Analysis of Smart Grid Optimal Scheduling considering the Demand Response of Different EV Owners

. Te escalating growth of electric vehicle (EV) load has emphasized the growing importance of efective scheduling strategies. Due to the discrepancies among EV owners, their responses to scheduling can difer signifcantly. Terefore, to achieve better scheduling results, it is crucial to consider the impact of these discrepancies on the optimal scheduling. Tis paper proposes a classifed scheduling method for diferent types of EV owners. According to charging and vehicle-to-grid (V2G) data of EV owners, the K-means clustering algorithm (K-means) is used to classify EV owners, and the demand response (DR) model is established based on the classifcation results. Te DR model is designed to account for the diverse responses of diferent EV owners, and the price elasticity, time gap elasticity, and preference time elasticity are important factors in the model. Tis paper adopts the maximization of smart grid’s revenue as the optimization objective through three approaches: (1) modifying the charging and V2G of EV; (2) obtaining V2G prices for all types of EV; and then (3) adjusting the power output of each unit. To evaluate the proposed method, the IEEE 10-unit system is employed for simulation, and the optimization problem is solved using the CPLEX solver. Compared to previous studies, the proposed classifed scheduling method exhibits signifcant improvements in terms of revenue maximization, load distribution among diferent types of EVs, generation cost savings, and load variance reduction.


Introduction
Power generation and transportation are two of the largest sources of energy consumption in the space [1].Fuel vehicle (FV) is the most widely used vehicle of transportation, and their low energy utilization efciency has resulted in signifcant energy waste.Te escalating adoption of electric vehicles (EVs) has resulted in a substantial shift of transportation load to the electrical grid.EVs have more advantages compared to FVs in terms of economy and environment [2].Replacing FVs with EVs is an efective method to reduce carbon emissions [3].Vehicle-to-grid (V2G) technology discharges EVs energy back to the smart grid [4].Due to the large number of EVs, the application of V2G can alleviate the problem that electric energy is not difcult to store, but the cost is relatively high.Alizadeh et al. [5] developed a two-layer optimization model for the management of charging and discharging of EVs in parking lots, exploring the application value of V2G.With the development of battery technology, the cost of battery loss decreases rapidly, which has signifcantly promoted the popularity of V2G [6].EVs with V2G can serve as fexible storage for smart grids, and Wei et al. [7], studying 300 EVs in three areas with two climate conditions, verifed the environmental and economic benefts of V2G.Coupling a large number of EVs with V2G into a smart grid makes full decarbonization of transportation possible [8].
With the development of science and technology, the ability to collect data and extract valuable insights from massive amounts of data has been improved [9].Various EV owners have diferent demands for EVs, and Roni et al. [10] conducted a study on EV charging in several areas in Seattle and found that the charging time of EVs in diferent regions varies.Based on power grid data, Yadav et al. [11] established an RBF-CNN-integrated model to predict short-term load and validated its results.Terefore, analyzing the behavior of EV owners is of critical importance.By analyzing the characteristics of EV owners, efective scheduling of EV charging can be achieved, which can improve the economy of the smart grid [12,13].
Classifying EV owners is an efective way to distinguish EV owners' discrepancies.Cluster analysis is a crucial classifcation method based on the correlation of data [14], which divides the data into multiple clusters according to the distance between various data points.Te K-means is the most commonly used clustering algorithm [15], and it has many advantages such as simplicity, convergence, scalability, and high efciency.Ren et al. [16] used K-means to analyze probabilistic power fow.Al-Obaidi et al. [17] used the Kmeans clustering algorithm to divide EV owners into 9 clusters based on four dimensions: time, location, charging duration, and time gap between charges.Soltani et al. [18] conducted a double-layer clustering for EV owners, and EV owners were divided into two groups based on their charging patterns in the morning and evening.Ten, each group was further divided based on whether they charge their EVs at their workplace or at home.Te classifcation of EV owners is conducive to distinguishing the characteristics among them and then scheduling their charging and V2G activities based on their respective characteristics.
Electric power load scheduling plays a crucial role in ensuring stable smart grid operation [19,20].Price-based demand response models (PBDRMs) are widely used in smart grid schedule study, and price guidance is the simplest and most efective scheduling method [21].Liu et al. [22] provided the elasticity curve of users, which refects the sensitivity of nonresponsive users to changes in prices.EV charging and V2G demand can be infuenced by price fuctuations in diferent time periods.A price elasticity matrix can be defned to refect the response of EV charging and V2G to price in each period.Te price elasticity of demand can be divided into two parts: (1) response to the price changes in this period, which is called self-elasticities, and (2) response to the price changes in the other period, which is called cross-elasticities [23].To illustrate the response of hourly demand to hourly price changes, a 24 × 24 price elasticity matrix was defned to refect the demand response (DR) to price changes in each period [24] and schedule the charging load of EV based on the price elasticity matrix [25].Te charging and V2G demand of EV owners are not only afected by the price but also by time.Lijesen [26] studied the impact of time on customers' DR and found that customers are more likely to accept schedules with minor changes in time, while they are less likely to accept schedules with signifcant changes in time, and various customers have diferent preferences for time [27].Te disorderly charging and V2G of EV will afect the reliability of the smart grid.Aalami et al. [28] established the demand response model of EV owners and calculated it for diferent power markets, efectively improving the reliability of the smart grid.Huang [29] employed a price elasticity matrix to quantify the impact of changes in electricity prices on EV charging and V2G behavior.
Te above literature review highlights the research status of related felds.Previous studies in the feld of classifcation and scheduling have made signifcant achievements.However, there is no integration of the results of these two felds when studying EV scheduling problems.Terefore, there is a need for further research to integrate classifcation and scheduling to better solve EV scheduling problems in the smart grid.
Previous studies usually used uniform prices to schedule all EV owners, but since EV owners have varied demand for EVs, they may have diferent responses to price changes.Applying the uniform pricing strategy to all EV owners may lead to some owners not responding to the schedule and not achieving the optimal scheduling efect.In contrast, a more targeted classifed scheduling based on the characteristics of EV owners can better manage the diverse EV loads, thereby efectively reducing the gap between peak and of-peak periods and increasing grid revenue.Tis paper proposes a classifed scheduling method that adjusts prices according to the characteristics of EV owners.Te main contributions are as follows: (1) To diferentiate various types of EV owners and extract their characteristics, this paper employs the K-means algorithm to classify EV owners into different types based on charging and V2G data; (2) To capture the varying responses of diferent EV owners to scheduling, this paper establishes DR models for diferent types of EV owners based on price elasticity, time preference elasticity, and time gap elasticity.By incorporating these factors, the models aim to refect the diverse behaviors of EV owners in response to price changes; (3) To demonstrate the signifcance of scheduling EV loads for the smart grid, the DR models of EV owners are incorporated into the smart grid model.Te maximization of revenue is adopted as the optimization objective, and these prices are used to guide their charging and V2G demand.
In conclusion, this paper presents an optimal scheduling strategy for EV loads.Trough the classifcation of EV owners and the implementation of dynamic pricing strategies, the study efectively addresses the diverse responses of EV owners.Moreover, the integration of DR models into the smart grid model optimizes revenue and guides charging behavior.
Te structure of the remaining paper is outlined as follows.Section 2 introduces EV data simulation and cluster analysis.Section 3 establishes the model of smart grid scheduling with EV demand response.In Section 4, a case study is conducted based on the charging data of EV users.Section 5 presents the conclusions and further work of this study.

EV Data Simulation and Cluster Analysis
2.1.EV Data Simulation.EV charging and V2G behaviors exhibit a high degree of randomness.To further investigate the scheduling of EV loads, a large amount of relevant data is required.In particular, the application of V2G is only applied in microgrids, and its scale is relatively small.Terefore, this paper uses Monte Carlo simulation to generate a substantial amount of charging and V2G data for EVs.Based on these data, a classifcation approach is applied to categorize the EVs.As per the statistical data of the 2009 National Household Travel Survey (NHTS2009) [10], the distribution function of EV driving mileage conforms to the lognormal distribution is expressed as follows: where L represents the EVs' driving distance; σ L is the standard deviation; and μ L is the mean value.EV owners do not necessarily recharge their EVs every day.Most EV owners recharge their EVs every 3-4 days.Terefore, the charging demand of EV owners is equal to the product of the driving mileage and the energy consumption per unit mileage, multiplied by the number of days between recharging.
Most EV owners charge V2G when they get home.Assuming that EV owners' get-home time is EV charging or V2G start time, according to NHTS2009 statistics, EV owners' get-home time meets the normal distribution which can be expressed as follows: where t represents the arrival time of an EV owner at home; σ t is the standard deviation; and μ t is the mean value.In this paper, it is assumed that the EV owner's arrival time at home is the starting time for charging.Tis paper assumes that the distribution functions for the V2G demand and V2G starting times of EV owners are similar, with diferences observed only in certain parameters.Te charging, V2G demand, and V2G time of each EV can be obtained through Monte Carlo simulation based on the probability distribution.
As shown in Figure 1, the distribution functions for various parameters are inputted, including EV driving mileage, home arrival time, V2G demand, and V2G time.Based on these distribution functions, the charging and V2G load as well as their corresponding time durations are extracted for each EV owner.Te charging demand of EV owners is prioritized over the V2G demand to ensure that their charging needs are met frst.During the data simulation, the charging status is recorded for each time period, with a value of 1 indicating a charging demand and 0 indicating no charging demand.V2G operations are only performed during time periods with a charging status of 0. Once the charging and V2G data for all EV owners are extracted, the results are outputted, completing the data simulation process.magnitude of the load, while the charging time determines the timing of the load.Moreover, the demand data provide insights into the behavioral patterns of EV owners, such as the intensity of EV usage inferred from the demand magnitude and the time periods of EV usage inferred from the demand time.

Classifcation of EV
EV data are multidimensional and massive.K-Means is a suitable method for classifying such data due to its ability to handle multidimensional and massive datasets.K-Means follows two principles for data classifcation: (1) minimizing the distance between points in the same cluster and (2) maximizing the distance between diferent cluster centers.It has the advantages of a simple principle and fast convergence speed.
According to the charging time and demand data of EV owners, the EV owners are divided into a clusters by K-means, with the EV owners in the 1-th cluster being the 1-th type of EV owners and the EV owners in the a-th cluster being the a-th type of EV owners.Similarly, according to V2G time and demand data of EV owners, the EV owners are divided into av clusters by K-means, with the EV owners in the av-th cluster being the av-th type of EV owners.EV charging obtains electric energy from the smart grid, while V2G releases EV's stored electric energy to the smart grid.Since the two types of data are relatively independent, the clustering of EV owners is divided into charging clusters and V2G clusters; for example, EV charging is divided into i-th type, while V2G is divided into j-th type.

Modeling of Smart Grid Scheduling with EV Demand Response
3.1.DR Model of EV Owners.EV owners' DR refers to the EV owners adjusting their electricity consumption in response to changes in electricity prices.Guiding EV loads in a reasonable method can be of great help to the smart grid.Te load demand of EV owners is mainly infuenced by two factors: time and price.Te impact of time on the load demand of EV owners can be further divided into two aspects: (1) Time preference elasticity of EV owners: diferent EV owners have diferent preferred time periods for charging and V2G.Tey are more willing to engage in charging or V2G activities during their preferred time periods.As a result, their response to price changes is more signifcant during these time periods, while it is relatively small outside of their preferred time periods.(2) Time gap elasticity of EV owners: time gap elasticity refers to the interval between price changes and the corresponding demand time periods.For example, when considering the impact of price changes at 10 o'clock on the demand at 6 o'clock, the time gap is 4 hours.Te price impact on the load demand of EV owners is refected in the fact that when prices change, consumers' demand for the product also changes accordingly, which is known as price elasticity.
Te response of a single EV owner to price guidance is difcult to refect; therefore, this paper takes a cluster of EV owners as the smallest unit for scheduling.Te total charge and V2G demand of cluster a-th and av-th EV owners in this period are equal to the sum of all EV charging demand d 0 a (t) and V2G demand d 0 av (t) of this cluster, as shown in the following equations, respectively: where d V a (t, v) is the charging demand of cluster a-th v-th EV owner and d V av (t, v) is the V2G demand of cluster a-th v-th EV owner.
Taking the cluster center to represent the characteristics of this cluster EV owners, the charging and V2G time of the cluster center can represent the charging and V2G time preference of these cluster EV owners.Te preference charging time elasticity E TL a (j) for cluster a-th EV owners at time j is stipulated as follows: where ∆t TL a (j) is the time gap between the a-th cluster center and the time of price change, and the time j may be later or earlier than time t, but the interval is within 12 hours; t a is the charging time of a-th cluster center.∆t TL a (j) is stipulated as follows: Te elasticity of preference V2G time E TL av (j) and the scheduling time gap ∆t TL av (j) are similar to charging, so the preference V2G time elasticity for cluster av-th EV owners at time j is stipulated as follows: EV owners also have diferent responses to price change times [26].Te response of demand time t to the scheduling time j is shown as follows: 4 International Transactions on Electrical Energy Systems where c and μ are two constant coefcients; ∆t is the scheduling time gap; the calculation for ∆t is similar to that of ∆t TL a (j); and it is stipulated as follows: Te response of EV owners' demand to scheduling time gap can be refected by a 24 × 24 matrix, and this matrix refects the fact that EV owners have lower responsiveness to price changes with longer scheduling time gaps, while their responsiveness to price changes is higher with shorter scheduling time gaps, and the scheduling time gap matrix is shown as follows: Te charging price elasticity E a (t, j) refects the response of EV owners to price.Te charging price elasticity of cluster a-th EV owners of the demand time t versus price change time j can be defned as follows: where ρ 0 (j) is the initial charging price at time j, which is equal to the initial electricity price, and d 0 a (t) is the initial charging demand of cluster a-th EV owners at time t.
Te load at each hour will be afected by the corresponding price variation at that hour, and the response of EV owners' charging demand to price changes throughout the day can be represented as a 24 × 24 matrix.In this matrix, each element of the matrix represents the degree of change in EV owners' charging demand in response to a price variation at a particular hour.
Te diagonal elements of this matrix are the selfelasticities that refect the response of charging demand to price change in the current period, and the of-diagonal elements are mutual elasticity that refect the response of charging demand to price change in other periods.
V2G price elasticity E av (t, j) of av-th EV owners can be defned as follows: where ρ 0 V2G (j) is the initial V2G price at time j and d 0 av (t) is the initial V2G demand of cluster av-th EV owners at time t.
Similar to the EV owners' charging price elasticity matrix, the EV owners' V2G price elasticity matrix is shown as follows:

Modeling of DR for EV Owners' Charging and V2G.
According to Section 3.1, the charging demand of EV owners will be afected by the price change, scheduling time gap, and preference time.Te DR model of cluster a-th EV owners charging can be expressed as follows: (24).
International Transactions on Electrical Energy Systems Te left side of equation ( 15) is the changing of cluster ath EV owners' charging demand, and the right side contains the price elasticity matrix, scheduling time gap elasticity matrix, and preference charging time elasticity.It can be seen that the DR model proposed in this paper not only considers the impact of price on demand but also considers the impact of price change time on demand.Te charging demand ∆d a (t) of cluster a-th EV owners in time t is expressed as follows: where ∆ρ a (j) is the change of charging a price for cluster ath EV owners at time j.
Te charging demand d a (t) of cluster a-th EV owners at time t after scheduling is equal to the initial demand added to the demand change, and it is expressed as follows: Also, the charging price ρ a (t) of cluster a-th EV owners at time t after scheduling is equal to the initial demand added to the demand change, and it is expressed as follows: Te DR model of cluster av-th EV owners V2G is similar to charging, so the V2G demand change ∆d av (t) is expressed as follows: where ∆ρ av (j) is the change of V2G price for cluster av-th EV owners at time j.Te V2G demand d av (t) of cluster av-th EV owners at time t after the schedule is expressed as follows: Also, the V2G price ρ av (j) of cluster av-th EV owners at time t after the schedule is expressed as follows: To ensure that the charging and V2G behavior of EV owners are feasible, certain parameters should be considered.First, it is necessary to ensure that the charging and V2G price fuctuations for EV owners are within a reasonable range, as shown in equations ( 22) and (23); second, in order to meet the demands of diferent types of EV owners, the charging and V2G load fuctuations of each type of EV owner should be limited, as shown in equations ( 24) and ( 25); fnally, constraints on the total EV charging and V2G load should be enforced, as shown in equations ( 26) and ( 27), respectively: where ρ min a is the lower limit of charging a price for cluster ath EV owners; ρ max a is the upper limit of charging a price for cluster a-th EV owners; ρ min av is the lower limit of V2G price for cluster av-th EV owners; and ρ max av is the upper limit of V2G price for cluster av-th EV owners.d min a (t) is the lower limit of charging demand for cluster a-th EV owners; d max a (t) is the upper limit of charging demand for cluster ath EV owners; d min av (t) is the lower limit of V2G demand for cluster av-th EV owners; and d max av (t) is the upper limit of V2G demand for cluster av-th EV owners.d min ch (t) is the lower limit of the sum of charging demand for all EV owners; d max ch (t) is the upper limit of the sum of charging demand for all EV owners; d min V2G (t) is the lower limit of the sum of V2G demand for all EV owners; and d max V2G (t) is the upper limit of the sum of V2G demand for all EV owners.

Optimization Objectives of Smart Grid Scheduling with EV Demand
Response.Tis paper adopts to maximize the revenues of smart grid, and the revenues C of smart grid are expressed as follows: where P Load (t) is the base load of the smart grid and C gen i (t) is the output cost of unit i. Te objective function can be divided into two parts: revenue and cost.Revenue includes both basic load and EV charge sales revenue, while cost includes output and V2G cost.
Te output cost of unit i consists of fuel and start-up costs.Te output cost of unit i is shown as follows: where a i , b i , and c i are three diferent coefcients of fuel cost; P i (t) is the output of unit i; U i (t) is the state variable of unit i, 1 is start, 0 is of; and S i (t) is the start-up cost of unit i.

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To ensure the stable operation of the smart grid, it is necessary to impose constraints on the generator units.Tese constraints include the output limits of the generator unit, as shown in equation (30); the load balance constraint, the sum of the generator unit output and the V2G output of EVs, equals the sum of the base load and the charging load of EVs, as shown in equation (31); the constraint on spinning reserve of generation units refers to the additional capacity provided by generation units within a certain period of time to ensure the stability operation for smart grid, as shown in equation (32); the constraint on the ramp rate of the generator unit, the output increase, and decrease of the generator unit should be within the rated range, as shown in equation (33); after starting or stopping the generator unit, it needs to meet a certain time requirement before it can start or stop again, as shown in equations ( 34) and (35).
where P min i is the minimum output of unit i, P max i is the maximum output of unit i; P Load (t) is the base load at time t; R i (t) is spinning reserve of unit i at time t; ∆P down i is the maximum output ramp-down rate for unit i; and ∆P up i is the maximum output ramp-up rate for unit i.

Numerical Studies
In this paper, IBM's CPLEX is used to fnd the optimal solution.A total of 7,000 EVs are assumed to be integrated into the IEEE 10-unit power system [30], and the generator units' data are given in Table 1.Te battery capacity of an EV is set as 100 kWh, the charging power is 6-30 kW, and the V2G power is 6-15 kW.We assumed that the basic load does not respond to electricity price changes.Te exchange rate between USD and RMB in this paper is 1 : 7.
Considering that V2G has not yet been implemented, the following Study A and Study B are included: Study A only considers the charging load of EVs, and the scheduling efects are analyzed.To demonstrate the advantages of the proposed classifcation-based scheduling method, two cases are designed, Case 1 uses the nonclassifcation method, and Case 2 uses the proposed classifcation method to schedule the charging load of EV owners.Study B considers the charging load and V2G load of EVs, the scheduling efects are simulated after the implementation of V2G, two cases are designed, Case 3 uses the nonclassifcation method to schedule the charging load and V2G load of EV owners, and Case 4 uses the proposed classifcation method to schedule the charging load and V2G load of EV owners.

Classifcation of EV Owners.
Figure 2 shows the clustering efects of EV owners' charging under diferent numbers of clusters, as illustrated in Figures 2(a)-2(d).Regardless of the number of EV owner clusters created, the charging periods for cluster centers are consistently distributed in the morning, noon, or night, fulflling the classifcation criteria.In terms of charging demand, according to the NHTS2009 statistics, the amount of EV owners with light and medium charging demand is more signifcant, so the classifcation of these EV owners should be more detailed.When the number of clusters is 4 or 6, the classifcation of charging demand is not detailed enough.However, when the number of clusters is 8 or 9, the classifcation of EV owners' charging demand is more accurate.To further compare the two, we can examine their respective silhouette coefcients.Te silhouette coefcient is used to evaluate the efectiveness of clustering.Its values range from − 1 to 1, where positive values indicate that data points within a cluster are more similar to each other than to data points in other clusters, and negative values suggest that data points might be better assigned to other clusters.A higher silhouette coefcient indicates a tighter and more efective clustering result.By comparing the silhouette coefcients at diferent numbers of clusters, we can determine the optimal number of clusters and select the best clustering result.Te vertical coordinate indicates the number of categories, and the horizontal coordinate indicates the size of the silhouette value.When number of clusters is 9, the silhouette coefcient has a lot of negative values, which indicates that many data points do not ft the cluster very well.
After comparison, it can achieve the best classifcation efect when the number of clusters is 8.According to Figure 2(c), clusters 3-th and 5-th are lightly charging EV owners, clusters 4-th, 6-th, 7-th, and 8-th are medium charging EV owners, and clusters 1-th and 2-th are heavy charging EV owners.In terms of charging time, clusters 3-th and 7-th EV owners charge in the morning, clusters 4-th and 8-th EV owners charge at the noon, and 5-th and 6-th EV owners charge at all periods.
Figure 3 shows the clustering efects of EV owners' V2G under diferent numbers of clusters, as illustrated in Figures 3(a)-3(d).In terms of V2G time, when the number of clusters is 9, the distribution of cluster centers becomes confused, and when the numbers of clusters are 8 and 6, the cluster centers are distributed in the morning, noon, or night.When the number of clusters is 4, the cluster centers are distributed in the morning and night.In terms of V2G demand, when the cluster is 6, the classifcation efect is best.
In terms of EV load, comparing the EV load before scheduling and after scheduling, the scheduling efect for EV owners is signifcant.In the frst valley period, the initial EV charging load is about 8300 kW, and the load increases to nearly 9000 kW after unclassifed scheduling and increases to nearly 10500 kW after classifed scheduling, respectively.From the frst transition period to the frst peak period, the initial EV charging load increases signifcantly from 8200 kW to 9200 kW and then stabilizes at 9000 kW, expanding the load gap of the peak between valleys.Te efect of unclassifed charge scheduling is small during this period, and the EV charging load slightly decreases at the end of the frst peak period, while the EV charging load signifcantly reduces after the classifed scheduling at the frst peak period, and the lowest point is only 7600 kW.

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Te initial EV charging load has a fuctuation in the second transition period, second peak period, and second valley period, decreasing to 8100 kW at 18:00, and stabilizing around 8700 kW at other periods.Te EV charging load increases to 9200 kW in the second transition section, then decreases to 7600 kW in the second peak period, and rapidly increases to 9000 kW in the second valley period after classifed scheduling.Te EV charging load gap between the peaks with valley efectively decreases after scheduling.Moreover, classifed scheduling is superior to unclassifed scheduling in all periods.
Te payof and load data of Study A are presented in Table 2. Te "revenue" column represents the revenue generated from selling electricity in the smart grid.Te "output cost" column represents the cost of power generation from the generator units.Te "charging load" column indicates the total load from EV charging.Te "load variance" column represents the variance of the total load in the smart grid.Te revenue of case 2 increases ¥1 × 10 5 than case 1.In terms of output cost, the output costs of the case 1 and the case 2 are close, and the output cost of case 2 is slightly lower than case 1 about ¥1 × 10 4 .Te charging load of case 1 decreases 5000 kWh compared to before scheduling.Te output costs of case 1 and case 2 are close, but the charging load of case 2 is larger, and it can be seen that the load distribution of case 2 has better economic benefts.Variance can refect the dispersion of data.Load variance refects the fuctuation of load, and the variance of case 2 is 7 × 10 7 smaller than that of case 1.When EV charging load only accounts for 2% of the base load, it shows that the classifed scheduling achieves good results in reducing the gap of the peak between valleys.
Te charging price of EV owners is shown in Figure 5, and the initial charging price is set as 0.3 ¥/kWh.According to Figure 5, case 1's range of price change is small.Te price slightly drops in the frst and second valleys and slightly rises in the frst and second peaks.In terms of case 2, the charging prices of clusters 1-th, 2-th, 3-th, and 7-th have signifcant fuctuation in a day, while the charging prices of clusters 4th, 5-th, 6-th, and 8-th fuctuate slightly.Te charging prices of clusters 1-th and 2-th EV owners sharply rise before 13:00, especially at 11:00 and 12:00, the charging price of cluster 2th EV owners closes to the upper limit of 0.6 ¥/kWh, and the charging price of cluster 1-th EV owners drops sharply to the lower limit of 0.2 ¥/kWh after 15:00.Te charging price of cluster 2-th EV owners drops sharply at 13:00 and drops sharply to the lower limit of 0.2 ¥/kWh after 14:00.Te charging prices of the clusters 3-th and 7-th EV owners drop sharply almost to the lower limit before 12:00.After 14:00, the charging price of these two clusters rises signifcantly, especially the charging price of the cluster 3-th EV owners rises to 0.58 ¥/kWh at 17:00, and the charging price of the cluster 7-th EV owners rises to 0.51 ¥/kWh at 20:00.Te charging price of cluster 4-th EV owners rises to 0.35 ¥/kWh from 10:00 to 14:00 and drops to 0.23 ¥/kWh.Te charging price of cluster 5-th EV owners drops slightly from 05:00 to 09:00 and rises after 12:00, and the price peak is at 20:00.Te charging price of cluster 6-th EV owners rises from 5:00 to 9: 00 and gets the highest point 0.36 ¥/kWh at 12:00.Te charging price of cluster 8-th EV owners drops all the time.International Transactions on Electrical Energy Systems Two trends can be seen from the charging prices of various EV owners: (1) the price increases during the period that the load of these EV owners is concentrated, and the price reduces during the period that the load of these EV owners is less; (2) the price will increase in peak periods and will reduce in valley periods.Figure 6 shows the load changes of various EV owners after scheduling where Figure 6(a) is the EV charging load stack diagram after unclassifed scheduling and Figure 6(b) is the EV charging load stack diagram of case 2. It can be seen in Figure 6(a) that the loads of clusters 1-th, 2-th, 3-th, 4-th, and 7-th EV owners are concentrated in a certain period, while the loads of clusters 5-th, 6-th, and 8-th EV owners are widely distributed in all periods.Te loads of clusters 1-th, 2th, and 4-th EV owners are mainly concentrated in the frst valley period, the frst transition period, and the frst peak period.It can be observed that the load periods of diferent types of EV owners remain almost unchanged, indicating the insufcient scheduling capability of unclassifed scheduling.After classifed scheduling, the loads of clusters 1-th, 2-th, and 4-th EV owners have more than 10% increase in the frst valley and about 10% decrease in the frst peak.Te loads of clusters 3-th and 7-th EV owners transfer some loads to the frst valley period, frst transition section, and frst peak period.Cluster 3-th EV owners transfer 1000 kW load to the frst valley period and 1200 kW load to the frst peak period.
Cluster 4-th EV owners transfer 1200 kW load to the frst valley period and 400 kW load to the frst peak period.Te loads of clusters 5-th, 6-th, and 8-th EV owners transfer from two peak periods to two valley periods.
By considering the price and load variations of diferent types of EV owners, it can be observed that unclassifed scheduling has a limited range of price changes due to the need for the responses of various types of EV owners.On the other hand, classifed scheduling only needs to consider the response of a specifc type of EV owner, allowing for larger price variations.As a result, unclassifed scheduling exhibits weaker scheduling capability because it lacks the ability to efectively guide diferent types of EV owners in shifting their loads to other time periods.Electric energy fows from the electric grid to EVs during EV charging.Terefore, guiding EV owners to increase charging during valley periods and decrease charging during peak periods is very useful for reducing the gap between peak and valley periods.
As shown in Figure 7, the charging scheduling efect of case 3 is poor, and the charging load decreases to 7700 kW in the frst valley period and increases to 10000 kW in the frst peak period.Te gap between peak and valley periods will aggravate after unclassifed scheduling while case 4 has a good scheduling efect on the charging load.Te load increases during the frst valley period, reaching a peak of around 10500 kW, and then decreases to 7500 kW during the frst and second peak periods.It then increases again to 9500 kW during the second valley period.
Electric energy fows from the EVs to the electric grid during EV V2G, so guiding EV owners to decrease V2G in the valley periods and increase V2G in the peak periods is very useful to reduce the gap between peaks with valley periods.In the frst valley period, the V2G decreases to 3600 kW after classifed scheduling.In terms of case 3, the V2G increases to 7000 kW in the frst transition period and decreases to 4500 kW in the second transition period.In contrast, the V2G fuctuation of case 4 is smoother.
Table 3 displays the payof and load data from Study B, wherein V2G load represents the total load of EVs V2G.Te revenue for Case 4 has improved by about ¥1.1 × 10 6 compared to Case 3.Meanwhile, the output cost of Case 4 is ¥1 × 10 5 less than Case 3. From Study B, it can be deduced that the disparities in both revenue and output cost between Case 3 and Case 4 are more pronounced than those in Study A. While the charging and V2G load for Case 3 are lower    International Transactions on Electrical Energy Systems the above observations, it can be concluded that after classifed scheduling, the distribution of EV charging load and V2G load becomes more reasonable, leading to a reduction of generation costs and an increase in the smart grid revenue.
As shown in Figure 8(a), the charging price of case 3 in valley periods rises by 0.02-0.05¥/kWh, and it leads to anincrease in the peak valley diference of EV charging load.
As shown in Figure 8(b), the V2G price of case 3 drops by 0.04 to 0.07 ¥/kWh in the frst and second valley periods and rises by 0.01 to 0.03 ¥/kWh in the frst and second peak periods.After unclassifed scheduling, the distribution of V2G is close to the basic load.Te V2G price change range of case 4 is − 0.1-0.16¥/kWh.Te V2G price of clusters 1-th and 4-th EV owners decreases to the lower limit of 0.3¥/kWh during the frst valley period, and the V2G price of clusters 5th and 6-th EV owners decreases to the lower limit too in the second peak period.By comparing case 3 and case 4, it can be seen that classifed scheduling has more signifcant potential in scheduling.
Figure 9 shows the charging and V2G load changes of various EV owners after scheduling where Figure 9(a) is the charging and V2G load stack diagram after unclassifed scheduling and Figure 9(b) is the EV charging and V2G load stack diagrams after the classifed schedule, respectively.It can be seen from Figure 9(a) that the clusters 1-th and 3-th EV owners' V2G are mainly distributed in the frst and second peak periods, the V2G of clusters 2-th and 6-th EV owners is mainly distributed in the frst and second valley periods, the V2G of cluster 4-th EV owners is mainly distributed in the frst valley period and the frst peak period, and the V2G of cluster 5-th EV owners is mainly distributed in the frst and second valley periods and the second peak period.As shown in Figure 9(b), after the classifed schedule, during the frst valley period, the V2G of cluster 2-th EV owners decreases to 1390 kW, accounting for about 20% of the initial V2G.During the frst peak period, the V2G of cluster 2-th EV owners increased by 2479 kW, the V2G of cluster 4-th EV owners increased by 565 kW, the V2G of cluster 5-th EV owners increased by 993 kW, and the V2G of cluster 6-th EV owners increases by 3394 kW.During the second peak period, the V2G of the clusters 2-th and 4-th EV owners increased, including 2155 kW of cluster 2-th EV owners and 957 kW of cluster 4-th EV owners.During the second valley period, the V2G of clusters 5-th and 6-th EV owners decreased, including 925 kW of clusters 5-th EV owners and 3157 kW of clusters 6-th EV owners.
From the above data, it can be seen that classifed scheduling allows for more targeted pricing strategies based on the characteristics of diferent EV owners, thereby   International Transactions on Electrical Energy Systems improving its ability to schedule EV loads.As a result, the distribution of EV charging load and V2G load becomes more reasonable.Tis more rational distribution of EV charging load and V2G load helps to reduce generation costs and increase the revenue of the smart grid.Te advantages of classifed scheduling are evident in various aspects, showcasing its benefts in multiple aspects.

Conclusion
Tis paper addresses the issue of insufcient scheduling capability of existing unclassifed EV load scheduling methods by proposing a method for classifying EV load scheduling based on the characteristics of EV owners.To better refect the response of diferent types of EV owners to scheduling, this paper expands upon the traditional price elasticity model by incorporating time preference time elasticity and time gap elasticity, comprehensively capturing the diverse responses of diferent EV owners to scheduling.Trough comparative analysis of relevant data, this paper achieves the following improvements compared to previous studies: With the increasing interaction between EVs and the smart grid, the advantages of classifed scheduling over unclassifed scheduling are also enhanced.
In addition, future work could further explore the following two aspects: (1) Te load characteristics of some EV owners may change, and it is necessary to further consider the transitions between diferent types of EV owners.(2) Since V2G is still in the theoretical research stage and lacks real-world data on EV charging and V2G load after V2G implementation, future research based on real data can further explore the usage characteristics of EV owners.
the 6 clusters, clusters 2-th, 3-th, and 5-th are light V2G EV owners, and clusters 1-th, 4-th, and 6-th are heavily V2G EV owners.In terms of V2G time, clusters 3-th and 4-th are EV owners V2G in the morning, clusters 2-th and 6-th are EV owners V2G at the noon, and clusters 1-th and 5-th are EV owners V2G at the night.

Figure 4 :
Figure 4: Base load and EV load.Te bar plot represents the basic load, and the point plot represents the EV charging load.

4. 3 .
Study B: EV Charging and V2G Scheduling.Study B considers EV charging and V2G, and it is divided into case 3 and case 4: case 3: unclassifed scheduling for EV charge and V2G; case 4: classifed scheduling for EV charge and V2G.

Figure 5 :
Figure 5: Charging price of EV owners.Te initial charging price is set as 0.3 ¥/kWh.Te curves in diferent colors are the charging prices of diferent EV owners.

Figure 6 :Figure 7 :
Figure 6: Stacking diagram of charging loads of EV owners.(a) Te charging load stack diagram after unclassifed scheduling.(b) Te charging load stack diagram after classifed scheduling.

Figure 8 :
Figure 8: Charging and V2G price of EV owners.Te initial charging price is set as 0.3 ¥/kWh, and the initial V2G price is set as 0.4 ¥/kWh.(a) Te charging price of EV owners.(b) Te V2G price of EV owners.

( 1 )
Expanded the boundaries of the traditional model: Tis paper extends the traditional EV owner DR model by considering the diferent responses of EV owners to time and price.(2) Proposed an improved scheduling method tailored for EV loads: Te proposed classifed scheduling method in this paper demonstrates stronger scheduling capability for EV loads compared to traditional unclassifed scheduling methods (demonstrated in Section 4.2).With EV load accounting for only 2%, there was an increase of 0.25% in revenue of the smart grid.Te classifed scheduling method formulates more targeted prices based on the characteristics of diferent types of EV owners, signifcantly improving the scheduling capability during preferred time periods and expanding the range of adjustable time.(3) By comparing Study A & Study B in Section 4, this paper showcases the stronger potential application of classifed scheduling after the implementation of V2G.

Figure 9 :
Figure 9: Stacking diagram of charging and V2G loads of EV owners.(a) Te charging and V2G load stack diagram after unclassifed scheduling.(b) Te charging and V2G load stack diagram after classifed scheduling.

Table 1 :
IEEE 10-unit parameter.Tis paper uses Monte Carlo simulation to simulate the charging load of 7000 EVs, accounting for about 2% of the base load.Te basic load and EV charging load are shown in Figure 4.2.Study A: EV Charging Schedule.Study A only considersEV charging, and it is divided into case 1 and case 2. (1) Case 1: unclassifed scheduling for EV charging; (2) case 2: classifed scheduling for EV charging.

Table 2 :
Payof and load data of Study A.
than those of Case 4, the output cost of Case 3 is higher than that of Case 4. Tis underscores the advantage of classifed scheduling in economic benefts.Additionally, the load variance in Case 4 is approximately 1% less than that in Case 3, indicating that classifed scheduling has advantages in narrowing the gap between peak and valley periods.From

Table 3 :
Payof and load data of Study B.