CN113609693B

CN113609693B - Heterogeneous vehicle owner charging behavior modeling method based on improved accumulation prospect theory

Info

Publication number: CN113609693B
Application number: CN202110929762.XA
Authority: CN
Inventors: 权轶; 陆军军; 冯万璐; 付波
Original assignee: Hubei University of Technology
Current assignee: Hubei University of Technology
Priority date: 2021-08-13
Filing date: 2021-08-13
Publication date: 2024-04-19
Anticipated expiration: 2041-08-13
Also published as: CN113609693A

Abstract

The invention belongs to the technical field of electric vehicle charging behavior control, and discloses a heterogeneous vehicle owner charging behavior modeling method based on an improved accumulated prospect theory, wherein the accumulated prospect theory is introduced to model electric vehicle charging behaviors, an electric vehicle real-time charging decision preference problem model is established by taking an accumulated prospect value of electric vehicle benefits as an evaluation index and taking electric vehicle charging time and charging capacity as sensitivity analysis parameters.

Description

Heterogeneous vehicle owner charging behavior modeling method based on improved accumulation prospect theory

Technical Field

The invention belongs to the technical field of electric vehicle charging behavior control, and particularly relates to a heterogeneous vehicle owner charging behavior modeling method based on an improved accumulation prospect theory.

Background

Currently, the number of electric vehicles is greatly increased, and the rising trend is kept, so that it is estimated that the electric vehicles will probably become one of the most numerous power grid loads in the future. At present, a disordered charging mode of the electric vehicle, namely, random charging at any time and any place, is easy to cause a large number of electric vehicles to charge in a concentrated manner in a power grid load peak period, so that a load peak value of a power grid is increased, higher requirements are provided for the power generation capacity and the power transmission capacity, the charging randomness of the electric vehicle is slightly disturbed, namely, the charging starting time and the charging capacity change can greatly influence the local power grid load, the influence of the electric vehicle charging on the power grid load is related to the scale of the electric vehicle, and the charging behavior of the electric vehicle is directly related to the electric vehicle, so that the analysis of the charging behavior of the electric vehicle has positive significance for solving the problem of overload of the power grid load.

Modeling is carried out on the charging behavior of the electric vehicle by a plurality of students, modeling is carried out on the required power of the charging of the electric vehicle by Wang Xiaoyin, and a benefit function of the charging of the electric vehicle owner is established, but the influence of initial charge distribution on the model is not analyzed in the model, luo Zhuowei analyzes different charging modes of different types of electric vehicles, and the initial charging time and the initial charge distribution are analyzed when the electric vehicle is charged and modeled, but the influence of irrational factors on the charging behavior of the electric vehicle is not analyzed; liang Yuanbo, modeling the charging behavior of the electric vehicle, and taking the minimum energy consumption as a target, but neglecting the influence of charging cost on the charging behavior of the electric vehicle; guo Jianlong is used for modeling the charging load of the electric vehicle, analyzing the influence of the starting charging time and the starting charging load, but the modeling basis is based on a rational vehicle owner and lacks analysis of the charging behavior of a non-rational vehicle owner; tian Liting establishes a statistical model for the power requirement of the electric vehicle, and the model analyzes the influence of random variables such as the starting charging time, charging power and the like of the electric vehicle, but ignores the influence of charging cost on charging selection; modeling the electric vehicle charging through the model, analyzing the influence of the electric vehicle charging behavior on the model, solving the model through an improved genetic algorithm, determining an optimization management strategy, optimizing the travel strategy of the electric vehicle by taking the minimum cost loss as a target when modeling the electric vehicle charging behavior through Hao Lili, wherein the model does not analyze the influence of irrational factors on the charging behavior, and taking the charging cost of a charging user as a charging target when guiding the charging behavior of the electric vehicle through the Wang Yi when preparing the electricity price strategy, wherein the expected utility theory and/or the random utility theory are used for quantifying the perception of the network uncertainty by the traveler. It is well known that these theories are based on the fact that the vehicle owner is fully rational and has a complete grasp of all charging information and charging results when making a charging decision. However, in real life, a person's behavior is often affected by factors such as his personality, mental state, risk preferences, and environmental factors. The results of practical experiments performed by behavioural scientists indicate that assumptions about the absolute rationality of individuals are not true in real life and that the decision maker's view of rationality is increasingly challenged.

The charging behavior of the electric vehicle has strong randomness and disorder, and the charging behavior can be influenced by the self-character and risk preference of the vehicle owner, so that the vehicle owner cannot achieve complete rationality when making an actual charging decision, and the expected utility theoretical model on the premise of complete rationality assumption cannot meet the actual requirement, so that a plurality of students at home and abroad try to find a new method to describe the limited rational behavior characteristics of the electric vehicle when making the charging decision.

The modeling of the electric vehicle charging is mostly based on the fact that the vehicle owner is completely rational and is performed under certain conditions, however, in real life, the vehicle owner cannot be completely rational, and the charging behavior of the electric vehicle is influenced by subjective factors such as an initial charge amount, a starting charging time, an arrival time and charging cost of objective factors, and subjective factors such as characteristics of the vehicle owner and risk preference. In order to solve the problem, the invention introduces an accumulated prospect theory to model the charging behavior of the electric vehicle. Modeling of a heterogeneous reference point of an accumulated prospect theory is lacking in China at present, so that in order to overcome the defects of the existing analysis on the setting of the reference point in the accumulated prospect theory and realize more accurate simulation of a charging decision of a vehicle owner, a new electric vehicle charging behavior control method is needed.

Through the above analysis, the problems and defects existing in the prior art are as follows:

(1) In the existing technical scheme for modeling the charging behavior of the electric vehicle, the minimum energy consumption is taken as a target, but the influence of the charging cost on the charging behavior of the electric vehicle is ignored; based on the rational car owners, the analysis of the charging behavior of the irrational car owners is lacking.

(2) The prior art ignores the influence of charging cost on charging selection; the model does not analyze the influence of irrational factors on the charging behavior, and the expected utility theory and/or the random utility theory are used for quantifying the perception of travelers on the network uncertainty.

(3) The charging behavior of the electric vehicle has strong randomness and disorder, and the expected utility theoretical model on the premise of complete rational assumption can not meet the actual demands.

(4) In the prior art, only one reference point is usually set when the behaviors of the irrational decision maker are analyzed based on the accumulated prospect theory, and the analysis of the heterogeneity reference point is lacked.

(5) The existing analysis lacks exploration of heterogeneous reference points with psychological perception, and the modeling of the heterogeneous reference points of the accumulated prospect theory is lacking in China.

The difficulty of solving the problems and the defects is as follows:

(1) The reference points are different from person to person and are influenced by a plurality of factors, and a heterogeneous reference point model with psychological perception is established by starting from two influencing factors of empirical psychological perception and psychological preference of the electric vehicle owners. The next effort is to analyze further influencing factors in different charging scenarios, however the complexity of the model increases.

(2) The traditional expected utility theoretical model only can describe the charging behavior of the rational car owners, and cannot explain the irrational charging behavior of irrational car owners.

The meaning of solving the problems and the defects is as follows:

(1) When an electric vehicle owner makes a charging decision, the charging behavior of the electric vehicle owner is a key factor with randomness and is interfered by very strong irrational factors, and the electric vehicle owner cannot accurately evaluate the current situation of the electric vehicle owner when making the charging decision, so that an inaccurate charging decision can be made, and therefore, the electric vehicle owner has very strong practical significance in researching the charging behavior of the irrational electric vehicle owner.

(2) The research on the charging behavior of the electric automobile has a certain reference significance for planning of a power distribution system, is favorable for analyzing how to better coordinate the stable operation of the power grid, and realizes peak clipping and valley filling.

Disclosure of Invention

Aiming at the problems existing in the prior art, the invention provides a heterogeneous vehicle owner charging behavior modeling method and system based on an improved accumulated prospect theory, and particularly relates to an electric vehicle real-time charging decision preference model based on an improved prospect theory of analyzing risk preference and heterogeneous reference points and a construction method thereof.

The invention is realized in such a way that a heterogeneous vehicle owner charging behavior modeling method based on an improved accumulated prospect theory comprises the following steps:

the method comprises the steps of taking an accumulated prospect value of electric vehicle benefits as an evaluation index, taking electric vehicle charging time and charging capacity as sensitivity analysis parameters, and establishing an electric vehicle charging decision preference problem model;

establishing a heterogeneity reference point model with psychological perception, and applying the heterogeneity reference point to the calculation of the accumulated foreground value.

Further, the heterogeneous vehicle owner charging behavior modeling method based on the improved accumulated prospect theory comprises the following steps of:

step one, establishing an electric vehicle charging decision preference model under random change of charging capacity and passenger order demands under different peak-to-average electricity price schemes by taking an accumulated prospect value of electric vehicle benefits as an evaluation index;

Step two, comprehensively evaluating the arrival time and the residual electric quantity, and establishing a reference experience perception model reflecting the objective current situation of the vehicle owner by using four psychological perception areas based on an experience psychological perception mode;

Step three, based on a reference experience perception model, establishing an analysis risk preference heterogeneous reference point model by introducing risk factors;

step four, taking a non-rational decision maker as an analysis object, combining objective perception of the decision maker with subjective risk preference, and establishing a heterogeneous reference point model with psychological perception;

and fifthly, applying the reference point model to the calculation of the accumulated foreground value.

Another object of the present invention is to provide a heterogeneous vehicle owner charging behavior modeling system based on an improved cumulative prospect theory, comprising:

The electric vehicle charging preference model construction module is used for constructing an electric vehicle charging preference model under the random change of charging capacity and guest bill demands under different peak-to-average electricity price schemes by taking the accumulated prospect value of the electric vehicle benefits as an evaluation index;

The system comprises a heterogeneous reference point model construction module with psychological perception, a reference experience perception model, a judgment module and a judgment module, wherein the heterogeneous reference point model construction module is used for comprehensively evaluating the arrival time and the residual electric quantity, and based on an experience psychological perception mode, four psychological perception areas are used for establishing a reference experience perception model reflecting the objective current situation of an owner.

Further, the heterogeneous reference point model construction module with psychological perception includes:

A psychological perception model building module based on current situation assessment and a heterogeneous reference point model building module for analyzing risk preference.

By combining all the technical schemes, the invention has the advantages and positive effects that: according to the heterogeneous vehicle owner charging behavior modeling method based on the improved accumulated prospect theory, the electric vehicle charging behavior is modeled based on the expected utility theory and the accumulated prospect theory, and the result shows that irrational factors of vehicle owners are analyzed under the accumulated prospect theory, compared with the traditional expected utility theory, the irrational factors of the vehicle owners are more accurate, however, the accumulated prospect theory can only describe the charging behaviors of the vehicle owners with the same risk preference, and in order to accurately describe the charging decision preference of heterogeneous vehicle owners, the invention provides a real-time charging decision preference model of the electric vehicle based on the improved prospect theory of analyzing risk preference and heterogeneous reference points. Firstly, an electric vehicle charging decision preference problem model is established by taking an accumulated prospect value of electric vehicle benefits as an evaluation index and taking electric vehicle charging time and charging capacity as sensitivity analysis parameters. And secondly, a variable reference point model for analyzing risk attitudes of heterogeneous vehicle owners is established, and the variable reference point is applied to foreground value calculation. The result shows that under the conditions of different risk preferences and heterogeneous reference points, the vehicle owners can show different charging decision behaviors, the simulation result is more practical, and the improved accumulation prospect theory is more accurate in describing the charging behaviors of the electric vehicle.

According to the invention, a decision model of a non-rational electric vehicle owner in charging is established based on an accumulated prospect theory, an expected utility theory is improved, but selection of a reference point in the accumulated prospect theory model has a larger influence on a prospect value calculation result, the reference point in the model represents a psychological expected benefit point of a charging decision maker, different people are analyzed to have different expected benefits in the future, a psychological reference point model is established, risk factors are introduced to describe risk preference attitudes of different people, the model is improved, the model is more practical, and the improved accumulated prospect theory decision model has a certain superiority in describing charging decision behaviors of the heterogeneous electric vehicle owner.

According to the invention, the heterogeneity of the vehicle owners is analyzed, the irrational people are used as the footholds for the different physiological perception of the current situation, the psychological perception coefficient is introduced, and the real-time charging behavior preference model of the electric vehicle based on the analysis risk preference and the improvement prospect theory of heterogeneous reference points is established. According to the invention, personal risk attitude preference is combined with heterogeneous reference points and is applied to accumulated prospect value calculation, so that the charging decision behaviors of non-rational electric vehicle owners for analyzing heterogeneous current psychological perception and different risk preference are analyzed.

The invention establishes an improved cumulative prospect theoretical model for analyzing risk preference and heterogeneous reference points. Meanwhile, an electric vehicle charging preference model with the accumulated prospect value of the electric vehicle benefits as an evaluation index and under different peak-to-average electricity price schemes and with the random change of charging capacity and passenger order requirements is established; by comprehensively evaluating the arrival time and the residual electric quantity, a reference experience perception model reflecting the objective current situation of the vehicle owner is established by using four psychological perception areas based on an experience psychological perception mode. On the basis, the risk heterogeneous reference perception model for analyzing the risk attitude of the heterogeneous vehicle owner is further established by introducing the risk factors; and taking a non-rational decision maker as an analysis object, combining psychological perception of the decision maker with subjective psychological preference, and establishing a non-rational person decision model for analyzing risk preference.

The invention takes the charging behavior of the electric vehicle as an analysis object and analyzes the finite rationality of the owner of the electric vehicle, introduces an accumulated prospect theory to model the charging behavior of the electric vehicle, proposes to take the accumulated prospect value of the electric vehicle income as an evaluation index, takes the charging time and the charging capacity of the electric vehicle as sensitivity analysis parameters, and establishes a real-time charging decision preference problem model of the electric vehicle, and the main work and the analysis results of the invention are as follows:

(1) According to the invention, the charging behavior of the owner of the electric vehicle is modeled based on the expected utility theoretical model, the passenger order quantity and the residual electric quantity are used as random variables, the electricity price multiple and the initial charge distribution are used as sensitivity parameters, the charging decision result of the owner of the electric vehicle under different arrival times is analyzed, and the simulation result shows that the charging decision result of the owner basically does not change when the electricity price multiple and the initial charge distribution change, so that the influence of irrational factors on the owner is limited under the expected utility theoretical model.

(2) The invention introduces the accumulated prospect theory to model the charging behavior of the electric vehicle, and the simulation result shows that when the electricity price multiple and the initial charge distribution change, the charging decision result of the electric vehicle owner changes to a certain degree and shows a certain regularity, so that the accumulated prospect theory model can better simulate the charging behavior of the non-rational vehicle owner.

(3) According to the method, a heterogeneous reference point model for analyzing the risk preference of the electric vehicle owner is established, and the heterogeneous reference points are applied to calculation of a foreground value, so that the result shows that the vehicle owner can show different charging decision behaviors under the conditions of different risk preference and heterogeneous reference points, the simulation result is more practical, and the simulation result of a desired effect theory and a cumulative foreground theory model is inaccurate.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments of the present invention will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.

Fig. 1 is a flowchart of a heterogeneous vehicle owner charging behavior modeling method based on an improved cumulative prospect theory provided by an embodiment of the invention.

FIG. 2 is a schematic diagram of a cost function provided by an embodiment of the present invention.

Fig. 3 is a schematic diagram of a weight function according to an embodiment of the present invention.

Fig. 4 is a schematic diagram of expected values of three charging schemes at 1 power price according to an embodiment of the present invention.

Fig. 5 is a schematic diagram of expected values of three charging schemes at 3 power rates provided by an embodiment of the present invention.

Fig. 6 is a schematic diagram of a structural framework of the cumulative foreground theory provided by the embodiment of the invention.

FIG. 7 is a graph showing cumulative prospect values at 1 time of electricity price according to the embodiment of the present invention.

FIG. 8 is a graph showing cumulative prospect values at 3-fold electricity prices provided by the embodiments of the present invention.

Fig. 9 is a schematic diagram of cumulative foreground values of the residual electric quantity at 0.2-0.35 according to the embodiment of the invention.

Fig. 10 is a schematic diagram of cumulative foreground values of the residual electric power at 0.35-0.5 according to the embodiment of the present invention.

Fig. 11 is a psychological security figure provided by an embodiment of the present invention.

Fig. 12 is a diagram showing the psychological security feeling after per unit value.

Fig. 13 is a diagram of psychological safety factor according to an embodiment of the present invention.

Detailed Description

The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.

Aiming at the problems existing in the prior art, the invention provides a heterogeneous vehicle owner charging behavior modeling method and system based on an improved accumulated prospect theory, and the invention is described in detail below with reference to the accompanying drawings.

As shown in fig. 1, the heterogeneous vehicle owner charging behavior modeling method based on the improved accumulated prospect theory provided by the embodiment of the invention comprises the following steps:

The electric vehicle charging behavior control system based on the improved accumulated prospect theory provided by the embodiment of the invention comprises:

The heterogeneous reference point model building module with psychological perception comprises:

The psychological perception model construction module based on the current situation assessment is used for comprehensively assessing the arrival time and the residual electric quantity and establishing a reference experience perception model reflecting the objective current situation of the vehicle owner by using four psychological perception areas based on the experience psychological perception mode.

And a heterogeneous reference point model construction module for analyzing risk preference. The risk heterogeneous reference perception model is used for establishing and analyzing the risk attitude of the heterogeneous vehicle owner by introducing risk factors based on the reference experience perception model.

The technical scheme of the invention is further described below by combining the embodiments.

1. The innovation points of the invention are as follows:

(1) The invention establishes an improved cumulative prospect theoretical model for analyzing risk preference and heterogeneous reference points. Meanwhile, an electric vehicle charging preference model with the accumulated prospect value of the electric vehicle benefits as an evaluation index and under different peak flat electricity price schemes and with the random change of charging capacity and passenger order requirements is established.

(2) By comprehensively evaluating the arrival time and the residual electric quantity, a reference experience perception model reflecting the objective current situation of the vehicle owner is established by using four psychological perception areas based on an experience psychological perception mode. On the basis, a risk heterogeneous reference perception model for analyzing the risk attitude of the heterogeneous vehicle owner is further established by introducing risk factors.

(3) And taking a non-rational decision maker as an object, combining psychological perception of the decision maker with subjective psychological preference, and establishing a non-rational person decision model for analyzing risk preference.

2. The technical scheme of the invention is further described below with reference to theoretical basis.

2.1 Theory of desired utility

The prior art proposes a desired utility function EU whose functional form can be expressed by the formula (1):

EU＝∑pμ#(1)

Wherein: p represents the probability of possible outcome of the alternative, μ represents the utility function of possible outcome of the alternative, EU represents the expected value of the alternative. The expected utility theory can be selected according to the expected value of each feasible decision item in theory, but the calculated result is more in a theoretical sense, because the result of the expected utility theory model is the selection made in a completely ideal state, namely, the charging information and the charging decision result are completely mastered by the vehicle owner, and the charging selection result is always the theoretical optimal charging scheme. The expected value is a description of a large number of repeatable uncertainty behavior characteristics, but in real life, because the expected value is influenced by risk factors and risk attitudes, repeatable experiments cannot be performed, and the expected value is limited by practical times, the theoretical result is far from the actual result, so that the theory cannot be applied to the charge behavior analysis of irrational vehicle owners.

2.2 Theory of prospect

Based on the traditional expected utility theory, there are many defects in analyzing the charging behaviors of irrational vehicle owners, for example, all electric vehicle owners are considered to be completely rational under the expected utility theory model, and always pursue the expected utility maximization, however, the prediction result obtained by the method is often quite different from the actual situation.

2.2.1 Cost function

The value function v (x) is independent of the actual value x of the result, the subjective value of the result for the decision maker is obtained, when the decision maker evaluates different results in each option, the decision maker perceives the subjective value v (x) of each result for him, rather than the actual value x, after determining the psychological reference point x ₀ of the decision maker, the decision maker perceives the result of each option as not an absolute value but a relative value, so that the value function of the foreground theory is generally defined as follows:

Wherein, alpha, beta (0 < alpha is less than or equal to 1,0< beta is less than or equal to 1) measures the sensitivity decreasing degree far from the psychological reference point x ₀, and the larger alpha, beta is, the more sensitive the decision maker is to risk; λ represents the loss avoidance factor and λ >1 is constant reflecting the fact that individuals are more sensitive to loss, and in one analysis of Kahneman and Tversky, when the parameter is α=β=0.88, λ=2.25 is more consistent with empirical data, and domestic analysts have established similar values.

As can be seen from fig. 2, the cost function v (x) is a strictly increasing function, the cost function curve is S-shaped, the cost function is a convex function in the "profit" part, the cost function is a concave function in the "loss" part, and the edge value caused by the change of the result gradually decreases along with the increase of the result per se; in the "loss" part, the edge value brought by the change of the result is gradually increased along with the increase of the result, which shows that the risk attitudes of a decision maker are different when the decision maker faces the "benefit" and the "loss", the decision maker is in risk avoidance when the decision maker faces the "benefit", the decision maker is in risk preference when the decision maker faces the "loss", and the decision maker is more sensitive to the "loss".

2.2.2 Weight functions

The second important influencing factor that determines the final value of each option is the weight, which is independent of the probability that the result will produce, but it represents no probability, which measures the extent to which each result affects its options, not just the likelihood that the result will occur.

The present invention employs the weight functions proposed by the Kahneman and Tversky teachings, and it can be known from the definition of the weight functions in the foreground theory that the weight function definition is different when a decision is faced with "benefit" and when a decision maker is faced with "loss":

when a decision maker faces a "loss":

Where p is the actual probability of the result, ω ⁺(p),ω^- (p) represents the subjective probability when the "gain" and "loss" are faced, the parameters γ, δ determine the curvature of the weight function, the smaller the corresponding value is, the greater the degree of curvature of the weight function is, and according to the general experimental data calibration, γ=0.61, δ=0.69 is generally taken.

As can be seen from fig. 3, the decision weight function is inverted S-shaped, and when the probability of a result is very small, the decision maker tends to amplify its probability, i.e. when the actual probability p is very small, the subjective probability of the decision maker will be greater than the actual probability ω (p) > p; when the probability of a result is large, the decision maker tends to reduce the probability of the result, that is, when the actual probability p is very large, the subjective probability of the decision maker is smaller than the actual probability ω (p) < p, which is shown that the decision maker tends to overestimate the low probability event under-estimate the medium-high probability event when making the actual decision. In addition, more specifically, the weight function is not continuous when ω (p) actual probability p is 0 and 1, but is abrupt, when the occurrence probability of the result is 0, ω (0) =0; when the occurrence probability of the result is 1, ω (1) =1, and thus the weight function ω (p) is a nonlinear function.

2.3 Cumulative prospect theory

While the foreground theory can describe the irrational decision behavior of the decision maker, the foreground theory also suffers from some drawbacks, and Kahneman and Tversky teach that in 1979, the weighting function suffers from some problems, assuming x > y >0,Then (x, p; y, q) is superior to/>If the preference is satisfied, there is: /(I)I.e./>, when y approaches xApproach/>And because ofΩ (p) must be linear, which is contrary to the fact that the weighting function ω (p) is a nonlinear function, so that the weighting function ω (p) in the foreground theory does not satisfy the first order dominance principle. To address this problem Kahneman and Tversky teachings propose cumulative prospect theory that improves on the weighting function of the prospect theory by using cumulative probability weights instead of individual probability weights. Kahneman and Tversky are defined foreground (Prospect) as an uncertainty event, assuming that a certain uncertainty alternative ψ consists of a series of combinations (x _i,p_i) and that-m.ltoreq.i.ltoreq.n is satisfied, for simple processing, the results of each foreground, x _i, are now sorted in ascending order, i.e. x _-m≤x_-m+1≤…≤x₀≤x₁≤…≤x_n, with positive subscripts used to represent positive possible results, negative subscripts used to represent negative possible results, 0 subscripts used to represent neutral possible results, what the decision maker perceives as "profit" when x _i>x₀, what the decision maker perceives as "loss" when x _i<x₀. In this case, the decision weight function/>, of the cumulative foreground theoryAnd/>The following can be defined:

Where p _i denotes a probability value of occurrence of the i-th positive state, p _n denotes a probability value of occurrence of the n-th positive state, p _-m denotes a probability value of occurrence of the m-th negative state, ω ⁺ and ω ^- are strictly increasing functions and satisfy ω ⁺(0)＝ω^-(0)＝0,ω⁺(1)＝ω^- (1) =1, Is a forward cumulative decision weight function, i.e. a cumulative decision weight function representing when a decision maker is faced with "benefits"/>A negative cumulative decision weight function, i.e., a cumulative decision weight function that represents when a decision maker is faced with "loss".

From the above description, the integrated cumulative prospect value for the alternative ψ is calculated as follows:

CPV＝CPV⁺+CPV^-#(8)

where CPV represents the actual aggregate cumulative prospect value, CPV ⁺ represents the cumulative prospect value of the "revenue" portion, and CPV ^- represents the cumulative prospect value of the "loss" portion.

2.4 Summary

When the electric vehicle charging behavior is modeled based on the expected utility theory, the vehicle owner is considered rational, the analysis of irrational factors is lacking, the foreground theory and the accumulated foreground theory can describe the decision behaviors of irrational decision makers, and compared with the expected utility theory, better effects can be obtained, however, the foreground theory does not meet the first-order dominant principle under certain special conditions, and can only be applied to the decision of few results.

3. Electric vehicle charging behavior based on expected utility theory:

(1) Assuming that the owner of the electric vehicle is completely rational, the charging information and the decision result are completely mastered, and the charging decision takes maximization of the benefit result as a charging decision target and cannot be influenced by the benefit change.

The electric automobile charging effect on the power grid is not only related to the vehicle scale, but also directly related to the electric automobile charging behavior, the electric automobile in China mainly comprises operation vehicles, buses and private vehicles through analysis of the development current situation and development planning of the electric automobile in China, the electric operation vehicles and buses realize large-scale operation, the private vehicles are fewer, the buses are used as public transportation means, the routes are relatively fixed, the rest time and the charging time are relatively fixed, the private vehicles are mainly used for going to and from work, leisure entertainment and the like, the corresponding charging places mainly comprise unit office parking lots, resident parking lots, market parking lots and the like, the relative travelling distance is short, and the private vehicle owners are sensitive to the charging cost, the electric automobile is often charged when the electric automobile owners have low electric prices in the valley period at night, the electric operation vehicles are used as important components of the electric automobile at present, the electric operation vehicles have the predetermined routes unlike the private vehicles and buses, the moving demands can be changed continuously according to the demands of customers, the moving distances are far higher than the private vehicles and the buses, and the random behavior of the electric operation on the buses on the journey and the bus is deeply analyzed.

(2) The main working time of the electric operation vehicle is the analysis time of the electric operation vehicle, which has a large influence on the power grid in the daytime and in the daytime, so that the electric operation vehicle is 9:00 am to 18:00 pm, the electric operation vehicle is required to be charged at least once in the daytime operation process according to the division rule of the peak-to-average time period of the Wuhan city, the peak-to-average time period of the electric operation vehicle is 9:00 am to 2:00 pm, the charging mode of the electric operation vehicle is analyzed according to Cao Weitao, the daily average driving mileage of the electric operation vehicle is 350-500km, the electric operation vehicle has fixed charging time at night, the safety and other factors are analyzed, the once-at-night charging is difficult to meet the operation requirement of one day, and the electric operation vehicle is required to be charged at least once in the daytime operation process, so that the electric operation vehicle is only analyzed in daytime, and the charging decision condition of the electric operation vehicle is not discussed.

In large and medium cities, different initial charging time is selected by the electric vehicle to have different influences on the power grid, when the electric vehicle is selected to charge in a peak period, the influence on the load of the power grid is aggravated, and when the electric vehicle is selected to charge in a normal period, the electric vehicle has almost no influence on the load of the power grid, so that the analysis of the charging decision behavior of the electric vehicle has positive significance in coordinating the stable operation of the power grid, and in the next section, the invention models the charging behavior of the electric vehicle.

(3) Electric vehicle charging behavior model based on expected utility theory

Yuan through analysis of the distribution of the residual electric quantity of the battery before charging, it is found that about three-quarters of pure electric taxi owners can charge when the residual electric quantity is between 20% and 50%, and the charging behavior of the electric operation vehicle is more concentrated when the residual electric quantity is between 0.2 and 0.5. Because the electric vehicle has strong randomness of the driving route, the distribution of the charging piles is not uniform, and when the residual electric quantity of the electric vehicle is lower than a certain value, the electric vehicle usually generates journey anxiety. The invention assumes that the initial electric quantity SOC _ini of the electric vehicle satisfies the uniform distribution between 0.2 and 0.5, the psychological safety electric quantity of the electric vehicle owner is 0.5, the psychological safety electric quantity means that the electric vehicle can be charged selectively when the residual electric quantity of the electric vehicle is lower than the psychological safety electric quantity, and the charging behavior of the electric vehicle can be stopped when the residual electric quantity of the electric vehicle is higher than the psychological safety electric quantity.

Table 1 parameter setting table

The parameter setting of the peak usual period is shown in table 1, and the invention assumes that the passenger flow rate p ₁ of each hour in the peak period obeys the poisson distribution of lambda=3, and the passenger flow rate p ₂ of each hour in the flat period obeys the poisson distribution of lambda=2; and in peak time, the unit price of the electric operation vehicle, namely the average income q ₁ of each guest is 30 yuan/person, the unit price of the electric operation vehicle in flat time, namely the average income q ₂ of each guest is 20 yuan/person, the electricity price of the electric vehicle in peak time is s ₁ yuan/degree, the electricity price of the electric vehicle in flat time is s ₂ yuan/degree, and the nine time periods from 9:00 am to 18:00 pm are divided into 18 time points on average as the value of the arrival time t, wherein the arrival time t represents the meaning that the residual electric quantity of the electric vehicle is lower than the psychological safety electric quantity at the time t, namely the charging requirement of the vehicle owner is generated at the time t.

The electric automobile is connected with the power grid at the moment of starting the charging process, the power is kept unchanged in the charging process, no discharging operation is performed, and the charging duration can be obtained:

Wherein:

q ₀ is the rated capacity of the battery of the electric vehicle;

SOC _lea is the cut-off power when the electric vehicle is charged, in the invention, SOC _lea =0.5 is the psychological safety power;

SOC _ini is the initial power of the electric vehicle when charging to the charging station;

P _EV is the charging power of the electric automobile;

T _char is the charging time, T ₁ is the peak period charging time, T ₂ is the normal period charging time, and T _char＝T₁+T₂;

θ _char is the charging efficiency of the electric vehicle;

In the model, an electric vehicle owner has three charging modes of scheme one peak period charging, scheme two-period charging and scheme three-span period charging, the electric vehicle owner has different charging options under different arrival times, when the electric vehicle arrives at the peak period, the electric vehicle owner has three charging modes of peak period, flat period and span period, if and only when the electric vehicle owner arrives at the peak period and the charging time is smaller than the peak period residual time, the option of span period charging is available, and when the electric vehicle arrives at the ordinary period, the charging option of the electric vehicle owner is relatively fixed, and only the option of usual period charging is available, so the electric vehicle owner is taken as an auxiliary decision.

The method analyzes the specificity of the electric operation vehicle, all charging behaviors of the vehicle owners take the maximization of the self-income as decision basis, so that the invention defines the income functions of the electric operation vehicle under three charging schemes, and the income functions of the electric operation vehicle without losing generality can be defined as follows under the assumption that the income of other time periods is the same under different charging schemes, the income of the electric operation vehicle consists of three parts of passenger carrying income, passenger loss and charging expense in charging time (without analyzing the electricity consumption and parking expense in the process of running the vehicle):

Y＝E-C₁-C₂#(12)

Y represents the actual revenue of the electric vehicle over nine time periods, where E represents the money earned by the electric vehicle passengers, C ₁ represents the electric vehicle charging cost, and C ₂ represents the passenger bill loss of the electric vehicle over the charging time period.

1) Electric operator car owner selects scheme revenue function when charging in peak period:

2) The owner of the electric operation car selects a scheme of gain function during two-period charging:

3) The owner of the electric operation car selects a scheme of a gain function when charging in a three-span period:

4)

When the expected utility theory is applied to analyze the charging behavior decision of the electric vehicle, the probability distribution P is used for representing the occurrence probability of each charging decision result; also, each charging decision result corresponds to a benefit function Y, which is used to represent the decision value, And the expected value of the benefit of the owner of the electric vehicle to the decision result is shown. Each vehicle owner wishes to make decisions that maximize the desired utility, i.e., the principle of maximizing the desired utility. Then for a certain charging scheme, Y _j is its desired utility; the expected value for each charging decision made by the owner of the electric vehicle can be expressed by equation (16) as follows:

EU_j＝∑(Y_ij,P_ij)#(16)

Wherein: y _ij represents the benefit of the ith random scenario under charging scheme j;

P _ij represents the probability of the ith random scenario under charging scheme j;

Wherein the method comprises the steps of Represents the expected value for each charging regime, j=1, 2,3,/>And/>The expected values of the scheme I, the scheme II and the scheme III are respectively expressed, and under the expected utility theoretical model, the electric vehicle owner can select the result with the maximum expected value as the charging selection, namely as shown in a formula (17):

(4) In order to analyze the influence of peak-to-average power price multiple on the charging behavior of the electric vehicle owner, the section designs the effectiveness of two case scene verification models, and compares and analyzes the charging decision results of the electric vehicle owner under different arrival time. When the first scene is that the peak flat power value multiple is 1, the residual electric quantity SOC _ini meets the uniform distribution between 0.2 and 0.5; and when the second scene is that the electricity price multiple is 3, the residual electric quantity SOC _ini meets the uniform distribution between 0.2 and 0.5. And comparing the charging decision results of the electric vehicle owners in different scenes, and further analyzing the influence of peak-to-average power price multiples on the charging behaviors of the electric vehicle owners.

(4.1) Parameter setting

Setting related parameters: in the invention, an exemplary electric operation vehicle BYD E6 is taken as an example, the battery capacity Q ₀ =60 KW.h of the electric vehicle, the rated power P ₀ =7 KW, the charging efficiency theta _char =0.95, the electric network is a price maker, the electric vehicle is an electric price complier, the electric network generally changes the peak flat price multiple to guide the charging behavior of the electric vehicle, the peak flat time interval is set according to the Wuhan city, the peak flat time interval is 9:00-2:00 pm, the peak flat time interval is 18:00 pm, the peak flat time interval of the Wuhan is set as an example, the electric price of the peak flat time interval is 1.1094 yuan/degree, and the electric price of the peak time interval is 1.19753 yuan/degree.

(4.2) Monte Carlo simulation method

The charging behavior of the electric operation vehicle is analyzed to be influenced by a plurality of randomness factors, and Monte Carlo simulation is adopted in the analysis. The Monte Carlo method is a method for performing calculation simulation by using random numbers, which is also called a random simulation method, and the main process when the method is applied is as follows: (1) Determining a probability model, wherein the probability model comprises passenger flow conforming to poisson distribution and passenger flow uniformly distributed; (2) Sampling from the above known probability distribution to generate random numbers; (3) Performing a simulation experiment, namely repeatedly simulating the random event for a plurality of times; (4) And carrying out statistical average on the random experiment result, and solving the frequency of occurrence of the random event as an approximate solution of the problem. In the case of the chapter, 10000 Monte Carlo simulations are performed on random factors in the section 3.3, so that expected values and accumulated prospect values of the electric vehicle at different moments of the day under various situations are obtained, and the charging decision behaviors of the electric vehicle at each moment are judged.

(4.3) Analyzing influence of electricity price on charging behavior of rational car owners

Scene one: the peak flat power factor is 1 without adopting any power price excitation strategy, and the residual power quantity SOC _ini satisfies the uniform distribution between 0.2 and 0.5, in which case the charging cost of the electric vehicle is the same in peak period charging and in normal period charging. In the charging decision, the owner of the electric vehicle only needs to refer to the expected passenger order quantity in different time periods, rationally analyzes the self charging requirement and makes a corresponding decision, and the charging decision result of the owner of the electric vehicle at each moment is shown in fig. 3.

Scene II: and introducing a power price excitation strategy, setting the peak period power price to be 3 times of the ordinary single power price, enabling the residual electric quantity SOC _ini to be uniformly distributed between 0.2 and 0.5, and observing decision difference of an electric vehicle owner. According to the initial data of 3.4.1, the flat period electricity price is 1.1094 yuan/degree, and the peak period electricity price is 3.3282 yuan/degree. At this time, the charging decision result of the owner of the electric vehicle at each moment.

As can be seen from the first scenario fig. 4, when the peak flat price multiple is 1 and the price excitation strategy is not introduced, the expected value of the second scenario is always the largest, and the vehicle owner tends to select the second scenario, namely, the second scenario is charged in the ordinary period; from the second scene, as can be seen from fig. 5, when the peak flat price multiple is 3 and the price excitation strategy is introduced, the decision of the vehicle owner is not changed, and the second scheme is always selected to charge in the ordinary period.

Specifically, when the peak flat valence multiple is 1, the scheme II is optimal except the time of 4, the scheme I is better than the scheme III, the relation of the three schemes in other time periods is the scheme II optimal, the scheme III is the worst, and the scheme I is the worst. And when the peak flat valence multiple is 3, although the scheme II is always the optimal choice, the decision subversion occurs within the period of 2.5 to 3. A situation where scheme one is better than scheme three occurs, both in the 2.5 to 3.5 period. In summary, under the desired utility theory, the decision maker would prefer to choose scheme two.

3.5. Under the expected utility theoretical model, the vehicle owner is completely rational, is not interfered by any irrational factors, always selects the maximization of the result income as a decision criterion, and always selects a scheme for charging in a two-period mode no matter how the peak flat power price multiple changes. In actual life, the vehicle owner is affected by irrational factors, however, under the expected utility theoretical model, the influence of irrational factors on the charging behavior of the electric vehicle cannot be reflected.

4. Electric vehicle charging behavior based on accumulated prospect theory:

And (4.1) modeling the charging behavior of the fully rational vehicle owner based on the expected utility theory, wherein the simulation result shows that when the power price multiple changes, the vehicle owner always selects the scheme II to charge in the ordinary period. It can be seen that the irrational factors have limited impact on the rational model targeting revenue maximization.

However, in real life, it is difficult for an individual to evaluate his own status and to make a rational decision. For the charging problem of the invention, the perception of the current situation of the vehicle owner determines the self-evaluation and directly influences the charging decision behavior. The resulting erroneous or improper decisions will lead to a reduction in operational revenue and in some cases even loss of revenue. Therefore, the self-perception modeling for the vehicle owners has great significance for ensuring stable and reliable benefits.

In order to better analyze the interference and influence of irrational factors on the charging decision of an electric vehicle owner, the method takes the current situation of the electric quantity of the owner and the mind perception expected by future income of the owner as analysis objects, introduces an accumulated prospect theoretical model to model irrational behaviors in the charging decision of the owner, and analyzes the mind perception of the owner and decision problems thereof under objective conditions of different residual electric quantity, arrival time, electricity price and the like.

(4.2) An electric vehicle charging behavior model based on an accumulated prospect theory: in actual life, an electric operation car owner is generally influenced by irrational factors when making a charging decision, so that inaccurate decisions can be made, the actual result is greatly different from the charging decision result of a complete rational car owner under the expected utility theoretical model frame, the problem is that benefits or losses exist for the car owner, and the uncertainty of load is increased for a power grid. When the electric vehicle charging behavior is modeled based on the accumulated prospect theory, the accumulated prospect theory can well describe the decision process of the vehicle owner when the vehicle owner faces uncertainty results and risks, so that the accumulated prospect theory is introduced to model the irrational charging behavior of the electric vehicle in this section.

Referring to an accumulated prospect theoretical model, the invention models the charging behavior of the electric vehicle in two stages: the editing phase and the evaluation phase, the charging behavior modeling framework is shown in fig. 6. In the editing stage, firstly determining possible benefit results of a vehicle owner under different charging schemes through a benefit function, then determining psychological reference points of the vehicle owner, taking expected values of benefits under current electricity price multiples as psychological reference points in an accumulated prospect theoretical model, then perceiving attributes of benefits under different charging schemes, namely converting the benefit results under different charging schemes into values relative to the reference points, judging whether the benefits belong to benefits or losses, analyzing actual probability generated by the benefit results according to a probability model, and finally converting the actual benefits and the actual probability into subjective benefits and subjective probability of the vehicle owner through a cost function and a weight function. In the evaluation stage, the accumulated prospect value under each charging scheme is calculated by an accumulated prospect value calculation method, the magnitude of the accumulated prospect value under each charging scheme is compared, and finally the optimal charging decision is made.

(4.2.1) Editing phase of the charging decision model

V (Y _ij) represents the subjective value of the owner of the electric vehicle to the ith random scene under the charging scheme j, Y _ij represents the actual benefit of the ith random scene under the charging scheme j,Representing the expected value under charging regime j,/>The calculation method of (2) can refer to the formula (16), wherein the alpha, beta and gamma parameters refer to the settings.

The vehicle owner can compare possible benefit results under each charging scheme with expected values when making decisions, when the benefit results are larger than the expected values, the vehicle owner feels 'benefits', when the benefit results are smaller than the expected values, the vehicle owner feels 'losses', the risk attitudes of the vehicle owner in the face of 'benefits' and in the face of 'losses' are different, and when the vehicle owner faces 'benefits':

When the owner faces a "loss":

Where P _ij represents the probability of the ith random scenario under charging regime j, ω ⁺(P_ij) and ω ^-(P_ij) represent the subjective probability weights in the face of "profit" and in the face of "loss", respectively, the parameters γ, δ refer to the setting of section 2.2.2. The subjective weight of the possible benefit result under each charging scheme is brought into the cumulative weight function, and the cumulative decision weight function is obtained:

Where the subscript j=1, 2,3 denotes three charging schemes, the subscript i denotes a certain possible scenario under charging scheme j, n denotes a possible outcome when the owner perceives a benefit under each charging scheme, m denotes a possible outcome when the owner perceives a loss under each charging scheme, Forward cumulative weight value representing ith random scene under charging scheme j,/>And the negative accumulated weight value under the ith random scene under the charging scheme j is represented.

(4.2.2) Evaluation phase of charging decision model

The value function v (Y _j) obtained by the calculation in the editing stage and the accumulated weight function pi _ij are brought into an accumulated foreground value calculation formula, so that a forward accumulated foreground value under the charging scheme j can be calculated:

Negative cumulative prospect value under charging regime j:

comprehensive accumulated prospect value under charging scheme j:

Wherein CPV _j represents the comprehensive cumulative prospect value under each charging scheme, j=1, 2,3, CPV ₁,CPV₂ and CPV ₃ represent the comprehensive cumulative prospect values of scheme one, scheme two and scheme three, respectively, and when making charging decisions, the electric vehicle owner generally tends to select the charging scheme with the largest comprehensive cumulative prospect value as the optimal charging selection, namely:

CPV＝MAX(CPV₁,CPV₂,CPV₃)#(26)

(4.3) example design

In order to better analyze the randomness factor in the decision, 10000 simulation is carried out on a possible scene by adopting a Monte Carlo method, the frequency of the simulation result is counted, the frequency data is regarded as the actual probability of the charging behavior, the profit result is regarded as the actual value, firstly, the actual profit and the actual probability are obtained according to the structural framework of the accumulated foreground theory, then the actual profit and the actual probability are converted into the subjective value and the subjective probability through a cost function and a weight function, then the accumulated foreground value calculation method is adopted, the accumulated foreground value of each charging scheme of the owner of the electric vehicle under different arrival time is solved, the charging decision behavior of the owner of the electric vehicle under each moment is judged, finally, the decision results under different scenes are compared, and the influence of peak-to-peak low price multiple and initial charge distribution on the charging behavior of the irrational vehicle owner is further analyzed.

(4.3.1) Analyzing the influence of electricity prices on the charging behavior of non-rational car owners: in order to analyze the influence of the peak flat power factor on the charging behavior of the irrational vehicle owner, the section designs the effectiveness of two case scene verification models, and compares and analyzes the charging decision results of the electric vehicle owner under different arrival time, wherein when the scene one is that the peak flat power factor is 1, the residual electric quantity SOC _ini meets the uniform distribution between 0.2 and 0.5; when the second scenario is that the peak flat power price multiple is 3, the residual electric quantity SOC _ini meets the uniform distribution between 0.2 and 0.5, and the charging decision results of the owners of the electric vehicle under the scenarios of different power price multiple are compared.

Scene one: the electricity price excitation strategy is not introduced, and when the peak flat electricity price multiple is 1 and the residual electric quantity SOC _ini meets the uniform distribution between 0.2 and 0.5, the charging cost of the electric vehicle in the peak period is the same as that in the normal period. When the electric car owner makes a charging decision, the electric car owner can refer to expected passenger orders in different time periods and can be influenced by irrational factors. At this time, the charging decision result of the owner of the electric vehicle at each moment is shown in fig. 7.

Scene II: and introducing an electricity price excitation strategy, wherein the SOC _ini of the residual electric quantity with the electricity price multiple of 3 satisfies the uniform distribution between 0.2 and 0.5, the charging cost of the electric vehicle in the peak period is greater than that in the flat period, and the charging decision result of the electric vehicle owner at each moment is shown in figure 9.

As can be seen from the first scene, fig. 7, when the peak flat power factor is 1, the second vehicle owner selection scheme is charged in the normal period within the period of 0 to 3.2, and the first vehicle owner selection scheme is charged in the peak period within the period of 3.2 to 5; as can be seen from scenario two fig. 8, the vehicle owner selection scheme charges for a flat period of time in the 0 to 3.5 period and the vehicle owner selection scheme charges for a peak period in the 3.5 to 5 period.

Specifically, when the peak flat power multiple is 1, the arrival time is within the period of 0 to 3.2, the optimal scheme of the vehicle owner is the scheme II, the scheme III is better than the scheme I, the arrival time is within the period of 3.2 to 5, the optimal scheme of the vehicle owner is the scheme I, and the scheme III is better than the scheme II; when the peak flat power multiple is 3, the arrival time is within the period of 0 to 3.5, the optimal choice of the vehicle owner is the scheme II, and the scheme III is better than the scheme II, and the optimal choice of the vehicle owner is the scheme I, and the scheme II is better than the scheme III, and the arrival time is within the period of 3.5 to 5. From the overall trend, when the arrival time is early, the vehicle owner tends to select scheme two to charge in the usual period, when the arrival time is late, the vehicle owner tends to charge in the peak period, and the comparison of scene one and scene two can be obtained, when the peak flat price multiple is the same, namely, when no price excitation strategy exists, the arrival time is 3.2 times later, the vehicle owner decision will change, and the vehicle owner tends to charge in the peak period; when the electricity price excitation strategy is introduced, when the peak electricity price multiple is 3, the charging decision of the vehicle owner changes after the arrival time is 3.5, the vehicle owner tends to charge in the peak time period of the scheme one, the charge time of the non-rational vehicle owner can be influenced by the peak electricity price multiple, and when the peak electricity price multiple is increased, the vehicle owner can select to charge in time in the peak time period later.

Under the accumulated prospect theoretical model framework, the vehicle owner can be interfered by irrational factors when making a charging decision, and the situation of inaccurate current estimation of the vehicle owner can occur when making the charging decision, so that an inaccurate charging decision is made. Under the expected utility theoretical model, when the power price multiple is improved, the charging behavior of the vehicle owner does not change, under the accumulated prospect theoretical model, when the power price multiple is improved, the charging behavior of the vehicle owner changes, so that compared with a rational vehicle owner, the irrational vehicle owner is more sensitive to the power price.

(4.3.2) Analyzing the effect of the initial charge distribution on the non-rational vehicle owner charging behavior: in order to analyze the influence of initial charge distribution on the charging behavior of an irrational vehicle owner, the section designs the effectiveness of a scene verification model of two cases, and compares and analyzes charging decision results of the electric vehicle under different arrival time, wherein the third scene is that the peak flat valence multiple is 3, and the residual electric quantity SOC _ini meets the uniform distribution between 0.2 and 0.35; the fourth scenario is that the peak flat power valence multiple is 3, and the residual electric quantity SOC _ini meets the uniform distribution between 0.35 and 0.5.

Scene III: when the peak flat power valence multiple is 3 and the residual electric quantity SOC _ini meets the uniform distribution between 0.2 and 0.35, the charging decision result of the electric vehicle owner at each moment is shown in figure 10.

Scene four: the peak-to-average power valence multiple 3 and the residual power SOC _ini meet the uniform distribution between 0.35 and 0.5, and the charging decision result of the electric vehicle owner at each moment is shown in figure 10.

As can be seen from fig. 8 of the third scenario, the remaining power SOC _ini satisfies the uniform distribution between 0.2 and 0.35, the arrival time is about 0 to 2.7, the optimal solution of the vehicle owner is the second solution, the arrival time is about 2.7 to 5, the optimal solution of the vehicle owner is the first solution, the second solution is better than the third solution, and when the arrival time is about 3.8, the optimal solution of the vehicle owner is the first solution, but the second solution and the third solution are overturned; from the scene four, as can be seen from fig. 10, the remaining power SOC _ini satisfies the uniform distribution between 0.35 and 0.5, and the charging decision of the vehicle owner is not changed in the whole peak period, that is, the arrival time is between 0 and 5, and the charging in the normal period is always selected in the scheme two. The comparison between the third scene and the fourth scene can be obtained, when the initial electric quantity distribution of the electric vehicle is low, the vehicle owner tends to charge in time earlier, and when the initial electric quantity distribution of the electric vehicle is high, the vehicle owner tends to charge in time later.

Under the expected utility theoretical model, when the initial charge distribution of the electric vehicle changes, the decision of the vehicle owner basically does not change, while under the accumulated prospect theoretical model, the vehicle owner is irrational, when the initial charge distribution of the electric vehicle changes, the charging decision of the vehicle owner changes greatly, and in comparison, the irrational vehicle owner is more sensitive to the change of the initial charge.

(4.4) Under the expected utility theoretical model, the vehicle owner is completely rational, only needs to analyze self charging requirements and final benefits under each charging decision, is less interfered by other factors, can always make optimal charging decisions in theory, when the electricity price multiple and the residual electric quantity change, the charging decision result of the vehicle owner basically does not change, under the accumulated prospect theoretical model, the vehicle owner is irrational and is interfered by strong irrational factors, the current situation of the vehicle owner is difficult to evaluate when making the charging decision, and also is difficult to make rational decisions, when the electricity price multiple and the initial electric charge distribution change, the charging decision of the vehicle owner is greatly changed, and compared with the rational vehicle owner, the irrational vehicle owner is more sensitive to the electricity price multiple and the residual electric quantity. Compared with the expected utility theory, the accumulated prospect theory analyzes the influence of irrational factors on the charging behavior, and is more in line with the actual result.

Although the influence of irrational factors on the charging behavior of the electric vehicle is analyzed, there is a basic assumption in the analysis that all electric vehicle owners have the same risk preference, which is impossible in real life, and the charging behaviors of different types of electric vehicle owners are different, and in this section, the analysis of the charging behaviors of heterogeneous owners is lacking, and in order to describe the charging behaviors of heterogeneous owners, the accumulated prospect theoretical model is improved in the next section.

5. Electric vehicle charging behavior analysis based on improved accumulation prospect theory

And (5.1) the invention introduces the accumulated prospect theory to model the charging behavior of the electric vehicle, and the simulation result shows that under the framework of the accumulated prospect theory model, the electricity price multiple and the initial charge distribution have larger influence on the charging decision behavior of the vehicle owner, so that compared with the expected utility theory, the accumulated prospect theory model can reflect the influence of irrational factors on the charging behavior, and is more in line with the actual result.

However, when the electric vehicle charging behavior is modeled based on the accumulated prospect theory, the vehicle owner is regarded as risk neutral, the influence of the risk preference attitude and the psychological perception effect of the vehicle owner on the reference point is not analyzed, the vehicle owner has the own current cognitive bias in the charging decision, and different types of vehicle owners have different risk preferences, so that the risk preference and the reference point of the vehicle owner are heterogeneous, and the vehicle owner can not well evaluate the own current situation and can make a decision under the non-rational model. This problem presents a risk of loss of revenue to the owners of the vehicle, and increases the uncertainty of the grid load for the grid.

In order to describe the charging behaviors of the heterogeneous vehicle owners with psychological perception more accurately, an improved accumulated prospect theory is introduced in the section to model the charging behaviors of the heterogeneous vehicle owners with psychological perception, and the influences of the current situation and risk preference attitudes on the charging behaviors of the electric vehicles are analyzed.

(5.2) Heterogeneous reference Point model with psychological perceptions

In the calculation of the cumulative foreground theory, the selection of the reference point is of vital importance. The selection of the reference points influences the calculation result of the accumulated prospect values, and has an important influence on travel decisions, in the past analysis, the reference points of the owners are generally considered to be homogeneous, heterogeneity of the reference points of the owners is rarely analyzed, in the calculation of the cost function, only one fixed reference point is generally considered, and the heterogeneity of the owners and the risk preference attitudes thereof are required to be analyzed to determine the reference points because different risk preference attitudes of different owners and psychological security sense are different, so that evaluation of future decisions of the owners is realized. Therefore, when the section determines the reference point, a variable reference point model for analyzing the risk attitude of the heterogeneous vehicle owner is established, so that the selection of the reference point is more in accordance with the decision of the heterogeneous non-rational person.

(5.2.1) Psychological perception model based on presence assessment: in many previous analyses, it was generally assumed that a decision maker has the same psychological perception effect under different environments, but this is impossible in real life, and under different current situations, the psychological perception of the vehicle owner is also different, and in this model, two objective factors that have a great influence on the psychological effect of the vehicle owner are the arrival time and the residual electric quantity, so by comprehensively evaluating the arrival time and the residual electric quantity arriving at the charging station, an electric vehicle current situation evaluation model is obtained, as shown in fig. 11, the psychological condition of the vehicle owner is reflected by four psychological perception areas, and on the basis of this, the psychological perception model based on the current situation evaluation is established by introducing the psychological safety factor 0 ζ.

The psychological security image obtained by per unit value-dividing the abscissa of fig. 11 is shown in fig. 12.

Ideally, the earlier the arrival time of the vehicle owner, the more the charging options are, the stronger the psychological safety sense is, otherwise, the later the arrival time is, the less the charging options are, the poorer the psychological safety sense is, and when the vehicle owner arrives after the moment 5, namely, arrives at ordinary times, the psychological safety sense of the vehicle owner can be obviously reduced. Also, the more the remaining power, the stronger the psychological safety feeling; the less the residual electric quantity is, the worse the psychological safety sense is, when the residual electric quantity is lower than 0.35, the psychological safety sense of the vehicle owner can be obviously reduced, and the vehicle owner can be more sensitive to the residual electric quantity. Therefore, the psychological feeling section is divided into four psychological feeling sections as shown in the above diagram, the section ④③②① is gradually deteriorated from strong, wherein the ④ section represents the section with the strongest psychological feeling and the ① section represents the section with the worst psychological feeling.

In the interval ④ in fig. 11, when the arrival time is earliest, the residual electric quantity is the largest, i.e. at the point a, the subjective profit expected by the vehicle owner is the largest, and when the arrival time is latest, the residual electric quantity is the smallest, i.e. at the point d, the subjective psychological profit expected by the vehicle owner is the smallest, and the subjective psychological profit expected by the vehicle owner in the remaining 3 intervals and the subjective psychological profit expected by the vehicle owner are the smallest can be found by the same method.

Therefore, in fig. 12, for four intervals, the lower right corner is the expected minimum point of subjective benefit of the vehicle owner, the upper left corner is the expected maximum point of subjective benefit of the vehicle owner, namely, the a, b, c, d point is the maximum point of subjective psychological expected benefit of the ④③②① interval, and the d, e, f, g point is the minimum point of subjective psychological expected benefit of the ④③②① interval.

The area projection is carried out on the four psychological safety sense areas in the figure 12 to obtain a psychological safety coefficient diagram, as shown in figure 13, on the basis of which the psychological safety coefficient zeta (0 is less than or equal to xi is less than or equal to 1) is defined, and zeta is the projection of the area subjected to per unit value by the four psychological sense areas, namely the product of the arrival time after per unit value and the residual electric quantity, and the larger zeta is the stronger the psychological safety of the owner of the electric vehicle, the smaller zeta is the poorer the psychological safety of the owner of the electric vehicle.

(5.2.2) Heterogeneous reference point model for analyzing risk preferences:

The risk preference is psychological attitudes and behavioral intentions of the vehicle owners shown by charging selection of the vehicle owners under the risk environment, the risk preference of the vehicle owners with different characteristics is different, all the vehicle owners are usually assumed to have the same risk preference in the previous analysis and are all of a risk neutral type, the vehicle owners with different types are not analyzed to have different risk preferences, the risk preference factors are introduced in the section to describe the vehicle owners with different types, and the risk preference factors are related to the reference point and the expected level, so the section models the correlation of the risk preference factors and the reference point.

Psychological benefit extremum table of vehicle owner under 23 times of electricity price

Table 2 shows the minimum value of subjective benefit and the maximum value of subjective benefit of the vehicle owner under three charging schemes in four psychological perception regions in a psychological perception model. In order to describe different risk attitudes of owners of different electric vehicles, risk preference factor risks are introducedRisk preference factor/>The larger represents the more optimistic the electric vehicle owner will be for the future, the risk preference factor/>Smaller indicates that the owner of the electric vehicle is pessimistic for the future.

When an electric vehicle owner makes a charging decision, the current situation is generally judged, the maximum value of subjective gain and the minimum value of subjective gain are determined, then a reference point is determined according to the risk preference attitude of the electric vehicle owner, and the reference point calculation formula is shown in (27):

Wherein I _ij denotes a reference point of an ith random scene under the charging scheme j, wherein subscripts j=1, 2,3 denote three charging schemes, subscript I denotes a possible scene under each charging scheme, I _jmin denotes a minimum value of a psychological safety interval under the charging scheme j, I _jmax denotes a maximum value of a psychological safety interval under the charging scheme j, Representing the risk preference factor for the vehicle owner.

(5.3) Heterogeneous vehicle owner charging behavior model based on improved cumulative prospect theory:

Under the framework of an improved accumulated prospect theory model, the modeling process of the charging behavior of the electric vehicle is similar to the modeling process under the framework of the accumulated prospect theory, and the modeling of the charging behavior of the electric vehicle mainly comprises two stages: the method comprises an editing stage and an evaluation stage, wherein the editing stage under the traditional cumulative prospect theory is improved by an improved cumulative prospect theory, after possible benefit results of owners under various charging schemes are determined through a benefit function, the owners can judge the current situation according to the current residual electric quantity and arrival time, then a reference point is determined according to the risk attitude of the owners of the electric car, then the attribute of benefits under different charging schemes is perceived, namely the benefit results under different charging schemes are converted into values relative to the reference point, whether the benefits belong to benefits or losses is judged, then the actual probability generated by the benefit results is analyzed according to a probability model, and finally the actual benefits and the actual probability are converted into subjective benefits and subjective probability of the owners through a value function and a weight function. In the evaluation stage, an improved accumulated prospect value under each charging scheme is calculated through an accumulated prospect value calculation method, the magnitude of the improved accumulated prospect value under various charging schemes is compared, and finally an optimal charging decision is made.

(5.3.1) Editing phase of charging decision model

The current concrete current situation and risk preference attitude can influence the selection of a reference point, the selection of the reference point under the framework of the improved accumulated prospect theoretical model can be determined jointly by the current situation and the risk preference of a vehicle owner, and the calculation formula of the I _ij can refer to the calculation method of the formula (27), wherein the alpha, beta and lambda parameters refer to the setting of the section 2.2.1.

(5.3.2) Evaluation phase of charging decision model

Under the framework of the improved accumulated prospect theoretical model, the evaluation phase is consistent with the evaluation phase of the accumulated prospect theoretical model.

(5.4) Example design

5.4.1 Comparison of decision results under different decision models

In order to analyze and compare three decision theory models of expected utility theory and accumulated prospect theory improved accumulated prospect theory, the section designs the effectiveness of two case scene verification models, and compares and analyzes charging decision results of electric vehicle owners at different arrival moments. When the first scene is that the peak flat power price multiple is 3, the residual electric quantity SOC _ini meets the uniform distribution between 0.2 and 0.35; and when the second scene is that the electricity price multiple is 3, the residual electric quantity SOC _ini meets the uniform distribution between 0.35 and 0.5.

Scene one: under the condition of 3 times of electricity price, the psychological safety is worse, namely the residual electric quantity SOC _ini meets the uniform distribution between 0.2 and 0.35, the arrival time t is in the [0,5] interval, and the improved accumulation prospect theory is in no risk preference, namely risk factorsWhen comparing the expected utility theory, the cumulative prospect theory and the improved cumulative prospect theory differ in charging decisions.

TABLE 3 decision results under different models

When the psychological safety is poor, and the psychological safety coefficient xi is in the [0.278,0.556] interval, when the arrival time is earlier in the [0,2.5] interval, the decision under the expected utility theory, the accumulated prospect theory and the improved prospect theory model is the same, and the scheme II is selected to charge in the ordinary period; when the arrival time t=3, under the expected utility theoretical model and the improved accumulated prospect theoretical model, the charging behavior of the vehicle owner is not changed, or the charging of the second scheme is selected in the ordinary period, and at the moment, the vehicle owner can select the first scheme to charge in the peak period under the accumulated prospect theoretical model; when the arrival time t is [4,5], the charging behavior of the vehicle owner is not changed under the expected utility theoretical model, and the vehicle owner decision result is the same under the accumulated prospect theory and the improved accumulated prospect theory model, and the charging is carried out in the peak period by the scheme I.

It can be seen that when the psychological safety feeling is poor and the psychological safety feeling coefficient ζ is in the [0.278,0.556] interval, when the arrival time is early, charging decisions under the three decision models are the same and are all selected to be charged in the usual period, but when the arrival time is late, the charging decisions under the three decision models are different, when the arrival time is late, the anxiety feeling generated by the psychology of the owner is stronger, and timely charging can be selected even if the owner encounters loss, so that the expected utility theory ignores people as non-rational people, the accumulated prospect theory and the improved accumulated prospect theory analyze the limited rationality of the owner of the electric vehicle, but the accumulated prospect theory does not analyze the cognition of the owner to the current situation, and the improved accumulated prospect theory model brings the psychological perception factors of the person into analysis, and can better reflect the non-rational decision behaviors of the person.

Scene II: under 3 times of electricity price, the psychological safety is strong, namely the residual electric quantity SOC _ini is uniformly distributed between 0.35 and 0.5, the arrival time t is in the [0,5] interval, and the improvement prospect theory has no risk preference, namely risk factors When comparing the expected utility theory, the cumulative prospect theory and the improved cumulative prospect theory differ in charging decisions.

When the psychological safety feeling is strong and the psychological safety feeling coefficient xi is in the [0.778,1] interval, the three decision models of the expected utility theory, the accumulated prospect theory and the improved accumulated prospect theory are the same in the charging decision result and have no change in the whole time period, and the scheme II is always selected to charge in the ordinary period.

When psychological security is strong, the car owner has strong future security, and at the moment, the car owner can reasonably analyze self charging requirements and the current situation, and make a reasonable charging behavior.

(5.4.2) Analyzing influence of risk preference on charging behavior

In order to analyze the influence of the risk preference attitude on the charging decision-making behavior, the risk conservation and the risk neutrality are compared under different physiological sensing intervals when the electricity price multiples are the same, and the charging decision-making results of risk preference type vehicle owners are different.

Scene III: under the condition of 3 times of electricity price, when the psychological safety sense is weaker, namely the residual electric quantity SOC _ini is between [0.2,0.35], the arrival time t is between [0,5], and the risk factorWhen 0.2, 0.5 and 0.8 are selected, risk conservation, risk neutral and risk preference type vehicle owners are respectively represented, and the charging decision results under different risk factors are compared to be different.

TABLE 4 decision results under different risk preferences

As can be seen from Table 4, the risk factors are setWhen the arrival time of the vehicle owner is 4, the charging decision is changed, and the charging is converted into the charging in the peak period from the charging in the normal period; at/>When the vehicle owner decides, the decision change occurs at the moment 3.5; at/>When the vehicle owner decides, the decision change occurs at the moment 3.

It can be seen that the charging decisions of owners of different types under different risk coefficients are different, the risk pursuit owners can charge in the earlier peak period with higher risk, and the risk conservation-oriented owners prefer to select to charge in the period with smaller risk at ordinary times.

The benefit of peak time is large, however, the loss of charging in the peak time is also large, and because the risk preference type vehicle owners are more adventure, the vehicle owners can charge in the peak time with larger risk in advance; the risk conservation type car owners are more sensitive to the loss, so the car owners can charge later at the normal time with smaller risk

Scene four: under the condition of 3 times of electricity price, the psychological safety is strong, namely the residual electric quantity SOC _ini meets the uniform distribution between 0.35 and 0.5, the arrival time t is in the [0,5] interval, and the risk factorWhen 0.2, 0.5 and 0.8 are selected, the charging decisions of the improved accumulation prospect theory under different risk factors are compared and are different.

The car owner has strong psychological safety sense, the psychological safety factor xi is in the [0.778,1] interval, the charging decision result under the three models is the same and has no change, the scheme II is always selected to charge in the usual period, the current situation of the car owner is better, the psychological safety sense is stronger, the interference of irrational factors is less, and the charging decision can be made more rationally.

(5.5) Under the framework of an improved accumulated prospect theoretical model, when the psychological safety is strong and the psychological safety coefficient xi is high, the car owner cannot generate journey anxiety in the future, and at the moment, the car owner is less interfered by irrational factors and can reasonably make a charging decision; when the psychological safety feeling is poor and the psychological safety feeling coefficient xi is small, the irrational factor interference suffered by the vehicle owner is strong at the moment, and the charging decisions of the vehicle owner are greatly different under different current situations. The accumulated prospect theory and the improved accumulated prospect theory can describe the irrational charging behavior of the vehicle owner, however, the accumulated prospect theory does not analyze the cognition of the vehicle owner to the current situation, and the improved accumulated prospect theory model brings the psychological perception factors of the person into analysis, so that the irrational decision-making behavior of the person can be reflected better.

The improved accumulation prospect theory can more accurately describe the charging decision-making behavior of the heterogeneous vehicle owners under uncertain conditions, and shows that the risk preference type vehicle owners prefer to charge in advance in peak periods with higher risks, and the risk conservation type vehicle owners prefer to charge when the risks are less in normal periods. Compared with the accumulated prospect theory, the improved accumulated prospect theory analyzes the influence of the risk preference attitude on the charging behavior, and the simulation result is more practical.

6. According to the method, the charging behavior of the electric vehicle is taken as an analysis object, the finite rationality of the owner of the electric vehicle is analyzed, the accumulated prospect theory is introduced to model the charging behavior of the electric vehicle, the accumulated prospect value of the electric vehicle benefits is taken as an evaluation index, the charging time and the charging capacity of the electric vehicle are taken as sensitivity analysis parameters, and a real-time charging decision preference problem model of the electric vehicle is established.

According to the invention, the charging behavior of the owner of the electric vehicle is modeled based on the expected utility theoretical model, the passenger order quantity and the residual electric quantity are used as random variables, the electricity price multiple and the initial charge distribution are used as sensitivity parameters, the charging decision result of the owner of the electric vehicle under different arrival times is analyzed, and the simulation result shows that the charging decision result of the owner basically does not change when the electricity price multiple and the initial charge distribution change, so that the influence of irrational factors on the owner is limited under the expected utility theoretical model.

The invention introduces the accumulated prospect theory to model the charging behavior of the electric vehicle, and the simulation result shows that when the electricity price multiple and the initial charge distribution change, the charging decision result of the electric vehicle owner changes to a certain degree and shows a certain regularity, so that the accumulated prospect theory model can better simulate the charging behavior of the non-rational vehicle owner.

According to the method, a heterogeneous reference point model for analyzing the risk preference of the electric vehicle owner is established, and the heterogeneous reference points are applied to calculation of a foreground value, so that the result shows that the vehicle owner can show different charging decision behaviors under the conditions of different risk preference and heterogeneous reference points, the simulation result is more practical, and the simulation result of a desired effect theory and a cumulative foreground theory model is inaccurate.

The foregoing is merely illustrative of specific embodiments of the present invention, and the scope of the invention is not limited thereto, but any modifications, equivalents, improvements and alternatives falling within the spirit and principles of the present invention will be apparent to those skilled in the art within the scope of the present invention.

Claims

1. The heterogeneous vehicle owner charging behavior modeling method based on the improved accumulated prospect theory is characterized by comprising the following steps of:

The method comprises the steps of taking an accumulated prospect value of electric vehicle benefits as an evaluation index, taking electric vehicle charging time and charging capacity as sensitivity analysis parameters, and establishing an electric vehicle charging decision preference model;

Establishing a heterogeneity reference point model with psychological perception, and applying the heterogeneity reference point to the calculation of the accumulated foreground value;

The heterogeneous vehicle owner charging behavior modeling method based on the improved accumulated prospect theory comprises the following steps:

step five, applying the reference point model to the calculation of the accumulated foreground value;

electric vehicle charging behavior model based on accumulated prospect theory includes:

The accumulated prospect theory is introduced to model the irrational charging behavior of the electric vehicle; based on an accumulated prospect theoretical model, modeling the charging behavior of the electric vehicle in two stages: an editing stage and an evaluation stage;

in the editing stage, determining possible profit results of the vehicle owners under different charging schemes through profit functions; determining a psychological reference point of an owner, and taking an expected value of the income under the current electricity price multiple as the psychological reference point in the accumulated prospect theoretical model; sensing the attribute of the benefits under different charging schemes, namely converting the result of the benefits under different charging schemes into a value relative to a reference point, and judging whether the benefits belong to the benefits or the losses; according to the actual probability generated by the probability model analysis income result, converting the actual income and the actual probability into subjective income and subjective probability of an owner through a cost function and a weight function;

in the evaluation stage, calculating an accumulated prospect value under each charging scheme by an accumulated prospect value calculation method, comparing the magnitude of the accumulated prospect value under each charging scheme, and finally making an optimal charging decision;

Wherein the value function v (x) takes the actual value x of the result as an independent variable, the obtained result is the subjective value of the result to the decision maker, when the decision maker evaluates different results in each option, he perceives the subjective value v (x) of each result to him instead of the actual value x, after determining the psychological reference point x ₀ of the decision maker, the decision maker perceives the result of each option as not an absolute value but a relative value, so the value function of the foreground theory is generally defined as follows:

Wherein, alpha, beta, 0< alpha is less than or equal to 1,0< beta is less than or equal to 1, the sensitivity decreasing degree away from the psychological reference point x ₀ is measured, and the larger alpha, beta represents the more sensitive the decision maker is to risk; λ represents a loss avoidance coefficient, and λ >1 is constant, reflecting the fact that the individual is more sensitive to loss;

The cost function v (x) is a strict increasing function, the cost function curve is in an S shape, a convex function is formed in a benefit part, a concave function is formed in a loss part, and the edge value caused by the change of the result gradually decreases along with the increase of the result in the benefit part; in the loss part, with the increase of the result, the edge value brought by the change of the result is gradually increased, the risk attitudes of a decision maker when facing the benefits and the losses are different, the decision maker when facing the benefits is in risk avoidance, the decision maker when facing the losses is in risk preference, and the decision maker is more sensitive to the losses;

The weight function comprises:

The second important influencing factor for determining the final value of each option is the weight, wherein the weight takes the probability generated by the result as an independent variable, the probability is not represented, and the influence degree of each result on the option where the result is positioned is measured, and the probability of the result occurs is measured;

By adopting the weight function, according to the definition of the weight function in the foreground theory, the definition of the weight function is different when the decision faces the benefit and when the decision faces the loss, and when the decision maker faces the benefit:

When a decision maker faces loss:

Wherein, p is the actual probability of the result occurrence, ω ⁺(p),ω^- (p) respectively represents the subjective probability when the gain and loss are faced, the parameters gamma and delta determine the curvature of the weight function, the smaller the corresponding value is, the greater the bending degree of the weight function is, the experimental data are calibrated, and gamma=0.61 and delta=0.69 are taken;

The decision weight function is inverted S-shaped, when the probability of a result is very small, the decision maker tends to amplify the probability of the result, and when the actual probability p is very small, the subjective probability omega (p) of the decision maker is larger than the actual probability p; when the probability of the generation of one result is larger, the decision maker tends to reduce the probability of the result, when the actual probability p is very large, the subjective probability omega (p) of the decision maker is smaller than the actual probability p, and the fact that the decision maker overestimates the low probability event to underestimate the medium and high probability event when making the actual decision is reflected; the weighting function is not continuous when ω (p) actual probability p is 0 and 1, but is abrupt, when the occurrence probability of the result is 0, ω (0) =0; when the occurrence probability of the result is 1, ω (1) =1, and the weight function ω (p) is a nonlinear function;

the cumulative prospect theory includes:

The cumulative prospect theory improves the weight function of the prospect theory, and cumulative probability weight is adopted; the foreground is an uncertainty event, assuming that a certain uncertainty alternative ψ consists of a series of combinations (x _i,p_i) and that-m.ltoreq.i.ltoreq.n is satisfied, the results of each foreground, x _i, are sorted in increasing order, i.e. x _-m≤x_-m+1≤…≤x₀≤x₁≤…≤x_n, where positive subscripts are used to represent positive possible results, negative subscripts are used to represent negative possible results, 0 subscripts are used to represent neutral possible results, the decision maker perceives a benefit when x _i>x₀, the decision maker perceives a loss when x _i<x₀, the decision weight function of the cumulative foreground theory AndThe definition is as follows:

Where p _i denotes a probability value of occurrence of the i-th positive state, p _n denotes a probability value of occurrence of the n-th positive state, p _-m denotes a probability value of occurrence of the m-th negative state, ω ⁺ and ω ^- are strictly increasing functions and satisfy ω ⁺(0)＝ω^-(0)＝0,ω⁺(1)＝ω^- (1) =1, Is a forward cumulative decision weight function, i.e. a cumulative decision weight function representing when a decision maker is faced with benefits,/>A negative cumulative decision weight function, namely a cumulative decision weight function representing when the decision maker is faced with loss;

The integrated cumulative foreground value for the alternative ψ is calculated as follows:

CPV＝CPV⁺+CPV^-；

wherein CPV represents the actual integrated cumulative prospect value, CPV ⁺ represents the cumulative prospect value of the "profit" portion, CPV ^- represents the cumulative prospect value of the "loss" portion;

the electric vehicle charging behavior model based on the accumulated prospect theory further comprises:

(1) Editing phase of charging decision model

Wherein v (Y _ij) represents the subjective value of the owner of the electric vehicle to the ith random scene under the charging scheme j, Y _ij represents the actual benefit of the ith random scene under the charging scheme j,Representing an expected value under a charging regime j;

The vehicle owner can compare possible benefit results under each charging scheme with expected values when making decisions, when the benefit results are larger than the expected values, the vehicle owner feels benefits, when the benefit results are smaller than the expected values, the vehicle owner feels losses, the risk attitudes of the vehicle owner in the face of benefits and the face of losses are different, and when the vehicle owner faces benefits:

When the owner of the vehicle faces loss:

wherein P _ij represents the probability of the ith random scenario under charging scheme j, ω ⁺(P_ij) and ω ^-(P_ij) represent subjective probability weights when facing benefit and facing loss, respectively; the subjective weight of the possible benefit result under each charging scheme is brought into the cumulative weight function, and the cumulative decision weight function is obtained:

Where j=1, 2,3 denotes three charging schemes, i denotes a certain possible scenario under charging scheme j, n denotes a possible result when the owner feels the benefit under each charging scheme, m denotes a possible result when the owner feels the loss under each charging scheme, Forward cumulative weight value representing ith random scene under charging scheme j,/>The negative accumulated weight value under the ith random scene under the charging scheme j is represented;

(2) Evaluation stage of charge decision model

The cost function v (Y _j) obtained by calculation in the editing stage and the accumulated weight function pi _ij are brought into an accumulated prospect value calculation formula, and a forward accumulated prospect value under the charging scheme j is calculated:

Negative cumulative prospect value under charging regime j:

comprehensive accumulated prospect value under charging scheme j:

Wherein, CPV _j represents the comprehensive cumulative prospect value under each charging scheme, j=1, 2,3, CPV ₁,CPV₂ and CPV ₃ represent the comprehensive cumulative prospect values of scheme one, scheme two and scheme three respectively, when making charging decisions, the electric vehicle owner tends to select the charging scheme with the largest comprehensive cumulative prospect value as the optimal charging selection, namely:

CPV＝MAX(CPV₁,CPV₂,CPV₃)；

Modeling the charging behavior of the electric vehicle by adopting an accumulated prospect theory, wherein under the framework of the accumulated prospect theory model, the power price multiple and the initial charge distribution have great influence on the charging decision behavior of the vehicle owner; modeling the charging behavior of the heterogeneous vehicle owners with psychological perception by adopting an improved accumulation prospect theory, and analyzing the influence of the current situation and risk preference attitude on the charging behavior of the electric vehicle;

Heterogeneous reference point model with psychological perception: when a reference point is determined, a variable reference point model for analyzing risk attitudes of heterogeneous vehicle owners is established, so that the selection of the reference point is more in accordance with the decision of heterogeneous non-rational persons;

Psychological perception model based on presence assessment: two objective factors with great psychological influence on the vehicle owner are arrival time and residual electric quantity, the situation assessment model of the electric vehicle is obtained by comprehensively assessing the arrival time and the residual electric quantity reaching a charging station, the psychological condition of the vehicle owner is reflected by four psychological feeling areas, and a psychological feeling model based on the situation assessment is established by adopting a psychological safety factor of 0-1;

carrying out per-unit on the abscissa and the ordinate to obtain a per-unit valued psychological safety image, dividing the per-unit valued psychological safety image into four psychological feeling sections, and gradually deteriorating the psychological safety of the section ④③②①, wherein the section ④ represents the section with the strongest psychological safety, and the section ① represents the section with the worst psychological safety;

In the interval ④, when the arrival time is earliest, the residual electric quantity is highest, namely, the subjective profit expected by the vehicle owner is highest at the point a, when the arrival time is latest, the residual electric quantity is lowest, namely, the subjective psychological profit of the vehicle owner is lowest at the point d, and the subjective psychological expected profit maximum point and the subjective psychological expected profit minimum point of the vehicle owner in the residual 3 intervals can be found by the same method;

Aiming at four intervals, the lower right corner is a subjective benefit expected minimum point of an owner, the upper left corner is a subjective benefit expected maximum point of the owner, namely a, b, c, d points are maximum value points of subjective psychological expected benefits of ④③②① intervals respectively, and d, e, f, g points are minimum value points of subjective psychological expected benefits of ④③②① intervals respectively;

The method comprises the steps of carrying out area projection on four psychological safety induction areas to obtain a psychological safety coefficient graph, defining a psychological safety induction coefficient zeta on the basis, wherein zeta is equal to or more than 0 and equal to or less than 1, and is the projection of the area subjected to per unit value by the four psychological induction areas, namely the product of the arrival time after per unit value and the residual electric quantity, wherein the larger zeta is the stronger the psychological safety induction of an electric vehicle owner, and the smaller zeta is the poorer the psychological safety induction of the electric vehicle owner;

Analyzing heterogeneous reference point models of risk preferences: the risk preference is psychological attitudes and behavioral intentions which are shown by the vehicle owners for charging and selecting the vehicle owners under a risk environment, the risk preference of the vehicle owners with different characteristics is different, different types of vehicle owners are described by adopting risk preference factors, the risk preference factors are related to reference points and expected levels, and the risk preference factors are related to the reference points for modeling;

limiting a reference point between a subjective benefit minimum value and a subjective benefit maximum value, firstly evaluating the current situation of an electric vehicle through residual electric quantity and arrival time, judging a psychological feeling zone where an electric vehicle owner is positioned, obtaining the subjective benefit minimum value and the subjective benefit maximum value of the owner, and adopting a risk preference factor to be 0-less than or equal to Risk preference factor/>The larger the electric vehicle owner, the more optimistic the future, the risk preference factor/>Smaller represents the more pessimistic the owner of the electric vehicle is about the future;

When an electric vehicle owner makes a charging decision, the current situation is firstly judged, the maximum value of subjective gain and the minimum value of subjective gain are determined, then a reference point is determined according to the risk preference attitude of the electric vehicle owner, and the reference point calculation formula is as follows:

Wherein I _ij denotes a reference point of an ith random scene under the charging scheme j, wherein subscripts j=1, 2,3 denote three charging schemes, subscript I denotes a possible scene under each charging scheme, I _jmin denotes a minimum value of a psychological safety interval under the charging scheme j, I _jmax denotes a maximum value of a psychological safety interval under the charging scheme j, Representing a vehicle owner risk preference factor;

Heterogeneous vehicle owner charging behavior model based on improved accumulation prospect theory: under the framework of an improved accumulated prospect theory model, the modeling process of the charging behavior of the electric vehicle is similar to the modeling process under the framework of the accumulated prospect theory, and the modeling of the charging behavior of the electric vehicle mainly comprises two stages: the method comprises the steps of editing and evaluating, determining possible benefit results of owners under various charging schemes through a benefit function, judging the current situation by the owners according to the current residual electric quantity and arrival time, determining a reference point according to risk attitudes of the owners of the electric vehicles, sensing attribute of benefits under different charging schemes, converting the benefit results under different charging schemes into values relative to the reference point, judging whether the benefits are benefit or loss, analyzing actual probability generated by the benefit results according to a probability model, and finally converting the actual benefit and the actual probability into subjective benefit and subjective probability of the owners through a cost function and a weight function; in the evaluation stage, calculating an improved accumulated prospect value under each charging scheme by an accumulated prospect value calculation method, comparing the values of the improved accumulated prospect values under various charging schemes, and finally making an optimal charging decision;

Editing stage of charging decision model:

the selection of the reference points can be influenced by the current specific current situation and risk preference attitudes, and the selection of the reference points under the improved accumulated prospect theoretical model frame can be jointly determined by the current situation and the risk preference of the vehicle owners;

evaluation stage of charging decision model: under the framework of the improved accumulated prospect theoretical model, the evaluation phase is consistent with the evaluation phase of the accumulated prospect theoretical model.

2. A heterogeneous vehicle owner charging behavior modeling system based on an improved accumulated prospect theory applying the heterogeneous vehicle owner charging behavior modeling method based on the improved accumulated prospect theory of claim 1, wherein the heterogeneous vehicle owner charging behavior modeling system based on the improved accumulated prospect theory comprises:

3. The heterogeneous vehicle owner charging behavior modeling system based on improved cumulative prospect theory of claim 2, wherein the heterogeneous reference point model building module with psychological perception comprises:

The psychological perception model construction module based on the current situation assessment is used for comprehensively assessing the arrival time and the residual electric quantity, and establishing a reference experience perception model reflecting the objective current situation of the vehicle owner by using four psychological perception areas based on the experience psychological perception mode;

A heterogeneous reference point model construction module for analyzing risk preference; the risk heterogeneous reference perception model is used for establishing and analyzing the risk attitude of the heterogeneous vehicle owner by introducing risk factors based on the reference experience perception model.