Optimal Charging Control of Electric Vehicle Fleets Based on Demand Aggregation and User-Oriented Disaggregation Respecting Data Privacy

With the share of electric vehicles (EVs) in the transportation sector rising, solutions for their power system and energy market integration are of increasing importance. In this context, aggregation entities are helpful for addressing the integration process of EV fleets. In this article, a novel methodology for day-ahead charging control of EV fleets is proposed. This includes the prediction of required energy used for charging purposes based on synthetic data and functionalities for optimized energy procurement in the day-ahead energy market to determine the aggregated charging schedule of the fleet. The aggregated charging schedule provides the basis for the proposed charging control algorithm for individual EVs. This algorithm allows for charging flexibility according to the user’s driving preferences while considering data privacy. To avoid data privacy conflicts, the scheduling of the individual charging is decoupled from the upcoming individual driving schedules of the users themselves. This means that the user is not asked to plan and submit expected driving profiles. Instead, realization is by a user-oriented disaggregation that uses the aggregated charging schedule as an input to coordinate the individual charging processes itself. The resulting integrative market solution allows to fulfill the contract positions in energy market participation. The simulation results verify the optimality of the proposed methodology for day-ahead operation and its applicability for aggregation entities that serve as an intermediate between the vehicle owners and electrical utilities or the energy market.

Optimal Charging Control of Electric Vehicle Fleets Based on Demand Aggregation and User-Oriented Disaggregation Respecting Data Privacy Flavio Gromann , Andreas F. Raab , and Kai Strunz Abstract-With the share of electric vehicles (EVs) in the transportation sector rising, solutions for their power system and energy market integration are of increasing importance.In this context, aggregation entities are helpful for addressing the integration process of EV fleets.In this article, a novel methodology for day-ahead charging control of EV fleets is proposed.This includes the prediction of required energy used for charging purposes based on synthetic data and functionalities for optimized energy procurement in the day-ahead energy market to determine the aggregated charging schedule of the fleet.The aggregated charging schedule provides the basis for the proposed charging control algorithm for individual EVs.This algorithm allows for charging flexibility according to the user's driving preferences while considering data privacy.To avoid data privacy conflicts, the scheduling of the individual charging is decoupled from the upcoming individual driving schedules of the users themselves.This means that the user is not asked to plan and submit expected driving profiles.Instead, realization is by a user-oriented disaggregation that uses the aggregated charging schedule as an input to coordinate the individual charging processes itself.The resulting integrative market solution allows to fulfill the contract positions in energy market participation.The simulation results verify the optimality of the proposed methodology for day-ahead operation and its applicability for aggregation entities that serve as an intermediate between the vehicle owners and electrical utilities or the energy market.
An aggregated charging schedule that results from smart charging strategies can be calculated by applying aggregation and optimization techniques.Concerning those optimization techniques, prior work dealt with forecasts and pooled data of EV users, e.g., the predicted driving energy demand, to calculate the aggregated charging schedule for the day-ahead operation [15], [22], [23].The optimization approaches in [24] and [25] consider risk aversion to obtain the aggregated charging schedule under uncertainty of energy prices, driving behavior of the users, and renewable energy generation.In [6] and [21], it was demonstrated that aggregation and optimization of the charging process of EVs can at the same time reduce the energy cost and form the basis for offering ancillary services of frequency regulation and peak load shaving.
The value of disaggregation of distributed energy resources was recognized in [26].With regard to smart charging strategies for EVs, disaggregation is performed to decompose the aggregated charging schedule into individual charging schedules.In [26], [27], [28], [29], and [30], the disaggregation of the aggregated charging schedule is achieved by an optimization process which minimizes the absolute difference between the aggregated charging schedule and the sum of the individual charging schedules.To do so, either detailed information on the individual driving behavior or the coordination in real-time between all the arising individual charging processes is required.A critical aspect hereby is the determination of the uncertain driving behavior of the users in terms of spatial and temporal dimensions.To obtain the necessary information, the usage of extensive transportation network simulation or of field-recorded driving cycles stamped with dwell times and locations was proposed [3], [31], [32], [33].Without access to this information, the driving behavior of the users was predicted [34], [35], [36], or the full information about the driving behavior was assumed [12], [18], [37], [38], [39], [40].While the accuracy of information on the driving behavior of the users varies, the assumption of full access to individual driving behavior of the users may conflict with the strive for data privacy.
This article presents a novel methodology for day-ahead operation of EV fleets to perform smart charging strategies under uncertain driving behavior of the users.To enhance data privacy, the proposed methodology is distinguished by three hallmarks.First, the method does not rely on individual driving data from identified users, such as geographical locations, arrival and departure times, or information about future trips, as, for example, required in [4], [12], and [23].Relevant driving behavior information is aggregated and predicted using synthetic data that are derived based on a general publicly available dataset.Users are not asked to deliver personal driving information for the upcoming day.
Second, the proposed method supports and implements user-oriented disaggregation and individual charging.Information sent from the aggregator to the EV users for the purpose of operation is not personalized, and all the EVs receive the same information.Nonetheless, each individual charging process operates independently and uses the aggregated charging schedule as an indirect control signal to determine charging time and charging power.Individual optimization of each single EV, as in [6], [9], and [12], is not necessary.Third, while EV users send information about their EVs' states of energy to the aggregator, this process is realized in an anonymized manner.There is no identification of the EV user to be included.Thus, the presented methodology, in particular the disaggregation process and information exchange considering data privacy, is fundamentally different from the prior ones that perform optimization from known personalized driving behavior data.
Within the methodology for day-ahead charging operation of EV fleets, presented in Section II, the organizational structure and the involved processes and interactions are introduced and specified.The driving energy demand calculation of EV fleets and the application for charging optimization are described in Section III.Section IV details the determination of the aggregated charging schedule of the fleet and its application to perform user-oriented disaggregation and individual EV charging.Extensive simulations and results are presented in Section V. Conclusions are drawn in Section VI.

II. METHODOLOGY FOR DAY-AHEAD CHARGING OPERATION OF EV FLEETS
With the aim to avoid data privacy conflicts during day-ahead charging operation of EV fleets, the proposed methodology combines the processes of demand aggregation, charging optimization, and user-oriented disaggregation.In this context, the EVS/A is introduced to coordinate and organize the day-ahead charging operation, as described in Section II-A.Section II-B details the related processes and interactions.

A. Organizational Structure
In the proposed organizational structure, as shown in Fig. 1, the main function of the EVS/A is to determine and manage the required energy demand for the charging of EVs.The EVS/A organizes and aggregates EVs into fleets.Each fleet represents a set of typical types of EV users of similar driving behaviors.As such, the fleets of private, commute, and business use types are considered.The use types are established by means of the driving activities of the EV users, which are categorized and introduced later in Appendix A. Within a fleet, EV usage is further categorized into clusters of technical EV characteristics, as detailed in Table I of Section III.For each fleet, the EVS/A combines the functions of managing and trading the energy demands, including data management, operating data acquisition, and maintenance planning.

B. Processes and Interactions
The processes and interactions for day-ahead charging operation of EV fleets are distinguished by two phases: first, the EV user classification and driving energy demand prediction phase, and second, the day-ahead charging optimization and implementation phase.In phase one, the EV fleet types are formed according to the main usage, e.g., "commute," and those fleets are subdivided into clusters according to the technical EV characteristics.Then, driving energy demand profiles are predicted.The profiles are then used in phase two for calculating the optimized charging schedule.
1) Phase One: The synthetic driving energy demand profiles are the main output of phase one, as shown in Fig. 2. Each of those profiles represents the predicted energy demand for driving over time.It is important to note that there is no direct monitoring of the EV users' driving behaviors themselves.The profiles are aggregated.This aggregation is suitable for the Fig. 2.
Phase one: EV user classification and driving energy demand prediction.
prediction of the driving energy demand of the fleet, as to be detailed and validated in Section III-B.
In a first step of the sequences of Fig. 2, the classification process is performed.Here, EV users that are members of the EVS/A are surveyed for their use types and their technical EV characteristics.With the information of the use type, an EV user is categorized into a certain fleet.On the basis of the technical EV characteristics such as the battery capacity and the maximal charging power, an EV user is categorized into a certain cluster, as discussed in Section III.An update of the fleets and the containing clusters is performed as soon as new EV users enter or when already participating EV users leave the EVS/A.This update is also necessary for the cases where the technical EV characteristics or the use types of participating EV users change.
Once the EV users have been categorized, synthetic driving energy demand profiles are generated in the prediction process as shown by the nested loops of Fig. 2. For the generation of synthetic profiles, as detailed later in Section III-A, the EVS/A manager takes into account: 1) the use type; 2) the number of EV users; 3) the predicted daily ambient temperature; and 4) the driving behavior of the considered use type.But instead of an extensive monitoring and recording of the actual behaviors of the EV users themselves, the information is taken from general datasets, covering wide driving statistics [41] of comparable use types.Then, the EVS/A manager forwards the synthetic profiles to the EVS/A optimizer in the upcoming phase two.
2) Phase Two: Phase two, as shown in Fig. 3, is composed of two main stages, hereafter referred to as optimization and implementation stages.In the optimization stage, the EVS/A optimizer first formulates the objectives and constraints for the charging optimization of the cluster as specified in Section IV.Then, the EVS/A optimizer aggregates the synthetic profiles and calculates the aggregated power schedule, also referred as optimal charging schedule, in the charging optimization process.The aggregate power schedule is forwarded to the EVS/A scheduler.On the basis of the aggregated power schedule, the EVS/A scheduler procures the required energy for charging in the day-ahead market.After the charging energy is procured, the EVS/A scheduler forwards the aggregated power schedule to the EVS/A optimizer.
In the implementation stage, the user-oriented disaggregation of the aggregated power schedule into individual power schedules is performed.As the EVS/A optimizer incorporates the delivery of charging power from renewable sources, as described in Section IV-A, it is appropriate to address uncertainty associated with renewable power generation in the forthcoming day.In response to this uncertainty, the EVS/A calculates a rolling horizon forecast update factor to account for deviations from renewable power generation in the aggregated power schedule, as detailed in Section IV-B.For the disaggregation, the actual state of energy of each grid-connected EV is forwarded to the EVS/A optimizer at every time step during the day.On the basis of the received individual states of energy, the EVS/A optimizer defines the set of grid-connected EVs and calculates the aggregated state of energy.Considering the individual states of energy, the EVS/A optimizer calculates a rolling horizon charging update factor as detailed in Section IV-B.Then, the EVS/A optimizer forwards the aggregated power schedule, the rolling horizon forecast update factor, the rolling horizon charging update factor, the cardinality of the set of grid-connected EVs, and the aggregated state of energy to the EVs.The rolling horizon forecast update factor, the rolling horizon charging update factor, the cardinality, the aggregated state of energy, and the aggregated power schedule are used as indirect control signals for the daily charging processes of the EVs.The detailed individual driving behavior of a user is not required and data privacy conflicts can be avoided.The disaggregation is detailed in Section IV-B.As a result of the daily charging processes, the EVS/A scheduler receives the actual power schedules from the EVs at the end of the day.Those power schedules are aggregated and referred to as actual scheduled charging power of the fleet.The EVS/A scheduler evaluates the accuracy between the actual scheduled charging power and the aggregated power as investigated in Section IV-C.The stronger the correlation of these schedules, the better the contracted position in the energy market is fulfilled.

III. USER CLASSIFICATION AND DRIVING ENERGY DEMAND COMPUTATION AND APPLICATION
As shown in the sequences of Fig. 2, the EVS/A considers different fleets together with their use types and clusters.A fleet is defined by the use type that represents a certain number n of EV users of similar driving behavior.Here, the use types "private," "commute," and "business" are considered as listed in Table I.To identify individual EV users within the fleet, the set of EV users H u,ev,f = {1, . . ., n} is introduced.
A fleet is subdivided into clusters according to the technical specifications of the EVs such as the battery capacity, the maximal charging power, and the charging efficiency.The clusters are defined and specified in Table I and represented by the set H cl,f = {short-range, mid-range, long-range}.To identify individual EV users within the cluster, the set of EV users of cluster j is introduced with H cl j , j ∈ H cl,f .This is a subset of the fleet set, H cl j ⊆ H u,ev,f .As an example, the cluster mid-range includes users of EVs with a battery capacity of 24.4 kWh, a maximal available charging power up to 7.4 kW, and a charging efficiency of 93 %.This information is applied in the optimization process to define the related constraints, as shown in the sequences of Fig. 3 and as mentioned in Section IV.

A. Driving Energy Demand Prediction
Following the sequences in Fig. 2, the EVS/A predicts the driving energy demands of the EV users by activity-based synthetic driving energy demand profiles.Each of these synthetic profiles consists of none, one, or multiple trips.Those trips are composed step by step from the entries of the driving energy demand E d,ev i (k) within the profile i at time step k.Regarding the trading period of the day-ahead market, the considered time horizon for the synthetic profiles is one day, Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Synthetic driving demand profiles of use type "commute" with variable numbers of EV users.and the considered time interval t is 0.25 h.Consequently, one day is divided into 96 time steps and is represented by the set of time steps H ts = {1, 2, . . ., 96}.Profiles with no trips are indicated by zero entries for all E d,ev The activity-based synthetic driving energy demand profiles cover the driving behaviors of EV users for distinct use types.The representation of the driving behavior is based on real measured driving behavior data of the MiD [41] study that cover wide driving statistics for Germany.These data are analyzed and processed as detailed in Appendixes A and B. The analyzed and processed data are then applied within a Monte Carlo simulation to generate activity-based synthetic driving energy demand profiles as detailed in Appendix C.

B. Driving Energy Demand Correlation
To evaluate the variability of various aggregated synthetic driving energy demand profiles, several fleets of different use types are investigated.The results are used to determine the variability in correlation to the number n of considered EV users of an EV fleet.The number of EV users is equal to the number of profiles.The aggregated synthetic driving energy demand profiles of an exemplary use type, as illustrated by power-over-time profiles, are shown in Fig. 4. It is observed that the variability decreases with higher numbers of EV users considered [29].
The degree of decreasing variability is determined by applying the formula of Pearson product-moment correlation described by (21) in Appendix E. It yields the correlation coefficient ρ d,f .The correlation is drawn to a highly aggregated reference fleet with synthetic driving energy demand profiles of 50 000 EV users as defined by E d,f 50 000 .The resulting correlation coefficients are depicted in Fig. 5.The gray-shaded area gives the acceptance area, indicated by a correlation coefficient of 0.9 ≤ ρ d,f ≤ 1. Numbers of ρ d,f ≥ 0.9 indicate high correlation, and ρ d,f = 1 shows perfect correlation.Taking the use type commute (B) as an example, a high correlation of ρ d,f equal to 0.9 can already be observed by considering just 150 EV users.From a size of about 1000 EV users and more, the value of ρ d,f increases and tends to values ≥ 0.96.A high value for the correlation coefficient indicates a small deviation between the predicted and actual driving energy demand profiles.
As expected, the higher the number of EV users becomes, the less volatile these profiles are.This observation suggests that the charging demand becomes more predictable as the number of the EV users increases.This relationship affects the charging optimization and implementation as shown in Fig. 3 of Section II-B and as analyzed in Section IV-C.

IV. EV CHARGING OPTIMIZATION AND IMPLEMENTATION
Within the methodology of EV fleet charging, optimization and implementation are important functions, as it has become evident from Fig. 3. First, the optimization, detailed in Section IV-A below, calculates the optimal power and state of energy schedule for each cluster of the fleet.Second, the resulting schedules are used in the implementation process that combines user-oriented disaggregation and individual EV charging, as described in Section IV-B.Third, the schedules of both the processes are analyzed by the accuracy evaluation in Section IV-C.

A. Aggregation and Charging Optimization
The optimization is modeled as a constrained linear programming problem with the aims of minimizing the total charging costs and prioritizing the utilization of contracted power for charging purposes.The objective function is formulated with the power P da to be assigned via the day-ahead market, the forecast day-ahead market price per amount of energy c da , and the charging efficiency η cl for cluster j and for all time steps k within the set H ts by min The minimization is subject to the constraints (2), ( 3), ( 5), and (6) as described in the following.
In practice, there may well be good reasons for the EVS/A to negotiate the delivery of a given amount of charging power from preferred power suppliers outside an energy exchange market place.A particular motivation could be the improvement of the carbon footprint of the fleet by obtaining power through a supplier that guarantees delivery from renewable sources.To actually integrate such a power purchasing agreement, the aggregated charging power P ch,cl j is the sum of the requested day-ahead market power and the renewable contracted power P ppa,re from a power purchasing agreement as follows: If the contracted power supplied by the renewable sources is sufficient to cover the demand on charging the EVs, the EVS/A does not need to buy further amount of power on the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
day-ahead market.However, if the contracted power supplied by the renewable sources is lower than the required P ch,cl j , the EVS/A has to purchase an additional amount of power P da j , which induces additional costs expressed by c da .
The aggregated charging power of the cluster j is limited by the cumulated maximal charging power P ch,max,ev i and the binary status of the grid connection con ev i of each individual EV i by For the considered cluster j, the state of energy SoE cl j is dependent on the aggregated rated energy capacity of the battery E bat,r,cl j , the aggregated charging power P ch,cl j , the driving energy demand E d,ev i of all the EVs considered, and the cluster cardinality |H cl j | as follows: Within ( 4), the aggregated rated energy capacity of the battery corresponds to the accumulation of the rated energy capacities of each battery E bat,r,ev i corresponding to individual EV i. Constraint ( 5) is introduced to maintain the state of energy within the minimum SoE min,cl and maximum SoE max,cl to guarantee sufficient energy for driving Furthermore, for the purpose of operation, it is often required to request a certain minimal setpoint of the state of energy as a function of time step k SoE cl j (k) ≥ SoE set,min,cl .
This constraint may be used to guarantee sufficiently charged batteries in accordance with expected trips.

B. Disaggregation and Charging Implementation
Once the optimization is completed, the following EV charging implementation process combines user-oriented disaggregation and individual EV charging.In the day-ahead consideration, there exists uncertainty about the renewable power generation in the forthcoming day.This uncertainty can be neglected in the intraday process of this forthcoming day by applying forecast updates on a rolling horizon basis every 15 min for the next 15-min period.For this purpose, P ppa,re j of the renewable power purchase agreement in (2) is to be replaced by P re j as the intraday update given the 15-min forecast of the available renewable power.For the short forecast interval of 15 min, P re j is assumed to be accurate and uncertainty neglected for this quantity.As a consequence, the aggregated charging power will be weighted by a rolling horizon forecast update factor that is calculated as follows and used in the individual charging process: Whenever individual EVs are connected to the grid, the aggregated charging schedule is used as a basis for disaggregation to derive control signals coordinating individual charging processes in terms of charging time and charging power.As such, the amount of charging power P ch,ev i for the EV of user i in the considered cluster j is obtained by the aggregated charging power P ch,cl j , the cardinality of grid-connected EVs, |H con,ev |, and the rolling horizon forecast update factor b rh j (k) in time step k as follows: with as the aggregated state of energy of grid-connected EVs; where d rh j is the rolling horizon charging update factor for the cluster j.Factor d rh j may be set equal to 1, or may be set using Algorithm 2 in Appendix F. When using d rh j equal to 1, the sum of the individual charging powers may not coincide with the aggregate charging power, because of the individual charging constraints ( 9) and (10) given below.The setting using Algorithm 2 takes into account that those individual charging powers not hitting the limits can be increased to compensate for the others hitting the limits.In this way, the sum of the individual charging powers can be adjusted to match the aggregated charging power.
The amount of charging power, as calculated by (8), is taken as the setpoint for the charging station.Then, the charging station performs the individual charging process.This individual charging process is subject to constraints as follows.First, the charging power of the EV of user i is limited by the maximal permissible charging power Second, the constraint maintains the state of energy of the EV of user i within reasonable ranges to allow for sufficient energy for driving.The state of energy SoE ev i in time step k may be obtained from metering.Alternatively, taking SoE ini i as the initial value, the state of energy for the individual EV of the user i is calculated by

C. Accuracy Evaluation
The accuracy of the proposed method for charging optimization and implementation is evaluated by comparing P ch,opt,f obtained from the optimization at the aggregated level (2) with P ch,sch,f as the sum of the individual disaggregated charging schedules (8).The optimal charging power and the actual scheduled charging power of the fleet are calculated by ( 12) and ( 13), respectively, at every time step k To assess the accuracy, a numerical analysis of the power deviation indicator λ ch,opt,sch is performed.The power deviation indicator represents the relative standard deviation between the optimal charging power of the fleet and the actual scheduled charging power of the fleet, and it is calculated by It is important to note that this accuracy validation considers fleet sizes of up to 100 000 EV users.The MiD study includes fewer applicable real-measured driving profiles.To close the gap between the number of real-measured profiles and the number of EV users considered, synthetic driving energy demand profiles are used.For that reason, synthetic driving energy demand profiles represent both the predicted and the actual driving energy demands as given in Figs. 2 and 3 of Section II.
In what follows, a numerical analysis of the accuracy evaluation is performed.In Section IV-C1, this is done without consideration of the rolling horizon charging update factor, i.e., the factor is set equal to 1.In Section IV-C2, the rolling horizon charging update factor is applied.
1) Rolling Horizon Charging Update Factor Equal to 1: As shown in Fig. 6(a), the accuracy evaluation is done for several fleets of different use types and numbers of users n.The values of the power deviation indicator are decreasing with higher numbers of EV users considered.Smaller values for λ ch,opt,sch indicate a higher accuracy of the cumulative charging power schedule of the individual EVs with respect to the optimum obtained for the aggregate.It can be observed in Fig. 6(a) that λ ch,opt,sch values drop below 0.01 with 1000 users and more across all the use types.This corresponds to a high correlation of the driving energy demand schedule profile and its optimum.The exemplary charging behavior for the fleet of the "commute" use type is shown in Fig. 6(b).The value for λ ch,opt,sch is 0.009 and indicates a very close matching between the actual scheduled charging power and the optimal counterpart.
2) Application of Rolling Horizon Charging Update Factor: The observed deviation between the optimal charging power and the actual scheduled charging power for a small number of users, as evaluated in Section IV-C1, can be attributed to the individual charging constraints ( 9) and ( 10).These constraints were not originally considered as individual constraints in the aggregation and charging optimization in Section IV-A.By applying the rolling horizon charging update factor with values greater than 1, as suggested in Appendix F, those deviations are practically eliminated.As a proof of concept, the accuracy evaluation of Fig. 6(a) is repeated and plotted again in Fig. 7(a) with the rolling horizon charging update factor obtained from Algorithm 2 in Appendix F.
A comparison of Figs.6(a) and 7(a) shows that the standard deviation between the optimal charging power and the actual scheduled charging power becomes smaller, thanks to the application of the rolling horizon charging update factor.The application of the rolling horizon charging update factor is particularly valuable for small fleet sizes.As such, Fig. 7(b) shows the optimized charging behavior for the fleet of the "commute" use type with 100 EV users.

V. CASE STUDY
In what follows, the performance of the charging optimization and implementation approach in day-ahead charging operation of EVs is validated, and its value is put into evidence.The simulation horizon is one week, and three selected days are presented in detail over a range of 72 h.It is shown how the predicted synthetic driving energy demand profiles as detailed in Section III can be applied in smart charging strategies for the operation of a fleet of the use type "commute."For the simulation of the actual charging behavior, a set of 1000 measured real-life driving energy demand profiles of conventional vehicle users are used as inputs.
The case study is structured as follows.In Section V-A, the input data and preliminary considerations are described.In Section V-B, a comparative analysis of the actual charging is carried out.Section V-C details the obtained results by assessing the charging schedules of selected EVs.

A. Preliminary Considerations
The EVS/A applies the objective function (1) to achieve cost-effective charging schedules while using solar power as a contracted input from a power purchasing agreement to improve the carbon footprint of the fleet.The constraint ( 2) is applied to consider both the power from the day-ahead market and the already contracted solar power for the charging purpose.For the day-ahead optimization, the forecast price signal and the already contracted power are to be known.In the case study, contracted solar power is considered, as given in Fig. 8(a).The shown price signal was taken from historical data of the European Energy Exchange.
In consideration of the battery life, the minimum SoE min is set to 0.1 p.u. and the maximum SoE max to 1.0 p.u., as discussed in [42].Those limits are enacted via the constraint (5).In addition, the constraint ( 6) is set to 0.8 p.u. for the hours 5, 29, and 53, which corresponds to 5:00 A.M. and time step k = 20 on each day, to obtain charged vehicles in the morning hours.
The synthetic and actual driving power demand profiles, along with the associated share of grid-connected EVs, are depicted in Fig. 8(b).The peak demand in the morning hours represents the driving behavior of the "commute" use type where EV users leave early in the morning and return from work in the evening.

B. Comparative Analysis of Charging Strategies
To obtain a base of comparison, the EVS/A first uses the synthetic driving energy demand profiles to determine the charging power in a UC scenario.This means that the charging process would start immediately once an EV user plugs in after the trip ends, and it would last until the EV gets disconnected or the EV's energy storage is fully charged.The resulting UC aggregated power schedule P ch,uc,f is depicted in Fig. 8(c) given by the dotted purple line.As expected, the curve characteristic of the UC aggregated power follows the characteristic of the driving power demand of Fig. 8(b) with a delay.The EVS/A may use the result of this UC scenario and set the maximal observed charging power as an additional constraint in the optimization process for the CC scenario to avoid additional network loads.This constraint condition is given by ( 3) in Section IV.
The actual schedule of the charging power profile P ch,sch,f of the CC scenario is indicated by the solid gray line of Fig. 8(c).The green arrows indicate the shift of the peak demand of the charging process toward the noon hours, when maximal solar power is available.
In addition, the solid purple line in Fig. 8(d) shows the SoE of the uncontrolled and the solid black line the SoE of the CC scenario.The solid red line and the boxplots in Fig. 8(d) represent the mean of the SoEs and the distribution of the individual SoEs in the CC scenario as a consequence of the implementation stage.
(a) First day from hour 0 to 24: On the first day, the contracted solar power is sufficient to cover 70 % of the daily driving demand.While in the uncontrolled case high SoE values are noted in Fig. 8(c), the SoE ranges between 0.7 and 0.91 p.u. to guarantee the up-and downward flexibility of the batteries in the case of CC.Consequently, compared with the UC scenario, 50 % more solar power is used.By inspection of Fig. 8(a) and (c), it can be seen that the remaining aggregated charging power is scheduled in the early morning and night hours to make use of low energy prices.
(b) Second day from hour 24 to 48: The contracted solar power on the second day suffices to cover 88 % of the daily driving demand.Additional charging power is required during night hours to fulfill the requirement of charged vehicles in the morning hours.In consequence of the forecast uncertainty, the forecast of the contracted solar power deviates from the solar power generation, as shown in Fig. 8(a).The actually available solar power generation is reduced from the originally contracted solar power by 13 %.As a result, the SoE is lowered to 0.76 p.u. at the end of day 2 in hour 96, and the targeted SoE of 0.8 p.u. for the end of the day is not fully reached.In comparison to the UC scenario, 40 % more solar Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.power is used.Thanks to the rolling horizon forecast update factor, the CC scenario can react accurately to fluctuations in renewable power generation.
(c) Third day from hour 48 to 72: As usual, the final SoE at the end of the second day serves as the initial SoE for the third day.On the third day, no solar power is contracted, and the required charging power is obtained from the energy market.Charging power is requested during the night and afternoon hours at the lowest energy prices available for the day, which ensures that vehicles are charged in the morning hours.A final SoE of 0.8 p.u. is reached at the end of the day.
Upon inspecting Fig. 8(a) and (c), it becomes evident that the actual scheduled charging power follows the optimized charging schedule P ch,opt,f in all the three illustrated days.In addition, it is shown that the fleet can handle fluctuations in renewable power generation without violating the optimized charging schedule.The value of the power deviation indicator λ ch,opt,sch is 0.0087 , and this indicates a very close matching between the actual scheduled charging power and the optimal counterpart.This result further confirms the observations in Section IV-C.

C. Analysis of Disaggregation and Individual EV Charging
Once the EVS/A has obtained the power and state of energy schedules of the optimization process, the results are used to procure the energy in the day-ahead market.The same schedules are used as indirect control signals to simultaneously perform disaggregation and individual EV charging.The charging powers of connected EVs are obtained as described by (8).Fig. 9(a) and (b) represents a selection of two chosen EV users with different driving behaviors to show the effects from applying the proposed method.The gray areas indicate the time intervals of connection.Negative power values refer to the power demand for driving, while positive values are indicative of charging.As can be seen, the selected EVs have different states of energy conditions during the day.This influences the individual charging power as described by (8).For example, the SoE ev 1 of EV 1 is 0.3 p.u. at hour 66, while the SoE con,ev,cl of the EV cluster is 0.7 p.u..This leads to a high weighting factor in (8), and the maximal charging power of 3.7 kW is used.The weighting factor decreases when SoE ev is equal or greater than SoE con,ev,cl .A decreased weighting factor lowers the charging power and the charging activity.This is particularly evidenced by the charging profile of EV 1 from hour 0 to 16.The application of the rolling horizon charging update factor is depicted by EV 2 between hours 65 and 68.During this period, EV 2 is charging, and while the SoE ev 2 increases, the charging power decreases.However, in hour 66, it suddenly increases again, contradicting the previous consideration.During this time, the rolling horizon charging update factor comes into play, and the available capacity of EV 2 is used.

VI. CONCLUSION
The large-scale integration of EVs relies both on a successful market integration and the provision of climate-friendly, cost-efficient, and user-friendly charging of EVs.In this sense, the proposed methodology for day-ahead charging operation plays a vital role, thanks to the coordinated application of aggregation and disaggregation when charging EVs.
As a first contribution, the organizational structure for the classification and management of EV fleets was identified and defined as part of the interaction between the EVS/A, the energy market, and the participating EV users.The EV users' driving behaviors and technical EV characteristics can be used by the EVS/A to classify EV users into fleets and clusters.Thus, each fleet represents an aggregated energy resource and enables the participation in the energy market for the acquisition of energy for charging purposes.For each fleet, the driving energy demand is predicted based on synthetic data that are representative of driving data from a comprehensive and publicly available dataset.The predicted driving energy demand is then used to calculate the optimal charging schedule for the fleet with the aim to use renewables and minimize the charging costs.
The optimal charging schedule builds the basis for the user-oriented disaggregation.This central part of the methodology and second contribution allows for the coordination of the individual charging of EVs.No specific individual driving behavior data from the EV users are requested, and, therefore, data privacy conflicts can be avoided.
It was successfully shown that the deviation between the contracted and the actual scheduled charging power, given by the sum of the individual charging powers, decreases with a higher number of EV users considered.Moreover, the superiority in handling and exploiting the up-and downward flexibility of the grid-connected EV batteries for the optimized energy procurement was quantified in a study case using real-life driving energy demand profiles.
The methodology brings together the processes of aggregation and disaggregation.On one hand, the process of aggregation enables the participation of aggregated EVs in the energy market for the usage as a predictable and flexible resource in the power system.On the other hand, the process of user-oriented disaggregation and individual EV charging accounts for user specific mobility needs and avoids data privacy conflicts.In sum, those features support the large-scale According to the MiD study [41], the daily driving profiles of the vehicle users are composed of trips.Each trip is assigned to certain driving activities.The driving activity is related to the destination of the trip.The study distinguishes more than 25 driving activities.Those activities are divided into five superordinate driving activities of "work," "commercial," "shopping," "leisure," and "accompany" as listed in Table II and represented by the set H a = {1, . . ., 5}.
An example profile is depicted in Fig. 10.The first trip is from home to the workplace.Due to the destination "workplace," the assignment of the driving activity is "work."The departure time of this trip is at 7:45 a.m., the arrival time is 8:15 a.m., and the driving distance is 17 km.The second trip is from the workplace to a shop.Accordingly, the driving activity is "shopping."The last trip starts from the shop and ends at home and is also assigned to the driving activity "shopping."When the home is a destination, then the activity is given by the starting point of the trip.Consequently, the driving activity "work" is considered when the trip starts at the workplace and ends at home.
Regarding the real measured driving profiles of the MiD study, the relative distribution of driving activities can be mapped onto use types "private," "commute," and "business," as developed in this article and shown in Table II.As an example, for the use type "commute" 62 % of trips are assigned to the driving activity "work."The remaining 38 % are spread across the driving activities "commercial" with 2 %, "shopping" with 17 %, "leisure" with 13 %, and "accompany" with 6 %.
The relative weighting of driving activities for distinct use types is taken into consideration for obtaining the temporal distributions of the departure times.For the use type "commute," this distribution is subdivided into daily time intervals as depicted in Fig. 11(a) for distinct driving activities.It can be observed that the majority of trips relates to the driving activity "work" with most trips starting in the morning hours when users travel to work.Furthermore, the distributions of driving distances of the considered driving activities are analyzed and depicted in Fig. 11(b) for several intervals of driving distance.It can be observed that most of the driving activities fall into the range of 0 -20 km.The frequency decreases toward higher distance ranges.For the driving activities "commercial" and "leisure," distances in excess of 150 km are not rare.
For the introduced distance intervals, the distribution of the trip time per km is analyzed and depicted in Fig. 11(c).The trip time per km is shown to increase with shorter driving distances because highways are used more often for longer distances.
Fleets are defined according to the considered use types.As an example, the use type "commute" leads to the definition of the cEV.The distributions of daily numbers of trips for the pEV, cEV, and bEV are depicted by the boxplots in Fig. 11(d).The average numbers of daily trips for those fleets are given by the red line in Fig. 11(d).An increasing number of daily trips leads to a higher average driving distance, as listed in Table III.For example, the average distance for the private use type is 29 km with 2.8 trips per day on average, as indicated by the red dot in Fig. 11(d).
The possible driving range per trip is constrained by the battery capacity.In Table III, the driving ranges in km for a trip are indicated for the considered clusters.For example, the range of trips of the cluster mid-range is from 0 to 150 km.Also given in Table III is the distribution of the vehicle numbers to be attributed to the three cluster types.The given Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.For the purpose of organization, the set of EV users per fleet H u,ev,f = {1, . . ., 1000} and the subset H cl j , ∀ j ∈ H cl,f , are arranged in ascending order.This means that the subset of the cluster short-range is defined as H cl short = {1, . . ., 670}, the cluster mid-range with H cl mid = {671, . . ., 860}, and the cluster long-range with H cl long = {861, . . ., 1000}.The evaluation of the driving behaviors discussed in this section is further used to generate the synthetic driving energy demand profiles for distinct use types.This is reflected in the sequences of Fig. 2 and is detailed in Section III-A.

B. Probability Distribution Estimation
For the representation of the probability distributions, the method of kernel density estimation (KDE) for discrete [43] and continuous [44], [45] observed data is suitable.In Fig. 12, the discrete KDE is applied to fit the data from profiles of the MiD study [41].It can be observed that the obtained nonparametric distribution for the number of daily trips P ndt matches the data.
In the same manner, the nonparametric distribution for the driving activity P a is obtained.As depicted in Fig. 13, the distribution shows how likely a certain driving activity, as observed in the MiD study, occurs.Result of continuous KDE method to obtain nonparametric distributions P δ a of driving distances for driving activities.
Result of continuous KDE method to obtain nonparametric distributions P tin,km (trip δ ] of trip time per km for intervals of driving distance.
The estimated nonparametric distributions for the departure time steps for the driving activities P ts,dep a are shown in Fig. 14.Due to the continuous values of the observed data, the continuous KDE method is used for the fitting purpose.
Using the continuous KDE method, the nonparametric distributions of the driving distances for the driving activities, P δ a , and the trip time per km for different intervals of driving distance, P tin,km (trip δ ] , are formulated and shown in Figs. 15 and 16.

C. Synthetic Driving Energy Demand Profiles
For the generation of synthetic driving energy demand profiles, Monte Carlo simulation (MC simulation) [25], [34], [46], [47] is used as clarified by Algorithm 1.The MC simulation is a technique to simulate the results of an experiment using random variables [48].Here, the results are daily driving energy demand profiles that are influenced by trips of a specific number n of EV users of distinct use types τ , as to be initialized in line 1 of Algorithm 1. Random variables are used to obtain the profile-related data, as performed within the for-loop from lines 5 to 13 of Algorithm 1.The profile-related data are the number of daily trips K in the vehicle user's profile i and, within each trip, for the selection of the driving activity a, a ∈ H a , the departure time step trip ts,dep , the driving distance trip δ , and the trip time interval per km trip tin,km .
The investigation of the driving behaviors in Appendix A is used to select and estimate the nonparametric probability distributions for the number of daily trips P ndt , the driving activities P a , the departure time steps for driving activities P ts,dep a , the driving distances for driving activities P δ a , and the trip times per km for intervals of driving distances P tin,km (trip δ ] as detailed in Appendix B and mentioned in line 2 of Algorithm 1.Each of these distributions is then used to Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
Algorithm 1 Monte Carlo simulation to generate synthetic daily driving energy demand profile for example use type "commute".
1: Initialize the number of EV users n and the use type τ 2: Estimate the nonparametric distributions of: (a) the number of daily trips P ndt as shown in Fig. 12, (b) the driving activities P a as shown in Fig. 13, (c) the departure time steps for driving activities P ts,dep a as shown in Fig. 14,  (d) the driving distances for driving activities P δ a as shown in Fig. 15, (e) the trip time per km for the intervals of driving distance 0-20 km, 20-50 km, 50-100 km, 100-150 km, and >150 km P tin,km (tri p δ ] as shown in Fig. 16 for the example of the use type commute τ = commute 3: Initialize counter i with i = 1 4: while i ≤ n do 5: Obtain a random number for the number of trips per day of EV user i with K ∼ P ndt [0, 13] 6: for k = 1 to K do Calculate the arrival time trip ts,arr by (16) 12: Calculate and assign synthetic driving energy demands for appropriate time steps with (15) and (18) 13: end for 14: i = i + 1 15: end while 16: Reorder synthetic driving energy demand profiles in ascending order, starting with the lowest energy demands 17: Calculate the grid connection by (17) generate according random numbers for the profile-related parameters as listed in lines 5 and 7-10 of Algorithm 1.These parameters are used to formulate the synthetic daily driving energy demand profile E d,ev i (k) of an EV user i in time steps k as given by ( 15) and ( 16)  Equation ( 15) also considers the specific driving energy demand E d,km,ev as detailed in Appendix D. Lines 11 and 12 of Algorithm 1 refer to the calculations made with those equations.The generation of trips and profiles is repeated until all the EV user profiles have been dealt with.The corresponding lines are indicated within the while-loop from lines 4 to 15 of Algorithm 1.
In line 16 of Algorithm 1, the daily driving energy demand profiles are rearranged in ascending order, starting with the lowest driving energy demands.According to the defined clusters in Appendix A, the rearrangement ensures that profiles with the lowest energy demands are assigned to the cluster short-range and profiles with the highest energy demands to the cluster long-range.Finally, the grid connection con ev i is introduced to identify possible time steps for charging as listed in line 17.The value for con ev i (k) is equal to 0 if the corresponding driving energy demand E d,ev i of the EV user i in the time step k is greater than zero.It is set to 1 otherwise.The mathematical relationship is as follows:

D. Specific Driving Energy Demand
The specific driving energy demand E d,km,ev per km is calculated as a function of the demands for the drive train E d,km,dr and for the auxiliary devices E d,km,aux by E d,km,ev (k) = E d,km,dr (k) + E d,km,aux (k). ( As confirmed in [49], the energy demands are functions of the ambient temperature T as follows: The functions are approximated from real measured data points in [49].The data points represent the energy demand during the drive per km for distinct values of the ambient temperature.The resulting polynomial coefficients α, β, γ , ϵ, ζ , and θ of the functions in (19) and (20) are defined and listed in Table IV.

E. Pearson Product-Moment Correlation
To measure the intensity of correlation between two variables, the Pearson's product-moment correlation coefficient is widely used [50].Here, the correlation coefficient ρ d,f n is introduced to measure the linear correlation between the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
Algorithm 2 Calculation of rolling horizon charging update factor for every time step k and cluster j.
1: Initialize variables and set d rh j equal to 1 2: while the sum of the individual charging power setpoints is not sufficiently close to the aggregated charging power do 3: Calculate charging power setpoints with (8) 4: For those setpoints of line 3 that exceed power constraint, set them to limit 5: Calculate SoE values expected for the next time step 6: For those setpoints of lines 3 and 4 that lead to SoE limit violations of line 5, adjust setpoints to avoid violations and adjust SoEs of line 5 with

F. Rolling Horizon Charging Update Factor
To compensate the deviation in the aggregated charging power at every time step k of the cluster j, the rolling horizon charging update factor d rh j is introduced.The calculation of the rolling horizon charging update factor is detailed in Algorithm 2. The value for the increment factor σ is set to 0.001 .

Fig. 1 .
Fig. 1.Organizational structure for classification and management of EV fleets.

Fig. 4 .
Fig. 4.Synthetic driving demand profiles of use type "commute" with variable numbers of EV users.

Fig. 5 .
Fig. 5. Correlation coefficient for private (A), commute (B), and business (C) use types for up to 50 000 EV users within the fleet.

Fig. 6 .
Fig. 6.Charging power deviation indicator for up to 50 000 EV users of different use types and optimized charging behavior for fleet B (use type: commute) with 1000 EV users; without rolling horizon charging update factor.

Fig. 7 .
Fig. 7. Charging power deviation indicator for up to 50 000 EV users of different use types and optimized charging behavior for fleet B (use type: commute) with 100 EV users; with rolling horizon charging update factor.

Fig. 8 .
Fig. 8. Day-ahead charging optimization and real-life charging implementation of fleet B (usage type: commute) with 1000 EV users.

Fig. 9 .
Fig. 9. Real-life individual EV charging for selected EVs of fleet B (use type: commute).

Fig. 10 .
Fig. 10.Example driving profile with multiple trips of different driving activities.TABLE II RELATIONSHIP OF USE TYPES AND DRIVING ACTIVITIES

Fig. 11 .
Fig. 11.Evaluation of driving behavior data of MiD study.

Fig. 14 .
Fig. 14.Result of continuous KDE method to obtain nonparametric distributions P ts,dep a of departure time steps for driving activities.

Fig. 15 .
Fig.15.Result of continuous KDE method to obtain nonparametric distributions P δ a of driving distances for driving activities.

TABLE I FLEETS
AND CORRESPONDING USE TYPES WITH TECHNICAL EV CHAR-ACTERISTICS OF CONTAINING CLUSTERS

TABLE III FLEETS
AND CORRESPONDING USE TYPES WITH EV CHARACTERISTICS OF CONTAINING CLUSTERS Fig. 12. Result of discrete KDE method to obtain nonparametric distribution P ndt of number of trips of vehicle users over day.

7 :
Increment d rhj by a number σ 8: end whiledriving energy demand E d,fn of the fleet with n users and the driving energy demand of the reference fleet E d,f 50 000 byρ d,f n = k∈H ts E d,f n (k) • E d,f 50 000 (k) − |H ts | • Ēd,f n • Ēd,f