection respectively.

[0049] In step 3, the evaluation of EV responsiveness specifically includes:

[0050] According to the demand response time T DR and the grid-connected period T of the i-th EV i Grid, calculate the time period during which the i-th EV can participate in demand response for:

[0051] T i DR =T DR ∩T i Grid (10);

[0052] According to the initial SOC value of the i-th EV connected to the charging pile and the expected value of charging end Calculate the shortest charging time t i,min :

[0053]

[0054] In formula (11): E i and P i,max They represent the battery capacity and maximum charging power of the i-th EV respectively.

[0055] like The charging demand response period T released by the power grid ch Or discharge demand response period T dis If there is overlap, the EV is considered to be responsive.

[0056]

[0057] In the above formula: EV pos,ch and EV pos,dis Respectively, in T ch and T dis The set of EVs that have the ability to respond during the time period; len(x) represents the number of elements in the set x; N represents the total number of electric vehicles;

[0058] In step 4, the specific steps of predicting the dispatchable capacity of the charging station are as follows:

[0059] First, the road network parameters and DR period are set, and the travel time and initial SOC of each EV are generated through Monte Carlo sampling. The OD matrix is ​​read to obtain the starting and ending point information; the OD matrix is ​​used to record the number of trips or travel distance from a starting point to an end point.

[0060] The Dijkstra algorithm is used to plan the driving route, the road travel time is calculated according to the speed-flow model, and the EV driving is simulated. According to formula (9), it is determined whether there is a charging demand. If so, the nearest charging station is selected to drive in and record the load information, and the demand response capability of the EV is reported.

[0061] In step 5, the outer DSO optimization model includes:

[0062] (1) DSO model:

[0063] The goal of DSO is to minimize its own operating costs, including the output cost of distributed gas turbine units and the cost of purchasing electricity from the main grid. The objective function is:

[0064]

[0065] In formula (14): F DSO is the DSO operating cost; dg For generator collection; is the generator output at node j during period t; a and b are energy production cost coefficients; ρ is the agreed electricity price for purchasing electricity from the main grid; S(0) represents the set of nodes connected to the main grid; P 0j,t Indicates the power purchased from the main grid during period t.

[0066] The DSO model satisfies power balance constraints and node voltage constraints:

[0067] 1) Power balance constraints:

[0068]

[0069] In formula (15) to formula (19): and They represent the charging and discharging power at node i during period t; P ij,t and Q ij,t They represent the active and reactive power flowing from node i to node j respectively; F(i) and S(i) represent the parent node and child node set of node i respectively; and represent the active and reactive base loads of the node respectively; and Respectively represent the upper and lower limits of the generator active power; and Respectively represent the upper and lower limits of the generator reactive power; P ij,max and P ij,min Respectively represent the upper and lower limits of line load;

[0070] 2) Node voltage constraints:

[0071]

[0072] In formula (20) and formula (21): V j,t represents the voltage at node j during period t; V i,t represents the voltage at node i during period t; Ω line and Ω node are distribution network lines and node sets respectively; R ij and X ijRespectively represent the line resistance and reactance between the distribution network branches ij; V i,max and V i,min Respectively represent the upper and lower limits of node voltage; P ij,t and Q ij,t They represent the active and reactive power flowing from node i to node j respectively.

[0073] (2) Model reconstruction:

[0074] DLMP reflects the marginal cost generated when the distribution network node increases the unit load. Therefore, DLMP is used as the purchase price and sales price of electricity from EVCS to DSO, which can be obtained by calculating the dual variable of formula (15). The outer DSO optimization model is reconstructed through the dual theory and KKT conditions to simplify the difficulty of solving the model. The specific steps are as follows:

[0075] A1: Take the dual variables of the constraint conditions as Lagrange multipliers and construct the Lagrangian function L of the lower model, as shown in formula (22):

[0076]

[0077] In formula (22), is the dual variable of formula (15); is the dual variable of formula (16); is the formula (17) The dual variable of is the formula (17) The dual variable of is the formula (18) The dual variable of is the formula (18) The dual variable of is P in formula (19) ij,min ≤P ij,t The dual variable of is P in formula (19) ij,t ≤P ij,max The dual variable of is the dual variable of formula (20); is V in formula (21) i,min ≤V i,t The dual variable of is V in formula (21) i,t ≤V i,max The dual variable of

[0078] represents the basic active load of node i during period t; P qi,t , represents the active power flowing from node q to node i during period t; P ij,t, represents the active power flowing from node i to node j during period t; represents the basic reactive load of node i during period t; Q qi,t , represents the active power flowing from node q to node i during period t; Q ij,t , represents the reactive power flowing from node i to node j during period t; P ij,t , represents the active power flowing from node i to node j during period t; V F(i),t represents the parent node voltage of node i during period t; Q ij,t represents the reactive power flowing from node i to node j during period t; V i,max and V i,min Respectively represent the upper and lower limits of the voltage of node i;

[0079] A2: Let the partial derivative of L with respect to each decision variable be equal to zero, and obtain the KKT condition:

[0080]

[0081] In the above formula, is the dual variable of formula (16); The node j dual variable of expression (15); The node i dual variable in (15); is P in formula (19) ij,min ≤P ij,t The dual variable of is P in formula (19) ij,t ≤P ij,max The dual variable of represents the dual variable of equation (20);

[0082] and P i dg,min Respectively represent the upper and lower limits of the generator active power; and Respectively represent the upper and lower limits of the generator reactive power Respectively represent the upper and lower limits of the line load between nodes i and j;

[0083] A3: Add KKT conditions to the constraints, and the outer DSO optimization model can be restated as:

[0084] OP:minobj.(14)

[0085]

[0086] In the above formula, OP represents the outer model; minobj.(14) represents the minimum value of formula (14).

[0087] A4: Linearization: Equations (28) to (35) contain complementary slack terms, which are converted into linear constraints using the Big M method. Take equation (28) as an example:

[0088]

[0089] In the above formula, M is a sufficiently large positive number; χ is a binary variable.

[0090] A5: Solve the outer DSO optimization model to obtain λ Pi,t That is DLMP, which is used as the electricity purchase cost and electricity selling price of the charging station.

[0091] In step 5, the inner EVCS-EV optimization model includes:

[0092] (1) EV user response willingness model:

[0093] Based on consumer psychology theory, the relationship between EV response willingness and price can be expressed by a piecewise linear function:

[0094]

[0095] Where: and They represent the EV charging and discharging demand responsiveness during period t; ch,high and π ch,low Respectively represent the upper and lower price thresholds that trigger charging demand response; π dis,high and π dis,low They represent the upper and lower price thresholds for triggering discharge demand response, respectively; represents the price value that triggers the charging demand response; Represents the price value that triggers discharge demand response.

[0096] When an EV meets the conditions of both response capability and response willingness, the EV is added to the response user cluster to accept the scheduling arrangement of the charging station.

[0097]

[0098] In formula (41) and (42), EV t res,ch and EV t res,dis They represent the set of EVs that respond to charging and discharging prices during period t; U(0,1) represents a random number uniformly distributed between [0,1]; T i Grid represents the time period during which the i-th EV is connected to the grid; EV pos,ch Indicates that in T ch The EV set with responsiveness during the time period; EV pos,dis Indicates that in Tdis The time period is the set of EVs that have the ability to respond; t represents the tth time period among the T time periods throughout the day; i represents the i-th EV.

[0099] (2)EVCS model:

[0100] The goal of EVCS is to maximize its own profits, including the revenue from electricity sales and the cost of electricity purchase. The objective function is:

[0101]

[0102] In formulas (43) to (45): They represent the profit, electricity sales revenue and electricity purchase cost of charging station n respectively; and is the charging and discharging power of charging station n during period t; determined by equations (46) to (47); and is the decision variable, which represents the charging and discharging price of the charging station; and They represent the electricity price of the charging station purchasing electricity from the power grid and the electricity price of the charging station selling electricity to the power grid respectively; The compensation cost obtained by the charging station for mobilizing EVs to participate in V2G; △t represents the time change. T represents that the whole day is divided into T time periods, and the maximum t is T.

[0103] The EVCS model constraints mainly include charging and discharging power constraints and charging and discharging electricity price constraints.

[0104] ①.Charge and discharge power constraints:

[0105]

[0106] In formulas (46) to (49): EV n represents the set of EVs in charging station n; represents the charging and discharging power of the i-th EV during period t, which is determined by the calculation part of the EV model; and They represent the charging and discharging states of the EV, respectively, and are determined by the calculation part of the EV model; and Respectively represent the maximum charging and discharging power of the charging station.

[0107] ②.Charge and discharge electricity price constraints

[0108]

[0109] In formulas (50) to (51): and They represent the upper and lower limits of the charging price of the charging station respectively; and They represent the upper and lower limits of the discharge price of the charging station respectively.

[0110] (3) EV model:

[0111] Assuming that the i-th EV is at charging station n, the EV arranges a charging plan according to the charging and discharging electricity prices released by EVCS, and the objective function is to minimize the charging cost:

[0112]

[0113] In formulas (52) to (55): represents the total charging cost of the i-th EV; and They represent the charging cost, discharging benefit and battery loss cost of EV respectively; is the decision variable, which represents the charging and discharging power of electric vehicle i during period t. Indicates charging. Indicates discharge; and are binary variables of the charging and discharging status of electric vehicle i during period t, 1 indicates charging / discharging, and 0 indicates not charging / discharging;

[0114] Determined by equation (56) and equation (57); c ch and c dis They represent the energy loss coefficient of battery charging and discharging respectively.

[0115]

[0116] The EV model mainly meets the charging and discharging power constraints, charging and discharging state constraints and power constraints.

[0117] a. Charge and discharge power constraints:

[0118]

[0119] In formula (58): represents the maximum power supported by the i-th EV; EV t res,dis represents the set of electric vehicles that respond to the discharge electricity price during period t.

[0120] b. Power Constraints:

[0121]

[0122] S i,min ≤S i,t ≤S i,max (62);

[0123] In formulas (59) to (62): represents the expected value of the i-th EV when charging is completed; represents the initial SOC value of the i-th EV connected to the charging pile; E i represents the battery capacity of the i-th EV; S i,t+1 represents the SOC of the i-th EV in period t+1; S i,t is the SOC of the i-th EV in period t; η ch and η dis Respectively represent the charging and discharging efficiency of EV; S i,min and S i,max They represent the minimum and maximum SOC values ​​of the i-th EV respectively.

[0124] (4) Reconstruction of the inner EVCS-EV optimization model:

[0125] The inner EVCS-EV optimization model can be viewed as a two-layer optimization problem, with EVCS at the upper layer and EV at the lower layer. When solving the EV objective function, the charging and discharging price of EVCS can be regarded as a constant. Therefore, EV optimization can be viewed as a linear problem, which is converted into EVCS constraint conditions through the Karush-Kuhn-Tucker (KKT) conditions. The KKT conditions are as follows:

[0126]

[0127]

[0128] 0≤S i,t -S i,min ⊥τ9≥0 (70);

[0129] 0≤S i,max -S i,t ⊥τ 10 ≥0(71);

[0130] In formulas (63) to (71): τ 1,t , τ 2,t , τ 3,t , τ 4,t , τ 5,t , τ 6,t , τ 7,t , τ 8,t , τ 9,t , τ 10,t are the dual variables of equations (58) to (62) respectively; and They represent the charging and discharging prices of charging station m respectively;

[0131] The game process between EVCS-EV can be transformed into a mixed integer linear programming problem:

[0132] IP:minobj.(43)

[0133]

[0134] In formula (72), IP represents the inner model; minobj.(43) represents the minimum value of formula (43);

[0135] Nonlinear terms in the EVCS model and It can be convexified by the McCormick envelope to For example:

[0136]

[0137] In formula (73): is the charging power of charging station n during period t; Indicates the lower limit of charging price of the charging station; Indicates the upper limit of charging price at the charging station; Indicates the maximum charging power of the charging station;

[0138] Through formula (73), the nonlinear term Replace with Equations (64) to (71) contain complementary relaxation terms, which can be linearized by the SOC information calculation method.

[0139] In step 5, the game equilibrium of the two-tier pricing model of charging stations based on the Stackelberg game is proved as follows:

[0140] When the two-tier pricing model of charging stations based on Stackelberg game meets the following conditions, there is a unique Nash equilibrium solution:

[0141] (1) The objective function of each subject in the game model is a non-empty, continuous function of its strategy set.

[0142] (2) The follower objective function is a continuous concave / convex function with respect to its strategy set.

[0143] prove:

[0144] (1) The objective functions of DSO, EVCS, and EV are all non-empty, continuous functions of their strategy sets, so Condition 1 is satisfied.

[0145] (2) The objective functions of EVCS and EV are linear functions of their strategy sets. According to the definition of convexity and concavity, linear functions are both convex functions and concave functions, so condition 2 is satisfied.

[0146] Therefore, the two-tier pricing model of charging stations based on Stackelberg game proposed in the present invention has a unique equilibrium solution, and the proof is complete.

[0147] In step 6, the two-layer game solution process is as follows:

[0148] The two-layer iterative method solves the inner EVCS-EV optimization model and the outer DSO optimization model in turn;

[0149] In the outer layer, solve the outer DSO optimization model and obtain the DLMP of each node (k) ; Each EVCS shall follow DLMP (k) Initialize the price, solve the inner EVCS-EV optimization model, and recalculate DLMP (k) ; If DLMP (k) -DLMP (k-1) <ε1, the DLMP clearing market of each node is determined, and the inner EVCS-EV optimization model is entered for solution. Otherwise, it is iterated again.

[0150] In the inner EVCS-EV optimization model, the user response willingness is first calculated based on the predicted EVCS dispatchable potential, and the EV response cluster is updated; then the inner EVCS-EV optimization model is solved to obtain the charging station price strategy and revenue F EVCS(a) If F EVCS (a) -F EVCS(a-1) <ε2, indicating that the strategy is optimal, and the EV load of the charging station and the node continues to be calculated, otherwise it is iterated again. The outer DSO optimization model and the inner EVCS-EV optimization model established in the present invention are both mixed integer programming, which can be solved by calling commercial solvers such as Gurobi.

[0151] The present invention provides a double-tier pricing method for electric vehicle charging stations based on multi-agent master-slave game, and the technical effects are as follows:

[0152] 1) The charging station pricing strategy proposed in the present invention can take into account the interests of all parties, increase the profit of EVCS and reduce the cost of EV and DSO;

[0153] 2) By optimizing the EVCS pricing strategy, the present invention can transfer EV loads in time and space, reduce peak loads, increase valley loads, and make the overall load distribution more balanced, thereby improving the stability and economy of the power system.

[0154] 3) Step 1 of the present invention uses a dynamic road network model to model the road network, and combines the speed-flow model to update the road network information in real time, which can describe the changing rules of traffic flow at different times. It is more practical to use the dynamically updated road network information to plan the EV driving path.

[0155] The advantage of step 1 is that it introduces the time dimension into the calculation of road section weights through dynamic road network modeling, and combines the speed-flow model and road characteristics to dynamically describe the law of traffic flow changes over time. Compared with traditional static models, this method improves the ability to describe actual traffic conditions, especially in situations with obvious dynamic characteristics such as peak and off-peak hours. In addition, the weight calculation formula organically combines multiple factors such as road length, vehicle speed, and traffic light delay, providing a basis for EV path planning, reflecting its flexibility in practical applications.

[0156] 4) Step 2 of the present invention introduces a Gaussian mixture model to describe the characteristics of the EV travel stage, and combines the analysis of the state of charge (SOC) and the probability of charging selection to provide multi-dimensional dynamic information support for modeling and optimization.

[0157] During the travel stage, the Gaussian mixture model is used to reflect the travel time distribution, which can characterize the travel patterns of different EV owners (such as private cars, taxis, etc.) through a weighted combination of multiple Gaussian distributions.

[0158] In the charging selection stage, a charging probability selection function is defined to describe the impact of SOC on charging behavior. Different SOC upper and lower limits are set for different EVs, reflecting that the lower the SOC, the higher the probability that EV users will choose to charge. This design is more in line with the actual dynamic charging needs of EVs.

[0159] 5) Step 3 of the present invention quantifies the participation capability of electric vehicles (EVs) in demand response through a mathematical model, combines the battery capacity, SOC initial state, and charging and discharging demand time window of the electric vehicle, and provides theoretical support for the dynamic load regulation of the power grid. The demand response time period that the EV can participate in is calculated by the formula EV charging time and the corresponding demand period released by the power grid, and combined with ti,min (the shortest charging time), the charging power, SOC state, and expected SOC of the EV are comprehensively considered, and the EV with objective response capability is added to the set EV. pos,ch and EV pos,dis , accept the dispatch of charging stations. This calculation method combines the dynamic behavior of EVs with the demand response of the power grid, adds individual EVs to the cluster, effectively distinguishes the orderly charging EV load from the disorderly charging EV load, and is suitable for the optimal dispatch of charging stations under the future large-scale EV grid connection.

[0160] 6) The advantage of step 4 of the present invention is that by predicting the dispatchable capacity of electric vehicle (EV) charging stations, the dynamic characteristics of the demand response period (DR) and the start-end OD matrix are integrated, and the Dijkstra algorithm is introduced to plan the optimal driving path, and the speed-flow model is combined to calculate the driving time, and the charging demand and demand response capacity of the EV are reported to the charging station, and the charging station arranges the dispatch plan according to the above information.

[0161] 7) The advantage of step 5 of the present invention is that it proposes a two-tier pricing model based on Stackelberg game, which integrates the interests of three major entities: electric vehicle charging stations (EVCS), electric vehicle users (EVs) and distribution network operators (DSOs), and solves the problem of multi-subject interest conflicts in the interaction between electric vehicles and power grids. By constructing an outer DSO optimization model and an inner EVCS-EV optimization model, the goals are to minimize DSO operating costs, maximize EVCS benefits, and minimize EV user costs, respectively, to achieve dynamic coordination and interest balance among the various entities.

[0162] The model adopts game theory methods, taking DSO as the leader, EVCS and EV as followers, and optimizing electricity price decisions through a two-layer game mechanism. The outer model reflects the real-time operating cost of the distribution network through DLMP (node ​​marginal price) and provides price signals for the inner layer; the inner model designs charging and discharging price strategies based on DLMP to optimize the charging station revenue and EV user charging costs. This top-down hierarchical optimization method combines the global cost of the power grid with the local revenue of the charging station and user behavior, forming an efficient decision-making mechanism.

[0163] Specifically, the advantages of step 5 mainly include the following aspects:

[0164] 1) Dynamic balance of multi-agent interests: Through the two-layer game model, step 5 fully considers the different interests of DSO, EVCS and EV users, solves the problem of interest imbalance in the traditional single-agent optimization model, and achieves the global optimality of the system.

[0165] 2) Flexible pricing strategy: By introducing a flexible charging and discharging pricing mechanism, the model can dynamically adjust the charging and discharging prices in different time periods, guiding EV users to charge during low-load periods and discharge during high-load periods, thereby effectively smoothing out grid load fluctuations and improving the stability of the power system.

[0166] 3) Strong practical applicability: The model not only regulates grid load, but also models EV user behavior in combination with the user response willingness model (based on consumer psychology), making the pricing strategy more in line with actual market demand and enhancing the application value of the model.

[0167] 4). Feasibility and uniqueness of game equilibrium: Through mathematical proof, the two-layer game model in step 5 has a unique Nash equilibrium solution in the strategy optimization process, which ensures the stability and credibility of the calculation results.

[0168] 5). Scalability: The two-layer game model framework in step 5 can be easily expanded to more complex multi-agent interaction scenarios, such as new energy access, grid storage optimization, etc., providing theoretical support for future energy Internet technologies.

[0169] 8) Step 6 of the present invention proposes a two-layer iterative solution method for solving the two-layer pricing model of charging stations based on Stackelberg game proposed in step 5. This step gradually approaches the global optimal solution in an iterative manner by alternately solving the outer DSO optimization model and the inner EVCS-EV optimization model, ensuring that the strategy adjustments of each subject in the dynamic game eventually converge to a stable and efficient equilibrium point. This two-layer iterative process ensures that the pricing strategy can dynamically adapt to changes in grid load and user behavior patterns, and has the following advantages:

[0170] 1) Flexibility and dynamic adaptability: The proposed method in step 6 simulates the interactive process of DSO, EVCS and EV: the outer model solves DLMP and dynamically reflects the load of the distribution network. In the inner model, EVCS sets charging and discharging prices according to DLMP, and users respond to the price strategy to optimize charging and discharging scheduling. The iterative method can update the strategy in real time. This flexibility makes the model more suitable for dynamic environments in actual scenarios.

[0171] 2) High computational efficiency: Step 6 greatly reduces the computational complexity of the model in Step 5 by decomposing the complex two-layer game problem into easy-to-handle inner and outer sub-problems and optimizing them using mature solvers (such as Gurobi). BRIEF DESCRIPTION OF THE DRAWINGS

[0172] The present invention will be further described below in conjunction with the accompanying drawings and examples;

[0173] Figure 1 This is a flow chart for predicting the dispatchable capacity of a charging station according to the present invention.

[0174] Figure 2 It is a two-layer game framework diagram of the EVCS pricing strategy of the present invention.

[0175] Figure 3 It is a double-layer iterative solution flow chart of the present invention.

[0176] Figure 4 This is the power-transportation coupling network diagram of the present invention.

[0177] Figure 5 It is a charging demand curve diagram of the present invention.

[0178] Figure 6 It is a graph of power grid load in various scenarios of the present invention.

[0179] Figure 7It is the price curve chart of EVCS#10 of the present invention.

[0180] Figure 8 This is the profit graph of EVCS#10 of the present invention.

[0181] Fig. 9 This is the EV cost diagram within EVCS#10 of the present invention.

[0182] Fig.10 This is the load diagram of the node where EVCS#10 of the present invention is located.

[0183] Fig.11 It is a diagram of the number of EVs participating in demand response according to the present invention.

[0184] Fig.12 It is a flow chart of the Dijkstra algorithm in the prediction of the dispatchable capacity of the charging station of the present invention. DETAILED DESCRIPTION

[0185] The present invention proposes a pricing strategy for electric vehicle charging stations that takes into account the interests of EVCS, EV and DSO. First, considering various factors that affect charging behavior, EV driving is simulated, the responsiveness of EV users is evaluated, and a charging station dispatchability prediction model is proposed; secondly, the interaction between the various subjects is discussed, and combined with the EV user response willingness and the node marginal electricity price theory, a two-layer pricing strategy for charging stations based on Stackelberg game is proposed: the outer layer clears the DLMP with the minimum DSO cost, and the inner layer optimizes and solves with the goal of maximizing EVCS benefits and minimizing EV travel costs; then the model is reconstructed using duality theory and KKT conditions, and an iterative algorithm is designed to solve it. Finally, the feasibility and effectiveness of the proposed strategy are verified by comparative analysis of examples.

[0186] The double-tier pricing method for electric vehicle charging stations based on multi-agent master-slave game is characterized by comprising the following steps:

[0187] Step 1: Build a road network model;

[0188] Step 2: Analyze the factors affecting EV charging behavior based on EV appearance time information, SOC information, and charging probability selection;

[0189] Step 3: Evaluate EV responsiveness;

[0190] Step 4: Forecast the dispatchable capacity of charging stations to provide basic data for pricing strategies;

[0191] Step 5: Establish a two-layer pricing model for charging stations based on Stackelberg game, including an outer DSO optimization model and an inner EVCS-EV optimization model;

[0192] Step 6: Solve the two-layer pricing model of charging stations based on Stackelberg game established in step 5 through a two-layer iterative method.

[0193] In step 1, the road network model is a dynamic road network model, which is expressed as:

[0194]

[0195] In formula (1), G represents the road network set; V represents the road network node set, with a total of u nodes; E represents the road segment set in the road network; H represents the time period set, dividing the whole day into T time periods; W represents the road segment weight set; v i represents the i-th road network node; u represents the number of nodes v ij represents the road section connecting the road network nodes i and j; t represents the tth time period among T time periods; T represents the division of the whole day into T time periods w ij (t) represents the road section v during the time period t ij The weight of

[0196] The connection relationship between nodes in the road network set G is described by the adjacency matrix D. The element d of the adjacency matrix D is ij The expression of (t) is:

[0197]

[0198] In formula (2): v j represents the jth road network node;

[0199] The travel time is selected as the road resistance for modeling, and the speed-flow model is introduced; the EV driving speed v ij The expression of (t) is:

[0200]

[0201] In formula (3): v ij,max is the zero flow velocity of road ij; C ij is the traffic capacity of road ij; Q ij (t) is the traffic volume of road ij in time period t; k1, k2, k3 are road grade adaptive coefficients; ω represents the road saturation coefficient

[0202] t period road section v ij The weight w ij The expression of (t) is:

[0203]

[0204] In formula (4): L ij is the length of road ij; R i is the waiting time for the traffic light at intersection i.

[0205] In the step 2,

[0206] 2.1: EV appearance period information, as follows:

[0207] The Gaussian mixture model is used to describe the distribution of EV travel time periods:

[0208]

[0209] In the above formula, t represents the travel time, f(t) represents the travel time distribution function; K represents the number of Gaussian distribution; χ i , μ i and σ i Respectively represent the weight, mean and standard deviation of the i-th Gaussian distribution; i represents the i-th Gaussian distribution;

[0210] is the probability density function of Gaussian distribution;

[0211] 2.2: SOC information, i.e. the initial state of charge of EV, is a random variable with Gaussian distribution, and its probability density function is:

[0212]

[0213] In formula (7), s represents the initial SOC of EV, f(s) represents the probability density function of the initial SOC of EV; μ s and σ s denote the mean and standard deviation respectively; is the probability density function of Gaussian distribution;

[0214] The power consumption of EV increases linearly with the driving distance. The SOC of EV at time t is:

[0215] S t =S t-1 -△l△S (8);

[0216] In formula (8): S t represents the SOC of EV at time t; S t-1 It represents the remaining power of EV at time t-1; Δl represents the driving distance of EV in the period [t-1, t]; ΔS represents the power consumption per kilometer.

[0217] 2.3: EV user charging behavior is mainly affected by the SOC value. The lower the SOC, the greater the probability that the user will choose to charge. The charging probability selection function is:

[0218]

[0219] In formula (9): S up and S downThey represent the upper and lower SOC thresholds that trigger charging selection respectively.

[0220] In step 3, the evaluation of EV responsiveness specifically includes:

[0221] According to the demand response time T DR and the grid-connected period T of the i-th EV i Grid , calculate the time period during which the i-th EV can participate in demand response for:

[0222] T i DR =T DR ∩T i Grid (10);

[0223] According to the initial SOC value of the i-th EV connected to the charging pile and the expected value of charging end Calculate the shortest charging time t i,min :

[0224]

[0225] In formula (11): E i and P i,max They represent the battery capacity and maximum charging power of the i-th EV respectively.

[0226] like The charging demand response period T released by the power grid ch Or discharge demand response period T dis If there is overlap, the EV is considered to be responsive.

[0227]

[0228] In the above formula: EV pos,ch and EV pos,dis Respectively, in T ch and T dis The set of EVs that have the ability to respond during the time period; len(x) represents the number of elements in the set x; N represents the total number of electric vehicles;

[0229] In step 4, the specific steps of predicting the dispatchable capacity of the charging station are as follows:

[0230] First, the road network parameters and DR period are set. The DR period represents the demand response period. The travel time and initial SOC of each EV are generated through Monte Carlo sampling. The OD matrix is ​​read to obtain the origin and destination information. The OD matrix, full name: Origin-Destination matrix, is used to record the number of trips or travel distances from a starting point to an end point.

[0231] The Dijkstra algorithm is used to plan the driving route, and the road travel time is calculated according to the speed-flow model. Fig.12 As shown in the figure, EV driving is simulated, and whether there is a charging demand is determined according to formula (9). If so, the nearest charging station is selected to drive in and record the load information, and the demand response capability of EV is reported. The process is as follows: Figure 1 shown.

[0232] The Dijkstra algorithm is used to plan the driving path, which includes the following steps:

[0233] 1 Initialization:

[0234] 1.1 Read the road network model G = (V, E, H, W), input the starting node i and the target node j

[0235] 1.2 Define a distance array d[v], which represents the shortest path distance from the starting point i to each node v∈V. The initial value is:

[0236] d[i]=0 (the distance from the starting point to itself is 0); d[v]=∞, v≠i.

[0237] 1.3 Create a Boolean array visited[v] with an initial value of False to record whether the node has been processed.

[0238] 1.4 Define a priority queue Q to store the nodes to be processed and their current shortest distances.

[0239] 2 Loop through the nodes in Q:

[0240] When the priority queue Q is not empty, perform the following steps:

[0241] 2.1 Take the node u with the smallest distance from the priority queue Q and mark visited[u] = True

[0242] 2.2 Traverse all adjacent nodes s of node u:

[0243] If v has not been visited yet, and d[u]+w us (t)<d[s], update the shortest distance: d[s]=d[u]+w us (t)

[0244] Add v and its new shortest distance to the priority queue Q.

[0245] 3 Termination conditions:

[0246] If the target node j is visited, stop the algorithm

[0247] 4. Output results:

[0248] The output array d[j] is the shortest distance from node i to node j.

[0249] In step 5, the outer DSO optimization model includes:

[0250] (1) DSO model:

[0251] The goal of DSO is to minimize its own operating costs, including the output cost of distributed gas turbine units and the cost of purchasing electricity from the main grid. The objective function is:

[0252]

[0253] In formula (14): F DSO is the DSO operating cost; dg For generator collection; is the generator output at node j during period t; a and b are energy production cost coefficients; ρ is the agreed electricity price for purchasing electricity from the main grid; S(0) represents the set of nodes connected to the main grid; P 0j,t Indicates the power purchased from the main grid during period t.

[0254] The DSO model satisfies power balance constraints and node voltage constraints:

[0255] 1) Power balance constraints:

[0256]

[0257] P ij,min ≤P ij,t ≤P ij,max (19);

[0258] In formula (15) to formula (19): and They represent the charging and discharging power at node i during period t; P ij,t and Q ij,t They represent the active and reactive power flowing from node i to node j respectively; F(i) and S(i) represent the parent node and child node set of node i respectively; and represent the active and reactive base loads of the node respectively; and Respectively represent the upper and lower limits of the generator active power; and Respectively represent the upper and lower limits of the generator reactive power; P ij,max and P ij,min Respectively represent the upper and lower limits of line load;

[0259] 2) Node voltage constraints:

[0260]

[0261] In formula (20) and formula (21): V j,t represents the voltage at node j during period t; V i,t represents the voltage at node i during period t; Ω line and Ω node are distribution network lines and node sets respectively; R ij and X ij Respectively represent the line resistance and reactance between the distribution network branches ij; V i,max and V i,min Respectively represent the upper and lower limits of node voltage; P ij,t and Q ij,t They represent the active and reactive power flowing from node i to node j respectively.

[0262] (2) Model reconstruction:

[0263] DLMP: distribution locational marginal price, DLMP reflects the marginal cost generated when the distribution network node increases the unit load. Therefore, DLMP is used as the purchase price and sales price of EVCS to DSO, which can be obtained by calculating the dual variable of formula (15). The outer DSO optimization model is reconstructed through the dual theory and KKT conditions to simplify the difficulty of solving the model. The specific steps are as follows:

[0264] A1: Take the dual variables of the constraint conditions as Lagrange multipliers and construct the Lagrangian function L of the lower model, as shown in formula (22):

[0265]

[0266] In formula (22), is the dual variable of formula (15); is the dual variable of formula (16); is the formula (17) The dual variable of is the formula (17) The dual variable of is the formula (18) The dual variable of is the formula (18) The dual variable of is P in formula (19) ij,min ≤P ij,t The dual variable of is P in formula (19) ij,t ≤P ij,max The dual variable of is the dual variable of formula (20); is V in formula (21) i,min ≤V i,t The dual variable of is V in formula (21) i,t ≤V i,max The dual variable of

[0267] represents the basic active load of node i during period t; P qi,t , represents the active power flowing from node q to node i during period t; P ij,t , represents the active power flowing from node i to node j during period t; represents the basic reactive load of node i during period t; Q qi,t , represents the active power flowing from node q to node i during period t; Q ij,t , represents the reactive power flowing from node i to node j during period t; P ij,t , represents the active power flowing from node i to node j during period t; V F(i),t represents the parent node voltage of node i during period t; Q ij,t represents the reactive power flowing from node i to node j during period t; V i,max and V i,min Respectively represent the upper and lower limits of the voltage of node i;

[0268] A2: Let the partial derivative of L with respect to each decision variable be equal to zero, and obtain the KKT condition:

[0269]

[0270] In the above formula, is the dual variable of formula (16); The node j dual variable of expression (15); The node i dual variable in (15); is P in formula (19) ij,min ≤P ij,t The dual variable of is P in formula (19) ij,t ≤P ij,max The dual variable of represents the dual variable of equation (20);

[0271] and P i dg,min Respectively represent the upper and lower limits of the generator active power; and Respectively represent the upper and lower limits of the generator reactive power Respectively represent the upper and lower limits of the line load between nodes i and j;

[0272] 0≤x⊥y≥0 means that the constraints x and y form a complementary relationship, which is equivalent to: x≥0 and y≥0 and x·y=0.

[0273] A3: Add KKT conditions to the constraints, and the outer DSO optimization model can be restated as:

[0274] OP:minobj.(14)

[0275]

[0276] In the above formula, OP represents the outer model; minobj.(14) represents the minimum value of formula (14).

[0277] A4: Linearization: Equations (28) to (35) contain complementary slack terms, which can be converted into linear constraints using the Big M method. Take Equation (28) as an example:

[0278]

[0279] In the above formula, M is a sufficiently large positive number; χ is a binary variable.

[0280] A5: Solve the outer DSO optimization model to obtain λ Pi,t That is DLMP, which is used as the electricity purchase cost and electricity selling price of the charging station.

[0281] In step 5, the inner EVCS-EV optimization model includes:

[0282] (1) EV user response willingness model:

[0283] Based on consumer psychology theory, the relationship between EV response willingness and price can be expressed by a piecewise linear function:

[0284]

[0285] Where: and They represent the EV charging and discharging demand responsiveness during period t; ch,high and π ch,low Respectively represent the upper and lower price thresholds that trigger charging demand response; π dis,high and π dis,low They represent the upper and lower price thresholds for triggering discharge demand response, respectively; represents the price value that triggers the charging demand response; Represents the price value that triggers discharge demand response.

[0286] When an EV meets the conditions of both response capability and response willingness, the EV is added to the response user cluster to accept the scheduling arrangement of the charging station.

[0287]

[0288] In formula (41) and (42), EV t res,ch and EV t res,dis They represent the set of EVs that respond to charging and discharging prices during period t; U(0,1) represents a random number uniformly distributed between [0,1]; T i Grid represents the time period during which the i-th EV is connected to the grid; EV pos,ch Indicates that in T ch The EV set with responsiveness during the time period; EV pos,dis Indicates that in T dis The time period is the set of EVs that have the ability to respond; t represents the tth time period among the T time periods throughout the day; i represents the i-th EV.

[0289] (2)EVCS model:

[0290] The goal of EVCS is to maximize its own profits, including the revenue from electricity sales and the cost of electricity purchase. The objective function is:

[0291]

[0292] In formulas (43) to (45): and They represent the profit, electricity sales revenue and electricity purchase cost of charging station n respectively; and is the charging and discharging power of charging station n during period t; determined by equations (46) to (47); and is the decision variable, which represents the charging and discharging price of the charging station; and They represent the electricity price of the charging station purchasing electricity from the power grid and the electricity price of the charging station selling electricity to the power grid respectively; The compensation cost obtained by the charging station for mobilizing EVs to participate in V2G; △t represents the time change. T represents that the whole day is divided into T time periods, and the maximum t is T.

[0293] The EVCS model constraints mainly include charging and discharging power constraints and charging and discharging electricity price constraints.

[0294] ①.Charge and discharge power constraints:

[0295]

[0296] In formulas (46) to (49): EV n represents the set of EVs in charging station n; represents the charging and discharging power of the i-th EV during period t, which is determined by the calculation part of the EV model; and They represent the charging and discharging states of the EV, respectively, and are determined by the calculation part of the EV model; and Respectively represent the maximum charging and discharging power of the charging station.

[0297] ②.Charge and discharge electricity price constraints

[0298]

[0299] In formulas (50) to (51): and They represent the upper and lower limits of the charging price of the charging station respectively; and They represent the upper and lower limits of the discharge price of the charging station respectively.

[0300] (3) EV model:

[0301] Assuming that the i-th EV is at charging station n, the EV arranges a charging plan according to the charging and discharging electricity prices released by EVCS, and the objective function is to minimize the charging cost:

[0302]

[0303] In formulas (52) to (55): represents the total charging cost of the i-th EV; and They represent the charging cost, discharging benefit and battery loss cost of EV respectively; is the decision variable, which represents the charging and discharging power of electric vehicle i during period t. Indicates charging. Indicates discharge; and are binary variables of the charging and discharging status of electric vehicle i during period t, 1 indicates charging / discharging, and 0 indicates not charging / discharging;

[0304] Determined by equation (56) and equation (57); c ch and c dis They represent the energy loss coefficient of battery charging and discharging respectively.

[0305]

[0306] The EV model mainly meets the charging and discharging power constraints, charging and discharging state constraints and power constraints.

[0307] a. Charge and discharge power constraints:

[0308]

[0309] In formula (58): represents the maximum power supported by the i-th EV; EV t res,dis represents the set of electric vehicles that respond to the discharge electricity price during period t.

[0310] b. Power Constraints:

[0311]

[0312] S i,min ≤S i,t ≤S i,max (62);

[0313] In formulas (59) to (62): represents the expected value of the i-th EV when charging is completed; represents the initial SOC value of the i-th EV connected to the charging pile; E i represents the battery capacity of the i-th EV; S i,t+1 represents the SOC of the i-th EV in period t+1; S i,t is the SOC of the i-th EV in period t; η ch and η dis Respectively represent the charging and discharging efficiency of EV; S i,min and S i,max They represent the minimum and maximum SOC values ​​of the i-th EV respectively.

[0314] (4) Reconstruction of the inner EVCS-EV optimization model:

[0315] The inner EVCS-EV optimization model can be viewed as a two-layer optimization problem, with EVCS at the upper layer and EV at the lower layer. When solving the EV objective function, the charging and discharging price of EVCS can be regarded as a constant. Therefore, EV optimization can be viewed as a linear problem, which is converted into EVCS constraint conditions through the Karush-Kuhn-Tucker (KKT) conditions. The KKT conditions are as follows:

[0316]

[0317]

[0318] 0≤S i,t -S i,min ⊥τ9≥0 (70);

[0319] 0≤S i,max -S i,t ⊥τ 10 ≥0(71);

[0320] In formulas (63) to (71): τ 1,t , τ 2,t , τ 3,t, τ 4,t , τ 5,t , τ 6,t , τ 7,t , τ 8,t , τ 9,t , τ 10,t are the dual variables of equations (58) to (62) respectively; and They represent the charging and discharging prices of charging station m respectively;

[0321] The game process between EVCS-EV can be transformed into a mixed integer linear programming problem:

[0322] IP:minobj.(43)

[0323]

[0324] In formula (72), IP represents the inner model; minobj.(43) represents the minimum value of formula (43);

[0325] Nonlinear terms in the EVCS model and It can be convexified by the McCormick envelope to For example:

[0326]

[0327] In formula (73): is the charging power of charging station n during period t; Indicates the lower limit of charging price of the charging station; Indicates the upper limit of charging price at the charging station; Indicates the maximum charging power of the charging station;

[0328] Through formula (73), the nonlinear term Replace with Equations (64) to (71) contain complementary relaxation terms, which can be linearized by the SOC information calculation method.

[0329] In step 5, the game equilibrium of the two-tier pricing model of charging stations based on the Stackelberg game is proved as follows:

[0330] When the two-tier pricing model of charging stations based on Stackelberg game meets the following conditions, there is a unique Nash equilibrium solution:

[0331] (1) The objective function of each subject in the game model is a non-empty, continuous function of its strategy set.

[0332] (2) The follower objective function is a continuous concave / convex function with respect to its strategy set.

[0333] prove:

[0334] (1) The objective functions of DSO, EVCS, and EV are all non-empty, continuous functions of their strategy sets, so Condition 1 is satisfied.

[0335] (2) The objective functions of EVCS and EV are linear functions of their strategy sets. According to the definition of convexity and concavity, linear functions are both convex functions and concave functions, so condition 2 is satisfied.

[0336] Therefore, the two-tier pricing model of charging stations based on Stackelberg game proposed in the present invention has a unique equilibrium solution, and the proof is complete.

[0337] In step 6, the two-layer game solution process is as follows:

[0338] The double-layer iterative method solves the inner EVCS-EV optimization model and the outer DSO optimization model in turn. The algorithm flow is as follows: Figure 3 shown.

[0339] In the outer layer, solve the outer DSO optimization model and obtain the DLMP of each node (k) ; Each EVCS shall follow DLMP (k) Initialize the price, solve the inner EVCS-EV optimization model, and recalculate DLMP (k) ; If DLMP (k) -DLMP (k-1) <ε1, the DLMP clearing market of each node is determined, and the inner EVCS-EV optimization model is entered for solution. Otherwise, it is iterated again.

[0340] In the inner EVCS-EV optimization model, the user response willingness is first calculated based on the predicted EVCS dispatchable potential, and the EV response cluster is updated; then the inner EVCS-EV optimization model is solved to obtain the charging station price strategy and revenue F EVCS(a) If F EVCS (a) -F EVCS(a-1) <ε2, indicating that the strategy is optimal, and the EV load of the charging station and the node continues to be calculated, otherwise it is iterated again. The outer DSO optimization model and the inner EVCS-EV optimization model established in the present invention are both mixed integer programming, which can be solved by calling commercial solvers such as Gurobi.

[0341] Step 7: Set up three scenarios for simulation to demonstrate the effectiveness of the method proposed in the present invention in improving the interests of various entities.

[0342] Example:

[0343] 1. Parameter settings:

[0344] The present invention selects the improved 41-node-72-section urban transportation network and the IEEE69-node distribution network to construct a coupling network. The network topology is shown in Figure 4 The main parameters are set as follows: The price coefficient of the unit's active output a = 9.0 × 10 -7 Yuan / (kW·h) 2 , b=0.4 yuan / (kW·h), ρ=0.9 yuan / (kW·h), the reference voltage is 12.66kV, and the reference power is 10MW. The number of electric vehicles is 20,000, the charging and discharging power is 40W, the battery charging and discharging efficiency is 95%, and the battery capacity is 80kWh; the battery charging and discharging loss coefficients are 0.01 yuan / kWh and 0.1 yuan / kWh respectively, the upper and lower limits of SOC are 0.95 and 0.1 respectively, the expected SOC is 0.85, and the S that triggers the charging selection is up and S down The EV travel period, OD matrix, initial SOC and other information are generated by Monte Carlo method to simulate EV driving. The demand response period is shown in Table 1, where the discharge demand response period λ inc =0.8 yuan / (kW·h).

[0345] Table 1 Demand response time

[0346]

[0347]

[0348] 2. EV charging demand forecast:

[0349] The grid load considering EV charging demand is as follows: Figure 5 As shown. Figure 5 It can be seen that the EV load gradually increases from 8:00, because EV users start to travel and go to work during this period, thus generating charging demand. At noon (12:00-15:00), the EV charging load reaches a peak, and overlaps with the peak period of the power grid load from 9:00-13:00, resulting in a "peak on peak" phenomenon. This is because this period is the lunch break, and car owners need to charge their EVs to meet afternoon travel needs. At night (0:00-6:00), since most EV owners are resting, the EV charging load gradually decreases, and a trough period occurs.

[0350] 3. Analysis of simulation results:

[0351] The present invention sets three scenarios: 1) EVs are charged disorderly and do not participate in DR; 2) EVs participate in DR, and EVCS adopts the time-of-use electricity price shown in Table 2; 3) EVs participate in DR, and EVCS adopts a text price strategy. The calculation results of EVCS profits, EV charging costs, and DSO operating costs under different scenarios are shown in Table 3. As can be seen from Table 3, compared with scenario 1, the EVCS profit under the scenario 2 scheme has increased, and the operating costs of EV users and DSO have decreased, which shows that after considering DR, EVCS can effectively guide EVs to participate in orderly charging and discharging, thereby improving the interests of various entities; compared with the time-of-use electricity price strategy of scenario 2, the strategy of scenario 3 increases EVCS profits by 13%, and reduces EV and DSO costs by 19.8% and 2.8% respectively. This is because the strategy proposed in the present invention optimizes the price strategy on the basis of the fixed time-of-use electricity price, which can better guide EVs to participate in orderly charging and discharging, and also shows the effectiveness of the method proposed in the present invention in improving the interests of various entities.

[0352] Table 2 Time-of-use electricity prices

[0353]

[0354] Table 3 Optimization results of each subject

[0355]

[0356] The distribution network load in each scenario is as follows: Figure 6 As shown in Figure 1, 10:00-13:00 and 19:00-21:00 are peak load periods for the power grid, and 3:00-6:00 and 14:00-17:00 are low load periods.

[0357] From the table analysis, it can be seen that by guiding EV to participate in orderly charging and discharging through DR, the grid load has been greatly reduced in both peak periods. This is because scenario 1 is disordered charging and no measures are taken to guide EV discharge. After considering DR, most EV users will choose to charge during non-peak periods to reduce their own costs. Scenario 3 optimizes the price strategy based on scenario 2, and can more flexibly guide EV to discharge during this period and transfer the charging load to other periods. It can be seen from the load curve of 1:00-6:00 that during the low load period at night, the strategy of scenario 2 has little effect on load increase. This is because under the fixed time-of-use electricity price strategy of scenario 2, the charging cost of EV from 3:00-6:00 is the same as that from 0:00 to 3:00, so it cannot flexibly guide EV to participate in orderly charging; while scenario 3 flexibly changes the price strategy to significantly increase the valley load. This shows that the strategy proposed in this invention can effectively guide EV to participate in the "peak shaving and valley filling" of the power grid and reduce load fluctuations.

[0358] To further analyze the relationship between DLMP, charging price and discharging price at different time periods throughout the day, take EVCS#10 at road network node 10 as an example, its price curve is as follows: Figure 7 As shown. Combined Figure 6 From the analysis, we can see that the DLMP curve and the load curve show a similar trend, which is consistent with the definition of DLMP, that is, the cost of increasing unit power. The charging prices set by the charging station throughout the 24 hours of the day are higher than DLMP to achieve their own profitability. During the charging demand response period of 1:00-5:00, since the grid load is at a low point, the EV charging load needs to be increased during this period to meet the "valley filling" demand. Therefore, the charging station sets a lower charging price during this period to guide EVs to charge in an orderly manner. During the 10:00-13:00 and 19:00-21:00 periods, the discharge price set by the charging station is significantly higher than the charging price. Figure 6 The load curve analysis shows that the load is high during this period, and the power grid has provided compensation measures for charging stations that mobilize EVs to participate in V2G. Therefore, charging stations set higher charging prices to encourage EVs to discharge to the grid. In the remaining periods of non-discharge demand response, since no incentive measures are set, the discharge prices set by charging stations are all the lowest values ​​allowed.

[0359] The profit of EVCS#10, the EV charging cost in EVCS#10, and the node load of EVCS#10 under scenario 2 and scenario 3 are shown as follows: Figure 8 to Figure 10 As shown. Figure 8 to Figure 10 It can be seen that the profit of EVCS under scenario 3 has increased in all periods of the day, the EV cost has significantly decreased during the discharge demand response period, and the node load has tended to be flat. During the discharge demand response period (10:00-13:00 and 19:00-21:00), the EV charging cost is negative, because the discharge price set by the charging station is significantly higher than the charging price. Scenario 3 attracts more EV users to discharge during this period, and the EV cost and node load are reduced overall. Furthermore, the profit of EVCS has increased significantly in the period before and after the discharge demand response, while the EV charging cost has increased slightly. This is because EV discharges to the grid or stops charging during the discharge demand response period, transferring part of the charging demand to the remaining periods adjacent to DR, resulting in an increase in the charging volume during these periods, which slightly increases the cost of EV users and increases the revenue of charging stations.

[0360] In scenario 3, the number of EVs participating in demand response is as follows: Fig.11 As shown. Combined Figure 7Analysis shows that during the charging demand response period (1:00-5:00), the number of EVs in the charging station is small, so the charging station sets a lower charging price to attract more EVs to transfer their charging needs to this period, and the lower the node load in this period, the lower the DLMP, so EVCS can set a lower charging price to attract EV charging; during the discharge demand response period 10:00-13:00, the number of EVs in the charging station is large, so even if a lower discharge price is set, a large number of EVs can be attracted to participate in orderly discharge. During the 19:00-21:00 period, due to the small number of EVs in the charging station, the charging station sets a higher discharge price to attract more EVs to participate in orderly discharge. This shows that the pricing strategy proposed in this invention can flexibly adjust the price of the charging station according to the number of EVs in the EVCS, guide EV users to participate in orderly charging and discharging, and thus enhance the interests of each subject.

Claims

1. A two-tier pricing method for electric vehicle charging stations based on multi-agent master-slave game, characterized by The following steps are involved: Step 1: Build a road network model; Step 2: Analyze the factors affecting EV charging behavior based on EV appearance time information, SOC information, and charging probability selection; Step 3: Evaluate EV responsiveness; Step 4: Predict the dispatchable capacity of the charging station; Step 5: Establish a two-layer pricing model for charging stations based on Stackelberg game, including an outer DSO optimization model and an inner EVCS-EV optimization model; Step 6: Solve the two-layer pricing model of charging stations based on Stackelberg game established in step 5 through a two-layer iterative method.

2. The double-tier pricing method for electric vehicle charging stations based on multi-agent master-slave game according to claim 1 is characterized by: In step 1, the road network model is a dynamic road network model, which is expressed as: In formula (1), G represents the road network set; V represents the road network node set, with a total of u nodes; E represents the road segment set in the road network; H represents the time period set, dividing the whole day into T time periods; W represents the road segment weight set; v i represents the i-th road network node; u represents the number of nodes v ij represents the road segment connecting the road network nodes i and j; t represents the tth time period among T time periods; T means dividing the whole day into T time periods w ij (t) represents the road section v during the time period t ij The weight of The connection relationship between nodes in the road network set G is described by the adjacency matrix D. The element d of the adjacency matrix D is ij The expression of (t) is: In formula (2): v j represents the jth road network node; The travel time is selected as the road resistance for modeling, and the speed-flow model is introduced; the EV driving speed v ij The expression of (t) is: In formula (3): v ij,max is the zero flow velocity of road ij; C ij is the traffic capacity of road ij; Q ij (t) is the traffic volume of road ij in time period t; k1, k2, k3 are road grade adaptive coefficients; ω represents the road saturation coefficient t period road section v ij The weight w ij The expression of (t) is: In formula (4): L ij is the length of road ij; R i is the waiting time for the traffic light at intersection i.

3. The double-tier pricing method for electric vehicle charging stations based on multi-agent master-slave game according to claim 1 is characterized by: In the step 2, 2.1: EV appearance period information, as follows: The Gaussian mixture model is used to describe the distribution of EV travel time periods: In the above formula, t represents the travel time, f(t) represents the travel time distribution function; K represents the number of Gaussian distribution; χ i , μ i and σ i Respectively represent the weight, mean and standard deviation of the i-th Gaussian distribution; i represents the i-th Gaussian distribution; is the probability density function of Gaussian distribution; 2.2: SOC information, i.e. the initial state of charge of EV, is a random variable with Gaussian distribution, and its probability density function is: In formula (7), s represents the initial SOC of EV, f(s) represents the probability density function of the initial SOC of EV; μ s and σ s denote the mean and standard deviation respectively; is the probability density function of Gaussian distribution; The power consumption of EV increases linearly with the driving distance. The SOC of EV at time t is: S t =S t-1 -△l△S (8); In formula (8): S t represents the SOC of EV at time t; S t-1 represents the remaining power of the EV at time t-1; Δl represents the driving distance of the EV in the period [t-1, t]; ΔS represents the power consumption per kilometer; 2.3: EV user charging behavior is mainly affected by the SOC value. The lower the SOC, the greater the probability that the user will choose to charge. The charging probability selection function is: In formula (9): S up and S down They represent the upper and lower SOC thresholds that trigger charging selection respectively.

4. The double-tier pricing method for electric vehicle charging stations based on multi-agent master-slave game according to claim 1 is characterized by: In step 3, the evaluation of EV responsiveness specifically includes: According to the demand response time T DR and the grid-connected period T of the i-th EV i Grid , calculate the time period during which the i-th EV can participate in demand response for: T i DR =T DR ∩T i Grid (10); According to the initial SOC value of the i-th EV connected to the charging pile and the expected value of charging end Calculate the shortest charging time t i,min : In formula (11): E i and P i,max They represent the battery capacity and maximum charging power of the i-th EV respectively; like The charging demand response period T released by the power grid ch Or discharge demand response period T dis If there is overlap, the EV is considered to be responsive; In the above formula: EV pos,ch and EV pos,dis Respectively, in T ch and T dis The set of EVs that have the ability to respond in the time period; len(x) represents the number of elements in the set x; N represents the total number of electric vehicles.

5. The double-tier pricing method for electric vehicle charging stations based on multi-agent master-slave game according to claim 3 is characterized by: In step 4, the specific steps of predicting the dispatchable capacity of the charging station are as follows: First, the road network parameters and DR period are set, and the travel time and initial SOC of each EV are generated through Monte Carlo sampling. The OD matrix is ​​read to obtain the starting and ending point information; the OD matrix is ​​used to record the number of trips or travel distance from a starting point to a destination. The Dijkstra algorithm is used to plan the driving route, the road travel time is calculated according to the speed-flow model, and the EV driving is simulated. According to formula (9), it is determined whether there is a charging demand. If so, the nearest charging station is selected to drive in and record the load information, and the demand response capability of the EV is reported.

6. The double-tier pricing method for electric vehicle charging stations based on multi-agent master-slave game according to claim 1 is characterized by: In step 5, the outer DSO optimization model includes a DSO model: The goal of DSO is to minimize its own operating costs, including the output cost of distributed gas turbine units and the cost of purchasing electricity from the main grid; the objective function is: In formula (14): F DSO is the DSO operating cost; dg For generator collection; is the generator output at node j during period t; a and b are energy production cost coefficients; ρ is the agreed electricity price for purchasing electricity from the main grid; S(0) represents the set of nodes connected to the main grid; P 0j,t Indicates the power purchased from the main grid during period t; The DSO model satisfies power balance constraints and node voltage constraints: 1) Power balance constraints: P ij,min ≤P ij,t ≤P ij,max (19); In formula (15) to formula (19): and They represent the charging and discharging power at node i during period t; P ij,t and Q ij,t They represent the active and reactive power flowing from node i to node j respectively; F(i) and S(i) represent the parent node and child node set of node i respectively; and represent the active and reactive base loads of the node respectively; and Respectively represent the upper and lower limits of the generator active power; and Respectively represent the upper and lower limits of the generator reactive power; P ij,max and P ij,min Respectively represent the upper and lower limits of line load; 2) Node voltage constraints: In formula (20) and formula (21): V j,t represents the voltage at node j during period t; V i,t represents the voltage at node i during period t; Ω line and Ω node are distribution network lines and node sets respectively; R ij and X ij Respectively represent the line resistance and reactance between the distribution network branches ij; V i,max and V i,min Respectively represent the upper and lower limits of node voltage; P ij,t and Q ij,t They represent the active and reactive power flowing from node i to node j respectively.

7. The double-tier pricing method for electric vehicle charging stations based on multi-agent master-slave game according to claim 6 is characterized by: DLMP reflects the marginal cost generated when the distribution network node increases the unit load. Therefore, DLMP is used as the purchase price and sales price of electricity from EVCS to DSO, which can be obtained by calculating the dual variables of formula (15). The outer DSO optimization model is reconstructed through the dual theory and KKT conditions to simplify the difficulty of solving the model. The specific steps are as follows: A1: Take the dual variables of the constraint conditions as Lagrange multipliers and construct the Lagrangian function L of the lower model, as shown in formula (22): In formula (22), is the dual variable of formula (15); is the dual variable of formula (16); is the formula (17) The dual variable of is the formula (17) The dual variable of is the formula (18) The dual variable of is the formula (18) The dual variable of is P in formula (19) ij,min ≤P ij,t The dual variable of is P in formula (19) ij,t ≤P ij,max The dual variable of is the dual variable of formula (20); is V in formula (21) i,min ≤V i,t The dual variable of is V in formula (21) i,t ≤V i,max The dual variable of represents the basic active load of node i during period t; P qi,t , represents the active power flowing from node q to node i during period t; P ij,t , represents the active power flowing from node i to node j during period t; represents the basic reactive load of node i during period t; Q qi,t , represents the active power flowing from node q to node i during period t; Q ij,t , represents the reactive power flowing from node i to node j during period t; P ij,t , represents the active power flowing from node i to node j during period t; V F(i),t represents the parent node voltage of node i during period t; Q ij,t represents the reactive power flowing from node i to node j during period t; V i,max and V i,min Respectively represent the upper and lower limits of the voltage of node i; A2: Let the partial derivative of L with respect to each decision variable be equal to zero, and obtain the KKT condition: In the above formula, is the dual variable of formula (16); The node j dual variable of expression (15); The node i dual variable in (15); is P in formula (19) ij,min ≤P ij,t The dual variable of is P in formula (19) ij,t ≤P ij,max The dual variable of represents the dual variable of equation (20); and P i dg,min Respectively represent the upper and lower limits of the generator active power; and Q i dg,min Respectively represent the upper and lower limits of the generator reactive power Respectively represent the upper and lower limits of the line load between nodes i and j; A3: Add KKT conditions to the constraints, and the outer DSO optimization model can be restated as: In the above formula, OP represents the outer model; minobj.(14) represents the minimum value of formula (14); A4: Linearization: Equations (28) to (35) contain complementary slack terms, which are converted into linear constraints using the Big M method. Take equation (28) as an example: In the above formula, M is a sufficiently large positive number; χ is a binary variable; A5: Solve the outer DSO optimization model to obtain λ Pi,t That is DLMP, which is used as the electricity purchase cost and electricity selling price of the charging station.

8. The double-tier pricing method for electric vehicle charging stations based on multi-agent master-slave game according to claim 1 is characterized by: In step 5, the inner EVCS-EV optimization model includes: (1) EV user response willingness model: Based on consumer psychology theory, the relationship between EV response willingness and price can be expressed by a piecewise linear function: Where: and They represent the EV charging and discharging demand responsiveness during period t; ch,high and π ch,low Respectively represent the upper and lower price thresholds that trigger charging demand response; π dis,high and π dis,low They represent the upper and lower price thresholds for triggering discharge demand response, respectively; represents the price value that triggers the charging demand response; represents the price value that triggers the discharge demand response; When an EV meets both the response capability and response willingness conditions, the EV is added to the response user cluster to accept the scheduling arrangement of the charging station; In formula (41) and (42), EV t res,ch and EV t res,dis They represent the set of EVs that respond to charging and discharging prices during period t; U(0,1) represents a random number uniformly distributed between [0,1]; T i Grid represents the time period during which the i-th EV is connected to the grid; EV pos,ch Indicates that in T ch The EV set with responsiveness during the time period; EV pos,dis Indicates that in T dis The set of EVs that have the ability to respond during a time period; t represents the tth time period among the T time periods throughout the day; i represents the i-th EV; (2)EVCS model: The goal of EVCS is to maximize its own profits, including the revenue from electricity sales and the cost of electricity purchase. The objective function is: In formulas (43) to (45): and They represent the profit, electricity sales revenue and electricity purchase cost of charging station n respectively; and is the charging and discharging power of charging station n during period t; determined by equations (46) to (47); and is the decision variable, which represents the charging and discharging price of the charging station; and They represent the electricity price of the charging station purchasing electricity from the power grid and the electricity price of the charging station selling electricity to the power grid respectively; The compensation cost obtained by the charging station for mobilizing EVs to participate in V2G; △t represents the time change; T represents the division of the whole day into T time periods, and the maximum t is T; The EVCS model constraints include charging and discharging power constraints and charging and discharging electricity price constraints; ①.Charge and discharge power constraints: In formulas (46) to (49): EV n represents the set of EVs in charging station n; represents the charging and discharging power of the i-th EV during period t, which is determined by the calculation part of the EV model; and They represent the charging and discharging states of the EV, respectively, and are determined by the calculation part of the EV model; and Respectively represent the maximum charging and discharging power of the charging station; ②.Charge and discharge electricity price constraints In formulas (50) to (51): and They represent the upper and lower limits of the charging price of the charging station respectively; and They represent the upper and lower limits of the discharge price of the charging station respectively; (3) EV model: Assuming that the i-th EV is at charging station n, the EV arranges a charging plan according to the charging and discharging electricity prices released by EVCS, and the objective function is to minimize the charging cost: In formulas (52) to (55): represents the total charging cost of the i-th EV; and They represent the charging cost, discharging benefit and battery loss cost of EV respectively; is the decision variable, which represents the charging and discharging power of electric vehicle i during period t. Indicates charging. Indicates discharge; and are binary variables of the charging and discharging status of electric vehicle i during period t, 1 indicates charging / discharging, and 0 indicates not charging / discharging; Determined by equation (56) and equation (57); c ch and c dis They represent the power loss coefficient of battery charging and discharging respectively; The EV model mainly meets the charging and discharging power constraints, charging and discharging state constraints, and power constraints; a. Charge and discharge power constraints: In formula (58): represents the maximum power supported by the i-th EV; EV t res,dis represents the set of electric vehicles that respond to the discharge electricity price during period t; b. Power Constraints: S i,min ≤S i,t ≤S i,max (62); In formulas (59) to (62): represents the expected value of the i-th EV when charging is completed; represents the initial SOC value of the i-th EV connected to the charging pile; E i represents the battery capacity of the i-th EV; S i,t+1 represents the SOC of the i-th EV in period t+1; S i,t is the SOC of the i-th EV in period t; η ch and η dis Respectively represent the charging and discharging efficiency of EV; S i,min and S i,max They represent the minimum and maximum SOC values ​​of the i-th EV respectively.

9. The double-tier pricing method for electric vehicle charging stations based on multi-agent master-slave game according to claim 8 is characterized by: The inner EVCS-EV optimization model reconstruction includes: The inner EVCS-EV optimization model can be regarded as a two-layer optimization problem, with EVCS at the upper layer and EV at the lower layer. When solving the EV objective function, the charging and discharging price of EVCS can be regarded as a constant. Therefore, EV optimization can be regarded as a linear problem, which is converted into the constraint conditions of EVCS through the Karush-Kuhn-Tucker (KKT) conditions. The KKT conditions are as follows: 0≤S i,t -S i,min ⊥τ9≥0 (70); 0≤S i,max -S i,t ⊥τ 10 ≥0(71); In formulas (63) to (71): τ 1,t , τ 2,t , τ 3,t , τ 4,t , τ 5,t , τ 6,t , τ 7,t , τ 8,t , τ 9,t , τ 10,t are the dual variables of equations (58) to (62) respectively; and They represent the charging and discharging prices of charging station m respectively; The game process between EVCS-EV can be transformed into a mixed integer linear programming problem: In formula (72), IP represents the inner model; minobj.(43) represents the minimum value of formula (43); Nonlinear terms in the EVCS model and It can be convexified by the McCormick envelope to For example: In formula (73): is the charging power of charging station n during period t; Indicates the lower limit of charging price of the charging station; Indicates the upper limit of charging price at the charging station; Indicates the maximum charging power of the charging station; Through formula (73), the nonlinear term Replace with Equations (64) to (71) contain complementary relaxation terms, which can be linearized by the SOC information calculation method.

10. The double-tier pricing method for electric vehicle charging stations based on multi-agent master-slave game according to claim 1 is characterized by: In step 6, the two-layer game solution process is as follows: The two-layer iterative method solves the inner EVCS-EV optimization model and the outer DSO optimization model in turn; Solve the outer DSO optimization model to obtain the DLMP of each node (k) ; Each EVCS shall follow the DLMP (k) Initialize the price, solve the inner EVCS-EV optimization model, and recalculate DLMP (k) ; If DLMP (k) -DLMP (k-1) <ε1, then the DLMP clearing market of each node is determined, and the inner EVCS-EV optimization model is entered for solution, otherwise it is re-iterated; In the inner EVCS-EV optimization model, the user response willingness is first calculated based on the predicted EVCS dispatchable potential, and the EV response cluster is updated; then the inner EVCS-EV optimization model is solved to obtain the charging station price strategy and revenue F EVCS(a) ; If F EVCS(a) -F EVCS(a-1) <ε2, indicating that the strategy is optimal, continue to calculate the EV load of the charging station and the node, otherwise reiterate; The established outer DSO optimization model and inner EVCS-EV optimization model are both mixed integer programming, which can be solved by calling commercial solvers such as Gurobi.

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