1. Introduction
Under the strategic promotion of the “dual-carbon” goal, the rapid popularization of electric cars has become a critical pathway toward sustainable energy development and carbon emission reduction. By 2024, the number of new energy vehicles in China had reached 31.4 million, with pure electric cars accounting for 22.09 million. This growth trajectory reflects the nation’s commitment to climate governance and energy structure transformation. However, the large-scale integration of electric cars into the power grid brings unprecedented challenges to system stability, power quality, and economic operation.
The charging behavior of electric cars exhibits high temporal randomness and spatial clustering effects, leading to expanding peak-valley differences in regional power grids—some urban distribution networks have recorded daily peak-valley rates exceeding 35%. The spatial distribution heterogeneity of charging load further amplifies these risks; urban centers face concentrated charging demand during evening hours, while suburban areas languish in low-load operation during nighttime valleys. Additionally, since the charging process of electric cars represents nonlinear load behavior, harmonic interference threatens grid equipment operation, exposing power systems to risks of increased reactive power losses and local overheating.
From an economic perspective, the stochastic fluctuations of large-scale electric car charging loads induce nonlinear changes in grid operation costs. Under traditional “supply-follows-demand” scheduling paradigms, an additional 15%-20% spinning reserve capacity must be reserved to control peak-valley differences, consequently amplifying the marginal operational cost of power systems. Furthermore, due to constraints in communication latency, control precision, and user acceptance, the economic value of vehicle-to-grid (V2G) interaction technologies remains underexploited, with utilization rates below 30%.
This article aims to develop a systematic framework encompassing electric car charging load prediction and scheduling strategies that integrate spatio-temporal distribution characteristics. The remainder of this article is organized as follows: Section 2 analyzes the spatio-temporal distribution characteristics of electric car charging load. Section 3 proposes a GCN-Transformer hybrid model for charging load forecasting. Section 4 establishes a scheduling strategy considering spatio-temporal distribution characteristics. Section 5 summarizes the concluding remarks and discusses directions for future research.
2. Spatio-Temporal Distribution Characteristics Analysis of Electric Car Charging Load
2.1 Temporal Characteristics of Charging Load
Charging loads generated by electric cars manifest evident daily periodic characteristics. During weekdays, morning and evening rush hours typically reach relatively higher levels of daily average load, forming a distinctive bimodal pattern. Conversely, non-working days tend to exhibit a single-peak pattern occurring around noon or nighttime. According to temporal classification, three typical patterns based on date attributes may be identified: workdays, weekends, and statutory holidays. Charging facility load intensity on workdays generally surpasses weekend levels, primarily attributable to the continuous charging demand stimulated by regular commuting movements between residential and workplace locations. During holiday periods, long-distance travel intensifies battery energy consumption in electric cars, which also induces concentrated charging demand phenomena.
Contemporary urban charging behavior appears to display a bimodal characteristic—morning and evening peak demand proportions respectively reach considerable levels of total daily demand, with overnight charging load peaks relatively elevated due to concentrated charging during lower electricity price valleys. Depending on regional developmental levels and various contributing factors, the emergence of these peaks may temporally shift or fluctuate. When undertaking prediction tasks, traditional autoregressive integrated moving average models neglect the discrepancies between workdays and holidays, thereby introducing prediction errors. An effective prediction model for electric cars must integrate multi-period temporal features and embed external variables to achieve dynamic correlation modeling.
2.2 Spatial Characteristics of Charging Load
The spatial dimension reveals pronounced non-uniform distribution in charging load. Based on urban functional zoning perspectives, transportation networks can be categorized into residential areas, commercial districts, and industrial zones. Charging load distribution is intimately connected to the geographical placement of urban functional areas. In residential zones, charging demand predominantly manifests as slow nighttime charging, with load density concentrated between 22:00 and 06:00. Commercial districts primarily require fast-charging services, and their midday load density significantly exceeds that of residential areas. Meanwhile, charging pile utilization rates vary notably based on urban development levels—central city charging pile utilization rates surpass 90%, whereas suburban facilities face underutilization challenges.
When performing prediction, capturing the spatial interconnections between regional charging facilities proves essential. Prediction models must integrate transportation network data and related spatial metrics to anticipate charging demand distribution patterns. Sole reliance on temporal dimension analysis fails to adequately address the spatial complexities inherent in electric car charging load behavior.
2.3 User Behavior and Environmental Factors
The non-uniform and differential nature of charging load spatio-temporal distribution ultimately stems from interactions between electric car users and various environmental factors. Although users demonstrate randomness in their charging behavior patterns influenced by multiple real-world factors, overall periodic variation tendencies persist, closely connected with local behavioral habits and work-life routines.
User travel patterns: Private electric car charging randomness markedly exceeds that of taxis and buses, with the latter presenting regular charging patterns due to fixed operational schedules. Private car users may be classified into three categories:
- Intercity commuting users: These exhibit significant spatial separation between residential and workplace locations, producing high-frequency, high-capacity charging demand during workdays while prioritizing fast-charging nodes along intercity routes.
- Transit intermittent users: Their proportion remains below 15% of total users, demonstrating low-frequency, low-capacity charging characteristics. From spatial distribution perspectives, their charging site choices highly correlate with transportation network topology structures.
- Urban resident users: Their charging behavior presents evident spatio-temporal coupling characteristics, typically reaching peak charging frequency before and after weekday commuting periods.
Environmental factors: Ambient temperature significantly influences charging load patterns of electric cars. In extreme heat or cold conditions, drivers typically activate temperature control systems to sustain cabin comfort, which directly accelerates traction battery energy consumption rates, triggering shortened charging demand cycles and intensified charging behavior. Under sunny conditions with short travel radii, residents prefer walking or non-motorized alternatives, consequently diminishing electric car utilization intensity. During rainfall or dusty weather—even for brief distances—motor vehicle usage proportions rise considerably from user convenience perspectives.
The charging load spatio-temporal distribution features result from multi-factor coupling characterization. Consequently, prediction and scheduling models that consider multiple contributing factors should be adopted. This work employs the GCN model which excels in spatial feature extraction, along with the Transformer model distinguished by outstanding temporal feature processing capabilities.
3. EV Charging Load Forecasting Model Using GCN-Transformer
3.1 Overall Model Architecture
To overcome limitations in traditional methods for interpreting spatio-temporal characteristics, this article proposes a comprehensive electric car charging load prediction model architecture composed of an input layer, GCN-based spatial feature extraction module, Transformer-based temporal modeling module, and output layer. The overall framework is illustrated as follows, where charging stations are modeled as graph nodes within the transportation network, constructing a dataset that contains node features and topological connections. The GCN module processes this graph-structured data for spatial feature extraction. Following this step, explicit positional encoding and gated fusion strategies achieve synergistic spatio-temporal feature modeling, enabling the model to capture complex patterns of electric car charging behavior effectively.
3.2 Related Definitions
According to charging station layouts and transportation network conditions, the topological relationships within a region may be abstracted as a graph structure. Charging stations positioned at different spatial locations function as load nodes:
$$G = (V, E)$$
where V represents the set of nodes in the charging station network, E is the edge set denoting spatial correlations between stations. When geographical proximity relationships exist between two stations, an edge is established as:
$$e_{ij} = \begin{cases} \frac{1}{h(v_i, v_j)} & \text{if } h(v_i, v_j) < 2.5\,\text{km} \\ 0 & \text{otherwise} \end{cases}$$
with $h(v_i, v_j)$ denoting the Haversine distance between stations $v_i$ and $v_j$. The spatio-temporal prediction objective may be defined as:
$$\hat{X}_{t+1:t+T} = F(G; X_{t-n:t})$$
where $X_{t-n:t}$ represents historical load sequences for the past $n$ timesteps, and the function $F$ models spatio-temporal dependencies, simultaneously capturing temporal dynamics and the spatial correlations inherent in topological structures.
3.3 GCN Module for Spatial Feature Extraction
The GCN module requires preparing node feature matrices and adjacency matrix inputs. The feature matrix at time step $t$ combines historical load values and environmental features for each charging station:
$$P_{i,t} = \left[P_{i,t}^{(1)}, P_{i,t}^{(2)}, \ldots, P_{i,t}^{(H)}\right] \in \mathbb{R}^{H}$$
where $E_{i,t} \in \mathbb{R}^{4}$ includes temperature, humidity, wind speed, and rainfall data. All station features follow a stacked arrangement to construct the node feature vector:
$$X_t = \begin{bmatrix} P_{1,t} & E_{1,t} \\ P_{2,t} & E_{2,t} \\ \vdots & \vdots \\ P_{N,t} & E_{N,t} \end{bmatrix} \in \mathbb{R}^{N \times F}$$
The adjacency matrix $A \in \mathbb{R}^{N \times N}$ encodes the edge weights $w_{ij}$ between stations. To ensure training stability and effective spatial aggregation, symmetric normalized Laplacian matrix transformation is applied:
$$\hat{A} = D^{-\frac{1}{2}}(A + I)D^{-\frac{1}{2}}$$
where $I$ denotes the identity matrix and $D$ is the degree matrix. The hierarchical graph convolution operation proceeds as:
$$H^{l+1} = \sigma(\hat{A} H^{l} W^{l})$$
3.4 Transformer Module Design
The Transformer encoder functions as the core component for capturing long-range dependencies in sequences through self-attention mechanisms. Unlike recurrent architectures, the Transformer achieves parallel sequence processing while effectively modeling long-distance dependencies—crucial for identifying prolonged temporal patterns in electric car charging data. Critical modifications for time-series forecasting purposes include: (1) replacing the Softmax output layer with Sigmoid functions to produce continuous-valued predictions; (2) incorporating rotary position embeddings; (3) applying gated fusion strategies for spatio-temporal integration.
Positional encoding with gated fusion:
$$X_t^{(pos)} = X_t \cdot R_t$$
where $R_t$ is a predefined rotation matrix providing temporal information injection. The gated fusion mechanism combines positional-encoded temporal features and GCN-extracted spatial features:
$$G_t = \sigma_g(W_g \cdot [X_t^{(pos)}; H^{(L)}] + b_g)$$
$$X_t^{(fused)} = \epsilon G_t \cdot X_t^{(pos)} + (1 – \epsilon G_t) \cdot H^{(L)}$$
where $\sigma_g$ denotes the sigmoid gating function, and $\epsilon$ indicates element-wise multiplication.
Multi-head self-attention: The core self-attention computation follows:
$$\text{Attention}(Q, K, V) = \text{Softmax}\left(\frac{QK^T}{\sqrt{d_k}} + M\right)V$$
where $Q$, $K$, V are projected query, key, and value matrices respectively, $d_k$ represents the dimension of the key vector, and $M$ is the causal mask matrix in decoder layers to prevent future information leakage:
$$M_{ij} = \begin{cases} 0 & \text{if } i \leq j \\ -\infty & \text{if } i > j \end{cases}$$
Multi-head attention: Multiple attention heads capture distinct relationship patterns:
$$\text{MultiHead}(H) = \text{Concat}[\text{head}_1; \ldots; \text{head}_M]W_O$$
$$\text{head}_m = \text{Attention}(QW_m^Q, KW_m^K, VW_m^V)$$
where $W_m^Q$, $W_m^K$, $W_m^V$ are projections for head $m$, and $W_O$ is the output projection matrix.
FFN and residual connections: Position-wise feed-forward networks inject nonlinear transformation capacity:
$$\text{FFN}(z) = \text{ReLU}(z W_1 + b_1)W_2 + b_2$$
Residual connections and layer normalization stabilize deep network training:
$$Z^{(l)} = \text{LayerNorm}(X^{(l-1)} + \text{MultiHead}(X^{(l-1)}))$$
$$H^{(l)} = \text{LayerNorm}(Z^{(l)} + \text{FFN}(Z^{(l)}))$$
The modified output layer applies Sigmoid activation for continuous-value predictions:
$$\hat{Y} = \sigma_{sigmoid}(H^{(L)} W_{out} + b_{out}) $$
with subsequent inverse normalization generating final charging load forecasts for electric cars.
3.5 Experimental Setup
The experiments utilize real-world electric car charging station data from a certain city in China, containing records from 15 geographically distributed stations. Sampling intervals are set at 15 minutes. Environmental data—temperature, humidity, rainfall, wind speed—are collected through the Open-Meteo API at corresponding station coordinates and timestamps. Additional date-type attributes identify workdays versus weekends. The dataset attributes may be summarized as follows:
| Feature Category | Feature Description | Dimension |
|---|---|---|
| Charging Station ID | Node index in graph matrix | Spatial |
| Station Coordinates | Latitude/longitude for adjacency matrix construction | Spatial |
| Historical Load | Time-series load at 15-min intervals | Temporal |
| Temperature | Regional ambient temperature | Environmental |
| Humidity | Regional relative humidity | Environmental |
| Rainfall | Regional precipitation intensity | Environmental |
| Wind Speed | Regional wind conditions | Environmental |
| Date Type | Workday vs. weekend vs. holiday classification | Behavioral |
Feature preprocessing includes Z-score normalization to stabilize training dynamics:
$$x^{\prime} = \frac{x – \mu}{\sigma}$$
where μ represents the feature mean and $\sigma$ is the standard deviation. The dataset is partitioned in an 80:20 ratio for training and validation. The experimental environment specifications are summarized below:
| Configuration Component | Specification Description |
|---|---|
| Operating System | Windows 11, 64-bit |
| Programming Language | Python 3.9.2 |
| Deep Learning Framework | TensorFlow 2.6 |
| GPU Hardware | NVIDIA RTX 3060 6GB |
| Processor | Intel i7, 14 cores, 2.30 GHz, 16.0 GB RAM |
The GCN module consists of 3 layers for spatial feature aggregation. The Transformer block implements 6 encoder-decoder layers with 4 parallel attention heads. Batch size is set to 48 with a Dropout layer at 0.1 probability for overfitting prevention. The Adam optimization algorithm updates parameters with an initial learning rate of 0.001 across 300 training epochs. The mean squared error (MSE) loss function serves as the training objective:
$$\mathcal{L}_{MSE} = \frac{1}{N} \sum_{i=1}^{N} (y_i – \hat{y}_i)^2$$
where $y_i$ represents actual charging load values and $\hat{y}_i$ denotes the predicted values for electric cars.
3.6 Result Analysis and Model Comparison
Through analyzing the thermal distribution map of urban charging stations, evident spatial heterogeneity exists across different station locations. Stations positioned in commercial districts display rapid charging demand throughout working hours. Residential area stations show concentrated nighttime charging patterns. Industrial zone stations operate consistently at lower loads. Highway stations experience periodic demand concentrated during specific travel windows. The load diagrams illustrate these spatial-temporal patterns, showing charging load values transitioning from lower ranges (depicted in blue) to higher demand (portrayed in red).
For comprehensive model evaluation, the proposed GCN-Transformer framework is benchmarked against BP, LSTM, and standalone GCN models. To evaluate load prediction at specific stations with different levels of electric car activity, these prediction profiles are compared:
| Model | RMSE | MAPE/kW | MAE/kW | R² |
|---|---|---|---|---|
| BP | 94.292 | 16.598 | 80.378 | 0.881 |
| GCN | 64.371 | 13.753 | 55.235 | 0.823 |
| LSTM | 55.328 | 8.325 | 45.363 | 0.855 |
| GCN-Transformer | 40.657 | 2.413 | 28.473 | 0.926 |
These quantitative results demonstrate that the GCN-Transformer hybrid model achieves superior performance across all evaluation criteria:
- RMSE: Reduced by 56.9% relative to BP baseline, validating the model’s strong non-linear relationship representation capability.
- MAPE: Decreased by 71% compared to LSTM, highlighting robustness to temporal fluctuations.
- MAE: Reduced by 48.5% relative to standalone GCN, confirming spatial feature extraction effectiveness.
- R²: Improved to 0.926, representing a 5.3% increase over the traditional BP model.
Experiments that systematically vary the number of nodes incorporated into the adjacency matrix reveal the significance of spatial correlations. When decreasing node counts, prediction errors show corresponding amplification at each station. This correlation indicates that inter-station dependencies carry predictive information—eliminating nodes removes the associative relationships contributing to accurate charging load forecasting. The model’s superior performance is attributable to the synergistic combination of GCN’s spatial perception and the Transformer’s global attention mechanism, enabling dual optimization of spatio-temporal characteristics.
4. Scheduling Strategy Considering Spatio-Temporal Distribution of Electric Cars
4.1 Problem Statement and Scheduling Framework
Large-scale integration of electric cars introduces significant operational challenges for distribution networks. Traditional scheduling strategies that neglect spatio-temporal dynamics often exacerbate load peak-valley differences and elevate system operational costs. Drawing from the spatio-temporal load characteristics accurately predicted by the GCN-Transformer model, a scheduling strategy that jointly accounts for user travel behavior, traffic conditions, and distribution network constraints is essential. This work thereby constructs an electric car scheduling spatio-temporal distribution model aimed at coordinating transportation and power systems effectively.
4.2 Modeling Spatial-Temporal Distribution of Electric Cars
User behavior modeling: The charging patterns of electric car users exhibit probabilistic distributions characterized by daily mileage patterns following normal distributions:
$$f(x) = \frac{1}{\sqrt{2\pi}\sigma}\exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right)$$
where μ indicates mean user travel distance and $\sigma$ is standard deviation. Based on statistical data, 68.3% of users exhibit daily mileage within the range $[\mu-\sigma, \mu+\sigma]$.
The number of electric cars participating in V2G services is:
$$N_{dch} = \gamma \cdot N_{EV}$$
with $\gamma$ as the percentage of consenting vehicle owners. For each participant, battery energy constraints preserve user charging expectations:
$$\sum_{t=t_{in}}^{t_{off}} U \cdot P(n,t) \cdot \Delta t \geq E_{off}^{EV} – E_{in}^{EV}$$
$$SOC_{min} \leq SOC(n,t) \leq SOC_{max}$$
$$P_{dch}^{EV,min} \leq P_{dch}^{EV}(n,t) \leq P_{dch}^{EV,max}$$
$$P_{ch}^{EV,min} \leq P_{ch}^{EV}(n,t) \leq P_{ch}^{EV,max}$$
where $E_{in}^{EV}$ is the initial energy upon grid connection, $E_{off}^{EV}$ is the expected departure energy, $SOC(n,t)$ is the battery state of charge for the n-th electric car at decision time $t$, and $P$ values denote charging/discharging power bounds.
Traffic network model: The transportation graph $G = (V, E, W)$ shares the identical geographic baseline with the charging station spatial association graph from the prediction module. Road travel time calculations:
$$w(t) = \frac{d_{ij}}{v_{road}(t)}$$
Speed characteristics across road levels and time periods:
| Time Period | Expressway Speed (km/h) | Arterial Road Speed (km/h) |
|---|---|---|
| Morning Peak (7:00–9:00) | 40 | 30 |
| Evening Peak (17:00–19:00) | 45 | 35 |
| Flat period (9:00–17:00) | 60 | 50 |
| Valley period (20:00–6:00) | 70 | 60 |
Energy consumption per unit mileage is formulated separately for four road levels, expressways, arterial roads, secondary roads, and branches:
$$E_{bes} = \begin{cases} 1.520 – 0.004v + 0.247/v & \text{expressway} \\ 5.492 – 0.004v + 0.179/v & \text{arterial} \\ 1.531 – 0.001v + 0.2/v & \text{secondary} \\ 1.553 – 0.02v + 0.208/v & \text{branch} \end{cases}$$
The shortest-time routing for scheduling decisions of electric cars is solved via Dijkstra’s algorithm:
$$dist(v) = \min_{u \in \mathcal{N}(v)}[dist(u) + W_e(u,v)]$$
subject to the range feasibility constraint:
$$\sum_{e \in P_{ab}} \frac{E_{unit}(v) \cdot d_{ab}}{\eta \cdot E_{SOC}} \leq E_{ab}^{EV} – E_{SOC}^{min}$$
Distribution network load model: The distribution network is modeled as a radial system where node power balance is:
$$P_i^G + P_i^M = P_i^L + \sum_{j \in B(i)} P_{ij}$$
with the AC power flow equations:
$$P_{ij} = V_i V_j (G_{ij}\cos\theta_{ij} + B_{ij}\sin\theta_{ij}) – G_{ij}V_i^2$$
$$Q_{ij} = V_i V_j (G_{ij}\sin\theta_{ij} – B_{ij}\cos\theta_{ij}) + B_{ij}V_i^2$$
Line losses are expressed as:
$$P_{loss,ij} = \frac{P_{ij}^2 + Q_{ij}^2}{V_i^2} \cdot R_{ij}$$
Here $V_i$ and $V_j$ denote voltage magnitudes, $\theta_{ij} = \theta_i – \theta_j$ is the phase angle difference, while $G_{ij}$, $B_{ij}$, $R_{ij}$, and $X_{ij}$ represent conductance, susceptance, resistance, and reactance parameters.
4.3 Spatio-Temporal Cooperative Optimization Objective
The constructed multi-objective optimization model aims to cooperatively reduce grid operation costs, smooth load fluctuations, and curtail network losses. Its composite objective function follows:
$$f_{total} = k_1 \cdot f_{fgc} + k_2 \cdot f_{netloss} + k_3 \cdot f_{traffic}$$
where the demand-side peak-valley penalty is:
$$f_{fgc} = p_{peak-valley} \cdot (\Delta P_{peak-valley}^{before} – \Delta P_{peak-valley}^{after})$$
network loss reduction benefits are:
$$f_{netloss} = \sum_{t=1}^{24} p_{netloss} \cdot E_{t}^{loss}$$
and comprehensive transportation energy cost is:
$$f_{traffic} = \sum_{t=1}^{24} \sum_{n=1}^{N_{EV(t)}} P_{dis}^{EV} \cdot d_{EV}(n,t)$$
The constraint set preserves safety limits:
$$V_{i}^{min} \leq V_i \leq V_{i}^{max}$$
$$P_{ij}^2 + Q_{ij}^2 \leq S_{ij,max}^{2}$$
$$V_i \geq V_{i,min} + \Delta V_{margin}$$
where a 5% voltage stability margin is reserved to manage load fluctuations in the network serving electric cars.
Multi-objective entropy weight normalization: To reconcile scale differences among objective functions, the decision matrix is established as:
$$\boldsymbol{E} = [K_1, K_2, K_3]^\top$$
where $K_1$ incorporates peak-valley mitigation, $K_2$ integrates total network loss energy, and $K_3$ includes total transport energy distance. Range-based normalization addresses dimensional inconsistency:
$$N_b = \frac{K_b – K_{b,min}}{K_{b,max} – K_{b,min}}$$
The entropy divergence coefficient measures information content:
$$d_b = 1 + \frac{1}{\ln n} \sum_{i=1}^{n} N_b^{(i)} \ln N_b^{(i)}$$
Dynamic weights incorporate spatio-temporal correction factors:
$$w_b = \frac{d_b \cdot \lambda_b(t,i)}{\sum_{b=1}^{3} d_b \cdot \lambda_b(t,i)}$$
The final normalized objective then becomes:
$$f_{total} = \sum_{b=1}^{3} w_b \cdot N_b$$
where small $w_1 N_1$ values prioritize peak load reduction, $w_2 N_2$ values minimize network losses, and $w_3 N_3$ values balance traffic energy consumption.
4.4 Improved Spatio-Temporal Adaptive Particle Swarm Optimization
Particle swarm optimization (PSO) is a swarm intelligence metaheuristic inspired by bird flocking and fish schooling behavior. Each particle represents a candidate solution updated iteratively according to:
$$v_{i}^{k+1} = \omega v_{i}^{k} + c_1 r_1 (pbest_i – x_{i}^{k}) + c_2 r_2 (gbest – x_{i}^{k})$$
$$x_{i}^{k+1} = x_{i}^{k} + v_{i}^{k+1}$$
where the inertia weight ω controls exploration-exploitation equilibrium. Standard PSO suffers premature convergence and limited global search capability in complex spatio-temporal scheduling contexts. To overcome these deficiencies, the following improvements are proposed:
(1) Temporal adaptive inertia weight:
$$\omega(t) = \omega_{max} – \frac{(\omega_{max} – \omega_{min}) \cdot \Delta\omega(t)}{T}$$
where $\Delta\omega(t)$ increases during peak periods to augment global search and decreases during valley periods for rapid convergence—enabling temporal differentiation matching load dynamics of electric cars.
(2) Spatial adaptive learning factors:
$$c_1(i) = c_{1,base} + \alpha \cdot \frac{P_{load}(i)}{P_{max}}$$
$$c_2(i) = c_{2,base} – \alpha \cdot \frac{P_{load}(i)}{P_{max}}$$
At high-load nodes, increasing $c_1$ emphasizes individual best experience. At low-load nodes, prioritizing $c_2$ accelerates convergence.
(3) Tent chaotic mapping initialization: To enhance population diversity and avoid premature local optima:
$$x_{i}^{(0)} = \begin{cases} 2x_{i-1} & \text{if } x_{i-1} < 0.5 \\ 2(1 – x_{i-1}) & \text{otherwise} \end{cases}$$
This mechanism guarantees uniform particle coverage across the solution space.
(4) Cauchy mutation operation: Standard Cauchy distributions with long-tail properties induce large-distance perturbations:
$$x_{i}^{k} = x_{i}^{k} + \beta \cdot e^{-k/T} \cdot C(0,1)$$
where the mutation intensity parameter β decreases with iteration count $k$, facilitating escape from stagnation while preserving convergence stability.
4.5 Case Studies and Numerical Analysis
Simulation experiments utilize the IEEE 33-node distribution network system interconnected with the corresponding urban transportation network topology. Charging infrastructure configuration includes 50 charging piles across strategically selected nodes as follows:
| Traffic Node Number | Area Type | Charging Pile Type | Quantity | Power Rating (kW) |
|---|---|---|---|---|
| 3 | Residential | Slow charger | 15 | 7 |
| 9 | Residential | Slow charger | 15 | 7 |
| 6 | Industrial | Fast charger | 10 | 120 |
| 11 | Transport hub | Ultra-fast charger | 5 | 250 |
| 14 | Transport hub | Ultra-fast charger | 5 | 250 |
| 15 | Commercial | Fast charger | 10 | 120 |
Three distinct scenarios are configured to validate the proposed strategy:
- Scenario 1 baseline: 200 electric cars, excluding traffic energy considerations, solved using standard PSO.
- Scenario 2: 200 electric cars with traffic energy costs incorporated, solved using standard PSO.
- Scenario 3: 200 electric cars including traffic energy costs, solved using the improved spatio-temporal adaptive PSO (ISTAPSO).
Voltage profile improvement: At distribution node 18, Scenario 1 shows voltage deviations in the range of -5.0% to -2.0%, breaching the lower voltage limit. In Scenario 3, deviation improves to a range of -3.0% to -1.5%, within the acceptable margin. This confirms optimized spatio-temporal charging/discharging of electric cars effectively balances power distribution, mitigating voltage violations in concentrated load zones.
Network loss reduction: At node 10, after implementing optimized routing strategy, network loss peaks decrease significantly, with the reduction of approximately 30.4% compared with the pre-dispatch baseline, demonstrating that the Dijkstra-based scheduling solution effectively reduces long-distance, high-impedance charging path selections.
Peak-valley mitigation: The system daily load profile transforms from an original evident bimodal shape to a smooth distribution after optimization:
| Scenario | Pre-dispatch Peak-valley (kW) | Post-dispatch Peak-valley (kW) | Network Loss (kW) | Grid Cost (CNY) | Traffic Cost (CNY) | Total Cost (CNY) |
|---|---|---|---|---|---|---|
| Scenario 1 | 2853.39 | 1508.42 | 35.20 | 68255.25 | 0 | 68255.25 |
| Scenario 2 | 2853.39 | 1303.84 | 28.84 | 62315.63 | 4212.43 | 66528.06 |
| Scenario 3 | 2853.39 | 1169.73 | 21.76 | 55828.97 | 4803.50 | 60632.47 |
Sensitivity analysis for different EV penetration rates:
| EV Load Percentage | User Participation γ | Peak-valley Reduction Rate | Total Cost (CNY) |
|---|---|---|---|
| 15% | 55% | 48% | 65820 |
| 25% | 65% | 59% | 60632 |
| 35% | 70% | 52% | 64210 |
As the electric car percentage increases from 15% to 25%, peak-valley reduction rates improve, indicating better load balancing. However, at 35% penetration, additional EV integration induces novel load concentration phenomena, diminishing peak-valley reduction efficiency.
Scheduling comparison analysis: The comparative evaluation demonstrates that:
- Scenario 1: Optimizing grid-side objectives only achieves 22% peak-valley reduction; however, excluding spatial factors causes elevated network losses and limited voltage improvement.
- Scenario 2: Adding path optimization achieves 41.8% peak-valley difference reduction, but static parameters constrain convergence.
- Scenario 3: Spatio-temporal adaptive weights with Cauchy mutation achieve 59% peak-valley reduction while achieving the lowest total cost of 60632.47 CNY—an 11% total cost reduction.
Through simulation, the spatio-temporal charging/discharging load distribution diagram verifies the strategy’s effectiveness in shaving peaks and filling valleys while supporting distribution infrastructure safety.
5. Conclusion and Future Work
5.1 Conclusion
This article investigates charging load prediction and scheduling strategy of electric cars considering spatio-temporal distribution characteristics. The main contributions are as follows:
(1) A comprehensive spatio-temporal distribution analysis: Electric car charging load characteristics are systematically analyzed from temporal, spatial, and user-environmental perspectives. The analysis reveals that charging load exhibits distinct periodic patterns influenced by multi-factor coupling, which establishes a theoretical framework for subsequent model developments.
(2) An effective GCN-Transformer prediction model: The graph neural network charge prediction model captures spatial dependencies among charging stations embedded within transportation network graph structures. By leveraging GCN spatial feature extraction and Transformer global attention mechanisms, the model achieves accurate spatio-temporal load forecasting. Experimental evaluation confirms: (i) excellent capability in capturing spatio-temporal charge heterogeneity; (ii) the GCN-Transformer model achieves 56.9% RMSE reduction relative to BP; (iii) 71% MAPE reduction relative to LSTM; (iv) R² improvement to 0.926. Spatial node influence analysis confirms that inter-station spatial correlations carry predictive information critical for forecasting accuracy.
(3) A scheduling strategy based on spatio-temporal coordination: A scheduling model jointly accounts for user behavioral spatio-temporal patterns, transportation network constraints, and distribution system operational conditions. A multi-objective optimization framework integrates grid operating costs, peak-valley mitigation incentives, network loss reductions, and traffic-related charging energy costs. The improved spatio-temporal adaptive PSO that combines dynamic inertia weight scheduling, adaptive learning factors, chaotic map initialization, and Cauchy mutation enhances both global exploration capability and local exploitation capacity. IEEE 33 bus simulations validate that the strategy reduces peak-valley differences by 59%, lowers network losses from 35.20 kW to 21.76 kW, improves voltage profiles within permissible margins, and achieves 11% total cost savings while simultaneously satisfying time-dependent and spatial constraints.
5.2 Future Work
The limitations of this study indicate several directions for future research:
- extended mobile storage integration: Fuel cell electric vehicles and mobile energy storage systems should be included in forecasting models, considering their distinct load profiles.
- Real-time data fusion: The current modeling depends on historical charging records. The integration of real-time traffic flow data with multi-source sensor streams would provide dynamic spatio-temporal modeling capability, enhancing prediction response.
- Multi-stakeholder collaborative frameworks: The scheduling model currently prioritizes grid-side economics. Future formulations should consider multi-party objectives incorporating user charging cost minimization, battery degradation quantification, and charging station revenue balancing to achieve equitable win-win outcomes across all participants.