Highway network charging station optimization method based on charging demand space-time distribution

Abstract

The invention discloses a highway network charging station optimization method based on charging demand space-time distribution, and belongs to the field of intelligent transportation, and the method comprises the steps: generating a road network vehicle driving track through collecting road network information and highway vehicle passing charging records; establishing an energy consumption model by combining the energy consumption of the electric vehicle; simulating the energy consumption condition through simulation software, obtaining the charging distribution of the electric vehicles, numbering each service area, establishing a site selection model, and obtaining a light storage and charging integrated charging station model; respectively calculating the satisfaction degree of the charging demand of each charging station, the reasonable allocation of power resources and the alleviation condition of road traffic congestion; based on a calculation result, establishing a charging station constant volume model; and solving an optimal capacity scheme. According to the method, an effective electric vehicle path and optimal charging station distribution are obtained through highway toll collection data, compared with a traditional technology, factors such as weather, driver anxiety electric quantity, traffic flow density, motor efficiency and user behaviors are also considered, and finally obtained results are more real and reliable.

Description

Technical Field

[0001] The present invention relates to the field of intelligent transportation, and in particular to a method for optimizing charging stations in a highway network based on the temporal and spatial distribution of charging demands. Background Art

[0002] The planning of highway charging stations is a complex system optimization problem with multiple nonlinear, multi-optimization objectives, and multi-constraint conditions, which is affected by multiple factors such as environment, policy, technology, economy, and transportation. For the planning of highway charging stations, the regulation is mainly carried out from two aspects: charging demand and reasonable allocation of resources. There are two main methods for charging demand. One is to study from the electric vehicle side, simulate electric vehicle travel based on Monte Carlo sampling, and then roughly estimate the charging demand in combination with the energy consumption model; the other method is to study from the charging station side, based on the traffic flow analysis near the charging station, combined with the queuing theory model, time series analysis model, etc., to model the arrival rate and charge state (historical data) of charging vehicles arriving at the service area, and then predict the charging demand.

[0003] However, the existing technology for electric vehicle research lacks the actual use data of electric vehicles as support and guidance. Electric vehicles are assumed to follow a unified travel pattern, and the calculation of energy consumption and charging amount is based on static data, resulting in the estimation of charging demand deviating from reality; the method studied from the charging station end has a good prediction effect for a single charging station, but lacks consideration of the randomness of travel and heterogeneity of charging behavior of electric vehicle users on highways, and has certain limitations in expanding the research to provincial highway networks. In addition, the existing technology for the method studied from the charging station end lacks an estimate of operating costs. At the same time, in actual situations, factors such as weather, driver anxiety, traffic density, motor efficiency and user behavior need to be considered. Therefore, there is an urgent need for a method that combines the methods of the electric vehicle end and the charging station end to analyze the actual situation. Summary of the invention

[0004] In order to solve the above problems, the present invention provides a method for optimizing charging stations in a highway network based on the spatiotemporal distribution of charging demand.

[0005] To implement the above technical solution, the details are as follows:

[0006] S1, collecting and processing road network data and highway toll collection record data, obtaining electric vehicle travel characteristic parameters and generating road network vehicle driving trajectories;

[0007] The characteristic parameters of electric vehicle travel include: time data and location data;

[0008] The specific steps of S1 are as follows:

[0009] S1.1. Obtain the experimental highway network model through open source maps; the steps are as follows:

[0010] S1.1.1. Obtain the road network model of the target province through the open source map software OpenStreetMap;

[0011] S1.1.2. Modify and organize the road network model of the target province using the road network editing software Netdit;

[0012] Modification and arrangement means only retaining the highway network model;

[0013] S1.1.3, setting the toll station locations, service area and parking area locations of the expressway network and the detector locations on the road sections as nodes and numbering them;

[0014] S1.2. Obtain the probability density curve of vehicles entering the expressway network through kernel density estimation; the steps are as follows:

[0015] S1.2.1. Discretize the time data of vehicles entering the expressway network through grid points and calculate the histogram of the time data;

[0016] Time data range R = [0h, 24h], where 0h corresponds to R as MIN and 24h corresponds to R as MAX;

[0017] S1.2.2. Normalize the probability density of the histogram and perform discrete cosine transform to obtain the frequency domain coefficient a k ; The expression is as follows:

[0018]

[0019] Where b k represents the kth interval; x s represents the sth data sample; A represents the total number of data samples; b represents the total number of partitioned intervals; M k represents the probability that the data sample falls into interval k; p k represents the normalized probability of the kth interval; p z Represents the normalized probability value of the index zth interval, z∈k;

[0020] S1.2.3. Calculate the optimal bandwidth h through the iterative calculation of the fixed point equation and perform smoothing on the histogram; the expression is as follows:

[0021]

[0022] R=MAX-MIN

[0023] Where R represents the time data range; t * represents the optimal smoothing parameter, and the expression is as follows:

[0024]

[0025] Where t represents the smoothing parameter; f(t) is the frequency domain smoothing function related to t, and the expression is as follows:

[0026]

[0027] In the formula, L represents the maximum order of iteration;

[0028] S1.2.4, the final probability density distribution is obtained by smoothing the frequency domain coefficients and inverse discrete cosine transform; the expression is as follows:

[0029]

[0030] In the formula, Represents the smoothed frequency domain coefficient; represents inverse discrete cosine transform;

[0031] S1.3, obtain the vehicle driving trajectory of the road network through the A* algorithm and the path allocation model; the steps are as follows:

[0032] S1.3.1. Obtain the starting and ending positions of the vehicle entering the expressway network based on the vehicle location data in the provincial expressway toll collection record data;

[0033] S1.3.2, the A* algorithm calculates the shortest path from the start point to the end point, taking into account the path choices of users midway, and applying random perturbations to the impedance of the road section in the mesoscopic traffic simulation software DynasTIM to expand the set of valid paths;

[0034] S2. Establish an energy consumption model based on the factors that affect the energy consumption of electric vehicles;

[0035] Factors that affect the energy consumption of electric vehicles include: motor conversion efficiency, internal equipment operating energy consumption and high-speed driving resistance (friction resistance, wind resistance, slope resistance);

[0036] The steps to build an energy consumption model are as follows:

[0037] S2.1. Based on the law of conservation of energy, consider the energy loss of the vehicle from two aspects: vehicle dynamics and motor dynamics. First, establish the driving equation of the electric vehicle, which is expressed as follows:

[0038] F t =F m +F k +F p +F j

[0039] In the formula, F t F is the driving force; m F is the friction resistance; kis air resistance; F p is the slope resistance; F j For acceleration resistance;

[0040] Through sorting, we can get:

[0041]

[0042] Where m is the mass of the vehicle; g is the acceleration of gravity; f is the road friction coefficient; α is the road slope angle; C D is the drag coefficient; A is the frontal area of ​​the vehicle; v s is the actual vehicle speed; δ is the rotation mass conversion coefficient;

[0043] S2.2. Establishing a driving energy consumption model under different driving conditions;

[0044] Different driving states include: vehicle uniform speed driving state, vehicle acceleration driving state and vehicle deceleration driving state; that is, according to the comparison of the current vehicle speed v s and target vehicle speed v m Determine different driving states of the vehicle;

[0045] The details are as follows:

[0046] S2.2.1. When the vehicle is moving at a constant speed (v s =v m ) state, the vehicle has no acceleration resistance, so the energy consumption expression of the electric vehicle at this time is as follows:

[0047]

[0048] Where η d is the motor conversion efficiency;

[0049] S2.2.2, when the vehicle accelerates (v s <v m ) or uphill state, the vehicle has acceleration resistance and needs to provide a net driving force for vehicle acceleration. Therefore, the energy consumption expression of electric vehicle acceleration drive is as follows:

[0050]

[0051] In the formula, ΔT is the torque added by the vehicle acceleration motor, and the expression is as follows:

[0052]

[0053] In the formula, r is the wheel radius; i0 is the speed ratio of the reducer;

[0054] ω n is the motor speed, the expression is as follows:

[0055]

[0056] Where i1 is the transmission ratio of the vehicle transmission system;

[0057] S2.2.3, when the vehicle is decelerating (v s >v m ) state, the vehicle regenerative braking system is started, there is no driving force, and the expression of the electric vehicle braking recovery energy is as follows:

[0058]

[0059] Where η r The efficiency of regenerative braking recovery;

[0060] S2.2.4. The energy consumption model of electric vehicles is integrated as follows:

[0061] P=P x1 +P x2 +P i -P x3

[0062] Where P x1 P is the energy consumption of electric vehicles; x2 Accelerate driving energy consumption for electric vehicles; x3 Recover energy from braking for electric vehicles; i Energy consumption for running the internal equipment of electric vehicles;

[0063] S2.3, target vehicle speed v in the driving energy consumption model under different driving conditions m Make corrections; the steps are as follows:

[0064] Specifically, the speed of simulated vehicles in the highway network is not always constant, and when rain, snow, fog, traffic congestion, etc. occur, it will affect the driver's visibility and vehicle grip, so the vehicle's speed and the driver's driving anxiety need to be corrected;

[0065] In addition, considering that drivers are worried about extreme weather and dense traffic, frequent starting and stopping or deceleration will cause range anxiety, which will lead to wrong judgments on the driver's charging decision, so the driver's anxious power also needs to be corrected;

[0066] Here are the steps:

[0067] S2.3.1. The correction expression of vehicle flow to vehicle speed is as follows:

[0068]

[0069] In the formula, v′ m is the target vehicle speed after traffic flow correction; vf is the free flow speed of vehicles; k m is the average density of the vehicle’s front influence region (SIR); k jam is the blocking density of the impact area in front of the vehicle; k min is the upper limit of the density of vehicles when they run at free flow speed; σ and β are the first parameter and the second parameter respectively;

[0070] S2.3.2 The weather correction expression for vehicle speed is as follows:

[0071]

[0072] In the formula, v′ m ′ is the target vehicle speed after weather correction; The correction factor of the weather from charging station i to i+1 on the vehicle speed is selected. Precipitation and snowfall are used as the scale calibration. The target vehicle speed is reduced as the precipitation and snowfall increase. The reduction range is 4%-14%.

[0073] S2.4, correct the anxiety power coefficient;

[0074] Considering that drivers are worried about extreme weather and dense traffic, frequent starting and stopping or deceleration may cause range anxiety, which may lead to misjudgment of the driver's charging decision, so the driver's anxious power level also needs to be corrected;

[0075] The weather correction expression for the anxiety power coefficient is as follows:

[0076]

[0077] In the formula, is the anxiety power coefficient of an electric vehicle driver at the highway charging station i+1 at time T; θ is the basic anxiety power coefficient under the assumption of good weather and reasonable traffic flow; It is the correction factor of the anxiety power coefficient caused by the weather and traffic flow from charging station i to i+1, ranging from 6% to 20%;

[0078] S3, input the parameters of S1 into the mesoscopic traffic simulation software DynasTIM, and run the energy consumption model of S2 in the software to track the vehicle's charge state in real time. The nodes selected by the vehicle for charging and the amount of electricity replenished at the nodes are calculated through the constructed charging scenario, and finally the spatiotemporal distribution of charging demand in each service area of ​​the highway network is obtained; the specific steps are as follows:

[0079] S3.1. Use traffic simulator to track the traffic status of expressway network or customize the network information;

[0080] Traffic simulators include: mesoscopic traffic simulation software DynasTIM;

[0081] Highway network traffic status or custom road network information including: highway network toll node location, lane speed limit information, road slope angle, air density, distribution station location and service area location and set charging station capacity;

[0082] S3.2, simulation of vehicle driving on the highway network;

[0083] S3.2.1. Set the parameters of different vehicle models in the routing file, including: vehicle weight, frontal area, speed, rotational mass conversion factor, motor energy conversion efficiency, rolling resistance coefficient, electric vehicle internal equipment operating energy consumption and maximum charge state;

[0084] S3.2.2. Put the vehicle into the road network based on the probability density curve of the vehicle entering the expressway network, and drive along the shortest path between the vehicle's starting point and end point and other valid paths;

[0085] S3.3, the energy consumption model is constructed to calculate the energy consumption and obtain the charging demand data of the vehicle;

[0086] Specifically, during the operation of the mesoscopic traffic simulation DynasTIM, the travel chain of vehicles on the highway network is as follows: Figure 4 , input the parameters of each node in the driving trajectory (the time from the previous node to this node, the driving distance and the driving speed) into the energy consumption model built in python to calculate the energy consumption, update the remaining power of the vehicle, and generate the correction factor based on the node parameters (weather information, traffic flow information of the node). According to S2.3 and S2.4, the speed and anxiety power coefficient of the vehicle are corrected, and the driving speed of the simulated vehicle after leaving the node is updated through the TraCI interface. It is updated in real time after each node is passed until the vehicle ends the simulation and leaves the road network;

[0087] S3.4. By obtaining the remaining power and anxiety power coefficient when the vehicle arrives at the node, the user charging decision is made according to the actual user driving habits and charging judgment to divide the scenarios; the details are as follows:

[0088] Scenario 1: When the driver arrives at a certain node, the state of charge of the electric vehicle is lower than the anxious power coefficient, and the driver chooses to replenish the power at this node; the expression is as follows:

[0089]

[0090] Scenario 2: When the driver reaches a certain node, the state of charge of the electric vehicle is higher than the anxiety power coefficient, and energy can still be replenished at the next node, so the driver chooses to continue moving forward; the expression is as follows:

[0091]

[0092] Scenario 3: When the driver arrives at a certain node, the state of charge of the electric vehicle is higher than the anxiety power coefficient, but the next node cannot be replenished, and the state of charge of the vehicle is lower than the anxiety power coefficient when arriving at the next node. The driver will choose to replenish the power at this node; the expression is as follows:

[0093]

[0094] When the driver chooses to replenish power at a node, charging is completed when the maximum state of charge is reached to 90%. The calculation formula for the replenished power is as follows:

[0095] Q=0.9SOC max -SOC i

[0096] In the calculation formula for scenarios 1, 2, 3 and supplementary power: SOC i SOC is the state of charge of the electric vehicle when it arrives at charging station i; max It is the maximum state of charge of the electric vehicle; is the anxiety power coefficient of an electric vehicle driver at charging station i on the highway network at time T;

[0097] After the vehicle is finished running in DynasTIM, the sum of the charging amount of the electric vehicle at each node is counted every hour, and the charging demand of all nodes is the spatiotemporal distribution of the charging demand in the study; at the same time, charging piles are set to run in some service areas, and the charging service time provided by the node and the waiting time for users to charge when the charging resources in the station are insufficient can also be obtained;

[0098] S4, according to the spatiotemporal distribution of charging demand of each service area in S3 and numbering each service area, select the service area nodes where charging stations need to be established through the maximum coverage site selection model;

[0099] Specifically, the optimization goal is to maximize the total charging demand of the covered demand points:

[0100]

[0101] Where Q is the total number of demand points; d q is the charging demand of demand point q;

[0102] Constraints are imposed on coverage, number of sites, and decision variables; the expressions are as follows:

[0103] Override constraints:

[0104] Site quantity constraints:

[0105] Where N is the total number of charging stations selected for construction; x pis the first binary variable, y p is the second binary variable and a pq is the third binary variable, and the expression is as follows:

[0106]

[0107]

[0108] The final output is the number of service areas selected for establishment, the total number is N;

[0109] S5. Establish a photovoltaic storage and charging integrated charging station model, and obtain the output result data of each unit when the photovoltaic storage charging station meets the charging load data of the selected charging station obtained in S3 and S4;

[0110] At present, the development prospects of charging stations are more inclined towards intelligent and digital multi-energy complementarity, and intelligent scheduling is achieved through technologies such as the Internet of Things, big data, and cloud computing. Among them, the photovoltaic storage charging station technology is relatively complete and has been widely put into use. The charging stations constructed in this article are all photovoltaic storage charging stations, which are mainly composed of intelligent control systems, photovoltaic units, energy storage units, distribution network interaction, and charging equipment;

[0111] The working status of each unit based on the charging load: when the photovoltaic power generation can meet the charging load, the energy storage system is charged first, and if there is surplus electricity, electricity is sold to the distribution network; on the contrary, if the photovoltaic power generation is not enough to support the charging load, the energy storage system is discharged, and if the charging load is still not met or the energy storage capacity is lower than the set value, electricity is purchased from the distribution network; the present invention requires the output result data of each unit to evaluate the operator's revenue;

[0112] The output models of each unit established are as follows:

[0113] S5.1. Establish a photovoltaic unit output model; the details are as follows:

[0114] The output power of photovoltaic cells is mainly affected by the light intensity, so the output model of photovoltaic units is expressed as:

[0115]

[0116] Where η pv is the photoelectric conversion efficiency; S is the area of ​​the photovoltaic unit; r(t) is the change of light intensity over time;

[0117] In the present invention, the mean and variance are calculated based on some historical data, 500 photovoltaic scene data are generated by Latin hypercube stratified sampling, and k-means clustering is reduced to ten scenes to reflect the uncertainty of photovoltaics; the details are as follows:

[0118] The mean and variance are calculated based on historical photovoltaic data. The expressions are as follows:

[0119]

[0120] σ t =u2(t)·μ t

[0121] In the formula, c represents the scaling ratio used to control the calculation of mean and variance, which is a constant; u2(t) represents the random factor generated by Latin hypercube sampling;

[0122] Generate photovoltaic output data of each photovoltaic storage charging station that obeys normal distribution, the expression is as follows:

[0123]

[0124] Where P pv1 (t) is the historical photovoltaic data; P pv2 (t) is the photovoltaic data of each photovoltaic storage charging station in the study;

[0125] S5.2. Establish the output model of the energy storage unit; the details are as follows:

[0126] The output model of the energy storage unit includes two states: charging and discharging;

[0127] The expression of the discharge state is as follows:

[0128]

[0129] The expression of the state of charge is as follows:

[0130]

[0131] Where η z is the conversion efficiency of the energy storage unit; η c , η dis E is the charging efficiency and discharging efficiency respectively; h is the rated capacity of the energy storage unit; P es (t) is the charge and discharge power;

[0132] Establish the battery model of energy storage unit, the expression is as follows:

[0133]

[0134] In the formula, SOC es (t) is the charge state of the energy storage unit in time period t;

[0135] S5.3. Establish a distribution network output model; the details are as follows:

[0136] Based on the charging load, as well as the output of photovoltaic and energy storage units, a distribution network output model is constructed; the expression is as follows:

[0137]

[0138] Where η t is the conversion efficiency; t is the line loss rate; is the charging demand of charging station i in time period t;

[0139] The constraints of the present invention on the energy storage unit include:

[0140] Energy storage power constraint: -P es (t) max ≤P es (t)≤P es (t) max

[0141] Energy storage state of charge constraint: 0.1E h ≤SOC es ≤0.9E h

[0142] Finally, the output results of each unit are obtained;

[0143] S6. Based on the results of S3, S4 and S5, the model is used to calculate the satisfaction degree of charging demand of each charging station, the reasonable allocation of power resources and the relief of road traffic congestion;

[0144] Specifically, S4 selects N charging stations, and the number of fast charging piles in each charging station is set E = {m1, m2, ..., m n}, n∈N, and each fast charging pile in the charging station (slow charging piles are not considered in the highway network service area) can work 24 hours a day;

[0145] The calculation process is as follows:

[0146] S6.1. Calculate the degree of satisfaction of charging demand; the details are as follows:

[0147]

[0148] In the formula, is the utilization rate of charging station i in time period t, which is specifically expressed as follows:

[0149]

[0150] In the formula, is the charging demand of charging station i in time period t (obtained by step S3.4); Q is is the maximum charging resource that can be provided in charging station i, which is specifically expressed as follows:

[0151] Q is =P f ·t is

[0152] Where P f is the charging power of the fast charging pile; t is The duration of the charging service provided by charging station i in time period t (obtained by step S3.4);

[0153] The average charging demand satisfaction of all charging stations can be expressed as:

[0154]

[0155] S6.2. Calculate the power resource allocation; the details are as follows:

[0156] The calculation expression of the power usage in the charging station is as follows:

[0157]

[0158] Where η f E is the energy conversion efficiency of the fast charging pile; io The power consumption of other power facilities in charging station i;

[0159] The entire photovoltaic charging station is mainly powered by the photovoltaic system, energy storage system, and distribution network. Therefore, the calculation expression of the power supply in the charging station is as follows:

[0160] E im =E i,pv +E i,es +E i,gr

[0161] In the formula, the photovoltaic system output model in each charging station is expressed as:

[0162]

[0163] In the formula, E i,pv is the power generation of the photovoltaic system in charging station i; η pv is the photoelectric conversion efficiency; S i is the area of ​​the photovoltaic unit in charging station i; r i (t) is the change of solar illumination intensity on the horizontal surface of charging station i over time;

[0164] The power transmission model from the distribution network to each charging station is approximately expressed as:

[0165]

[0166] Where η t is the conversion efficiency; tis the line loss rate; therefore, the average distribution of power resources in all charging stations can be expressed as:

[0167]

[0168] S6.3. Calculate traffic relief conditions; details are as follows:

[0169]

[0170] Where U i is the congestion index of the road section between charging station i and the previous charging station; is the actual traffic flow through the road section during time period t (obtained through traffic monitoring equipment); is the road capacity that can pass through the road section in time period t (a fixed value set for each road in the traffic simulation road network model); is the average speed of vehicles passing through charging station i during time period t; V i,free is the free flow speed of vehicles passing charging station i without congestion;

[0171] S7. Based on the data of S5 and the calculation results of S6, a charging station capacity determination model is established to determine the daily net profit after all charging stations in the road network are put into use; that is, the entropy weights of the three aspects of the adaptability of charging resources and charging demand, power resource allocation, and traffic relief are calculated by the entropy weight method to establish a road performance evaluation model; based on cooperative game, an overall profit model brought by all charging stations after they are put into operation is established; and the maximization of road performance and the maximization of benefits are taken as the objective function;

[0172] Here are the steps:

[0173] S7.1. Establish a road performance evaluation model by entropy weight method;

[0174] The expression of the road performance evaluation model established by the entropy weight method is as follows:

[0175] f1=ω1·v1(N)+ω2·v2(N)+ω3·v3(N)

[0176] In the formula, ω1, ω2, and ω3 are the weights of the three indicators of the charging demand satisfaction degree, the average distribution of power resources, and the traffic relief situation of the charging station;

[0177] S7.2. Establishing operator profit model through cooperative game;

[0178] The daily revenue function after all charging stations in the road network are put into use is established through the cooperative game model. First, the revenue expression of each charging station is as follows:

[0179]

[0180] In the formula, ct The unit price of the charging service provided by the charging station to the user during time period t;

[0181] The daily cost of each charging station includes four parts: photovoltaic system operation and maintenance cost, energy storage system operation and maintenance cost, electricity purchase cost from the distribution network, and station facility operation and maintenance cost;

[0182] The operation and maintenance cost of the photovoltaic system is expressed as follows:

[0183]

[0184] In the formula, c pv is the unit operation and maintenance price of the photovoltaic system; is the output power of the photovoltaic system of charging station i in time period t; Δt is the unit length of time period t (1 hour);

[0185] The operation and maintenance cost of the energy storage system is expressed as follows:

[0186]

[0187] In the formula, c E E is the unit capacity operation and maintenance cost of the energy storage system; im Configure the energy storage capacity of charging station i; c p is the unit transmission cost of the energy storage system; is the output power of the energy storage system of charging station i during time period t;

[0188] The interaction cost expression of the distribution network is as follows:

[0189]

[0190] In the formula, The unit price that the charging station buys and sells from the distribution network during time period t; The power purchased and sold by charging station i from the distribution network during time period t;

[0191] The cost expression of the in-station infrastructure is as follows:

[0192] C i,inst =c f ·m i +c o

[0193] In the formula, c f is the operation and maintenance price of a single fast charging pile; m i is the number of fast charging piles in charging station i; c o is the fixed operation and maintenance cost of other facilities in the charging station (a set constant item);

[0194] Therefore, the daily net profit function after all charging stations in the entire road network are put into use is:

[0195]

[0196] S8. Solve the optimization objective of S7 through the NSGA-II algorithm, then obtain the ideal allocation plan based on the Shapley value, and use the Topsis method to find the optimal solution that is closest to the ideal allocation plan in the Pareto solution set. The decision variable corresponding to the optimal solution is the optimal capacity plan; the steps are as follows:

[0197] S8.1. Obtain the spatiotemporal distribution diagram of charging demand in the highway network through SUMO. The specific data has been obtained through step S3.4.

[0198] S8.2. According to the average charging demand over 24 hours, set the ideal capacity range of each charging station and formulate the form of each solution in the algorithm x={m1,m2,…,m i ,…,m n}, where each value m i Represents the number of charging piles installed in the corresponding node, all of which are even variables;

[0199] S8.3, according to the maximum population size N pop Generate an initial population and check whether the generated initial solution meets the capacity interval constraint. If not, regenerate until the initial population size reaches N. pop ;

[0200] S8.4. Calculate the first function f1 and the second function f2 of all individual fitness, and get two groups and The tournament algorithm selection operator is used to randomly select individuals from the initial population. The two with the highest fitness function win and are selected. Then, the crossover operator and mutation operator are used to generate offspring individuals. The new individuals are tested again to see if they meet the capacity interval constraint. If they do, they are retained in the offspring population until the offspring population also reaches the maximum population size N. pop ;

[0201] S8.5. Merge the parent population and the child population through the elite strategy, and use the fast non-dominated sorting algorithm to obtain the sorting hierarchy of the new population after the merger;

[0202] According to the sorting level, the population of each level is taken out from low to high and put into the new population. If the number of the new population exceeds the maximum population when a certain level is taken, the crowding degree of the individuals in the level is calculated, and the individuals are taken out in order from low to high according to the crowding degree until the number of the new population reaches the maximum population.

[0203] S8.6, if the number of iterations does not reach the maximum number of iterations Genmax , then go to S7.4, otherwise terminate the algorithm and output the Pareto frontier solution;

[0204] S8.7. All charging stations are members of the alliance s, N = {1, 2, ..., n}, and a set of constant solutions x0 = {a, a, ..., a} are taken to calculate the daily revenue function f2 as the characteristic function of the cooperative game of alliance members, that is:

[0205] v(s)=f2(x0)

[0206] Then n charging stations jointly play the game, and the allocation scheme y={y1,y2,…,y n} satisfies the following formula:

[0207]

[0208]

[0209] Where |s| is the number of elements in set s (equal to n); y i is the Shapley value of i; v(s / i) is the revenue of alliance s minus charging station i; [v(s)-v(s / i)] is the marginal contribution of charging station i to alliance s; based on the Shapley value of each charging station, we get a set of ideal solutions Combining the topsis idea, we can find the solution closest to the ideal solution from the Pareto frontier solution set, which is the optimal solution.

[0210] Beneficial effects of the present invention

[0211] The present invention can obtain effective traffic routes and flow rates through expressway entrance and exit toll data, which effectively guarantees the authenticity and reliability of the experiment.

[0212] At the same time, in the energy consumption model, most studies have considered that weather factors will aggravate the shortening of the actual range of EVs. However, the energy consumption model of electric vehicles on highway networks is affected by many factors, such as the density of traffic ahead, motor efficiency, internal equipment operation, and EV user behavior habits. Therefore, the present invention considers combining vehicle dynamics and motor dynamics to construct energy consumption models according to different situations, and at the same time constructs a charging behavior scenario for drivers passing by charging stations;

[0213] Under the background of smart grid and multi-energy complementary charging station technology, the present invention establishes an output model of each unit of a photovoltaic storage and charging integrated charging station, and calculates the output result data of each unit based on the charging load and photovoltaic power generation, which is convenient for the evaluation of the operator's daily profit in the subsequent optimization of the charging station capacity model.

[0214] The optimization research of charging stations can be experimented on the premise of the currently constructed charging resources, adopting the policy of less charging and more stopping, which is conducive to cost saving. BRIEF DESCRIPTION OF THE DRAWINGS

[0215] Figure 1 is a flow chart of the steps of the present invention;

[0216] Figure 2 It is a schematic diagram of the probability density curve of a car entering a highway according to the present invention;

[0217] Figure 3 A schematic diagram of the shortest path and effective path set of the present invention;

[0218] Figure 4 It is a relationship curve schematic diagram of the present invention;

[0219] Figure 5 It is a time-space distribution diagram of charging demand of the present invention; wherein, part (a) is a schematic diagram of the time-space distribution path of charging demand; part (b) is a three-dimensional column diagram of the time-space distribution of charging demand;

[0220] Figure 6 This is a system structure diagram of the photovoltaic storage and charging integrated power station of the present invention;

[0221] Figure 7 The photovoltaic output data diagram of the present invention; wherein, part (a) is a schematic diagram of photovoltaic power generation under 500 scenarios; part (b) is a schematic diagram of the quantity under each cluster; part (c) is a schematic diagram of photovoltaic power generation under 10 scenarios after reduction; part (d) is a schematic diagram of the probability distribution under each scenario; part (e) is a schematic diagram of the photovoltaic uncertainty output power;

[0222] Figure 8 This is the output result diagram of each unit in the photovoltaic storage charging station;

[0223] Fig. 9 Schematic diagram of the convergence results of the NSGA-II algorithm. DETAILED DESCRIPTION

[0224] The present invention is further described in detail below in conjunction with specific embodiments.

[0225] A method for optimizing charging stations in a high-speed road network based on the spatiotemporal distribution of charging demand specifically comprises the following steps:

[0226] S1, collecting and processing road network data and highway toll collection record data, obtaining electric vehicle travel characteristic parameters and generating road network vehicle driving trajectories;

[0227] The characteristic parameters of electric vehicle travel include: time data and location data;

[0228] The specific steps of S1 are as follows:

[0229] S1.1. Obtain the experimental highway network model through open source maps; the steps are as follows:

[0230] S1.1.1. Obtain the road network model of the target province through the open source map software OpenStreetMap;

[0231] In this experimental example, the road network map of Shandong Province is selected as the experimental object;

[0232] S1.1.2. Modify and organize the road network model of the target province using the road network editing software Netdit;

[0233] Modification and arrangement means only retaining the highway network model;

[0234] S1.1.3, setting the toll station locations, service area and parking area locations of the expressway network and the detector locations on the road sections as nodes and numbering them;

[0235] S1.2. Obtain the probability density curve of vehicles entering the expressway network through kernel density estimation; the steps are as follows:

[0236] S1.2.1. Discretize the time data of vehicles entering the expressway network through grid points and calculate the histogram of the time data;

[0237] Time data range R = [0h, 24h], where 0h corresponds to R as MIN and 24h corresponds to R as MAX;

[0238] S1.2.2. Normalize the probability density of the histogram and perform discrete cosine transform to obtain the frequency domain coefficient a k ; The expression is as follows:

[0239]

[0240] Where b k represents the kth interval; x s represents the sth data sample; A represents the total number of data samples; b represents the total number of partition intervals, which is 24; M k represents the probability that the data sample falls into interval k; p k represents the normalized probability of the kth interval; p z Represents the normalized probability value of the index zth interval, z∈k;

[0241] S1.2.3. Calculate the optimal bandwidth h through the iterative calculation of the fixed point equation and perform smoothing on the histogram; the expression is as follows:

[0242]

[0243] R=MAX-MIN

[0244] Where R represents the time data range; t * represents the optimal smoothing parameter, and the expression is as follows:

[0245]

[0246] Where t represents the smoothing parameter; f(t) is the frequency domain smoothing function related to t, and the expression is as follows:

[0247]

[0248] In the formula, L represents the maximum order of iteration;

[0249] S1.2.4, the final probability density distribution is obtained by smoothing the frequency domain coefficients and inverse discrete cosine transform; the expression is as follows: Figure 2 As shown;

[0250]

[0251] In the formula, Represents the smoothed frequency domain coefficient; represents inverse discrete cosine transform;

[0252] S1.3, obtain the vehicle driving trajectory of the road network through the A* algorithm and the path allocation model; the steps are as follows:

[0253] S1.3.1. Obtain the starting and ending positions of the vehicle entering the expressway network based on the vehicle location data in the provincial expressway toll collection record data;

[0254] S1.3.2, the A* algorithm calculates the shortest path from the starting point to the end point, taking into account the user's path choice midway, and applying random perturbations to the road section impedance in the mesoscopic traffic simulation software DynasTIM to expand the set of valid paths; the specific results are as follows Figure 3 As shown;

[0255] S2. Establish an energy consumption model based on the factors that affect the energy consumption of electric vehicles;

[0256] Factors that affect the energy consumption of electric vehicles include: motor conversion efficiency, internal equipment operating energy consumption and high-speed driving resistance (friction resistance, wind resistance, slope resistance);

[0257] The steps to build an energy consumption model are as follows:

[0258] S2.1. Based on the law of conservation of energy, consider the energy loss of the vehicle from two aspects: vehicle dynamics and motor dynamics. First, establish the driving equation of the electric vehicle, which is expressed as follows:

[0259] F t =F m +Fk +F p +F j

[0260] In the formula, F t F is the driving force; m F is the friction resistance; k is air resistance; F p is the slope resistance; F j For acceleration resistance;

[0261] Through sorting, we can get:

[0262]

[0263] Where m is the mass of the vehicle; g is the acceleration of gravity; f is the road friction coefficient; α is the road slope angle; C D is the drag coefficient; A is the frontal area of ​​the vehicle; v s is the actual vehicle speed; δ is the rotation mass conversion coefficient;

[0264] S2.2. Establishing a driving energy consumption model under different driving conditions;

[0265] Different driving states include: vehicle uniform speed driving state, vehicle acceleration driving state and vehicle deceleration driving state; that is, according to the comparison of the current vehicle speed v s and target vehicle speed v m Determine different driving states of the vehicle;

[0266] The details are as follows:

[0267] S2.2.1. When the vehicle is moving at a constant speed (v s =v m ) state, the vehicle has no acceleration resistance, so the energy consumption expression of the electric vehicle at this time is as follows:

[0268]

[0269] Where η d is the motor conversion efficiency;

[0270] S2.2.2, when the vehicle accelerates (v s <v m ) or uphill state, the vehicle has acceleration resistance and needs to provide a net driving force for vehicle acceleration. Therefore, the energy consumption expression of electric vehicle acceleration drive is as follows:

[0271]

[0272] In the formula, ΔT is the torque added by the vehicle acceleration motor, and the expression is as follows:

[0273]

[0274] In the formula, r is the wheel radius; i0 is the speed ratio of the reducer;

[0275] ω n is the motor speed, the expression is as follows:

[0276]

[0277] Where i1 is the transmission ratio of the vehicle transmission system;

[0278] S2.2.3, when the vehicle is decelerating (v s >v m ) state, the vehicle regenerative braking system is started, there is no driving force, and the expression of the electric vehicle braking recovery energy is as follows:

[0279]

[0280] Where η t The efficiency of regenerative braking recovery;

[0281] S2.2.4. The energy consumption model of electric vehicles is integrated as follows:

[0282] P=P x1 +P x2 +P i -P x3

[0283] Where P x1 P is the energy consumption of electric vehicles; x2 Accelerate driving energy consumption for electric vehicles; x3 Recover energy from braking for electric vehicles; i Energy consumption for running the internal equipment of electric vehicles;

[0284] S2.3, target vehicle speed v in the driving energy consumption model under different driving conditions m Make corrections; the steps are as follows:

[0285] Specifically, the speed of simulated vehicles in the highway network is not always constant, and when rain, snow, fog, traffic congestion, etc. occur, it will affect the driver's visibility and vehicle grip, so the vehicle's speed and the driver's driving anxiety need to be corrected;

[0286] In addition, considering that drivers are worried about extreme weather and dense traffic, frequent starting and stopping or deceleration will cause range anxiety, which will lead to wrong judgments on the driver's charging decision, so the driver's anxious power also needs to be corrected;

[0287] Here are the steps:

[0288] S2.3.1. The correction expression of vehicle flow to vehicle speed is as follows:

[0289]

[0290] In the formula, v′ m is the target vehicle speed after traffic flow correction; v f is the free flow speed of vehicles; k m is the average density of the vehicle’s front influence region (SIR); k jam is the blocking density of the impact area in front of the vehicle; k min is the upper limit of the density of the vehicle when it runs at the free flow speed; σ and β are the first parameter and the second parameter respectively; the detailed parameter settings are shown in Table 1 of the attached figure;

[0291] Table 1 Density-vehicle speed model parameters

[0292]

[0293] The density-vehicle speed result is as follows Figure 3 As shown;

[0294] S2.3.2 The weather correction expression for vehicle speed is as follows:

[0295]

[0296] In the formula, v′ m ′ is the target vehicle speed after weather correction; The correction factor of the weather from charging station i to i+1 on the vehicle speed is selected. Precipitation and snowfall are used as the scale calibration. The target vehicle speed is reduced as the precipitation and snowfall increase. The reduction range is 4%-14%.

[0297] S2.4, correct the anxiety power coefficient;

[0298] Considering that drivers are worried about extreme weather and dense traffic, frequent starting and stopping or deceleration may cause range anxiety, which may lead to misjudgment of the driver's charging decision, so the driver's anxious power level also needs to be corrected;

[0299] The weather correction expression for the anxiety power coefficient is as follows:

[0300]

[0301] In the formula, is the anxiety power coefficient of an electric vehicle driver at the highway charging station i+1 at time T; θ is the basic anxiety power coefficient under the assumption of good weather and reasonable traffic flow, and its value is 0.3; It is the correction factor of the anxiety power coefficient caused by the weather and traffic flow from charging station i to i+1, ranging from 6% to 20%;

[0302] S3, input the parameters of S1 into the mesoscopic traffic simulation software DynasTIM, and run the energy consumption model of S2 in the software to track the vehicle's charge state in real time. The nodes selected by the vehicle for charging and the amount of electricity replenished at the nodes are calculated through the constructed charging scenario, and finally the spatiotemporal distribution of charging demand in each service area of ​​the highway network is obtained; the specific steps are as follows:

[0303] S3.1. Use traffic simulator to track the traffic status of expressway network or customize the network information;

[0304] Traffic simulators include: mesoscopic traffic simulation software DynasTIM;

[0305] Highway network traffic status or custom road network information including: highway network toll node location, lane speed limit information, road slope angle, air density, distribution station location and service area location and set charging station capacity;

[0306] S3.2, simulation of vehicle driving on the highway network;

[0307] S3.2.1. Set the parameters of different vehicle models in the routing file, including vehicle weight, frontal area, speed, rotational mass conversion coefficient, motor energy conversion efficiency, rolling resistance coefficient, electric vehicle internal equipment operating energy consumption and maximum charge state. The specific parameter values ​​of the experiment are shown in Table 2;

[0308] Table 2 Energy consumption model parameters

[0309]

[0310] S3.2.2. Put the vehicle into the road network based on the probability density curve of the vehicle entering the expressway network, and drive along the shortest path between the vehicle's starting point and end point and other valid paths;

[0311] S3.3, the energy consumption model is constructed to calculate the energy consumption and obtain the charging demand data of the vehicle;

[0312] Specifically, during the operation of the mesoscopic traffic simulation DynasTIM, the travel chain of vehicles on the highway network is as follows: Figure 4 , input the parameters of each node in the driving trajectory (the time from the previous node to this node, the driving distance and the driving speed) into the energy consumption model built in python to calculate the energy consumption, update the remaining power of the vehicle, and generate the correction factor based on the node parameters (weather information, traffic flow information of the node). According to S2.3 and S2.4, the speed and anxiety power coefficient of the vehicle are corrected, and the driving speed of the simulated vehicle after leaving the node is updated through the TraCI interface. It is updated in real time after each node is passed until the vehicle ends the simulation and leaves the road network;

[0313] S3.4. By obtaining the remaining power and anxiety power coefficient when the vehicle arrives at the node, the user charging decision is made according to the actual user driving habits and charging judgment to divide the scenarios; the details are as follows:

[0314] Scenario 1: When the driver arrives at a certain node, the state of charge of the electric vehicle is lower than the anxious power coefficient, and the driver chooses to replenish the power at this node; the expression is as follows:

[0315]

[0316] Scenario 2: When the driver reaches a certain node, the state of charge of the electric vehicle is higher than the anxiety power coefficient, and energy can still be replenished at the next node, so the driver chooses to continue moving forward; the expression is as follows:

[0317]

[0318] Scenario 3: When the driver arrives at a certain node, the state of charge of the electric vehicle is higher than the anxiety power coefficient, but the next node cannot be replenished, and the state of charge of the vehicle is lower than the anxiety power coefficient when arriving at the next node. The driver will choose to replenish the power at this node; the expression is as follows:

[0319]

[0320] When the driver chooses to replenish power at a node, charging is completed when the maximum state of charge is reached to 90%. The calculation formula for the replenished power is as follows:

[0321] Q=0.9SOC max -SOC i

[0322] In the calculation formula for scenarios 1, 2, 3 and supplementary power: SOC i SOC is the state of charge of the electric vehicle when it arrives at charging station i; max It is the maximum state of charge of the electric vehicle; is the anxiety power coefficient of an electric vehicle driver at charging station i on the highway network at time T;

[0323] After the vehicle runs in DynasTIM, the sum of the charging amount of the electric vehicle at each node is counted every hour. The charging demand of all nodes is the spatiotemporal distribution of the charging demand in the study. The results are shown in Figure 5 (a) and (b); At the same time, charging piles are set to operate in some service areas, and the charging service time provided by the node and the waiting time for users to charge when the charging resources in the station are insufficient can be obtained;

[0324] Figure 5 The size of the circle in part (a) reflects the amount of charging required.

[0325] Depend on Figure 5 As can be seen from part (b), the temporal and spatial distribution of charging demand in the service area is not uniform, showing “peak and valley” driving, which is in line with the travel patterns of users;

[0326] S4, according to the spatiotemporal distribution of charging demand of each service area in S3 and numbering each service area, select the service area nodes where charging stations need to be established through the maximum coverage site selection model;

[0327] Specifically, the optimization goal is to maximize the total charging demand of the covered demand points:

[0328]

[0329] Where Q is the total number of demand points; d q is the charging demand of demand point q;

[0330] Constraints are imposed on coverage, number of sites, and decision variables; the expressions are as follows:

[0331] Override constraints:

[0332] Site quantity constraints:

[0333] Where N is the total number of charging stations selected for construction, which is 85% of the total number of service areas in this implementation; x p is the first binary variable, y p is the second binary variable and a pq is the third binary variable, and the expression is as follows:

[0334]

[0335] The final output is the number of service areas selected to be established, the total number is N.

[0336] S5. Establish a photovoltaic storage and charging integrated charging station model, and obtain the output result data of each unit when the photovoltaic storage charging station meets the charging load data of the selected charging station obtained in S3 and S4;

[0337] At present, the development prospects of charging stations are more inclined towards intelligent and digital multi-energy complementarity, and intelligent scheduling is achieved through technologies such as the Internet of Things, big data, and cloud computing. Among them, the photovoltaic storage charging station technology is relatively complete and has been widely put into use. The charging stations constructed in this article are all photovoltaic storage charging stations, which are mainly composed of intelligent control systems, photovoltaic units, energy storage units, distribution network interaction and charging equipment. The system block diagram is as follows Figure 6 shown.

[0338] The working status of each unit based on the charging load: when the photovoltaic power generation can meet the charging load, the energy storage system is charged first, and if there is surplus electricity, electricity is sold to the distribution network; on the contrary, if the photovoltaic power generation is not enough to support the charging load, the energy storage system is discharged, and if the charging load is still not met or the energy storage capacity is lower than the set value, electricity is purchased from the distribution network; the present invention requires the output result data of each unit to evaluate the operator's revenue;

[0339] The output models of each unit established are as follows:

[0340] S5.1. Establish a photovoltaic unit output model; the details are as follows:

[0341] The output power of photovoltaic cells is mainly affected by the light intensity, so the output model of photovoltaic units is expressed as:

[0342]

[0343] Where η pv is the photoelectric conversion efficiency; S is the area of ​​the photovoltaic unit; r(t) is the change of light intensity over time;

[0344] The present invention does not have the light intensity data of all regions in the province, but the difference in sunlight intensity between provinces is not large, and the sunlight intensity roughly obeys the normal distribution over time; therefore, the present invention calculates the mean and variance based on some historical data, uses Latin hypercube stratified sampling to generate 500 photovoltaic scene data, and kmeans clustering is reduced to ten scenes to reflect the uncertainty of photovoltaics; the details are as follows:

[0345] The mean and variance are calculated based on historical photovoltaic data. The expressions are as follows:

[0346]

[0347] σ t =u2(t)·μ t

[0348] Wherein, c represents the scaling ratio used to control the calculation of the mean and variance, which is a constant and is set to 1 in this embodiment; u2(t) represents the random factor generated by Latin hypercube sampling;

[0349] Generate photovoltaic output data of each photovoltaic storage charging station that obeys normal distribution, the expression is as follows:

[0350]

[0351] Where P pv1 (t) is the historical photovoltaic data; P pv2 (t) is the photovoltaic data of each photovoltaic storage charging station in the study;

[0352] S5.2. Establish the output model of the energy storage unit; the details are as follows:

[0353] The output model of the energy storage unit includes two states: charging and discharging;

[0354] The expression of the discharge state is as follows:

[0355]

[0356] The expression of the state of charge is as follows:

[0357]

[0358] Where η z is the conversion efficiency of the energy storage unit; η c , η dis E is the charging efficiency and discharging efficiency respectively; h is the rated capacity of the energy storage unit; P es (t) is the charge and discharge power;

[0359] Establish the battery model of energy storage unit, the expression is as follows:

[0360]

[0361] In the formula, SOC es (t) is the charge state of the energy storage unit in time period t;

[0362] S5.3. Establish a distribution network output model; the details are as follows:

[0363] Based on the charging load and the output of photovoltaic and energy storage units, a distribution network output model is constructed; the expression is as follows:

[0364]

[0365] Where η t is the conversion efficiency; t is the line loss rate; is the charging demand of charging station i in time period t;

[0366] The constraints of the present invention on the energy storage unit include:

[0367] Energy storage power constraint: -P es (t) max ≤P es (t)≤P es (t) max

[0368] Energy storage state of charge constraint: 0.1E h ≤SOC es ≤0.9E h

[0369] Finally, the output results of each unit are obtained, such as Figure 8 As shown;

[0370] S6. Based on the results of S3, S4 and S5, the model is used to calculate the satisfaction degree of charging demand of each charging station, the reasonable allocation of power resources and the relief of road traffic congestion;

[0371] Specifically, S4 selects N charging stations, and the number of fast charging piles in each charging station is set E = {m1, m2, ..., m n}, n∈N, and each fast charging pile in the charging station (slow charging piles are not considered in the highway network service area) can work 24 hours a day;

[0372] The calculation process is as follows:

[0373] S6.1. Calculate the degree of satisfaction of charging demand; the details are as follows:

[0374]

[0375] In the formula, is the utilization rate of charging station i in time period t, which is specifically expressed as follows:

[0376]

[0377] In the formula, is the charging demand of charging station i in time period t (obtained by step S3.4); Q is is the maximum charging resource that can be provided in charging station i, which is determined by the number of fast charging piles in the station, and is specifically expressed as follows:

[0378] Q is =P f ·t is

[0379] Where P f is the charging power of the fast charging pile; t is The duration of the charging service provided by charging station i in time period t (obtained by step S3.4);

[0380] The average charging demand satisfaction of all charging stations can be expressed as:

[0381]

[0382] S6.2. Calculate the power resource allocation; the details are as follows:

[0383] The calculation expression of the power usage in the charging station is as follows:

[0384]

[0385] Where η f E is the energy conversion efficiency of the fast charging pile; io is the power consumption of other power facilities in charging station i; the entire photovoltaic storage charging station is mainly powered by the photovoltaic system, energy storage system, and distribution network, so the calculation expression of the power supply in the charging station is as follows:

[0386] E im =E i,pv +E i,es +E i,gr

[0387] In the formula, the photovoltaic system output model in each charging station is expressed as:

[0388]

[0389] In the formula, E i,pv is the power generation of the photovoltaic system in charging station i; η pv is the photoelectric conversion efficiency; S i is the area of ​​the photovoltaic unit in charging station i; r i (t) is the change of solar illumination intensity on the horizontal surface of charging station i over time;

[0390] The power transmission model from the distribution network to each charging station is approximately expressed as:

[0391]

[0392] Where η t is the conversion efficiency; δ t is the line loss rate; therefore, the average distribution of power resources in all charging stations can be expressed as:

[0393]

[0394] S6.3. Calculate traffic relief conditions; details are as follows:

[0395]

[0396] Where U i is the congestion index of the road section between charging station i and the previous charging station; is the actual traffic flow through the road section during time period t (obtained through traffic monitoring equipment); is the road capacity that can pass through the road section in time period t (a fixed value set for each road in the traffic simulation road network model); is the average speed of vehicles passing through charging station i during time period t; V i,free is the free flow speed of vehicles passing charging station i without congestion;

[0397] S7. Based on the data of S5 and the calculation results of S6, a charging station capacity determination model is established to determine the daily net profit after all charging stations in the road network are put into use; that is, the entropy weights of the three aspects of the adaptability of charging resources and charging demand, power resource allocation, and traffic relief are calculated by the entropy weight method to establish a road performance evaluation model; based on cooperative game, an overall profit model brought by all charging stations after they are put into operation is established; and the maximization of road performance and the maximization of benefits are taken as the objective function;

[0398] Here are the steps:

[0399] S7.1. Establish a road performance evaluation model by entropy weight method;

[0400] The expression of the road performance evaluation model established by the entropy weight method is as follows:

[0401] f1=ω1·v1(N)+ω2·v2(N)+ω3·v3(N)

[0402] In the formula, ω1, ω2, and ω3 are the weights of the three indicators of the charging demand satisfaction degree, the average distribution of power resources, and the traffic relief situation of the charging station;

[0403] S7.2. Establishing operator profit model through cooperative game;

[0404] The daily revenue function after all charging stations in the road network are put into use is established through the cooperative game model. First, the revenue expression of each charging station is as follows:

[0405]

[0406] In the formula, c t The unit price of the charging service provided by the charging station to the user during time period t;

[0407] The daily cost of each charging station includes four parts: photovoltaic system operation and maintenance cost, energy storage system operation and maintenance cost, electricity purchase cost from the distribution network, and station facility operation and maintenance cost;

[0408] The operation and maintenance cost of the photovoltaic system is expressed as follows:

[0409]

[0410] In the formula, c pv is the unit operation and maintenance price of the photovoltaic system; is the output power of the photovoltaic system of charging station i in time period t; Δt is the unit length of time period t (1 hour);

[0411] The operation and maintenance cost of the energy storage system is expressed as follows:

[0412]

[0413] In the formula, c E E is the unit capacity operation and maintenance cost of the energy storage system; im Configure the energy storage capacity of charging station i; c p is the unit transmission cost of the energy storage system; is the output power of the energy storage system of charging station i during time period t;

[0414] The interaction cost expression of the distribution network is as follows:

[0415]

[0416] In the formula, The unit price that the charging station buys and sells from the distribution network during time period t; The power purchased and sold by charging station i from the distribution network during time period t;

[0417] The cost expression of the in-station infrastructure is as follows:

[0418] C i,inst =c f ·m i +c o

[0419] In the formula, c f is the operation and maintenance price of a single fast charging pile; m i is the number of fast charging piles in charging station i; c o is the fixed operation and maintenance cost of other facilities in the charging station (a set constant item);

[0420] Therefore, the daily net profit function after all charging stations in the entire road network are put into use is:

[0421]

[0422] S8. Solve the optimization objective of S7 through the NSGA-II algorithm, then obtain the ideal allocation plan based on the Shapley value, and use the Topsis method to find the optimal solution that is closest to the ideal allocation plan in the Pareto solution set. The decision variable corresponding to the optimal solution is the optimal capacity plan; the steps are as follows:

[0423] S8.1. Obtain the spatiotemporal distribution diagram of charging demand in the highway network through SUMO. The specific data has been obtained through step S3.4.

[0424] S8.2. According to the average charging demand over 24 hours, set the ideal capacity range of each charging station and formulate the form of each solution in the algorithm x={m1,m2,…,m i ,…,m n}, where each value m iRepresents the number of charging piles installed in the corresponding node, all of which are even variables;

[0425] S8.3, according to the maximum population size N pop Generate an initial population and check whether the generated initial solution meets the capacity interval constraint. If not, regenerate until the initial population size reaches N. pop ;

[0426] S8.4. Calculate the first function f1 and the second function f2 of all individual fitness, and get two groups and The tournament algorithm selection operator is used to randomly select individuals from the initial population. The two with the highest fitness function win and are selected. Then, the crossover operator and mutation operator are used to generate offspring individuals. The new individuals are tested again to see if they meet the capacity interval constraint. If they do, they are retained in the offspring population until the offspring population also reaches the maximum population size N. pop ;

[0427] S8.5. Merge the parent population and the child population through the elite strategy, and use the fast non-dominated sorting algorithm to obtain the sorting hierarchy of the new population after the merger;

[0428] According to the sorting level, the population of each level is taken out from low to high and put into the new population. If the number of the new population exceeds the maximum population when a certain level is taken, the crowding degree of the individuals in the level is calculated, and the individuals are taken out in order from low to high according to the crowding degree until the number of the new population reaches the maximum population.

[0429] S8.6, if the number of iterations does not reach the maximum number of iterations Gen max , then go to S7.4, otherwise terminate the algorithm and output the Pareto frontier solution; the results are shown in Table 3. The convergence effect is as follows Fig. 9 As shown;

[0430] Table 3 Pareto frontier solutions

[0431]

[0432]

[0433] S8.7. All charging stations are members of the alliance s, N = {1, 2, ..., n}, and a set of constant solutions x0 = {a, a, ..., a} are taken to calculate the daily revenue function f2 as the characteristic function of the cooperative game of alliance members, that is:

[0434] v(s)=f2(x0)

[0435] Then n charging stations jointly play the game, and the allocation scheme y={y1,y2,…,y n} satisfies the following formula:

[0436]

[0437] Where |s| is the number of elements in set s (equal to n); y i is the Shapley value of i; v(s / i) is the revenue of alliance s minus charging station i; [v(s)-v(s / i)] is the marginal contribution of charging station i to alliance s;

[0438] Based on the Shapley value of each charging station, a set of ideal solutions is obtained Combining the topsis idea, we can find the solution closest to the ideal solution from the Pareto frontier solution set, which is the optimal solution.

[0439] In summary, the present invention obtains effective electric vehicle routes and optimal charging station distribution through highway toll data, and then considers the distribution of charging stations in the highway network. The present invention also considers factors such as weather, driver anxiety, traffic density, motor efficiency and user behavior, and the final result is more real and reliable.

Claims

1. A method for optimizing charging stations in a high-speed road network based on the spatiotemporal distribution of charging demand, characterized in that: The following steps are involved: S1, collecting and processing road network data and highway toll collection record data, obtaining electric vehicle travel characteristic parameters and generating road network vehicle driving trajectories; S2. Establish an energy consumption model based on the factors that affect the energy consumption of electric vehicles; S3, input the parameters of S1 into the mesoscopic traffic simulation software DynasTIM, and run the energy consumption model of S2 in the software to track the vehicle's charge state in real time. Through the constructed charging scenario, the nodes selected by the vehicle for charging and the amount of electricity replenished at the nodes are calculated, and finally the spatiotemporal distribution of charging demand in each service area of ​​the highway network is obtained; S4, according to the spatiotemporal distribution of charging demand of each service area in S3 and numbering each service area, select the service area nodes where charging stations need to be established through the maximum coverage site selection model; S5. Establish a photovoltaic storage and charging integrated charging station model, and obtain the output result data of each unit when the photovoltaic storage charging station meets the charging load data of the selected charging station obtained in S3 and S4; S6. Based on the results of S3, S4 and S5, the model is used to calculate the satisfaction degree of charging demand of each charging station, the reasonable allocation of power resources and the relief of road traffic congestion; S7. Based on the data of S5 and the calculation results of S6, a charging station capacity determination model is established to determine the daily net profit after all charging stations in the road network are put into use; That is, the entropy weights of the three aspects of the compatibility between charging resources and charging demand, power resource allocation, and traffic relief are calculated through the entropy weight method to establish a road performance evaluation model; the overall benefit model brought by the operation of all charging stations is established based on cooperative game theory; the maximization of road performance and the maximization of benefits are solved as objective functions; S8. Solve the optimization objective of S7 through the NSGA-II algorithm, then obtain the ideal allocation plan based on the Sharpe force value, and use the Topsis method to find the optimal solution in the Pareto solution set that is closest to the ideal allocation plan. The decision variable corresponding to this solution is the optimal capacity plan.

2. A method for optimizing charging stations in a high-speed road network based on the spatiotemporal distribution of charging demand according to claim 1, characterized in that: The steps of collecting and processing road network data and highway toll collection record data to obtain electric vehicle travel characteristic parameters and generate road network vehicle driving trajectories are as follows: S1.

1. Get the experimental highway network model through the open source map. The steps are as follows: S1.1.

1. Obtain the road network model of the target province through the open source map software OpenStreetMap; S1.1.

2. Modify and organize the road network model of the target province using the road network editing software Netdit; Modification and arrangement means only retaining the highway network model; S1.1.3, setting the toll station locations, service area and parking area locations of the expressway network and the detector locations on the road sections as nodes and numbering them; S1.

2. Obtain the probability density curve of vehicles entering the expressway network through kernel density estimation; the steps are as follows: S1.2.

1. Discretize the time data of vehicles entering the expressway network through grid points and calculate the histogram of the time data; S1.2.

2. Normalize the probability density of the histogram and perform discrete cosine transform to obtain the frequency domain coefficient a k ; The expression is as follows: Where b k represents the kth interval; x s represents the sth data sample; A represents the total number of data samples; b represents the total number of partitioned intervals; M k represents the probability that the data sample falls into interval k; p k represents the normalized probability of the kth interval; p z Represents the normalized probability value of the index zth interval, z∈k; S1.2.

3. Calculate the optimal bandwidth h through the iterative calculation of the fixed point equation and perform smoothing on the histogram; the expression is as follows: R=MAX-MIN Where R represents the time data range; t * represents the optimal smoothing parameter, and the expression is as follows: Where t represents the smoothing parameter; f(t) is the frequency domain smoothing function related to t, and the expression is as follows: In the formula, L represents the maximum order of iteration; S1.2.4, the final probability density distribution is obtained by smoothing the frequency domain coefficients and inverse discrete cosine transform; the expression is as follows: In the formula, represents the smoothed frequency domain coefficient; represents inverse discrete cosine transform; S1.3, obtain the vehicle driving trajectory of the road network through the A* algorithm and the path allocation model; the steps are as follows: S1.3.

1. Obtain the starting and ending positions of the vehicle entering the expressway network based on the vehicle location data in the provincial expressway toll collection record data; S1.3.2, the A* algorithm calculates the shortest path from the starting point to the end point, taking into account the user's path choice midway, and applies random perturbations to the road section impedance in the mesoscopic traffic simulation software DynasTIM to expand the set of valid paths.

3. The method for optimizing charging stations in a high-speed road network based on the spatiotemporal distribution of charging demand according to claim 1, characterized in that: The steps of establishing the energy consumption model by combining the factors that affect the energy consumption of the electric vehicle are as follows: S2.

1. Based on the law of conservation of energy, consider the energy loss of the vehicle from two aspects: vehicle dynamics and motor dynamics. First, establish the driving equation of the electric vehicle, which is expressed as follows: F t =F m +F k +F p +F j In the formula, F t F is the driving force; m F is the friction resistance; k is air resistance; F p is the slope resistance; F j For acceleration resistance; Through sorting, we can get: Where m is the mass of the vehicle; g is the acceleration of gravity; f is the road friction coefficient; α is the road slope angle; C D is the drag coefficient; A is the frontal area of ​​the vehicle; v s is the actual vehicle speed; δ is the rotation mass conversion coefficient; S2.

2. Establishing a driving energy consumption model under different driving conditions; Different driving states include: vehicle uniform speed driving state, vehicle acceleration driving state and vehicle deceleration driving state; that is, according to the comparison of the current vehicle speed v s and target vehicle speed v m Determine different driving states of the vehicle; The details are as follows: S2.2.

1. When the vehicle is running at a constant speed, there is no acceleration resistance. Therefore, the energy consumption of the electric vehicle is expressed as follows: Where η d is the motor conversion efficiency; S2.2.

2. When the vehicle is accelerating or going uphill, the vehicle has acceleration resistance and needs to provide a net driving force for vehicle acceleration. Therefore, the energy consumption expression of electric vehicle acceleration driving is as follows: In the formula, ΔT is the torque added by the vehicle acceleration motor, and the expression is as follows: In the formula, r is the wheel radius; i0 is the speed ratio of the reducer; ω n is the motor speed, the expression is as follows: Where i1 is the transmission ratio of the vehicle transmission system; S2.2.

3. When the vehicle is decelerating, the vehicle regenerative braking system is activated and there is no driving force. At this time, the expression of the electric vehicle's braking recovery energy is as follows: Where η r The efficiency of regenerative braking recovery; S2.2.

4. The energy consumption model of electric vehicles is integrated as follows: P=P x1 +P x2 +P i -P x3 Where P x1 P is the energy consumption of electric vehicles; x2 Accelerate driving energy consumption for electric vehicles; x3 Recover energy from braking for electric vehicles; i Energy consumption for running the internal equipment of electric vehicles; S2.3, target vehicle speed v in the driving energy consumption model under different driving conditions m Make corrections; the steps are as follows: S2.3.

1. The correction expression of vehicle flow to vehicle speed is as follows: In the formula, v′ m is the target vehicle speed after traffic flow correction; v f is the free flow speed of vehicles; k m is the average density of the impact area in front of the vehicle; k jam is the blocking density of the impact area in front of the vehicle; k min is the upper limit of the density of vehicles when they run at free flow speed; σ and β are the first parameter and the second parameter respectively; S2.3.2 The weather correction expression for vehicle speed is as follows: In the formula, v′ m ′ is the target vehicle speed after weather correction; The correction factor of the weather from charging station i to i+1 on the vehicle speed is selected. Precipitation and snowfall are used as the scale calibration. The target vehicle speed is reduced as the precipitation and snowfall increase. The reduction range is 4%-14%. S2.4, correct the anxiety power coefficient; Considering that drivers are worried about extreme weather, frequent starting and stopping or deceleration will cause range anxiety, which will lead to wrong judgments on the driver's charging decision, so the driver's anxious power also needs to be corrected; The weather correction expression for the anxiety power coefficient is as follows: In the formula, is the anxiety power coefficient of an electric vehicle driver at the highway charging station i+1 at time T; θ is the basic anxiety power coefficient under the assumption of good weather and reasonable traffic flow; It is the correction factor of the anxiety power coefficient due to the weather and traffic flow from charging station i to i+1, ranging from 6% to 20%.

4. The method for optimizing charging stations in a high-speed road network based on the spatiotemporal distribution of charging demand according to claim 1, characterized in that: The parameters of S1 are input into the mesoscopic traffic simulation software DynasTIM, and the energy consumption model of S2 is run in the software to track the charge state of the vehicle in real time. The nodes selected by the vehicle for charging and the amount of electricity replenished at the nodes are calculated through the constructed charging scenario, and finally the spatiotemporal distribution of charging demand in each service area of ​​the highway network is obtained; the specific steps are as follows: S3.

1. Use traffic simulator to track the traffic status of expressway network or customize the network information; Traffic simulators include: mesoscopic traffic simulation software DynasTIM; Highway network traffic status or custom road network information including: highway network toll node location, lane speed limit information, road slope angle, air density, distribution station location and service area location and set charging station capacity; S3.2, simulation of vehicle driving on the highway network; S3.2.

1. Set the parameters of different vehicle models in the routing file, including: vehicle weight, frontal area, speed, rotational mass conversion factor, motor energy conversion efficiency, rolling resistance coefficient, operating energy consumption of internal equipment of electric vehicles and maximum state of charge; S3.2.

2. Put the vehicle into the road network based on the probability density curve of the vehicle entering the expressway network, and drive along the shortest path between the vehicle's starting point and end point and other valid paths; S3.3, the energy consumption model is constructed to calculate the energy consumption and obtain the charging demand data of the vehicle; S3.

4. By obtaining the remaining power and anxiety power coefficient when the vehicle arrives at the node, the user charging decision is made according to the actual user driving habits and charging judgment to divide the scenarios; the details are as follows: Scenario 1: When the driver arrives at a certain node, the state of charge of the electric vehicle is lower than the anxious power coefficient, and the driver chooses to replenish the power at this node; the expression is as follows: Scenario 2: When the driver reaches a certain node, the state of charge of the electric vehicle is higher than the anxiety power coefficient, and energy can still be replenished at the next node, so the driver chooses to continue moving forward; the expression is as follows: Scenario 3: When the driver arrives at a certain node, the state of charge of the electric vehicle is higher than the anxiety power coefficient, but the next node cannot be replenished, and the state of charge of the vehicle is lower than the anxiety power coefficient when arriving at the next node. The driver will choose to replenish the power at this node; the expression is as follows: When the driver chooses to replenish power at a node, charging is completed when the maximum state of charge is reached to 90%. The calculation formula for the replenished power is as follows: Q=0.9SOC max -SOC i In the calculation formula for scenarios 1, 2, 3 and supplementary power: SOC i SOC is the state of charge of the electric vehicle when it arrives at charging station i; max It is the maximum state of charge of the electric vehicle; is the anxiety power coefficient of an electric car driver at charging station i on the highway network at time T.

5. The method for optimizing charging stations in a high-speed road network based on the spatiotemporal distribution of charging demand according to claim 1, characterized in that: According to the spatiotemporal distribution of charging demand in each service area in S3, each service area is numbered, and the service area nodes where charging stations need to be established are selected through the maximum coverage site selection model, as follows: The optimization goal is to maximize the total charging demand of the covered demand points: Where Q is the total number of demand points; d q is the charging demand of demand point q; Constraints are imposed on coverage, number of sites, and decision variables; the expressions are as follows: Override constraints: Site quantity constraints: Where N is the total number of charging stations selected for construction; x p is the first binary variable, y p is the second binary variable and a pq is the third binary variable, and the expression is as follows:

6. The method for optimizing charging stations in a high-speed road network based on the spatiotemporal distribution of charging demand according to claim 1, characterized in that: The photovoltaic storage charging integrated charging station model is established, and the charging load data of the selected charging station obtained by S3 and S4 is used to obtain the output result data of each unit when the photovoltaic storage charging station meets these loads, as follows: The output models of each unit established are as follows: S5.

1. Establish a photovoltaic unit output model; the details are as follows: The output power of photovoltaic cells is mainly affected by the light intensity, so the output model of photovoltaic units is expressed as: Where η pv is the photoelectric conversion efficiency; S is the area of ​​the photovoltaic unit; r(t) is the change of light intensity over time; S5.

2. Establish the output model of the energy storage unit; the details are as follows: The output model of the energy storage unit includes two states: charging and discharging; The expression of the discharge state is as follows: The expression of the state of charge is as follows: Where η z is the conversion efficiency of the energy storage unit; η c , η dis E is the charging efficiency and discharging efficiency respectively; h is the rated capacity of the energy storage unit; P es (t) is the charge and discharge power; Establish the battery model of energy storage unit, the expression is as follows: In the formula, SOC es (t) is the charge state of the energy storage unit in time period t; S5.

3. Establish a distribution network output model; the details are as follows: Based on the charging load, as well as the output of photovoltaic and energy storage units, a distribution network output model is constructed; the expression is as follows: Where η t is the conversion efficiency; t is the line loss rate; is the charging demand of charging station i in time period t; The constraints of the energy storage unit include: Energy storage power constraint: -P es (t) max ≤P es (t)≤P es (t) max ; Energy storage state of charge constraint: 0.1E h ≤SOC es ≤0.9E h .

7. The method for optimizing charging stations in a high-speed road network based on the spatiotemporal distribution of charging demand according to claim 1, characterized in that: According to the results of S3, S4, and S5, the calculation process of calculating the satisfaction degree of charging demand of each charging station, the reasonable allocation of power resources, and the relief of road traffic congestion through the model is as follows: S6.

1. Calculate the degree of satisfaction of charging demand; the details are as follows: In the formula, is the utilization rate of charging station i in time period t, which is specifically expressed as follows: In the formula, is the charging demand of charging station i in time period t; Qis is the maximum charging resource that can be provided in charging station i, which is specifically expressed as follows: Q is =P f ·t is Where P f is the charging power of the fast charging pile; t is is the charging service duration of charging station i in time period t; The average charging demand satisfaction of all charging stations can be expressed as: S6.

2. Calculate the power resource allocation; the details are as follows: The calculation expression of the power usage in the charging station is as follows: Where η f E is the energy conversion efficiency of the fast charging pile; io The power consumption of other power facilities in charging station i; The entire photovoltaic charging station is mainly powered by the photovoltaic system, energy storage system, and distribution network. Therefore, the calculation expression of the power supply in the charging station is as follows: AND im =And i,pv +E i,es +E i,gr In the formula, the photovoltaic system output model in each charging station is expressed as: In the formula, E i,pv is the power generation of the photovoltaic system in charging station i; η pv is the photoelectric conversion efficiency; S i is the area of ​​the photovoltaic unit in charging station i; r i (t) is the change of solar illumination intensity on the horizontal surface of charging station i over time; The power transmission model from the distribution network to each charging station is approximately expressed as: Where η t is the conversion efficiency; t is the line loss rate; therefore, the average distribution of power resources in all charging stations can be expressed as: S6.

3. Calculate traffic relief conditions; details are as follows: Where U i is the congestion index of the road section between charging station i and the previous charging station; is the actual traffic flow through the road section during time period t; is the road capacity that can pass through the road section in time period t; is the average speed of vehicles passing through charging station i during time period t; V i,free is the free flow speed of vehicles passing charging station i without congestion.

8. The method for optimizing charging stations in a high-speed road network based on the spatiotemporal distribution of charging demand according to claim 1, characterized in that: The steps of establishing a charging station capacity determination model based on the data of S5 and the calculation result of S6 to determine the daily net profit after all charging stations in the road network are put into use are as follows: S7.

1. Establish a road performance evaluation model by entropy weight method; The expression of the road performance evaluation model established by the entropy weight method is as follows: f1=ω1·v1(N)+ω2·v2(N)+ω3·v3(N) In the formula, ω1, ω2, and ω3 are the weights of the three indicators of the charging demand satisfaction degree, the average distribution of power resources, and the traffic relief situation of the charging station; S7.

2. Establishing operator profit model through cooperative game; The daily revenue function after all charging stations in the road network are put into use is established through the cooperative game model. First, the revenue expression of each charging station is as follows: In the formula, c t The unit price of the charging service provided by the charging station to the user during time period t; The daily cost of each charging station includes four parts: photovoltaic system operation and maintenance cost, energy storage system operation and maintenance cost, electricity purchase cost from the distribution network, and station facility operation and maintenance cost; The operation and maintenance cost of the photovoltaic system is expressed as follows: In the formula, c pv is the unit operation and maintenance price of the photovoltaic system; is the output power of the photovoltaic system of charging station i in time period t; Δt is the unit length of time period t; The operation and maintenance cost of the energy storage system is expressed as follows: In the formula, c E E is the unit capacity operation and maintenance cost of the energy storage system; im Configure the energy storage capacity of charging station i; c p is the unit transmission cost of the energy storage system; is the output power of the energy storage system of charging station i during time period t; The interaction cost expression of the distribution network is as follows: In the formula, The unit price that the charging station buys and sells from the distribution network during time period t; The power purchased and sold by charging station i from the distribution network during time period t; The cost expression of the in-station infrastructure is as follows: C i,inst =c f ·m i +c o In the formula, c f is the operation and maintenance price of a single fast charging pile; m i is the number of fast charging piles in charging station i; c o Fixed operation and maintenance costs for other facilities in the charging station; Therefore, the daily net profit function after all charging stations in the entire road network are put into use is:

9. The method for optimizing charging stations in a high-speed road network based on the spatiotemporal distribution of charging demand according to claim 1, characterized in that: The steps of solving the optimization objective of S7 by using the NSGA-II algorithm, obtaining the ideal allocation plan based on the Sharpe force value, and finding the optimal solution that is closest to the ideal allocation plan in the Pareto solution set by using the Topsis method, and the decision variable corresponding to the optimal solution is the optimal capacity plan are as follows: S8.

1. Obtain the spatiotemporal distribution diagram of charging demand in the highway network through SUMO. The specific data has been obtained through step S3.

4. S8.

2. According to the average charging demand over 24 hours, set the ideal capacity range of each charging station and formulate the form of each solution in the algorithm x={m1,m2,…,m i ,…,m n }, where each value m i Represents the number of charging piles installed in the corresponding node, all of which are even variables; S8.3, according to the maximum population size N pop Generate an initial population and check whether the generated initial solution meets the capacity interval constraint. If not, regenerate until the initial population size reaches N. pop ; S8.

4. Calculate the first function f1 and the second function f2 of all individual fitness, and get two groups and The tournament algorithm selection operator is used to randomly select individuals from the initial population. The two with the highest fitness function win and are selected. Then, the crossover operator and mutation operator are used to generate offspring individuals. The new individuals are tested again to see if they meet the capacity interval constraint. If they do, they are retained in the offspring population until the offspring population also reaches the maximum population size N. pop ; S8.

5. Merge the parent population and the child population through the elite strategy, and use the fast non-dominated sorting algorithm to obtain the sorting hierarchy of the new population after the merger; According to the sorting level, the population of each level is taken out from low to high and put into the new population. If the number of the new population exceeds the maximum population when a certain level is taken, the crowding degree of the individuals in the level is calculated, and the individuals are taken out in order from low to high according to the crowding degree until the number of the new population reaches the maximum population. S8.6, if the number of iterations does not reach the maximum number of iterations Gen max , then go to S7.4, otherwise terminate the algorithm and output the Pareto front solution; S8.

7. All charging stations are members of the alliance s, N = {1, 2, ..., n}, and a set of constant solutions x0 = {a, a, ..., a} are taken to calculate the daily revenue function f2 as the characteristic function of the cooperative game of alliance members, that is: v(s)=f2(x0) Then n charging stations jointly play the game, and the allocation scheme y={y1,y2,…,y n } satisfies the following formula: Where |s| is the number of elements in set s; y i is the Sharpe value of i; v(s / i) is the revenue of alliance s minus the revenue of charging station i; [v(s)-v(s / i)] is the marginal contribution of charging station i to alliance s.

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