1. Introduction Reference [ 5] identified six operational charging patterns for electric taxis using high-dimensional clustering. Reference [ 1] constructed user profiles in a campus setting by integrating fuzzy C-means clustering with feature aggregation. Reference [ 6] modeled group demand using a combination of Gaussian mixture models and K-means clustering. Reference [ 7] applied clustering techniques on millions of charging sessions to identify temporal load patterns and generate group-level charging profiles. Reference [ 8] developed a real-time, role-aware behavior model using 5G system data, capturing dynamic differences across user categories such as private cars and ride-hailing vehicles. Reference [ 4] proposed an explainable machine learning framework that accurately forecasts plugged-in status and power demand at charging stations, achieving an F1 score of 0.97. Although various electric vehicle charging behavior response models have been proposed in previous studies, most of them consider only a single dimension (e.g., price or time-of-day) and mainly focus on aggregate-level modeling. The novelty of this study lies in the following three aspects [ 9, 10]: (1) We construct a three-variable response function model that simultaneously incorporates price sensitivity (α), time-of-day preference (β), and weekend preference (γ), which represents an important extension beyond existing single- or two-variable models. (2) We propose a comprehensive framework of individual-level parameter estimation combined with unsupervised clustering. Personalized behavioral parameters are extracted for each user using nonlinear least squares (NLS), followed by K-means clustering on the parameter vector (Q 0, α, β, γ) to identify five interpretable behavioral patterns. (3) We provide rigorous quantitative validation through benchmark comparisons and performance metrics (RMSE, MAPE, R 2), demonstrating the superiority of the proposed model in both predictive accuracy and behavioral interpretability. These contributions offer valuable theoretical support and methodological tools for charging operators to implement differentiated pricing and precise resource allocation. 2. Construction of User Response Function Model 2.1. Data Description and Processing Data were obtained from a public charging station platform in Guangdong, including order ID, user ID, start time, electricity volume, and cost. After cleaning, the variables p (unit price), h (start hour), ω (weekend indicator), and q (charging volume) were derived. The function f(h) was produced by normalizing the timestamp. Details are provided in the experimental section [ 11]. The electric vehicles involved are primarily private passenger battery electric vehicles (BEVs), with battery capacities mainly ranging from 30 to 80 kWh, and the most common range being 40–60 kWh (corresponding to mainstream compact and mid-size EVs from BYD, Tesla, and local brands in the Chinese market). After data cleaning, the charging volume q per session is predominantly concentrated between 10 and 50 kWh, consistent with partial to full charging cycles for these battery sizes. The public charging stations consist of 7 kW AC slow chargers and 60–150 kW DC fast chargers (commonly 120 kW). This mixed charging infrastructure significantly influences charging duration and time-of-day preferences, as users of fast chargers tend to complete sessions during convenient daytime periods. 2.2. Basic Structure of the Price Response Function The user’s willingness to charge decreases with increasing prices, and the model employs an exponential response function [ 12]. q ( p ) = Q 0 ⋅ e − α ( p − 1 ) (1) Here, q(p) represents the expected charging quantity at the unit electricity price p, Q0 is the benchmark charging quantity, and α is the user’s price sensitivity coefficient. 2.3. Incorporation of Time-of-Day Preference Factor Among them, β > 0 indicates a preference for charging during high-demand periods f(h), while β < 0 indicates a preference for off-peak or atypical periods. Based on three months of actual order data, the 24 h charging power variation curve for each day over the three months was plotted, along with its average normalized period preference function f(h) as shown in Figure 1. Figure 1 shows that 06:00–08:00, 12:00, and 19:00–21:00 are the three peak periods. Since the valley-price period typically begins after midnight, users can charge their vehicles at a lower electricity cost during this period. As a result, a considerable number of users tend to initiate charging sessions around 00:00, leading to an increase in both charging frequency and aggregated charging demand. The piecewise function f(h) is obtained by fitting the average normalized period preference curve of all users, as shown in Equation (3). f ( h ) = 0.97 − 0.1767 h , 0 ≤ h ≤ 3 0.2 sin π ( h − 3 ) 9 + 0.44 , 3 ≤ h ≤ 12 0.12 sin π ( h − 12 ) 7 + 0.44 , 12 ≤ h ≤ 19 0.44 − 0.115 ( h − 19 ) , 19 ≤ h ≤ 23 (3) The function declines in the early morning (0–3 a.m.), peaks between 6 and 8 a.m., gradually rises from 12 to 19 p.m., and fluctuates during 19–23 p.m. Its shape aligns well with users’ actual charging curves, indicating strong representational capacity for charging behavior. It should be noted that the f(h) function was fitted from three months of real charging-order data from a public charging platform in Guangdong Province. Its shape strongly depends on local EV usage patterns and charging infrastructure conditions, and therefore needs recalibration for different regions and charging environments. 2.4. Behavioral Differences on Weekends To account for users’ preference for slow charging or concentrated recharging on weekends, a weekend indicator variable ω is introduced, and a three-variable response model is constructed as shown in Equation (4). q ( p , h , ω ) = Q 0 ⋅ e − α ( p − 1 ) ⋅ ( 1 + β f ( h ) + γ ω ) (4) Here, w = 1 indicates the weekend, w = 0 indicates a working day, and γ represents the user’s preference coefficient for weekends, with a value of γ approaching 1 indicating a stronger preference for charging on weekends [ 16]. 2.5. Parameter Value Range In order to enhance the interpretability and numerical stability of the model, this article combines the results of batch fitting for actual orders, setting the empirical value ranges for each parameter as follows. Q0 ∈ [10, 80] (unit: kWh) represents the average charging amount for users, with values outside the range typically indicating abnormal or special users; α ∈ [0, 5]: to avoid excessive sensitivity to prices, in line with economic implications; β ∈ [−1, 1]: to prevent extreme values in the time response function; γ ∈ [−1, 1]: balancing the model’s expressive capability with real behavior, with most users concentrated in [−0.5, 0.5] and a minority exhibiting extreme preferences around ±1. The above range is based on empirical estimates; although it is not a rigid constraint, it can provide a useful prior for subsequent clustering and optimization, preventing model distortion. 3. Parameter Extraction and Classification Method 3.1. User Parameter Extraction Method In order to achieve the personalized construction of user behavior modeling, this article fits parameters individually for each user based on the response function structural formula (4), extracting individual behavioral characteristics as shown in Equation (5). θ i = [ Q 0 i , α i , β i , γ i ] (5) Using nonlinear least squares (NLS), the fitting is done by minimizing the sum of the squares of the residuals between the predicted and actual power as shown in Equation (6) [ 17]. m i n θ i = ∑ j = 1 n i [ q i j o b s − q i ( p j , h j , w j ) ] 2 (6) Here, ni represents the historical order quantity of user i, q ijobs represents the time charging quantity of the j-th order of that user, and (p j, h j, w j) correspond to the electricity price, time period, and weekend identifier of the respective order. This paper introduces the root mean square error (RMSE) to measure the accuracy of the predictive function (p, h, ω) in fitting the actual charging behavior qi, with the calculation formula being given in Equation (7). R M S E = 1 n ∑ i = 1 n ( q i − q ^ i ) 2 (7) Among them, n is the number of users, qi is the actual response value of the i-th user, and q i is the predicted value of the i-th user. The fitting process involves preprocessing user orders to retain valid records (p, h, w, q) and remove anomalies, computing f(h) for each order and substituting it into the response model. The LM algorithm iteratively minimizes residuals to estimate optimal parameters with balanced convergence and robustness. Parameters beyond empirical limits are boundary-corrected, and samples above the RMSE threshold are discarded to improve fitting quality. 3.2. Construction and Normalization of Response Features The fitted parameters θ i reflect the user’s baseline charging demand (Q0), price sensitivity (α), time preference (β), and weekend charging tendency (γ). To eliminate the dimensional differences affecting clustering, this paper performed Z-score normalization on all features. 3.3. User Clustering Method This article uses the K-means algorithm to cluster model the user behavior parameter vector (Q0, α, β, γ), and evaluates the effects of different cluster numbers k using the Calinski–Harabasz index, with results shown in Figure 2 [ 18]. When k = 5, the Calinski–Harabasz index reaches its maximum value, indicating optimal classification performance. Therefore, this paper adopts k = 5 as the final number of user classifications and outputs the category label for each user [ 19]. 3.4. Interpretation of Classification Results Each clustering category represents user groups that are similar in behavioral response characteristics. Section three will conduct a visual analysis combining typical parameter distributions, response curves, and weekend preferences, and assign behavioral labels such as ‘frequent commuter type’, ‘night preference type’, and ‘price-sensitive type’. 4. Fitting of User Response Features and Analysis of Behavioral Patterns 4.1. Analysis of the Overall Distribution of Response Parameters This study employs the three-variable response function q(p,h,w) to model user behavior, estimating Q0, α, β, and γ via nonlinear least squares. Model accuracy is evaluated by RMSE, while visual analysis clarifies parameter effects on charging behavior ( Figure 3). Figure 3 shows that Q0 is mostly concentrated between 10 and 50 kWh, with individual users reaching up to 80 kWh, reflecting the differences in base load; α is predominantly distributed between 0 and 3, indicating that most users are sensitive to prices, with some values truncated at the upper limit of 5. The time preference coefficient β ∈ [−1, 1] has some users clustered around β = 1, possibly influenced by boundary effects. To further verify the time preference characteristics, this paper statistically analyses the peak charging periods of users, with results shown in Figure 4. Figure 4 shows that most users charge during late night (0–6 am), midday (12–2 pm), and evening (6–10 pm), consistent with β estimates. The bimodal β distribution around −1 and +1 indicates preferences for off-peak versus high-demand periods. This confirms the empirical validity of the model’s time preference mechanism and highlights significant heterogeneity in users’ time selection. In addition, the γ parameter approximates a normal distribution, centered around 0, with some users showing a marked preference for weekends. The RMSE is predominantly distributed between 5 and 15 kWh, indicating that the model’s predictive performance is relatively good. 4.2. Parameter Correlation Analysis In order to explore the cooperative or mutually exclusive relationships between various parameters, this paper conducted a pairwise parameter correlation heatmap analysis of the fitted α, β, γ, and Q0, with the results shown in Figure 5 [ 20]. Figure 5 shows that the overall correlation between parameters is relatively weak, possessing independent modeling value. To further verify the independence of clustering variables and explore potential behavioral relationships, this paper presents Figure 6, which displays scatter plots of α against β and γ, β against γ, and Q0 against γ, intuitively illustrating the correlation trends among the variables. Figure 6 shows scatter plots with linear or LOWESS fitting of α, β, γ, and Q0, with shading denoting the 95% confidence interval. The results indicate α and β are weakly positively correlated, implying price-sensitive users often display strong time concentration. A slight negative slope for α ∈ [0, 0.7] reflects rigid-demand users with dispersed times. α and γ are nearly flat but slightly rising, suggesting price-sensitive users retain adjustment potential on weekends. β and γ exhibit a mild positive correlation, indicating limited weekend timing differences. Q0 and γ show a slight negative correlation, implying high-load users behave stably on weekends while low-load users fluctuate more. Overall, the variables show no strong dependence, supporting their treatment as independent dimensions for behavioral profiling and clustering. To explore the relationship between model fitting error and the sensitivity of benchmark electricity quantity to price, this paper presents a scatter plot of α, Q0, and RMSE, as shown in Figure 7. Figure 7 shows pairwise relationships among α, Q0, and RMSE. Overall, α and RMSE are weakly correlated, but error fluctuations increase near α ≈ 0 or 5, implying reduced stability under extreme price responses. α and Q0 exhibit a clear negative correlation, suggesting price-sensitive users have lower base loads and necessity-driven users weaker elasticity. Q0 positively correlates with RMSE, indicating high-load users display more complex behavior and higher fitting errors. Thus, strong price sensitivity → lower load → more stable fitting. These findings provide a basis for subsequent clustering and strategy evaluation. 4.3. Analysis of the Three-Variable Relationship in the Response Function To examine the moderating effects of α, β, and γ on the response function q, we fix Q0 = 40, p = 1.2, f(h) = 0.7, and w = 0 (working day), compute q for all users, and plot parameter–q curves ( Figure 8). Despite fixed p, α reflects user price sensitivity: larger α implies greater demand reduction at the same price. In Figure 8, the red, blue, and green lines represent the relationships between q and α, β, and γ, respectively, allowing a direct comparison of the effects of price sensitivity, time preference, and weekend preference on charging demand. α is negatively correlated with q, indicating higher price sensitivity reduces demand. β shows a weak positive correlation, with stronger time preferences yielding slightly higher responses. γ is negatively correlated, suggesting stronger weekend preferences weaken price responsiveness. Overall, price sensitivity, time preference, and weekend behavior exert distinct moderating effects on charging demand. To intuitively reveal the interactive effects of price sensitivity and time period preference on charging response quantity, this paper simulates the two-dimensional distribution surface of q as α and β vary based on the response function, with the results shown in Figure 9. In Figure 9, the horizontal axis denotes α (price sensitivity), the vertical axis β (time preference), and color the simulated response power q. A clear trend of “high upper left, low lower right” is observed: lighter colors indicate larger q. The results show q decreases markedly with increasing α, confirming price sensitivity suppresses demand, whereas q rises with β, implying users with stronger time preferences respond more positively during specific periods. These findings validate the independent moderating roles of α and β. The following article presents a three-dimensional scatter plot of q as it varies with α, β, and γ ( Figure 10), comprehensively illustrating the joint regulatory effects of the three parameters on q. Figure 10 simulates the 3D relationship between response q and parameters α, β, and γ (weekend preference). The axes correspond to α, β, and γ, while color denotes q, with lighter colors indicating stronger responses. Overall, q decreases markedly as α rises, whereas β and γ show slight increases, confirming α’s dominant suppressive effect and the weaker positive roles of β and γ. These results validate the joint regulatory influence of the three parameters on charging behavior. 4.4. Behavioral Characterization of Clustered User Types To further characterize differences in user response behavior, K-means clustering divided users into five categories. PCA reduced the four response parameters (Q0, α, β, γ) to two dimensions for visualization ( Figure 11). Color-coded labels illustrate the distribution of different user types in feature space. In Figure 11, different colors represent five categories of users: Type 1 (Commuting-Dominant), Type 2 (elastic energy-saving), Type 3 (Weekend-Switching), Type 4 (Night-Preferential), and Type 5 (discount-sensitive). In the PCA space, each user category forms relatively separate clusters, with high-frequency commuters and weekend flexible switchers being concentrated, while night preference users show greater internal heterogeneity. This indicates that the method is effective in extracting and distinguishing user behavioral characteristics, supporting the validity of the clustering modeling approach. After completing the classification of the five types of users, this article calculates the proportion of each type of user and their mean values across the four dimensions of Q0, α, β, and γ ( Table 1) to reflect the behavioral parameter differences among the various types of users. Table 1 presents user type proportions and mean parameter values. Most users show price-driven or elastic behaviors, with discount-sensitive users dominant and night-preference users few. Behavioral parameters differ markedly: high-frequency commuters exhibit the highest Q0 and lower α, focusing on fixed weekday slots; elastic energy-saving users have low Q0 with high price and time sensitivity; weekend switchers shift behavior across weekdays and weekends; night-preference users display the lowest Q0 but high α and β, concentrating on late-night low-price charging; and discount-sensitive users charge during discounts, showing strong elasticity. This classification highlights distinct patterns in demand, price response, temporal choice, and weekend behavior. In order to clarify the distribution of time preferences for different types of users, we calculated the proportion of each user category and the charging frequency during each hour, normalized the data, and fitted a curve using cubic spline interpolation, with the results shown in Figure 12. Figure 12 depicts hourly charging patterns (0–23 h) with normalized frequency, colored by user type. Type 1 shows pronounced morning and evening peaks (7–9, 18–20 h). Type 2 charges frequently at 23:00 and prefers off-peak hours, exploiting price flexibility. Type 3 exhibits evening peaks and dual day–night preference with high elasticity. Type 4 concentrates on 0–6 h, peaking at midnight, reflecting low-price sensitivity and delayed charging. Type 5 displays dispersed behavior with secondary peaks at night and late afternoon, aligned with discount periods [ 21]. To analyze the parameter distribution characteristics of each user type, we employed the Kernel Density Estimation (KDE) method to plot the probability density curves for each parameter of every user type, which ‘smooths’ the distribution and extends into areas beyond the actual data, as shown in Figure 13. Figure 13 presents parameter distributions with normalized density by user type. For Q0, high-frequency commuters show the widest right-shifted span, reflecting high demand; night-preference users cluster at 5–10 kWh, while others lie mid-range. In α, commuters cluster near 0 (price-insensitive); night-preference users show higher values; elastic and discount-sensitive users respond moderately via timing or discounts; weekend-switchers remain centered. β is negative for commuters and night-preference types, indicating peak avoidance, but positive for elastic and discount-sensitive users, showing responsiveness to timing; weekend-switchers exhibit flat distributions. γ concentrates near 0 for commuters and night-preference users, while elastic users display bimodality, and discount-sensitive users skew right, reflecting weekend activity. Weekend-switchers are expected to polarize, but limited weekend orders yield values around 0. Figure 14 further validates their weekday–weekend behavior. Figure 14 illustrates weekday and weekend charging for switching users: the blue bars denote order counts and the orange line indicates average energy. Users placed 1762 weekday orders (24.33 kWh each) and 661 weekend orders (25.86 kWh each). Although weekend volume is lower, the higher per-order demand highlights distinct behavioral shifts, validating γ in capturing weekday–weekend differences. Figure 13 illustrates user distributions across key response parameters, and, together with clustering results, corroborates the validity of user type division. 4.5. Model Validation and Parameter Interpretability Analysis 4.5.1. Verification of Trend Consistency To assess model discrimination on new samples, we analyzed average charging amounts qfor different user types using doubled simulated data, as shown in Figure 15. Figure 15 shows distinct mean q differences across user types: high-frequency commuters have the highest values, while night-preference and energy-saving users are lowest. This pattern aligns with the original sample, confirming the model’s discriminatory power and generalizability to large-scale unseen data. In order to verify the distribution of different types of simulation parameters, statistical analysis of the parameter distribution for the expanded data was conducted, as shown in Figure 16. The simulated data follow similar parameter trends to real data: commuters show high Q0/low α, while night-preference users exhibit high α/low Q0, with type-specific β and γ. Yet, simulated distributions are more concentrated and idealized, lacking real data’s variability. Thus, simulation aids model validation, whereas real data better captures behavioral complexity. 4.5.2. Validation of Parameter Adjustment Mechanism To assess parameter explanatory power, scenario-based conditions are set and user response changes fitted to parameter values. Specifically, price is raised from p = 1.0 to 1.4, and the response change Δq is analyzed against α, as shown in Figure 17. Figure 17 illustrates the relationship between the price sensitivity parameter α and the charging response change Δq = q(1.4) − q(1.0) under a fixed price increment Δp = 0.4. The blue line represents the fitted trend of the simulated data. Simulation points show a clear negative trend: higher α values correspond to larger demand reductions when prices rise, indicating stronger responsiveness and confirming α’s explanatory power for dynamic price fluctuations. To validate the effect of the time preference coefficient β, with electricity price fixed at p = 1.2 and ω = 0 (weekdays), only the starting charging time h is varied. It shifts from the user’s historical preference hpast to 14:00, and the response variation Δq is analyzed against β ( Figure 18). Figure 18 demonstrates the relationship between the change in simulated response power Δq and the user time preference parameter β when all users’ charging starting periods are adjusted from their historical peak h_past to 14:00 (h = 14). The red line represents the fitted trendline of the simulated data. The overall trendline shows a slight positive slope, indicating that users with a larger β experience a slightly greater decline in charging amount |Δq| after the time adjustment, which is consistent with the model’s design of β positively regulating time sensitivity. In order to verify the impact of the weekend preference coefficient γ on user charging behavior, we fixed the electricity price p = 1.2 and the initial charging period h = h_past, only varying the weekend indicator variable ω (i.e., changing from weekdays to weekends or from weekends to weekdays). We calculated the variation in charging response Δq for each user between weekends and weekdays, and performed a fitting analysis with the corresponding γ values as shown in Figure 19. Figure 19 illustrates the relationship between the difference in charging response amount Δq on workdays (w = 0) and weekends (w = 1) and the user’s weekend preference parameter γ. The orange line represents the fitted trendline of the simulated data. The overall trend indicates that as γ increases, the absolute value of Δq increases, suggesting that γ effectively characterizes the differences in charging behavior between weekends and workdays in the model, thereby validating γ’s explanatory power regarding the differences in behavior based on day type. 4.5.3. Validation of Parameter Interpretability Through Representative Users As shown in Figure 20a, the charging quantity of the high-price-sensitive user decreases noticeably as the electricity price increases, indicating a strong response to price signals. In contrast, the low-price-sensitive user shown in Figure 20b maintains a relatively stable charging quantity despite variations in electricity prices. These observations are consistent with the estimated α values. Figure 20c,d further illustrate the influence of the time preference parameter β. Users with large positive or negative β values exhibit clear charging preferences toward specific time periods. For all representative users, the predicted charging quantities closely follow the observed charging patterns, demonstrating that the estimated parameters can effectively capture heterogeneous charging behaviors across different user types. 4.6. Quantitative Validation and Benchmark Comparison To quantitatively evaluate the effectiveness of the proposed three-variable response function model, this study designs the following benchmark comparison experiments: (1) Price-only model: Considers only the price factor, simplified as q(p) = Q 0 × e^(−alpha·(p − 1)) (setting β = 0, γ = 0); (2) Time-only model: Considers only the time-of-day preference, simplified as q(h) = Q 0 × (1 + β × f(h)) (setting α = 0, γ = 0, with p = 1); (3) Traditional K-means baseline: Directly applies K-means clustering to user statistical features (mean charging volume, temporal distribution, weekend ratio, etc.). All the models use the same dataset split (80% training set and 20% test set, divided chronologically). The evaluation metrics include RMSE, MAPE, and R 2. The predictive performance was assessed using three metrics: root mean square error (RMSE, already defined in Equation (7)), Mean Absolute Percentage Error (MAPE), and the coefficient of determination (R 2). MAPE and R 2 are defined as follows: MAPE = 100 n ∑ i = 1 n q i − q ^ i q i (8) R 2 = 1 − ∑ i = 1 n q i − q ^ i 2 ∑ i = 1 n q i − q ପ୍ତ 2 (9) The results are shown in Table 2. As shown in Table 2, the proposed model achieves a reduction of approximately 27.8% in the RMSE test, 26.1% in the MAPE test, and an improvement of 14.3% in the R 2 test compared to the best baseline model. These results quantitatively demonstrate that jointly modeling price, time-of-day, and weekend preferences significantly enhances both predictive accuracy and generalization capability. 5. Conclusions This paper proposes a three-variable charging response framework for electric vehicle (EV) user behavior modeling and classification. By jointly considering electricity price, time-of-day preference, and weekend preference, the proposed model provides a unified description of heterogeneous charging behaviors and enables interpretable characterization of individual user preferences. Using real charging-order data, four behavioral parameters—baseline charging demand (Q 0), price sensitivity (α), time preference (β), and weekend preference (γ)—are estimated via nonlinear least squares. The results reveal significant user heterogeneity in charging demand, temporal preference, and price responsiveness. Based on these estimated parameters, K-means clustering identifies five representative user categories (Commuting-Dominant, elastic energy-saving, Weekend-Switching, Night-Preferential, and discount-sensitive), revealing distinct charging preferences and behavioral characteristics across different user groups. Furthermore, parameter validation confirms that the estimated parameters possess clear behavioral meanings and effectively explain variations in user charging responses. Benchmark comparisons demonstrate that the proposed framework outperforms conventional methods in predictive performance, achieving a 28% reduction in the RMSE test, a 26% reduction in the MAPE test, and a 14% improvement in the R 2 test compared with the strongest baseline model. From a practical perspective, the identified charging preferences reveal that many EV users tend to concentrate charging activities during specific periods, particularly during evening hours and low-price periods. While such behavior may reduce charging costs and improve user convenience, it can also lead to charging station congestion, increased waiting times, uneven infrastructure utilization, and potential stress on local distribution networks. Therefore, the proposed framework can provide valuable support for charging demand forecasting, differentiated pricing strategies, demand-side management, and long-term charging infrastructure planning. By enabling a better understanding of heterogeneous user behaviors, the model offers a useful decision-support tool for charging network operators and energy management systems. Several limitations remain in the current study. The proposed model primarily considers electricity price, time-of-day preference, and weekend effects, while other potentially influential factors, such as weather conditions, travel purposes, battery state-of-charge, charging station characteristics, distribution grid capacity constraints, charging station power limits, and vehicle-to-grid (V2G) interactions, are not explicitly incorporated. In addition, only conventional benchmark models are considered in the comparative analysis. Future research will focus on integrating user behavior prediction with dynamic pricing mechanisms, charging reservation systems, and load-balancing control strategies, while incorporating richer behavioral features and advanced machine learning approaches. Future studies will also investigate nonlinear behavioral response formulations, time-varying behavioral parameters, and adaptive learning mechanisms to better capture the evolution of user preferences and the complex relationships between charging demand and behavioral characteristics while maintaining model interpretability. Such integration may help charging infrastructure operators proactively mitigate congestion risks, improve service quality, and enhance the operational efficiency of EV charging systems under high-demand conditions. Author Contributions Conceptualization, Y.X.; methodology, Y.X.; formal analysis, Y.X.; resources, Y.X.; visualization, Y.X., X.T.; data curation, X.T.; validation, X.T.; writing—original draft preparation, X.T.; writing—review and editing, W.L. All authors have read and agreed to the published version of the manuscript. Funding This research received no external funding. Data Availability Statement The data presented in this study are not publicly available due to privacy, ethical, and commercial confidentiality restrictions associated with user-level data obtained from a public electric vehicle charging station operated by a third-party enterprise. These data contain sensitive user charging behavior records and are subject to data protection agreements. The data supporting the findings of this study are available from the corresponding author upon reasonable request, subject to approval from the data provider. Conflicts of Interest The authors declare no conflict of interest. References Figure 1. The daily 24-h charging volume change curve and normalized preference over a three-month period. Figure 1. The daily 24-h charging volume change curve and normalized preference over a three-month period. Figure 2. Cluster validation via Calinski–Harabasz index. Figure 2. Cluster validation via Calinski–Harabasz index. Figure 3. Distribution of estimated user response parameters (Q 0, α, β, γ) across all EV users. Figure 3. Distribution of estimated user response parameters (Q 0, α, β, γ) across all EV users. Figure 4. Distribution of user’s peak charging hour. Figure 4. Distribution of user’s peak charging hour. Figure 5. Correlation heatmap of user response parameters (Q 0, α, β, γ). Figure 5. Correlation heatmap of user response parameters (Q 0, α, β, γ). Figure 6. Pairwise relationships among α, β, γ, and Q 0 in user behavior modeling. Figure 6. Pairwise relationships among α, β, γ, and Q 0 in user behavior modeling. Figure 7. Relationships among α, Q 0, and RMSE in user response modeling. Figure 7. Relationships among α, Q 0, and RMSE in user response modeling. Figure 8. Impacts of α, β, and γ on simulated charging demand q. Figure 8. Impacts of α, β, and γ on simulated charging demand q. Figure 9. Simulated q surface as function of α and β. Figure 9. Simulated q surface as function of α and β. Figure 10. Simulated q as function of α, β, γ. Figure 10. Simulated q as function of α, β, γ. Figure 11. User clustering visualization via PCA (Q0, α, β, γ). Figure 11. User clustering visualization via PCA (Q0, α, β, γ). Figure 12. Hourly charging behavior curves by user type. Figure 12. Hourly charging behavior curves by user type. Figure 13. Distributions of Q 0, α, β, and γ across five user types. Figure 13. Distributions of Q 0, α, β, and γ across five user types. Figure 14. Weekday vs. weekend charging behavior of weekend switchers. Figure 14. Weekday vs. weekend charging behavior of weekend switchers. Figure 15. Mean simulated q per user type (simulated expand data). Figure 15. Mean simulated q per user type (simulated expand data). Figure 16. KDE curves of Q 0, α, β, and γ per user type. Figure 16. KDE curves of Q 0, α, β, and γ per user type. Figure 17. Δq as a function of α in user response modeling. Figure 17. Δq as a function of α in user response modeling. Figure 18. Δq as a function of β in user response modeling. Figure 18. Δq as a function of β in user response modeling. Figure 19. Δq as a function of γ in user response modeling. Figure 19. Δq as a function of γ in user response modeling. Figure 20. Representative fitting examples for users with different α and β values. Figure 20. Representative fitting examples for users with different α and β values. Table 1. Proportions and mean parameters of different user types. Table 1. Proportions and mean parameters of different user types. No. User Type Q0 Mean α Mean β Mean γ Mean Proportion 1 Commuting-Dominant 50.03 0.24 −0.70 0.008 17.6% 2 Elastic-Energy-Saving 10.88 0.83 0.64 0.62 25.1% 3 Weekend-Switching 23.16 0.60 0.60 0.30 19.2% 4 Night-Preferential 6.92 3.43 0.95 0.03 7.9% 5 Discount-Sensitive 12.90 0.52 0.87 −0.17 30.2% Table 2. Performance comparison of different models on training and test sets. Table 2. Performance comparison of different models on training and test sets. Model Train RMSE (kWh) Train MAPE (%) Train R 2Test RMSE (kWh) Test MAPE (%) Test R 2Price-only 13.5 31.5 0.58 14.1 33.9 0.57 Time-only 11.8 26.3 0.69 13.4 27.8 0.65 Traditional K-means 9.9 22.1 0.74 11.5 25.3 0.70 Proposed (3-var Response) 7.4 16.2 0.79 8.3 18.7 0.80 Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. © 2026 by the authors. Published by MDPI on behalf of the World Electric Vehicle Association. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
