Charging station pricing method considering flexibility of electric vehicle and distributed power supply

Abstract

The invention relates to the technical field of charging station infrastructure pricing schemes, in particular to a charging station pricing method considering flexibility of an electric vehicle and a distributed power supply, and the method comprises the steps: building a comprehensive charging pricing model; the flexibility range of boundary nodes of operators of the power distribution and power transmission system is obtained by using distributed energy; obtaining a balance condition of pricing and profit of the non-cooperative electric vehicle charging stations through a game theory method, and obtaining a pricing model of N electric vehicle charging stations participating in competition in a market sharing environment; and establishing a closed expression of the service price of the electric vehicle charging station along with the profit, and performing mathematical analysis. According to the method, a plurality of electric vehicle charging stations adopt a comprehensive charging pricing model to realize profit maximization, the balance condition of each charging station in the smart power grid is solved in a non-cooperative mode by adopting a game theory method, and the reliability of the profit of each participant during balance is analyzed and researched through the game theory method.

Description

Technical Field

[0001] The present invention relates to the technical field of pricing schemes for electric vehicle charging infrastructure, and in particular to a charging station pricing method that takes into account the flexibility of electric vehicles and distributed power sources. Background Art

[0002] Greenhouse gas emissions have always been a focus of global social attention. Traditional fuel-driven transportation accounts for about a quarter of the world's total greenhouse gas emissions. Due to its significant environmental benefits and the development of battery technology, electric vehicles (EVs) are becoming increasingly popular among stakeholders such as consumers, researchers, manufacturers, and regulatory agencies. However, due to the lack of charging infrastructure for electric vehicles, consumers have weak purchasing power and the market penetration of electric vehicles is limited. Therefore, in order to increase the share of electric vehicles in the transportation industry, it is necessary to develop charging infrastructure at a faster pace to meet the growing demand for electric vehicle charging.

[0003] The current emerging charging market will motivate various competitive charging service providers to invest in the deployment of charging stations (CS) in order to obtain greater profits in the potential common market. Due to the development of fast charging technology and the growing demand for charging, the traditional static CS charging strategy is now increasingly popular among researchers, charging service providers (CSPs) and electric vehicle owners. A scholar proposed a study on the optimal placement of electric vehicle charging stations (EVCs), simulating the oligopoly market scenario through Bayesian game, using clustering-based methods and traffic network graphs to find the optimal placement strategy of CS. However, this study did not consider the non-cooperative market scenario, so that the entire market is considered to be dominated by a few EVCs. Another study showed the pricing of CS using a two-stage Stackelberg game, in which the uniqueness of CS selection is established so that electric vehicles occupy a larger share in the charging industry. The competitive charging pile providers strive to choose the appropriate pricing for the fixed strategic location of their electric vehicle charging piles in order to maximize profits, but the scheme only considers two CSs, and the model is difficult to generalize to N CSs. Another scholar proposed an optimal pricing scheme for public EV charging, in which the power distribution network (PDN) and the urban transportation network (UTP) are considered to be interdependent, and it is assumed that all EVCs in an urban area belong to one company and the charging network operator (CNO), and the CNO will find an optimal price to maximize the total charging revenue.

[0004] In the above studies and works, the necessary conditions for prices, i.e., the requirement that all available CS remain profitable in the market, are not elaborated in detail, indicating that the relevant problems are optimized by methods based on numerical techniques. Therefore, no explicit closed-form expression for the utility of non-cooperative EV control systems is explored. In addition, no set of prices to reach equilibrium is explicitly provided; on the other hand, in practical situations, drivers are very familiar with the energy demand patterns of their EVs, and EV drivers do not trust control systems due to the anxiety associated with rapidly changing prices. Due to critical time and energy constraints, EVs only prefer EV control systems that are close to them. The proposed model does not require real-time information of EVs; rather, it is based on the expected values ​​of EV energy demand and travel costs as well as other relevant parameters. Summary of the invention

[0005] The purpose of the present invention is to overcome the defects of the prior art and propose a charging station pricing method that takes into account the flexibility of electric vehicles and distributed power sources, wherein multiple electric vehicle charging stations (EVCs) adopt a comprehensive charging pricing model to maximize their profits, and use game theory methods to find the equilibrium conditions of each charging station in the smart grid in a non-cooperative manner, and apply the proposed model to the following two situations: when multiple EVCs are already located in different locations and when a new charging service provider (CSP) wants to enter the market by establishing its own EVCs in existing competitive EVCs. According to the equilibrium price of the charging station, the Nash equilibrium profit of the charging station is obtained, which to a certain extent can illustrate the reliability of analyzing and studying the NE price and the profit of each participant (EVCs) at equilibrium through game theory methods.

[0006] To achieve the above object, the present invention adopts the following specific technical solutions:

[0007] The present invention provides a charging station pricing method considering the flexibility of electric vehicles and distributed power sources, comprising the following steps:

[0008] S1. Establish a comprehensive charging pricing model, including the charging price composition of charging stations and the profits of electric vehicle charging stations (EVCs).

[0009] S2, using distributed energy resources (DER) to obtain the flexibility range of the distribution and transmission system operator (TSO-DSO) boundary nodes;

[0010] S3. The equilibrium conditions of pricing and profit of non-cooperative EVCs are obtained through game theory, and the pricing model of N competing EVCSs in a market sharing environment is obtained by using Hotelling's game method.

[0011] S4. Establish a closed expression for EVCs service price and EVCs profit and conduct mathematical analysis.

[0012] Furthermore, in step S1, the charging price of the electric vehicle comprises energy cost, service cost, travel cost and waiting cost;

[0013] The expression for energy cost is as follows:

[0014]

[0015] In the formula, Indicates EVCs O n The cost of energy provided, η n Indicates EVCs O n Cost per unit of energy generated, δ k represents energy demand;

[0016] The expression of service cost is as follows:

[0017]

[0018] In the formula, Indicates EVCs O n Cost of services provided, represents the fixed cost per unit of energy; for all n Charging electric cars, remain unchanged;

[0019] The expression for travel cost is as follows:

[0020] use Indicates that an electric car arrives at O n The driving energy consumed at the point C k Indicates u k The travel cost per unit distance, Indicates u k With O n The distance between k Modeled as a random variable with uniform distribution, C k The expected value of μ ;

[0021] The expression of waiting cost is as follows:

[0022] EV k Replace in EVCs O n The effective waiting cost of waiting in line is expressed as C ω represents the waiting cost per unit time, is the waiting time of EVCs, and the waiting time of EVCs is modeled as a random variable that obeys an exponential distribution. n The expected waiting time is denoted as Γ n ;

[0023] Energy costs and service costs are part of EV u k To EVCs O n The direct costs are paid by u, while the travel costs and waiting costs are paid by u k Indirectly generated, electric vehicles k Replace O n The effective charging cost of charging is expressed as:

[0024]

[0025]

[0026] Located in k EV u k With EVCs O n The distance between them is:

[0027]

[0028] Furthermore, in step S1, the EVCs profit is as follows:

[0029] EVCs n The revenue collected without charging a specific EV is O n The charging energy cost is EV's profit is Specific EVCs O n The total profit can be calculated from O n The sum of the profits of the electric vehicles collected is obtained;

[0030] EVCs n The captured length segment is defined as the demand length (DL), denoted by Ψ n , O n The expected total profit is: Where Π n O n The expected total profit, E{·} represents the expectation, Indicates EVCs O n The terminal cost is ρ, which represents the number of electric vehicles located within a unit distance; EVCs need to exchange their charging price components regularly. And the expected waiting time (Γ n) to achieve NE by investigating the choice patterns of EV drivers in a common market, assuming that all EV drivers know the common market parameters of expected travel cost, expected waiting cost and EV density.

[0031] Furthermore, step S2 specifically includes the following steps:

[0032] S21. Calculate the flexibility cost of loads and generators:

[0033]

[0034]

[0035] Where ΔP k L , ΔQ k L , ΔLP i G and ΔQ i G represents the amount of active and reactive power flexibility activated from each load k and generator i, c k PL 、c k QL 、c i PG 、c i QG A function representing the activation cost per MWh or Mvarh of flexibility; the activation price is derived directly from the price in the offer submitted by the market agent to the flexibility market;

[0036] S22. Calculate rOLTC transformer flexibility cost:

[0037]

[0038] Where Δtap ij t j represents the tap change of each OLTC connecting nodes i and j, c t OLTC The cost of is the cost function of changing the OLTC location to its neighbor;

[0039] S23. Calculate the flexibility cost of reactive power compensator:

[0040]

[0041] Where ΔQ c position The position is associated with the position change of each reactive compensator c, and the corresponding cost function is given by c c RCGiven, only condenser based power compensators are considered.

[0042] Furthermore, in step S3, the process of establishing the pricing model of the N competing EVCSs is as follows:

[0043] N EVCs are users, with O n Indicates; by user O n Price selection made O n Action at NE Indicates: User O n The utility of n Defined as O n The expected profit of user O n The utility on NE is denoted as Π n * ;

[0044] Considering the decision-making of game participants at the beginning of the game, the existence of NE in the proposed game model is analyzed. A network element is a cross section. For each user O n ,

[0045] Under the market share condition, electric vehicles are in O n and O n+1 Between the positions, consider two adjacent EVCsO n and O n+1 EV u k , there exists a point s k , so that l n k <l n+1 , the electric car is at point O n and O n+1 The charging cost of each EV is equal to the critical point (CP), at which the EV can choose two adjacent EVCSsO n and O n+1 Any one of them, CP is the decision point of EV related to the adjacent EVCs, EV u k The problem of finding CP can be expressed as: for adjacent user O n and O n+1 , find CP as:

[0046] Adjacent participant O n and O n+1 , CP D of n∈{1,2,…,N-1} n,n+1 (x), belongs to the class with energy requirement δ k and the unit distance travel cost C​k EV u k , expressed as:

[0047]

[0048] In the formula, η n Indicates O n The unit energy consumption, and Respectively represent O n and O n+1 Waiting time; C ω is the waiting cost per unit time;

[0049] Under the market sharing condition, the two adjacent CPs D n,n+1 (x) and D n-1,n (x) between EVs will find EVCsO n is the most cost-effective, among which D n,n+1 (x) is the adjacent EVCsO n and O n+1 CP; D n-1,n (x) is EVCs O n-1 and O n Corresponding CP;

[0050] For u k EVCs n The charging cost provided will be greater than EVCs O n+1 , if EV is located at D n,n+1 (x), then EV reaches EVCs O n The distance is less than EVCs O n+1 distance.

[0051] Furthermore, the closed-form expression of EVCs service price and EVCs profit is established as follows:

[0052] Under market sharing conditions, participant O n Action belongs to a given compact set, and In the formula,

[0053] Located between two adjacent CPs D n,n+1 (x) and D n-1,n (x) between EVs will find EVCsO n is the most cost-effective among all EVCs, so, substituting D n,n+1(x) Get the DL expression Q of EVCs n , n∈{1,2…N};

[0054]

[0055] EVCs n Service price Compared with other EVCsO -n Price P f-n The utility representation of can be simplified as:

[0056]

[0057] User O n The reaction function is obtained by differential utility Π n Behavior Get, record as The utility corresponding to the NE behavior gives the NE utility of each user, and the user's reaction function is:

[0058]

[0059] in,

[0060] Further, consider a three-player game where each player Q n , n∈{1,2…N} actions on NE for:

[0061]

[0062] In the formula,

[0063] Each participant n NE Utility for:

[0064]

[0065] In the formula, J 1 =(η 3 +4η 2 -5η 1 ), J 2 =(2η 3 -4η 2 +2η 1 ), J 3 =(-5η 3 +4η 2 +η 1 );

[0066] A participant’s NE price depends not only on its own strategic position but also on the fixed strategic positions of other participants, as a special case of symmetric EVCs positions, where Π 1 * =Π 3 * , at NE, participant O 1 The price and 3 The same price as NE 1 and O 3 The utility is equal.

[0067] The present invention can achieve the following technical effects:

[0068] The charging station pricing method provided by the present invention considers the flexibility of electric vehicles and distributed power sources, models the electric vehicle charging nodes as non-cooperative selfish nodes, and maximizes profits by selecting appropriate service costs in the electric vehicle charging costs, while the electric vehicles minimize the charging costs by selecting the most cost-effective electric vehicle charging nodes. Based on the location of the transportation system, the expected waiting time, energy costs, service costs and transportation costs, the criteria for electric vehicles to select transportation systems are derived, and the non-cooperative behavior of EVCs is considered using game theory methods. A closed expression of EVCs service prices following EVCs profits is established, and the results are verified by mathematical analysis and simulation. However, since CSPs are non-cooperative in typical electric vehicle charging competition market scenarios, electric vehicle owners do not have to follow any centralized decision to select EVCs, but can independently select cost-effective CSPs. Therefore, the present invention proposes a solution using game theory methods and considers the selfish and rational behavior of electric vehicles. In addition, the Hotelling game provides a suitable closed-form expression for the NE condition in a non-cooperative environment. The results of the model are compared with the social welfare scenario (SWPS). The results show that the utility of the model is higher than that of the SWPS for all EVCs. The proposed strategy does not limit the number of charging points deployed by EVCs. However, increasing the number of charging points will reduce the expected waiting time of electric vehicles in specific EVCs (Little's law), and the waiting cost will be reduced. Therefore, more electric vehicles will choose EVCs. Setting up additional charging points is equivalent to increasing the terminal cost of EVCs, so the trade-off between terminal cost and profit will be observed by EVCs. The proposed pricing method is effective for achieving the NE condition for discrete-time dynamic market scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 is a flow chart of a charging station pricing method considering the flexibility of electric vehicles and distributed power sources provided in accordance with an embodiment of the present invention;

[0070] Figure 2 is a schematic diagram of flexibility areas with different maximum flexibility costs provided by an embodiment of the present invention;

[0071] Figure 3 It is EVCsO provided according to an embodiment of the present invention. 1 ,O 2 ,O 3 The intersection of the reaction functions gives the price diagram of EVCs at NE;

[0072] Figure 4 is a schematic diagram illustrating the influence of PQ interdependence and specific network characteristics on flexibility regions according to an embodiment of the present invention;

[0073] Figure 5 is a schematic diagram of an optimal EVCs selection algorithm for electric vehicles provided according to an embodiment of the present invention;

[0074] Figure 6 Schematic diagram of a Nash equilibrium algorithm for a Hotelling game between non-cooperative EVCs provided according to an embodiment of the present invention. DETAILED DESCRIPTION

[0075] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In the following description, the same modules are represented by the same reference numerals. In the case of the same reference numerals, their names and functions are also the same. Therefore, the detailed description thereof will not be repeated.

[0076] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0077] The embodiment of the present invention provides a charging station pricing method that takes into account the flexibility of electric vehicles and distributed power sources. The process is as follows: Figure 1 As shown, the specific steps are as follows:

[0078] Step 1: Establish a comprehensive charging pricing model.

[0079] A charging station pricing approach for EVs with distributed generation flexibility is considered, in which multiple static EV companies engage in a price war to attract more EVs for charging in order to maximize profits. A discrete-time dynamic model provides a more natural framework to describe the actual situation, where market parameters can be assumed to be static over a time interval. EVs are selfish and approach the EVCs that provide charging at the lowest charging cost. A comprehensive charging pricing model is established by assuming that the grid is connected to all EV charging stations to provide the required energy.

[0080] Step 1.1: Components of charging price for electric vehicles: Consider an electric vehicle with energy demand represented by δ k , for example, to select a specific EVCs for charging, then the EVCs selection criteria for EVs depends on the following components:

[0081] a) Energy costs: EVCs O n Energy cost components provided It means that where η n Indicates EVCs O n Cost per unit of energy generated (grid energy cost).

[0082] b) Service cost: EVCs O n Energy cost components provided It means that in is a fixed unit of energy. n Charging electric cars, Remain unchanged.

[0083] c) Travel expenses: Indicates that an electric car arrives at O n The driving energy consumed at this point is Among them C k Indicates u k The travel cost per unit distance, Indicates u k With O n The distance between k is modeled as a random variable with uniform distribution, C k The expected value of μ .

[0084] d) Waiting cost: EV u k Replace in EVCs O n The effective waiting cost of waiting in line is expressed as Defined as: Among them C ω represents the waiting cost per unit time, is the waiting time of EVCs, and the waiting time of EVCs is modeled as a random variable that obeys an exponential distribution. n The expected waiting time is denoted as Γ n .

[0085] Energy costs and service costs are partly considered as EV u k To EVCs O n The direct cost is paid by u, while the transportation cost and waiting cost are partly paid by uk Therefore, electric vehicles k Replace O n The effective charging cost of charging is expressed as: but:

[0086]

[0087] Among them, located at s k EV u k With EVCs O n The distance between them is:

[0088]

[0089] By selecting an EVCs O i / O j EV u k The profit of , i≠j, is defined as:

[0090] Step 1.2: Profits of EVCs: EVCs need to periodically exchange (display) their charging price components and the expected waiting time (Γ n ) to realize NE.

[0091] EVCs n Revenue collected without charging a specific EV is considered O n The charging energy cost is Therefore, the profit of EV is Specific EVCs O n The total profit can be calculated from O n The sum of the profits collected by all electric vehicles is given by n The expected value of total profit is all the values ​​close to O. n The expected value of the total profits of electric vehicles. n The captured length segment is defined as the demand length (DL), denoted by Ψ n Therefore, O n The expected total profit is: Where Π n O n The expected total profit, E{·} represents the expectation, Indicates EVCs O n The terminal cost is ρ, which represents the number of electric vehicles located per unit distance. EVCs need to exchange (display) their charging price components regularly. And the expected waiting time (Γ n ) to achieve NE. By investigating the choice patterns of EV drivers in a common market, it is assumed that all EV drivers know common market parameters such as expected travel cost, expected waiting cost and EV density.

[0092] Step 2: Due to the significant increase in the penetration of distributed renewable energy in the distribution network, which has led to an increase in technical problems in the transmission and distribution systems, and the lack of power flow coordination at the system operator interface, the flexibility provided by distributed energy resources (DER) is used to estimate the flexibility range of the distribution and transmission system operator (TSO-DSO) boundary nodes. The specific steps are as follows:

[0093] Step 2.1: The range of flexibility available at the TSO-DSO boundary node depends on the different types of flexible resources connected to the distribution network and is divided into three categories:

[0094] 1) Market-based, including active power flexibility provided by aggregators or other market participants (e.g. loads, storage, DRES) in short-term flexibility markets (e.g. traditional reserve markets) or in medium-term flexibility;

[0095] 2) Network assets usually owned by DSOs, such as on-load tap changers (OLTCs), transformers, reactive power compensators;

[0096] 3) Regulated flexibility.

[0097] Step 2.2: The activation of flexibility constitutes a service provided by the corresponding resource and therefore has an associated cost, so the flexibility of different resources is calculated using different cost formulas:

[0098] 1)r Load and generator flexibility costs:

[0099]

[0100]

[0101] Where ΔP k L , ΔQ k L , ΔP i G and ΔQ i G represents the amount of active and reactive power flexibility activated from each load k and generator i (e.g. DRES), c k PL 、c k QL 、c i PG、c i QG Function representing the activation cost per MWh or Mvarh of flexibility; the activation price is derived directly from the price in the offer submitted by the market agent to the flexibility market.

[0102] 2)rOLTC transformer flexibility cost:

[0103]

[0104] Where Δtap ij t j represents the tap change of each OLTC connecting nodes i and j, c t OLTC The cost (in m) is the cost function of changing the OLTC location to its neighbor. This scheme proposes an optimal reactive power dispatch model and tries to minimize the global cost (i.e., taking into account the required cost) to adjust the control device set points.

[0105] 3)r Reactive power compensator flexibility cost:

[0106]

[0107] Among them, ΔQ c position The position is associated with the position change of each reactive compensator c, and the corresponding cost function is given by c c RC are given (in nanometers), where only condenser-based power compensators are considered. The cost of a synchronous compensator with continuously varying can be calculated using the formulas defined for the load and generator in (3) and (4), respectively. Each cost function varies with the direction (i.e., upward or downward) and magnitude of the requested flexibility, as well as the market offer of the flexibility operator. While the current version of the algorithm considers a quadratic cost function, it would be straightforward to include a different relationship and the effectiveness of the proposed approach would not be affected by such variations.

[0108] Step 2.3: Output by extracting a set of benefits in the active power and reactive power flexibility diagrams.

[0109] Figure 2 Four different flexibility regions are presented. Each corresponds to a maximum flexibility cost. Therefore, each region shows a feasible point area that can be achieved at the TSO-DSO boundary node by maximizing the corresponding flexible resource activation cost, and the active area grows with the cost that the user is willing to pay. If flexibility is not activated, the system will be at the predetermined operating point ( Figure 2 The visualization provided by the flexibility map provides important support for the following aspects, such as:

[0110] 1) estimates the minimum cost of moving the operating point from a predetermined location to a predetermined location and the other is to activate the flexible resources available in the distribution network without violating any technical constraints.

[0111] 2) Supporting the fulfilment of regulatory requirements in terms of reactive power ratios in the TSO-DSO interface, flexibility zones provide a range of viable alternatives for forecasting operating points and can help decision makers find the best way to comply with pre-defined values. This last aspect is relevant for several countries.

[0112] Step 3: Model the electric vehicle as a selfish node. Since electric vehicles prefer to provide the electric vehicle with the lowest charging cost, the equilibrium conditions of pricing and profit of multiple non-cooperative EVCS are obtained by using the game theory method, and the appropriate pricing model of N competing EVCSs in a market sharing environment is found by using Hotelling's game method. The specific steps are as follows:

[0113] Step 3.1: First consider a market sharing environment where N EVCs compete in a price war to maximize their expected profits. For the game model considering non-cooperative games between N EVCs, the existence of NE can be proved. Therefore, this scenario can be modeled as a static game with the following elements:

[0114] 1) User: N EVCs are users, with O n express;

[0115] 2) Action: By user O n Price selection made Participant O n Action at NE express;

[0116] 3) Utility: Use Π n Indicates that user O n The utility of n Defined as O n The expected profit of user O n The utility on NE is denoted as Π n * .

[0117] Considering the decision-making of game participants at the beginning of the game, the existence of NE in the proposed game model is analyzed. A network element is a cross section. So that for each user O n ,

[0118] Under the market share condition, electric vehicles are in O n and O n+1Some electric vehicles will think that O n More cost-effective, and the remaining electric vehicles will find O n+1 More cost-effective. Consider two adjacent EVCs O n and O n+1 EV u k Therefore, there exists a point s k , so that l n k <l n+1 , the electric car is at point O n and O n+1 The charging cost of each EV is equal to the critical point (CP), at which the EV can choose two adjacent EVCs. n and O n+1 Therefore, CP is the decision point of EV with respect to the adjacent EVCs, EV u k The problem of finding CP can be expressed as:

[0119] (P1) For neighboring user O n and O n+1 , find CP as:

[0120] Lemma 1: Adjacent participant O n and O n+1 , CP D of n∈{1,2,…,N-1} n,n+1 (x), belongs to the class with energy requirement δ k and the unit distance travel cost C k EV u k , expressed as:

[0121]

[0122] In the formula, η n Indicates O n The unit energy consumption, and Respectively represent O n and O n+1 Waiting time; C ω is the waiting cost per unit time.

[0123] Proof: Consider a point s k EV u∈[0,L] k , only when , point s k ,l n k <l​​n+1 With adjacent EVCs O n and O n+1 , CPD of n∈{1,2,…N-1} n,n+1 (x). n k <l n+1 , we get |s k -l n |=(s k -l n ) and |s k -l n+1 |=l n+1 -s k In addition, Substitute (1) into and You can get direct results.

[0124] Lemma 2: Under the market sharing condition, the two adjacent CPs O n,n+1 (x) and D n-1,n (x) between EVs will find EVCs O n is the most cost-effective, among which D n,n+1 (x) are adjacent EVCs O n and O n+1 CP; D n-1,n (x) is EVCs O n-1 and O n Corresponding CP.

[0125] Proof: Consider an electric car u k , its energy requirement δ k and the unit distance travel cost C k Located at point s k , where l n k <l n+1 . Further, consider point s k With D n,n+1 (x). Therefore, from (P1) we get Using formula (1), we can get:

[0126]

[0127] Consider a point s′ where l n <s′<l n+1 , s′ k , therefore, |s k -l n |>|s′-l n | and |s k -l n+1 ​​​|<|s′-l n+1 Substituting these relations into equation (8), we obtain:

[0128]

[0129] It can be seen from formula (9) that for EV u k , EVCs O n Provides charging cost lower than EVCs O n+1 , because when EV is located at D n,n+1 (x), then EV reaches EVCs O n The distance is less than EVCs O n+1 Furthermore, when s′ is located at CP D n,n+1 (x), then we have s′>s k For l n <s′<l n+1 . Therefore, there is |s k -l n |<|s′-l n | and |s k -l n+1 |>|s′-l n+1 |, from formula (4) we can get:

[0130]

[0131] For u k EVCs n The charging cost provided will be greater than EVCs O n+1 , if EV is located at D n,n+1 (x), then EV reaches EVCs O n The distance is less than EVCs O n+1 The above parameters can be used in all CPs D n,n+1 (x),n∈{1,2,…,N-1}, to obtain the result.

[0132] Step 4: Summarize Lemma 1 and Lemma 2 in Step 3 and establish a closed expression for EVCs service price and EVCs profit, followed by a detailed mathematical analysis. The specific steps are as follows:

[0133] Step 4.1: The proposed charging station pricing strategy is effective for achieving the NE condition of the EV and DG flexibility scenario, where the parameters can be considered static over a time interval that depends on the market behavior.

[0134] Lemma 3: Under market sharing conditions, participant O n Action belongs to a given compact set, and in,

[0135] From Lemma 1 and Lemma 2, we can conclude that the D n,n+1 (x) and D n-1,n EVs between (x) will find EVCs O n is the most cost-effective among all EVCs, so substituting Lemma 1 into D n,n+1 (x), and obtain the DL expression Q of EVCs n , n∈{1,2…N}, is:

[0136]

[0137] Substituting equation (11) into Ψ n , substitute formula (10) into D n,n+1 (x), then EVCs O n Service price Compared with other EVCs O -n Price The utility representation of can be simplified as:

[0138]

[0139] Proof: Consider two adjacent users O n and O n+1 , assuming that the entire market is occupied by participants O n+1 Occupation, only when O n Charging costs provided Greater than O n+1 Charging costs provided Therefore, for the k EV u k , The relationship can be written as follows from equations (1) and (2):

[0140]

[0141] After rearranging the terms, equation (13) can be written as:

[0142]

[0143] If k > n+1 , then formula (14) can be written as:

[0144]

[0145] If k <l n , then formula (15) can be written as:

[0146]

[0147] If l n k <l n+1 , then formula (16) can be expressed as:

[0148]

[0149] For l n k <l n+1 , Formula (17) shows that the entire market is occupied by participant O n+1 Occupy, then Must be greater than and at least greater than Expression l n k <l n+1 can be equivalently written as:

[0150] (l n -l n+1 )<(l n+1 +l n -2s k )<(l n+1 -l n ); (18)

[0151] Therefore, from the above equations (15) to (18), it can be concluded that under the following conditions, all markets are O n+1 occupied:

[0152]

[0153] Using similar arguments, user O n Will capture all markets if:

[0154]

[0155] For EVCs O n and O n+1 In the shared market, equations (19) and (20) are not valid. Under the market share, we have:

[0156]

[0157] Rearranging (21) yields Lemma 3.

[0158] ​​​Lemma 4: Under market sharing conditions and the set of actions satisfying Lemma 3, there exists a unique pure strategy NE(5) describing the utility.

[0159] User O n The reaction function is recorded as This is done by differentiating the utility Π n Behavior Further, we need to solve the reaction function to find the NE action spectrum. The utility corresponding to the NE behavior gives the NE utility of each user, and the user's reaction function is

[0160]

[0161] in,

[0162] Proof: From formula (12), we can see that This shows that the analytical utility Π n Relative to their effects n∈(1,2…N) is concave (quasi-concave). In addition, from Lemma 3, we can see that the action n∈(1,2…N) is compact. Therefore, under compact action sets and concave utility, the existence of pure strategy NE is proved.

[0163] Consider a three-player game where each player Q n , n∈{1,2…N} actions on NE for:

[0164]

[0165] In the formula,

[0166] Each participant n NE Utility for:

[0167]

[0168] In the formula, J 1 =(η 3 +4η 2 -5η 1 ), J 2 =(2η 3 -4η 2 +2η 1 ), J 3 =(-5η 3 +4η 2 +η 1 ).

[0169] The trilinear relationship obtained in Equation (23) shows that the NE price of a participant depends not only on its own strategic position, but also on the fixed strategic positions of other participants in the game. As a special case of symmetric EVCs positions, Then we can get from formula (6) From formula (24), we can get 1 * =Π 3 * Therefore, at NE, participant O 1 The price and 3 The price is the same, and it is more intuitive that at NE O 1 and O 3 The utility is equal.

[0170] Proof: Consider N = 3in(6), the reaction function is:

[0171]

[0172]

[0173]

[0174] By solving the above linear equations (25) to (27), we can get the corresponding participant O n NE Action This proves formula (23). Furthermore, the utility obtained by formula (12) is Substituting N=3, we obtain the NE utility expressed by equation (24).

[0175] Step 4.2: Since the proposed charging station pricing strategy is effective for considering the flexibility of electric vehicles and distributed power sources, where the parameters can be considered static within a time interval depending on market behavior, the algorithm and specific parameters of this embodiment are as follows:

[0176] like Figure 3 Shown: EVCsO 1 ,O 2 ,O 3 The reaction function satisfies equation (22), and the intersection point gives the price of EVCs at NE.

[0177] parameter:

[0178] N=3,L=12km,l 1 =2km,l 2 =6km,l 3 =10km,C k ∈[0.5,1.5]($ / km),ρ=50 / km,μ 1=60(kWh),σ=5.77(kWh),Γ 1 =Γ 2 =0.4(hr),Γ 3 =0.5(hr),C ω =4$ / h,η 1 =η 2 =η 3 =0.3 ($ / kWh).

[0179] The effect of PQ interdependence and specific network characteristics on the flexibility region is illustrated in Figure 4 As shown in the figure, the optimal EVCs selection algorithm for electric vehicles is as follows: Figure 5 As shown in the figure, the Nash equilibrium algorithm of the Hotelling game between non-cooperative EVCs is as follows: Figure 6 shown.

[0180] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0181] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

[0182] The above specific implementations of the present invention do not constitute a limitation on the protection scope of the present invention. Any other corresponding changes and modifications made based on the technical concept of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A charging station pricing method considering the flexibility of electric vehicles and distributed power sources, characterized in that: The steps include: S1. Establish a comprehensive charging pricing model, including the charging price composition of charging stations and the profits of electric vehicle charging stations (EVCs). S2, using distributed energy resources (DER) to obtain the flexibility range of the distribution and transmission system operator (TSO-DSO) boundary nodes; S3. The equilibrium conditions of pricing and profit of non-cooperative EVCs are obtained through game theory, and the pricing model of N competing EVCSs in a market sharing environment is obtained by using Hotelling's game method. S4. Establish a closed expression for EVCs service price and EVCs profit and conduct mathematical analysis.

2. The charging station pricing method considering the flexibility of electric vehicles and distributed power sources according to claim 1 is characterized in that: In step S1, the charging price of the electric vehicle includes energy cost, service cost, travel cost and waiting cost; The expression of energy cost is as follows: In the formula, Indicates EVCs O n Provided energy cost component, η n Indicates EVCs O n Cost per unit of energy generated, δ k represents energy demand; The expression of the service cost is as follows: In the formula, Indicates EVCs O n Cost of services provided, represents the fixed cost per unit of energy; for all n Charging electric cars, remain unchanged; The expression of the travel cost is as follows: use Indicates that an electric car arrives at O n The driving energy consumed at the point C k Indicates u k The travel cost per unit distance, Indicates u k With O n The distance between k Modeled as a random variable with uniform distribution, C k The expected value of μ ; The expression of the waiting cost is as follows: EV k Replace in EVCs O n The effective waiting cost of waiting in line is expressed as C ω represents the waiting cost per unit time, is the waiting time of EVCs, and the waiting time of EVCs is modeled as a random variable that obeys an exponential distribution. n The expected waiting time is denoted as Γ n ; Energy costs and service costs are part of EV u k To EVCs O n The direct costs are paid by u, while the travel costs and waiting costs are paid by u k Indirectly generated, electric vehicles k Replace O n The effective charging cost of charging is expressed as: Located in k EV u k With EVCs O n The distance between them is:

3. The charging station pricing method considering the flexibility of electric vehicles and distributed power sources according to claim 2 is characterized in that: In step S1, the EVCs profit is as follows: EVCs n The revenue collected without charging a specific EV is O n The charging energy cost is EV's profit is Specific EVCs O n The total profit can be calculated by O n The sum of the profits of the electric vehicles collected is obtained; EVCs n The captured length segment is defined as the demand length (DL), denoted by Ψ n , O n The expected total profit is: Where Π n O n The expected total profit, E{·} represents the expectation, Indicates EVCs O n The terminal cost is ρ, which represents the number of electric vehicles located within a unit distance; EVCs need to exchange their charging price components regularly. And the expected waiting time (Γ n ) to achieve NE by investigating the choice patterns of EV drivers in a common market, assuming that all EV drivers know the common market parameters of expected travel cost, expected waiting cost and EV density.

4. The charging station pricing method considering the flexibility of electric vehicles and distributed power sources according to claim 1 is characterized in that: Step S2 specifically includes the following steps: S21. Calculate the flexibility cost of loads and generators: In the formula, ΔP k L , ΔQ k L , ΔP i G and ΔQ i G represents the amount of active and reactive power flexibility activated from each load k and generator i, c k PL 、c k QL 、c i PG 、c i QG A function representing the activation cost per MWh or Mvarh of flexibility; the activation price is derived directly from the price in the offer submitted by the market agent to the flexibility market; S22. Calculate rOLTC transformer flexibility cost: Where Δtap ij t j represents the tap change of each OLTC connecting nodes i and j, c t OLTC The cost of is the cost function of changing the OLTC location to its neighbor; S23. Calculate the flexibility cost of reactive power compensator: Where ΔQ c position The position is associated with the position change of each reactive compensator c, and the corresponding cost function is given by c c RC Given, only condenser based power compensators are considered.

5. The charging station pricing method considering the flexibility of electric vehicles and distributed power sources according to claim 1 is characterized in that: In step S3, the process of establishing the pricing model of N competing EVCSs is as follows: N EVCs are users, with O n Indicates; by user O n Price selection made O n Action at NE Indicates: User O n The utility of n Defined as O n The expected profit of user O n The utility on NE is denoted as Π n * ; Considering the decision-making of game participants at the beginning of the game, the existence of NE in the proposed game model is analyzed. A network element is a cross section. For each user O n , Under the market share condition, electric vehicles are in O n and O n+1 Between the positions, consider two adjacent EVCs O n and O n+1 EV u between k , there exists a point s k , so that l n k <l n+1 , the electric car is at point O n and O n+1 The charging cost of each EV is equal to the critical point (CP), at which the EV can choose two adjacent EVCSsO n and O n+1 Any one of them, CP is the decision point of EV related to the adjacent EVCs, EV u k The problem of finding CP can be expressed as: for adjacent user O n and O n+1 , find CP as: ​ Adjacent participant O n and O n+1 , CP D of n∈{1,2,…,N-1} n,n+1 (x), belongs to the class with energy requirement δ k and the unit distance travel cost C k EV u k , expressed as: In the formula, η n Indicates O n The unit energy consumption, and Respectively represent O n and O n+1 Waiting time; C ω is the waiting cost per unit time; Under the market sharing condition, the two adjacent CPs D n,n+1 (x) and D n-1,n (x) between EVs will find EVCs O n is the most cost-effective, among which D n,n+1 (x) are adjacent EVCs O n and O n+1 CP; D n-1,n (x) is EVCs O n-1 and O n Corresponding CP; For u k EVCs n The charging cost provided will be greater than EVCs O n+1 , if EV is located at D n,n+1 (x), then EV reaches EVCs O n The distance is less than EVCs O n+1 distance.

6. The charging station pricing method considering the flexibility of electric vehicles and distributed power sources according to claim 1 is characterized in that: Step S4, establish a closed expression of EVCs service price and EVCs profit as follows: Under market sharing conditions, participant O n Action belongs to a given compact set, and In the formula, Located between two adjacent CPs D n,n+1 (x) and D n-1,n EVs between (x) will find EVCs O n is the most cost-effective among all EVCs, so, substituting D n,n+1 (x) Get the DL expression Q of EVCs n , n∈{1,2…N}; EVCs n Service price Compared with other EVCs O -n Price The utility representation of can be simplified as: User O n The reaction function is obtained by differential utility Π n Behavior Get, record as The utility corresponding to the NE behavior gives the NE utility of each user, and the user's reaction function is: in, 7. The charging station pricing method considering the flexibility of electric vehicles and distributed power sources according to claim 6 is characterized in that: Consider a three-player game where each player Q n , n∈{1,2…N} actions on NE for: Each participant n NE Utility for: In the formula, J1=(n3+4n2-5n1), J2=(2n3-4n2+2n1), J3=(-5n3+4n2+n1); The NE price of a participant depends not only on its own strategic position, but also on the fixed strategic positions of other participants, as a special case of symmetric EVCs positions, where l1=L-l3, At NE, the price of participant O1 is the same as the price of O3, and at NE the utilities of O1 and O3 are equal.

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