CN113887032A - Electric automobile ordered charging and discharging control method based on Lagrange distributed algorithm - Google Patents

Abstract

The invention relates to an electric automobile ordered charging and discharging control method based on a Lagrange distributed algorithm, and belongs to the technical field of new energy. The method comprises the following steps: s1: establishing an orderly charging and discharging boundary condition of an electric automobile cluster; s2: establishing an optimization objective function at a power grid side and a user side; s3: establishing a cluster scheduling constraint condition of the electric vehicle; s4: obtaining an optimal solution by continuously updating the Lagrange multiplier; s5: and orderly charging and discharging scheduling of regional electric automobile clusters is realized. The strategy provided by the invention can not only dispatch the electric automobile to realize peak clipping and valley filling, but also ensure that the electric automobile obtains reasonable income by adjusting the charging and discharging time period of the electric automobile cluster. The control strategy provided by the invention can ensure that the electric automobile does not influence the driving requirement of an electric automobile user while participating in V2G, and is beneficial to the popularization of the V2G technology.

Description

Electric automobile ordered charging and discharging control method based on Lagrange distributed algorithm

Technical Field

The invention belongs to the technical field of new energy, and relates to an electric automobile ordered charging and discharging control method based on a Lagrange distributed algorithm.

Background

The electric vehicle and power grid interaction technology is focused on by researchers, and research focuses mainly on the aspects that the electric vehicle participates in power grid peak shaving, frequency modulation, and stabilization of renewable energy fluctuation and the like. Documents [1-3] mainly study formulation of charging and discharging electricity prices and setting of charging and discharging time periods of the electric vehicle in the process of participating in V2G demand response, and example analysis shows that both economy of a power grid and income of electric vehicle users after participating in V2G are improved; documents [4-5] research auxiliary service functions provided by the electric vehicle in the V2G process, including establishment of a peak and frequency modulation model and formulation of a control strategy of the electric vehicle on a power grid; document [6] adopts a method of electric vehicle cluster classification to coordinate electric vehicle charging and discharging and distributed energy output, thereby not only ensuring the benefits of electric vehicle owners, but also improving the operation performance of a power distribution network; document [7] proposes orderly charging of electric vehicles from a temporal and spatial perspective to achieve peak clipping and valley filling; documents [8-9] establish a layered and partitioned framework for electric vehicles, provide an electric vehicle cluster demand response control strategy on the basis, and verify that the provided control strategy can realize the electric vehicle cluster demand response function through examples; document [10] proposes a distributed electric vehicle control strategy based on battery constraints, power grid constraints and electric vehicle owner constraints, which dynamically manages the charging and discharging behavior of each electric vehicle group according to the real-time grid connection condition of the electric vehicle; documents [11-12] propose a response evaluation model of electric vehicle participation V2G from an electric vehicle clustering perspective based on a time-of-use electricity price and electric vehicle V2G battery loss model. Document [13] compares the charging and discharging of the electric vehicle V2G with a random charging model, and verifies that the large-scale electric vehicle can perform the peak clipping and valley filling functions on the load of the power grid in the charging and discharging mode of V2G.

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[5]H.Liang,Y.Liu,F.Li,et al."Dynamic Economic/Emission Dispatch Including PEVs for Peak Shaving and Valley Filling,"in IEEE Transactions on Industrial Electronics,vol.66,no.4,pp.2880-2890,April 2019.

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[10] Sunbong, permissive park, Thangjia, etc. electric vehicle cluster charging load modeling and capacity boundary control strategy based on demand response [ J ] grid technologies, 2016,40(09): 2638-.

[11]Singh S N,Irfan A A.Optimal charging and discharging for EVs in a V2G participation under critical peak conditions[J].IET Electrical Systems in Transportation,2018,8:136-143.

[12] Book filling, Sun Yingyun. electric vehicle cluster V2G considering time-of-use electricity price and battery loss responds to cost analysis [ J ]. electric power system and its automatic chemical report, 2017,29(11):39-46.

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In summary, in order to solve the adverse effect of the rapid development of the electric vehicle on the power grid, the ordered scheduling strategy of the electric vehicle is always a research hotspot. Although various strategies are adopted to achieve different targets in various electric vehicle ordered charging and discharging models which are proposed at present, most of the models only start from the perspective of a power grid layer or a user layer, and the attention on the uncertainty of electric vehicle user behaviors and the balance of benefits of upper and lower layers is insufficient. Aiming at the problems, the invention introduces a Lagrange multiplier of machine learning, establishes an electric vehicle ordered charging and discharging control model based on a Lagrange distributed algorithm, and realizes ordered charging and discharging control on the electric vehicle so as to optimize benefits of a power grid, an operator and an electric vehicle user.

Disclosure of Invention

In view of this, the present invention provides an electric vehicle ordered charging and discharging control method based on a lagrangian distributed algorithm. The method comprises the steps of introducing a Lagrange multiplier, establishing an electric vehicle ordered charging and discharging control model based on a Lagrange distributed algorithm, analyzing the schedulable potential of electric vehicle users in a regional power grid, analyzing regional market benefits (including the power grid, vehicle owners and operators) through simulation results, evaluating the operation effect in the region, and ensuring sustainable operation in the region. The development of the research lays a solid foundation for the development of the commercial popularization of the next large-scale charge and discharge application of the electric automobile.

In order to achieve the purpose, the invention provides the following technical scheme:

the electric automobile ordered charging and discharging control method based on the Lagrange distributed algorithm comprises the following steps:

s1: establishing an orderly charging and discharging boundary condition of an electric automobile cluster;

s2: establishing an optimization objective function at a power grid side and a user side;

s3: establishing a cluster scheduling constraint condition of the electric vehicle;

s4: obtaining an optimal solution by continuously updating the Lagrange multiplier;

s5: and orderly charging and discharging scheduling of regional electric automobile clusters is realized.

Optionally, the S1 specifically includes:

s11: establishing SOC boundary conditions of the electric vehicle;

under the condition of ordered charging and discharging, the electric automobile has two states in the t-th time period, and a state variable, namely a charging state lambda is introduced_n,tIn the discharge state mu_n,t：

The total charge and discharge load of the electric automobile is the superposition of the charge load and the discharge load of the electric automobile at a certain moment, namely:

the electric automobile can not be charged and discharged at the same time at a certain moment, and lambda_n,tAnd mu_n,tMutual exclusion, represented as:

the discharge benefit problem is that the SOC at the beginning of discharge is greater than 0.5, and if the electric automobile is charged and discharged once a day, the discharge starting time of the electric automobile is deduced as follows:

in the formula, t_startRepresenting the starting discharge time of the electric automobile; the condition whether the battery can be discharged is determined by the home arrival SOC and the home arrival time of the electric automobile; after the electric vehicle is discharged, the duration of the complete discharge of the battery needs to be calculated as shown in the following formula:

wherein T represents a maximum discharge time period, SOC_startA battery SOC indicating a discharge start time;

the electric vehicle cannot be discharged until the discharge time is cut off, and in the discharge process, enough time needs to be left for charging to meet the expected SOC when the electric vehicle leaves the home the next day, and the expected SOC when the electric vehicle leaves the home on the second day is assumed to be 0.9:

in the formula, T_exceptIndicating the length of time for charging to a desired SOC, SOC_tShowing the current SOC after the electric automobile arrives at home, if the electric automobile does not meet the discharging condition in the process and does not participate in discharging, then the SOC_except＝SOC_t；

S12: calculating the acceptance of a user to a power grid electricity price compensation mechanism;

after the electric automobile is charged and discharged, the system needs a user to continuously provide electric energy due to high demand on the electric energy, and the system is regulated and controlled by a certain compensation means; user voluntarily selects whether to accept systemThe system takes the acceptance degree of the user as one of the indexes of the scheduling priority; get the compensation price of electricity p_m0.23 yuan/kWh; meanwhile, the unit battery loss compensation rate B of the part exceeding the declared capacity is taken_m0.5 yuan/kWh; defining the acceptance degree delta of the electric vehicle user to the power grid price compensation mechanism as follows:

C_eindicating the user's profit under the compensation mechanism, C_pRepresents the cost of the electric vehicle:

wherein p is a constant representing the fundamental compensation given by the grid to attract users to participate in the scheduling, p_cFor charging electricity rates:

s13: calculating the depreciation loss of the battery;

definition of depreciation loss B_rComprises the following steps:

B_lossthe average battery loss cost per charge and discharge was taken to be 0.26 yuan, and r was 5% of the residual value.

Optionally, the S2 specifically includes:

grid-side target: managing the charging behavior of the electric automobile by taking the minimum mean square error of the load of the power grid as a power grid side optimization target; the load mean square error is the sum of the variances of each time period under the basic load of the power grid and the total charge and discharge load of the electric automobile, and is expressed as follows:

in the formula P_ld,totalThe total power load of the power grid at the moment T, wherein T is a research time period;

user side target: fully considering the benefits of users, charging the electric automobile when the electricity price is lowest, and discharging the electric automobile when the electricity price is highest; the total charge and discharge cost of the user comprises two parts, wherein one part is the charge required to be paid by the user in charging and the charge obtained in subsidy in discharging, namely charge and discharge cost C_CDAnother part is the cost of battery depletion C, which is the cost of battery depletion during battery participation in a single discharge of V2G_V2GThe objective function is as follows:

min f₂＝min(C_CD-C_V2G) (12)

wherein, C_CDIs the cost of charging and discharging, C_V2GThe battery loss cost is calculated according to the following formula:

in the formula, S_tPositive values indicate charging electricity prices, negative values indicate discharging subsidy electricity prices, C_n,V2GThe single battery loss is caused when the nth electric automobile participates in V2G, and the cost of charging loss is ignored; the total cost of single loss of the battery participating in charge and discharge is as follows:

the added weight coefficient represents the bias ratio of the two objective functions, and the simplified objective function is as follows:

in the formula (f)_1max、f_1min、f_2max、f_2minRespectively representing the global maximum and minimum of daily load variance during disordered charging of the electric automobile and the maximum and minimum of charging cost during disordered charging, and determining the maximum and minimum according to the optimization algorithm of each single objective function; a and b are weight coefficients of two objective functions of a power grid side and a user side, represent preference degrees of the two objective functions, are also called preference coefficients, and satisfy the following formula

Optionally, the S3 specifically includes:

s31: calculating the declared scheduling capacity;

obtaining a schedulable time period T according to declaration information of a user_dAnd schedulable capacity S_d，S_dCalculated by the formula (18);

S_d＝S_B.max-S_B.min (18)

wherein S is_B.max、S_B.minRespectively represent the upper and lower limits of the capacity;

s32: calculating the credit degree of the electric automobile participating in the dispatching plan;

wherein the content of the first and second substances,

the average daily declared capacity of the electric automobile is shown,

average actual scheduling capacity in the day ahead; if the credit rating is large enough, taking 1, if the credit rating is too small, taking 0; let ρ be_down＝0.15，ρ_up＝0.95；

S33: calculating the responsiveness of the electric automobile to a power price mechanism;

the electricity price electricity quantity elasticity is adopted to express the response degree of the user to an electricity price mechanism, as shown in a formula (20);

wherein S, Delta S is capacity and relative increment thereof, P, Delta P is power and relative increment thereof; p, Δ p are the electricity price and its relative increment;

introducing an elastic coefficient of cross electricity price electricity quantity as formula (21), and representing the response of electricity quantity at the moment i to electricity price at the moment j;

from time 1 to t, there are:

defining the execution degree of the electric vehicle user participating in the power grid dispatching plan as follows:

μ＝βε+(1-β)δ (23)

beta represents a proportion coefficient and can be determined by a weighting method;

under the compensation mechanism, the charging and discharging of the electric automobile are guided by an economic means, so that the load fluctuation caused by large-scale electric automobile grid connection can be relieved, and the effects of peak clipping and valley filling can be achieved;

s34: establishing an index evaluation system;

the target of the index evaluation model is to make preferential relative comparison and sequencing among a plurality of evaluation objects in a discourse domain and determine the weight of each evaluation index;

giving weights to all indexes so as to obtain a dispatching sequence of the electric automobile; wherein, the larger the benefit index is, the more priority is to scheduling; the smaller the cost index, the more prioritized the scheduling.

Optionally, the S4 specifically includes:

the integer programming problem is described as follows

Absorbing the constraint condition multiplied by a Lagrange multiplier lambda into a target function, and changing the complex constraint into a format with b-Ax being less than or equal to 0; the deformed functional form is then:

wherein λ is a non-negative number, b-Ax is a non-positive number, and the product of the two is defined as a non-positive number; for the same set of solutions, Z_LR≤Z_IPThe LR problem is used as a lower bound of the original problem, and the final goal is to obtain the lower bound which is closest to the original IP problem; needs to find Z_LR(λ) maximum value of the problem; for Z_LR(λ) each λ value corresponds to a Z_LRThe optimum value of (lambda) is obtained when what is now required is to be solved_LRA maximum value of (λ); z corresponding to each lambda_LR(lambda) is used as the lower bound of the original IP problem, the optimal value of the lower bound, namely the maximum value is the final value, and the process of continuously searching the optimal lower bound is the process of continuously updating the Lagrange multiplier;

handle Z_LRThe direction of rise in a certain neighborhood of λ is called the sub-gradient, which is denoted as sⁱTo indicate that in the LR problem, can pass through sⁱ＝b-AxⁱObtaining a specific sub-gradient numerical value; the maximum Z is obtained by continuously updating the value of lambda by a sub-gradient algorithm_LRObtaining a set of solutions closest to the optimal solution; the specific iteration steps are as follows:

s41: randomly selecting a group of Lagrange multipliers as initial values, and taking all values as 0;

s42: for lambdaⁱCorresponding sⁱArbitrarily take a sub-gradient sⁱIf s isⁱ0, then λⁱStopping calculation when the optimal solution is reached, and if the optimal solution is not reached, updating lambdaⁱValue of (A)ⁱ⁺¹＝max(λⁱ+θ,sⁱ0), i ═ i +1, repeat S42:

there are four methods to decide to stop the iteration:

(1) stopping iteration when the iteration times reach T;

(2) when s isⁱWhen the value is equal to 0, stopping iteration; by sⁱThe rank of (2) is less than or equal to a certain fixed value to determine the standard of stopping iteration;

(3) when Z is_LR(i)＝Z_IP(i) When the current problem is solved, stopping iteration, wherein the upper bound and the lower bound of the original problem are equal and the optimal target value is reached;

(4) when lambda isⁱOr Z_LRWhen they do not change more than a fixed value within a specified number of steps, the objective function value is considered to be unlikely to change, and the iteration is stopped.

Optionally, the S5 specifically includes:

at the moment of access of the electric automobile, the battery is charged or discharged, the power of the battery discharged to the power grid is the same as the discharge power of the battery in normal running, and the following reference indexes are added:

1) the declared capacity influences the demand of the power dispatching plan, and if the declared capacity is too low, the power grid basically does not consider participating in the dispatching plan;

2) when the number of the electric vehicles participating in the coordinated dispatching plan is large enough, the comprehensive evaluation value is higher than 0.5 for vehicle full dispatching;

3) in the index evaluation system model, vehicles with high credit degree and participation degree are called preferentially;

4) the vehicle which is called by priority can not participate in scheduling charging and discharging for more than 3 times a day.

The invention has the beneficial effects that: the invention provides an electric vehicle ordered charging and discharging strategy based on a Lagrange distributed algorithm, and examples verify that electric vehicles in a region can fully support the stable operation of a power grid through cluster ordered scheduling, and the influence of various information of electric vehicles declared by a user on the establishment of a scheduling plan by an agent is analyzed. The method comprises the steps of establishing a system evaluation index model of an electric automobile cluster by taking declared scheduling capacity, user credit, battery breakage and user participation of the electric automobiles as evaluation indexes, solving an optimal solution based on a Lagrangian distributed algorithm, obtaining a priority order of scheduling of each electric automobile in the cluster, and determining actual schedulable capacity of agents at different nodes in each time period. And finally, orderly charging and discharging scheduling is realized for the electric automobiles in the cluster by combining the automobile-using requirements of the electric automobiles, so that the efficient optimal configuration of the power grid resources is effectively promoted, the consumption of new energy is promoted, and the stable operation of the power grid is guaranteed. By example simulation, the following conclusions are drawn:

(1) the charging and discharging time periods of the electric automobile cluster are adjusted through the strategy provided by the invention, so that the electric automobiles can be dispatched to realize peak clipping and valley filling, and the electric automobiles can be ensured to obtain reasonable benefits.

(2) The control strategy provided by the invention can ensure that the electric automobile does not influence the driving requirement of an electric automobile user while participating in V2G, and is beneficial to the popularization of the V2G technology.

Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.

Drawings

For the purposes of promoting a better understanding of the objects, aspects and advantages of the invention, reference will now be made to the following detailed description taken in conjunction with the accompanying drawings in which:

FIG. 1 is an electric vehicle cluster index evaluation system;

FIG. 2 is a flow chart of a Lagrangian distributed algorithm

FIG. 3 is a load influence curve of orderly charging and discharging of an electric vehicle on a power grid

FIG. 4 is a graph showing a comparison of gains for different control strategies.

Detailed Description

The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention in a schematic way, and the features in the following embodiments and examples may be combined with each other without conflict.

Wherein the showings are for the purpose of illustrating the invention only and not for the purpose of limiting the same, and in which there is shown by way of illustration only and not in the drawings in which there is no intention to limit the invention thereto; to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.

The same or similar reference numerals in the drawings of the embodiments of the present invention correspond to the same or similar components; in the description of the present invention, it should be understood that if there is an orientation or positional relationship indicated by terms such as "upper", "lower", "left", "right", "front", "rear", etc., based on the orientation or positional relationship shown in the drawings, it is only for convenience of description and simplification of description, but it is not an indication or suggestion that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes, and are not to be construed as limiting the present invention, and the specific meaning of the terms may be understood by those skilled in the art according to specific situations.

1. Electric automobile cluster ordered charging and discharging boundary condition

1) SOC boundary condition of electric vehicle

Under the condition of ordered charging and discharging, considering that the electric automobile can have two states in the t-th time period, a state variable, namely a charging state lambda is introduced_n,tIn the discharge state mu_n,t：

The total charge and discharge load of the electric automobile is the superposition of the charge load and the discharge load of the electric automobile at a certain moment, namely:

the electric automobile can not be charged and discharged at the same time at a certain moment, so lambda_n,tAnd mu_n,tMutual exclusion, which can be expressed as:

the purpose of orderly charging and discharging is to stabilize the load fluctuation of the power grid and improve the user income, so that the electric automobile is scheduled to be charged in the load valley period of low electricity price and discharged in the load high period of high electricity price, and the electric automobile is planned to be discharged in the load peak interval as much as possible and charged in the time of low electricity price. Meanwhile, considering the discharge benefit problem, the SOC at the beginning of discharge is greater than 0.5, and the electric vehicle is considered to be charged and discharged once a day, and according to the above analysis, the discharge starting time of the electric vehicle can be deduced as follows:

in the formula, t_startIndicating the starting discharge time of the electric vehicle. From the above equation, the condition whether the battery can be discharged is determined by the home-arriving SOC and the home-arriving time of the electric vehicle. After the electric vehicle is discharged, the duration of the complete discharge of the battery needs to be calculated as shown in the following formula:

wherein T represents a maximum discharge time period, SOC_startIndicating the battery SOC at the discharge start time.

The electric vehicle cannot be discharged until the discharge time is cut off, and in the discharge process, enough time needs to be left for charging to meet the expected SOC when the electric vehicle leaves the home the next day, and the expected SOC when the electric vehicle leaves the home on the second day is assumed to be 0.9:

in the formula, T_exceptIndicating the length of time for charging to a desired SOC, SOC_tShowing the current SOC after the electric automobile arrives at home, if the electric automobile does not meet the discharging condition in the process and does not participate in discharging, then the SOC_except＝SOC_t。

2) Acceptance of user to power grid price compensation mechanism

After the electric automobile is charged and discharged, the system needs a user to continuously provide electric energy due to high demand on the electric energy, and the system is regulated and controlled by a certain compensation means. The user can voluntarily choose whether to accept the compensation of the system, and the system can be used as one of the indexes of the scheduling priority according to the acceptance degree of the user. Taking herein the compensation price p_mIt was 0.23 yuan/kWh. Meanwhile, the unit battery loss compensation rate B of the part exceeding the declared capacity is taken_mIs 0.5 yuan/kWh. Defining the acceptance degree delta of the electric vehicle user to the power grid price compensation mechanism as follows:

C_eindicating the user's profit under the compensation mechanism, C_pRepresents the cost of the electric vehicle:

wherein p is a constant representing the fundamental compensation given by the grid to attract users to participate in the scheduling, p_cFor charging electricity rates:

3) depreciation and loss of battery

The battery loss caused by repeated charge and discharge is an important factor influencing the participation of the electric automobile in power grid dispatching, so the user declaration information received by the electric automobile agent also comprises the battery depreciation condition of the vehicle, and the depreciation loss B is defined_rComprises the following steps:

B_lossthe average battery loss cost per charge and discharge was taken to be 0.26 yuan, and r was 5% of the residual value.

2. Optimization objective function of power grid side and user side

Grid-side target: and managing the charging behavior of the electric automobile by taking the minimum mean square error of the load of the power grid as a power grid side optimization target. The minimization of the load mean square error can avoid large-scale charging of users in the load valley period, thereby achieving the purpose of smoothing the load curve of the power grid. The load mean square error is the sum of the variances of each time interval under the basic load of the power grid and the total charge and discharge load of the electric automobile, and the process can be expressed as follows:

in the formula P_ld,totalThe total power load of the power grid at the moment T, and the research time period T.

User side target: and fully considering the benefit of the user, the electric automobile is charged when the electricity price is the lowest, and the electric automobile is discharged when the electricity price is the highest. The total charge and discharge cost of the user comprises two parts, wherein one part is the charge required to be paid by the user in charging and the charge obtained in subsidy in discharging, namely charge and discharge cost C_CDIn addition, anotherOne part is the cost of battery loss when the battery participates in single V2G discharge, namely the battery loss cost C_V2GThe objective function is as follows:

min f₂＝min(C_CD-C_V2G) (12)

wherein, C_CDIs the cost of charging and discharging, C_V2GThe battery loss cost is calculated according to the following formula:

in the formula, S_tPositive values indicate charging electricity prices, negative values indicate discharging subsidy electricity prices, C_n,V2GThe battery loss is single when the nth electric automobile participates in V2G, and the battery charging loss cost is low, so the charging loss cost is ignored. According to the analysis of the battery loss model, the total cost of the single loss of the battery participating in charge and discharge is as follows:

when solving the problem of nonlinear programming of multi-objective functions, because sub-objectives and sub-objectives of the multi-objective optimization problem conflict with each other, the optimal solution of each sub-objective cannot be obtained generally, and only an optimal compromise solution closest to the ideal solution can be obtained, so that each objective is optimized as much as possible. The multi-objective function can be converted into a single objective function, but the objective functions cannot be directly operated due to different dimensions, so that the objective functions need to be normalized, a linear weighting method is adopted in the following formula, namely, a weighting coefficient is added to represent the weight ratio of the two objective functions, and the simplified objective functions are as follows:

in the formula (f)_1max、f_1min、f_2max、f_2minThe method is characterized in that the method respectively represents the global maximum and minimum of daily load variance during disordered charging of the electric automobile and the maximum and minimum of charging cost during disordered charging, and the maximum and minimum can be determined according to the optimization algorithm of each single objective function. a and b are weight coefficients of two objective functions of a power grid side and a user side, represent preference degrees of the two objective functions, are also called preference coefficients, and satisfy the following formula

3. Electric vehicle cluster scheduling constraint condition

Before an electric vehicle user responds to participate in a power grid interactive scheduling plan, the electric vehicle needs to set the SOC upper and lower limits of a battery when the vehicle is connected to the power grid when the electric vehicle is connected to the power grid, and provides reporting information such as reporting of a charging and discharging state, a corresponding time period, battery loss and the like for the power grid. Meanwhile, the power grid can determine real-time scheduling arrangement according to past reporting information of the electric automobile and the execution degree of the reporting plan.

1) Reporting scheduling capacity

According to the declaration information of the user, the schedulable time interval T can be obtained_dAnd schedulable capacity S_d，S_dCalculated by equation (18).

S_d＝S_B.max-S_B.min (18)

Wherein S is_B.max、S_B.minRespectively representing the upper and lower capacity limits.

2) Credit degree of electric automobile participating in dispatching plan

In order to enable the electric automobile to travel more in accordance with the dispatching plan, the concept of 'honest membership' is introduced in the calculation of the dispatchable capacity. And on the basis of a fuzzy mathematical theory, defining a membership function of the credit degree of the electric automobile user as rho (x), and counting the reported capacity of the electric automobile into the available capacity according to the proportion of the credit degree. Specifically, as shown in formula (19):

wherein the content of the first and second substances,

the average daily declared capacity of the electric automobile is shown,

the average actual scheduled capacity in the day ahead. If the credit rating is sufficiently high, 1 is taken, and if it is too low, 0 is taken. Let us denote herein p_down＝0.15，ρ_up＝0.95。

3) Responsiveness of electric automobile to electricity price mechanism

The participation degree of the vehicle owner to the power grid dispatching interactive plan is individual conscious behaviors. The extent to which the electric vehicle is involved in the plan for V2G interaction is therefore considered here on the user side.

The response of the electric vehicle to the electricity price means that the user selects different charging periods according to the electricity price. The electricity load is transferred between the high and low electricity price periods to reduce the electricity cost. According to the demand response theory, the electricity price change can cause the change of the electricity demand of the user, so the electricity price elasticity is adopted to express the response degree of the user to the electricity price mechanism, as shown in formula (20).

Wherein S, Delta S is capacity and relative increment thereof, P, Delta P is power and relative increment thereof; p, Δ p are the electricity prices and their relative increments.

Considering that the response behavior of the electric automobile is related to the current electricity price and the electricity price in the adjacent time period, the elasticity coefficient of the electric quantity of the cross electricity price is introduced as formula (21), and the elasticity coefficient represents the response of the electric quantity at the moment i to the electricity price at the moment j;

therefore, from time 1 to t, there are:

therefore, the execution degree of the electric vehicle user participating in the power grid dispatching plan is defined as follows:

μ＝βε+(1-β)δ (23)

beta represents a ratio coefficient and can be determined by a weighting method.

Under the compensation mechanism, the charging and discharging of the electric automobile are guided by an economic means, so that the load fluctuation caused by large-scale electric automobile grid connection can be relieved, and the effects of peak clipping and valley filling can be achieved.

4) Index evaluation system

The goal of the index evaluation model is to determine the weights of the evaluation indexes by making a preferential relative comparison and ranking between the evaluation objects in the domain. An evaluation index system can be established as shown in fig. 1:

and giving weights to each index so as to obtain the dispatching sequence of the electric automobile. Wherein, the larger the benefit index is, the more priority is to scheduling; the smaller the cost index, the more prioritized the scheduling.

4. Solving algorithm

The basic idea of the lagrangian algorithm is: the constraint condition which causes the problem to be difficult is absorbed into the objective function, so that the problem is easier to solve. When the combinatorial optimization problem is a Non-Polynomial Deterministic (NP) problem, under existing constraint conditions, there is often no Polynomial time algorithm for solving the optimal solution, but after some constraints are reduced in the original problem, the difficulty of solving the problem is greatly reduced, and the original problem after the constraints are reduced can also obtain the optimal solution within Polynomial time. For the linear integer programming problem, after some hard constraint conditions are absorbed into the objective function, the problem generally becomes easier to solve, and at this time, the quality of the solution completely depends on the parameter before the constraint conditions absorbed into the objective function, and the parameter is called as a lagrange multiplier and can also be called as a penalty factor. The optimal solution is obtained by continuously updating the lagrangian multiplier.

We can describe the integer programming problem as the following form

The constraint conditions multiplied by the Lagrangian multiplier lambda are absorbed into the objective function, and the complex constraint is changed into a format with b-Ax less than or equal to 0.

The deformed functional form is then:

where λ is a non-negative number and b-Ax is a non-positive number, so that the product of the two is always a non-positive number. For the same set of solutions, Z_LR≤Z_IPTherefore, the LR problem can be used as a lower bound of the original problem, and our final goal is to find the lower bound that is closest to the original IP problem. Therefore, we need to find Z_LR(λ) maximum value of the problem. For Z_LR(λ) each λ value corresponds to a Z_LRThe optimum value of (lambda) can be obtained when what is now required is found_LRMaximum value of (λ). As can be seen from the above explanation, Z corresponds to each λ_LRAnd (lambda) can be used as a lower bound of the original IP problem, the optimal value (maximum value) of the lower bound is the final value which we want to obtain, and the process of continuously searching the optimal lower bound is the process of continuously updating the Lagrangian multiplier. In the process, the Lagrange multiplier can be updated by using a sub-gradient algorithm, and heuristic algorithms such as a genetic algorithm and a particle swarm algorithm can also be applied.

We turn Z_LRThe direction of rise in a certain neighborhood of λ is called the sub-gradient, which is denoted as sⁱTo indicate that in the LR problem, can pass through sⁱ＝b-AxⁱSpecific values of the minor gradient were obtained. The maximum Z is obtained by continuously updating the value of lambda through a sub-gradient algorithm_LRAnd obtaining a group of solutions closest to the optimal solution.

The Lagrangian dual problem is that Z is desired_LRThe lower bound (lambda) is as large as possible, so that it is necessary to be Z_LRThe rising direction of (lambda) gradually approaches the optimal value, and the idea of gradient descent is the same as that of nonlinear programming, and the secondary gradient is Z_LRThe optimization algorithm of the direction subgradient rising in a certain neighborhood of lambda is based on Z_LRThe concave function of (λ) is structured.

The iteration steps are as follows:

step 1: a group of lagrange multipliers is arbitrarily selected as an initial value, and in general, all the lagrange multipliers are 0

Step 2: for lambdaⁱCorresponding sⁱArbitrarily take a sub-gradient sⁱIf s isⁱ0, then λⁱStopping calculation when the optimal solution is reached, and if the optimal solution is not reached, updating lambdaⁱValue of (A)ⁱ⁺¹＝max(λⁱ+θ,sⁱ0), i ═ i +1, Step2 is repeated.

For the stopping principle of the iteration, there are four methods that can be used as the criterion for stopping the iteration.

(1) And stopping iteration when the iteration number reaches T. This is the simplest principle, and the iteration is stopped when a fixed iteration step is reached, regardless of the quality of the solution, so that the complexity of the calculation is easily controlled, but the quality of the solution cannot be guaranteed.

(2) When s isⁱWhen 0, the iteration is stopped. This is the most ideal situation, but in practical calculations such a result is often difficult to achieve due to the complexity of the problem and the computational errors of the computer itself, and is often used as sⁱIs less than or equal to a certain fixed value to determine the criterion for stopping iteration.

(3) When Z is_LR(i)＝Z_IP(i) And stopping iteration, wherein the upper bound and the lower bound of the original problem are equal and the optimal target value is reached.

(4) When lambda isⁱOr Z_LRWhen they do not change more than a fixed value within a specified number of steps, the objective function value is considered to be unlikely to change, and the iteration is stopped.

In summary, the Lagrangian relaxation algorithm can be divided into two stages. In the first stage, the optimal lower bound is found by the sub-gradient. In the second stage, if the optimal solution is not feasible, the optimal solution needs to be feasible for different problems, the feasible methods used are also different, and the method for correcting the infeasible solution needs the problem itself to be judged. The coefficient correction method is a feasible method of a Lagrange relaxation algorithm, and realizes the feasibility of an infeasible solution by correcting a Lagrange multiplier according to a certain rule.

The process of solving the optimal solution for ordered charging and discharging using the lagrangian algorithm is shown in fig. 2.

5. Ordered charging and discharging scheduling strategy for regional electric vehicle cluster

At the moment of connecting the electric automobile, the battery can be charged or discharged, and it is assumed here that the power of the battery when discharging to the power grid is the same as the discharge power when normally driving, which is a limit that the SOC of the discharging electric automobile should reach a certain standard and the electric quantity after discharging should be guaranteed that no anxiety is generated in the owner of the electric automobile, so as to ensure that the discharging behavior to the power grid is realized on the premise that the vehicle using behavior of the user is not influenced, and in addition, the following reference indexes are also added:

1) the declared capacity influences the demand of the power dispatching plan, and if the declared capacity is too low, the power grid basically does not consider participating in the dispatching plan;

2) when the number of electric vehicles participating in the coordinated dispatching plan is sufficiently large, vehicles having a comprehensive evaluation value higher than 0.5 are dispatched as fully as possible.

3) In the index evaluation system model, the comprehensive weight coefficient of the two indexes, namely the user participation degree and the credit degree, is higher, so that vehicles with higher credit degree and participation degree are preferentially called;

4) the vehicle which is called preferentially participates in the dispatching plan more actively, the battery damage degree is slightly high, and although the obtained V2G compensation is correspondingly high, the power grid and the automobile user should be aware that the vehicle is not suitable for frequently participating in dispatching charging and discharging in order to protect the vehicle.

When the electric automobile participates in the power grid dispatching interaction, the declaration information and the day-ahead participation condition of the electric automobile are the key for determining the real-time dispatching sequence, and meanwhile, the calling arrangement of the electric automobile is further adjusted according to the dispatching requirement issued by the power grid, so that the influence of large-scale electric automobile cluster grid connection is reduced, and real-time ordered dispatching is realized.

6. Example simulation

6.1 example background

To verify the effectiveness of the electric vehicle charging and discharging strategy presented herein. The transformer has a base load and an electric automobile load under a regional distribution transformer, and the rated capacity of the transformer is 5000 kVA. The holding capacity of each regional electric automobile is 200, the battery capacity of each electric automobile is 64kWh, the minimum SOC of each battery is 0.3, the electric automobiles are charged and discharged in a conventional charging mode, the maximum charging power is 7kW, and the charging efficiency is 0.9; the maximum discharge power was 7kW, and the discharge efficiency was 0.85. The charging price of the electric automobile adopts the time-of-use price of the residents in Kunming, namely peak power price 0.8892 yuan/kWh at 7:00-12:00 and 17:00-21:00, namely peak power price 0.6142 yuan/kWh at 12:00-17:00 and 21:00-24:00, and valley power price 0.3393 yuan/kWh at 0:00 to the next day 7:00, and the discharging price of the electric automobile adopts the reference time-of-use price, namely peak power price 1.4 yuan/kWh, flat power price 0.9 yuan/kWh, valley power price 0.2 yuan/kWh, and SOC when the user of the electric automobile desires to leave the charging pile is set to 0.9 as shown in Table 1.

TABLE 1 scene parameter settings

6.2 electric automobile ordered charging and discharging simulation result analysis

The load influence of the ordered charging and discharging, the ordered charging and the unordered charging of the electric vehicle on the power grid is shown in fig. 3.

As can be seen from fig. 3, compared with the disordered charging, the charging load of the electric vehicle after the ordered charging is distributed in the flat time period and the valley time period, but the peak time period and the power of the original load curve are not obviously changed, and the ordered charging strategy does not realize peak clipping but has an obvious valley filling effect. When the electric automobile is controlled by orderly charging and discharging, two peak values of a load curve at about 8-11 points and 18 points are obviously reduced, and the peak-valley difference is reduced by 8.52 percent compared with the disordered charging.

6.3 electric automobile ordered charging and discharging benefit analysis

The load curve variance and peak-to-valley difference under different control modes and the user revenue comparison of the electric vehicle are shown in table 2, table 3 and fig. 4 respectively. As can be seen from table 2, table 3, and fig. 4, although the total benefit of the electric vehicle user is only 28.5 yuan during the ordered charging and discharging, 2344.2 yuan is saved compared with the case of the unordered charging, and it can be seen that the electric vehicle in the V2G mode can obtain a certain benefit through the ordered charging and discharging.

TABLE 2 load variance and Peak-to-valley Difference

TABLE 3 electric vehicle user revenue comparison

Finally, the above embodiments are only intended to illustrate the technical solutions of the present invention and not to limit the present invention, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all of them should be covered by the claims of the present invention.

Claims (6)

1. The electric automobile ordered charging and discharging control method based on the Lagrange distributed algorithm is characterized by comprising the following steps of: the method comprises the following steps:

s1: establishing an orderly charging and discharging boundary condition of an electric automobile cluster;

s2: establishing an optimization objective function at a power grid side and a user side;

s3: establishing a cluster scheduling constraint condition of the electric vehicle;

s4: obtaining an optimal solution by continuously updating the Lagrange multiplier;

s5: and orderly charging and discharging scheduling of regional electric automobile clusters is realized.

2. The electric vehicle ordered charging and discharging control method based on the Lagrange distributed algorithm according to claim 1, characterized in that: the S1 specifically includes:

s11: establishing SOC boundary conditions of the electric vehicle;

under the condition of ordered charging and discharging, the electric automobile has two states in the t-th time period, and a state variable, namely a charging state lambda is introduced_n,tIn the discharge state mu_n,t：

The total charge and discharge load of the electric automobile is the superposition of the charge load and the discharge load of the electric automobile at a certain moment, namely:

the electric automobile can not be charged and discharged at the same time at a certain moment, and lambda_n,tAnd mu_n,tMutual exclusion, represented as:

the discharge benefit problem is that the SOC at the beginning of discharge is greater than 0.5, and if the electric automobile is charged and discharged once a day, the discharge starting time of the electric automobile is deduced as follows:

in the formula, t_startRepresenting the starting discharge time of the electric automobile; the condition whether the battery can be discharged is determined by the home arrival SOC and the home arrival time of the electric automobile; after the electric vehicle is discharged, the duration of the complete discharge of the battery needs to be calculated as shown in the following formula:

wherein T represents a maximum discharge time period, SOC_startA battery SOC indicating a discharge start time;

the electric vehicle cannot be discharged until the discharge time is cut off, and in the discharge process, enough time needs to be left for charging to meet the expected SOC when the electric vehicle leaves the home the next day, and the expected SOC when the electric vehicle leaves the home on the second day is assumed to be 0.9:

in the formula, T_exceptIndicating the length of time for charging to a desired SOC, SOC_tShowing the current SOC after the electric automobile arrives at home, if the electric automobile does not meet the discharging condition in the process and does not participate in discharging, then the SOC_except＝SOC_t；

S12: calculating the acceptance of a user to a power grid electricity price compensation mechanism;

after the electric automobile is charged and discharged, the system needs a user to continuously provide electric energy due to high demand on the electric energy, and the system is regulated and controlled by a certain compensation means; the user voluntarily selects whether to accept the compensation of the system, and the system takes the acceptance degree of the user as one of the indexes of the scheduling priority; get the compensation price of electricity p_m0.23 yuan/kWh; meanwhile, the battery loss of unit electric quantity exceeding the declared capacity part is takenCost compensation charge rate B_m0.5 yuan/kWh; defining the acceptance degree delta of the electric vehicle user to the power grid price compensation mechanism as follows:

C_eindicating the user's profit under the compensation mechanism, C_pRepresents the cost of the electric vehicle:

wherein p is a constant representing the fundamental compensation given by the grid to attract users to participate in the scheduling, p_cFor charging electricity rates:

s13: calculating the depreciation loss of the battery;

definition of depreciation loss B_rComprises the following steps:

B_lossthe average battery loss cost per charge and discharge was taken to be 0.26 yuan, and r was 5% of the residual value.

3. The electric vehicle ordered charging and discharging control method based on the Lagrange distributed algorithm as claimed in claim 2, wherein: the S2 specifically includes:

grid-side target: managing the charging behavior of the electric automobile by taking the minimum mean square error of the load of the power grid as a power grid side optimization target; the load mean square error is the sum of the variances of each time period under the basic load of the power grid and the total charge and discharge load of the electric automobile, and is expressed as follows:

in the formula P_ld,totalThe total power load of the power grid at the moment T, wherein T is a research time period;

user side target: fully considering the benefits of users, charging the electric automobile when the electricity price is lowest, and discharging the electric automobile when the electricity price is highest; the total charge and discharge cost of the user comprises two parts, wherein one part is the charge required to be paid by the user in charging and the charge obtained in subsidy in discharging, namely charge and discharge cost C_CDAnother part is the cost of battery depletion C, which is the cost of battery depletion during battery participation in a single discharge of V2G_V2GThe objective function is as follows:

min f₂＝min(C_CD-C_V2G) (12)

wherein, C_CDIs the cost of charging and discharging, C_V2GThe battery loss cost is calculated according to the following formula:

in the formula, S_tPositive values indicate charging electricity prices, negative values indicate discharging subsidy electricity prices, C_n,V2GThe single battery loss is caused when the nth electric automobile participates in V2G, and the cost of charging loss is ignored; the total cost of single loss of the battery participating in charge and discharge is as follows:

the added weight coefficient represents the bias ratio of the two objective functions, and the simplified objective function is as follows:

in the formula (f)_1max、f_1min、f_2max、f_2minRespectively representing the global maximum and minimum of daily load variance during disordered charging of the electric automobile and the maximum and minimum of charging cost during disordered charging, and determining the maximum and minimum according to the optimization algorithm of each single objective function; a and b are weight coefficients of two objective functions of a power grid side and a user side, represent preference degrees of the two objective functions, are also called preference coefficients, and satisfy the following formula

4. The electric vehicle ordered charging and discharging control method based on the Lagrange distributed algorithm according to claim 3, characterized in that: the S3 specifically includes:

s31: calculating the declared scheduling capacity;

obtaining a schedulable time period T according to declaration information of a user_dAnd schedulable capacity S_d，S_dCalculated by the formula (18);

S_d＝S_B.max-S_B.min (18)

wherein S is_B.max、S_B.minRespectively represent the upper and lower limits of the capacity;

s32: calculating the credit degree of the electric automobile participating in the dispatching plan;

wherein the content of the first and second substances,

electric automobile with indicationThe average reported capacity before the day is used,

average actual scheduling capacity in the day ahead; if the credit rating is large enough, taking 1, if the credit rating is too small, taking 0; let ρ be_down＝0.15，ρ_up＝0.95；

S33: calculating the responsiveness of the electric automobile to a power price mechanism;

the electricity price electricity quantity elasticity is adopted to express the response degree of the user to an electricity price mechanism, as shown in a formula (20);

wherein S, Delta S is capacity and relative increment thereof, P, Delta P is power and relative increment thereof; p, Δ p are the electricity price and its relative increment;

introducing an elastic coefficient of cross electricity price electricity quantity as formula (21), and representing the response of electricity quantity at the moment i to electricity price at the moment j;

from time 1 to t, there are:

defining the execution degree of the electric vehicle user participating in the power grid dispatching plan as follows:

μ＝βε+(1-β)δ (23)

beta represents a proportion coefficient and can be determined by a weighting method;

under the compensation mechanism, the charging and discharging of the electric automobile are guided by an economic means, so that the load fluctuation caused by large-scale electric automobile grid connection can be relieved, and the effects of peak clipping and valley filling can be achieved;

s34: establishing an index evaluation system;

the target of the index evaluation model is to make preferential relative comparison and sequencing among a plurality of evaluation objects in a discourse domain and determine the weight of each evaluation index;

giving weights to all indexes so as to obtain a dispatching sequence of the electric automobile; wherein, the larger the benefit index is, the more priority is to scheduling; the smaller the cost index, the more prioritized the scheduling.

5. The electric vehicle ordered charging and discharging control method based on the Lagrange distributed algorithm according to claim 4, characterized in that: the S4 specifically includes:

the integer programming problem is described as follows

Absorbing the constraint condition multiplied by a Lagrange multiplier lambda into a target function, and changing the complex constraint into a format with b-Ax being less than or equal to 0;

the deformed functional form is then:

wherein λ is a non-negative number, b-Ax is a non-positive number, and the product of the two is defined as a non-positive number; for the same set of solutions, Z_LR≤Z_IPThe LR problem is used as a lower bound of the original problem, and the final goal is to obtain the lower bound which is closest to the original IP problem; needs to find Z_LR(λ) maximum value of the problem; for Z_LR(λ) each λ value corresponds to a Z_LRThe optimum value of (lambda) is obtained when what is now required is to be solved_LRA maximum value of (λ); z corresponding to each lambda_LR(lambda) is used as the lower bound of the original IP problem, the optimal value of the lower bound, namely the maximum value is the final value, and the process of continuously searching the optimal lower bound is the process of continuously updating the Lagrange multiplier;

handle Z_LRAt λThe direction of rise in a certain neighborhood is called the sub-gradient, which is denoted as sⁱTo indicate that in the LR problem, can pass through sⁱ＝b-AxⁱObtaining a specific sub-gradient numerical value; the maximum Z is obtained by continuously updating the value of lambda by a sub-gradient algorithm_LRObtaining a set of solutions closest to the optimal solution; the specific iteration steps are as follows:

s41: randomly selecting a group of Lagrange multipliers as initial values, and taking all values as 0;

s42: for lambdaⁱCorresponding sⁱArbitrarily take a sub-gradient sⁱIf s isⁱ0, then λⁱStopping calculation when the optimal solution is reached, and if the optimal solution is not reached, updating lambdaⁱValue of (A)ⁱ⁺¹＝max(λⁱ+θ,sⁱ0), i ═ i +1, repeat S42:

there are four methods to decide to stop the iteration:

(1) stopping iteration when the iteration times reach T;

(2) when s isⁱWhen the value is equal to 0, stopping iteration; by sⁱThe rank of (2) is less than or equal to a certain fixed value to determine the standard of stopping iteration;

(3) when Z is_LR(i)＝Z_IP(i) When the current problem is solved, stopping iteration, wherein the upper bound and the lower bound of the original problem are equal and the optimal target value is reached;

(4) when lambda isⁱOr Z_LRWhen they do not change more than a fixed value within a specified number of steps, the objective function value is considered to be unlikely to change, and the iteration is stopped.

6. The electric vehicle ordered charging and discharging control method based on the Lagrange distributed algorithm according to claim 5, characterized in that: the S5 specifically includes:

at the moment of access of the electric automobile, the battery is charged or discharged, the power of the battery discharged to the power grid is the same as the discharge power of the battery in normal running, and the following reference indexes are added:

1) the declared capacity influences the demand of the power dispatching plan, and if the declared capacity is too low, the power grid basically does not consider participating in the dispatching plan;

2) when the number of the electric vehicles participating in the coordinated dispatching plan is large enough, the comprehensive evaluation value is higher than 0.5 for vehicle full dispatching;

3) in the index evaluation system model, vehicles with high credit degree and participation degree are called preferentially;

4) the vehicle which is called by priority can not participate in scheduling charging and discharging for more than 3 times a day.

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