1. Introduction and Research Background
In the context of the deeply promoted “dual-carbon” strategy and the rapid popularization of electric vehicles, the precise prediction and optimized scheduling of electric vehicle charging loads hold significant importance for grid stability and the optimal allocation of grid resources. The large-scale integration of electric vehicles into the power system poses new challenges to the safe, stable, and economical operation of the grid. This research focuses on addressing the limitations of traditional prediction methods, which struggle to effectively integrate the spatio-temporal distribution characteristics of charging loads, thereby resulting in suboptimal prediction accuracy. Furthermore, conventional scheduling strategies fail to adequately respond to spatio-temporal dynamic changes, leading to issues such as increased peak-valley load differences, elevated network losses, and rising operational costs. To tackle these challenges, this study proposes a novel charging load prediction and scheduling strategy considering the spatio-temporal distribution characteristics of electric vehicles.
To address the deficiencies of existing electric vehicle charging load prediction methods that cannot adequately extract spatio-temporal features, leading to reduced accuracy and excessive training durations, this thesis develops a hybrid prediction model based on Graph Convolutional Network (GCN) and Transformer integration. Moreover, to mitigate the grid-side issues caused by large-scale electric vehicle integration, an optimized scheduling strategy for electric vehicles is introduced, which considers their spatio-temporal distribution to balance grid economics and stability.
2. Temporal and Spatial Characteristics of Electric Vehicle Charging Loads and Underlying Theories
2.1 Temporal Distribution Characteristics
The temporal characteristics of charging loads demonstrate a pronounced diurnal cyclicality. During workdays, peak demands generally align with morning and evening rush hours, exhibiting a bimodal distribution. Conversely, weekends often present a single-peak pattern during midday or nighttime. Charging loads in different functional zones show significant variance at different times, reflecting the complex temporal dynamics that need careful consideration in my predictive model.
2.2 Spatial Distribution Characteristics
Spatially, charging loads are not uniformly distributed across urban areas. They exhibit patterns strongly correlated with city functional zoning. Residential areas commonly show concentrated nighttime slow-charging, whereas commercial districts evidence high daytime fast-charging demands. This non-uniformity is further amplified by road connectivity and traffic flow, making spatial features critical inputs for both load prediction and optimal scheduling.
2.3 User and Environmental Factor Analysis
The spatio-temporal heterogeneity originates chiefly from the stochastic but pattern-following behaviors of electric vehicle users. This is coupled with external conditions such as ambient temperature and meteorological events, which directly affect the range and energy consumption of electric vehicles. Thus, for high-precision predictions, factors like weather data and holiday schedules must be incorporated alongside historical charging data.
3. The GCN-Transformer Charging Load Prediction Framework
3.1 Overall Model Architecture
Traditional forecasting methods lack the capability to characterize both topological spatial correlations and long-range temporal dependencies effectively. To overcome this, I constructed a hybrid model where electric vehicle charging stations are conceptualized as graph nodes over the transportation network. Road connectivity establishes edge features, enabling the construction of a specialized graph dataset. This structure paves the way for spatial feature extraction via GCN. The temporal dynamics are captured through a Transformer encoder enhanced with explicit positional encoding and gating fusion mechanisms.
3.2 Problem Formalization
The spatial topology of the charging infrastructure is abstracted into a graph:
$$G = (V, E)$$
where $V=\{v_1,v_2,…,v_N\}$ denotes the set of nodes (charging stations), and $E$ symbolizes the spatially correlated edges between stations. To define the edge weights, I utilized the Haversine distance $h(v_i, v_j)$ between stations $v_i$ and $v_j$, establishing a spatial adjacency rule that only connects stations within a 2.5 km radius:
$$
e_{ij} =
\begin{cases}
\frac{1}{h(v_i, v_j)}, & \text{if } h(v_i, v_j) < 2.5\text{ km} \\
0, & \text{otherwise}
\end{cases}
$$
For time-series data spanning $T$ time steps, defining $X_t \in \mathbb{R}^{N}$ as the load values at time $t$, the spatio-temporal prediction task is to learn a mapping $f$ that predicts the next $T$ frames based on previous data:
$$\left[\hat{X}_{t+1}, \dots, \hat{X}_{t+T}\right] = f_\theta\left(G; X_{t-n}, \dots, X_t\right)$$
3.3 GCN Module for Spatial Feature Extraction
I defined the node feature matrix by concatenating historical load data $P_{i,t}$ with exogenous environmental features such as temperature $T_{i,t}$, humidity $M_{i,t}$, wind speed $W_{i,t}$, and rainfall $R_{i,t}$:
$$E_{i,t} = [T_{i,t}, M_{i,t}, W_{i,t}, R_{i,t}]$$
$$X_t = \begin{bmatrix} P_{1,t} & E_{1,t} \\ P_{2,t} & E_{2,t} \\ \vdots & \vdots \\ P_{N,t} & E_{N,t} \end{bmatrix} \in \mathbb{R}^{N \times F}$$
To maintain numerical stability during training, I applied a symmetric normalization to the adjacency matrix:
$$\hat{A} = D^{-\frac{1}{2}}(A + I)D^{-\frac{1}{2}}$$
where $I$ is the identity matrix for self-loops and $D$ is the degree matrix. The GCN layer is then expressed as:
$$H^{(l+1)} = \sigma\left(\hat{A} H^{(l)} W^{(l)}\right)$$
Here, $H^{(l+1)}$ is the output of the convolution, $W^{(l)}$ constitutes the trainable weights of the layer, and $\sigma(\cdot)$ is a non-linear activation function. This operation intrinsically allows nodes to aggregate information from their neighboring charging stations, thereby capturing local spatial dependencies caused by geographic proximity and similar functional zones.
3.4 Transformer Module for Temporal Dependency Modeling
To identify long-term dependencies within historical sequences, while avoiding vanishing gradients, I deployed a Transformer. For handling positional information alongside input, I applied rotary position encoding:
$$X_t^{(pos)} = X_t \cdot R_t$$
where the temporal feature matrix $R_t$ is a pre-defined rotation matrix. The spatial features obtained from the GCN, denoted $H_{space}^{(L)}$, are then projected forward and fused with the temporally-encoded load data by introducing an adaptive gating weight $G_g$:
$$G_g = \sigma\left(W_g \cdot \text{Concat}(X_t^{(pos)}, H_{space}^{(L)})\right)$$
$$X_{fused} = (1 – \epsilon)G_g \odot X_t^{(pos)} + \epsilon(1 – G_g) \odot H_{space}^{(L)}$$
Attention weights between different time periods were computed using multi-head self-attention. Assuming $Q$, $K$, and $V$ are the queries, keys, and values derived from the input sequences, and $d_k$ is the dimension of the keys, the attention output is mathematically defined as:
$$\text{Attention}(Q,K,V) = \text{Softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V$$
In the standard Transformer architecture used in this prediction model, the decoder cannot use future time-step information when outputting load data. This is attained through a masked multi-head attention mechanism that incorporates a mask matrix $M_{mask}$:
$$\text{Attention}(Q,K,V) = \text{Softmax}\left(\frac{QK^T + M_{mask}}{\sqrt{d_k}}\right)V$$
where elements in $M_{mask}$ that correspond to future time steps are set to negative infinity, ensuring information leakage is prevented. Subsequently, the output is processed through a Feed-Forward Neural Network (FFN) to add non-linearity, enhancing the expressiveness of the temporal features.
3.5 Dataset Description and Pre-processing
I validated the model using charging station data from a Chinese city, covering 15 distinct charging stations. The dataset included power consumption and environmental information, with most data being recorded at 15-minute intervals for effective time-series alignment.
| Feature Category | Input Variable | Temporal/Spatial Classification |
|---|---|---|
| Station Metadata | Station Name and/or ID | Spatial Feature |
| Geography | Longitude & Latitude Coordinates used for graph construction | Spatial Feature |
| Historical Trend | Historical load profiles per charging station | Temporal Feature |
| Exogenous Climate | Temperature at station location | External Factor |
| Exogenous Climate | Humidity at station location | External Factor |
| Exogenous Climate | Rainfall intensity at station location | External Factor |
| Exogenous Climate | Wind speed at station location | External Factor |
| Calendar Variable | Working day/Holiday identification identifier | User behavior driver |
After collecting the data, I focused my efforts on high-quality normalization. A Z-score standardization process was applied to the feature vectors to scale them to a zero mean and unit variance before feeding them into the deep learning graph, which stabilizes the gradient flow during backpropagation:
$$x’ = \frac{x – \mu_x}{\sigma_x}$$
where $x$ represents the raw data, $\mu_x$ is the mean, and $\sigma_x$ is the standard deviation. Additionally, to scale extreme values in the target labels, a Min-Max normalization maps them into a range adequate for the final activation function:
$$x’ = \frac{x – x_{\min}}{x_{\max} – x_{\min}}$$
My experimental configuration was based on a Windows 11 operating system, utilizing Python 3.9.2 as the coding language and TensorFlow 2.6 as the deep learning framework. The computational hardware relied upon an NVIDIA RTX 3060 GPU (6 GB). For hyperparameters, I fixed the context length, configured the GCN module with 3 layers for spatial aggregation, and designed a 6-layer Transformer encoder–decoder structure. Four parallel attention heads were implemented in the Multi-Head Self-Attention to capture more diversified variable associations. The batch size was set to 48, with an initial learning rate of 0.001 supported by the Adam optimizer. The loss function objective was the Mean Squared Error (MSE):
$$\mathcal{L}_{MSE} = \frac{1}{N}\sum_{i=1}^{N}(y_i – \hat{y}_i)^2$$
where $y_i$ denotes the actual charging load, and $\hat{y}_i$ corresponds to the prediction value.
3.6 Spatial Distribution Analysis and Heat Map Analytics
| Station Cluster Category | Representative Station ID | Dominant Charging Peak Type |
|---|---|---|
| Commercial District Zone | 1, 2, 4, 13, 14 | Daytime high demands (9:00–21:00) |
| Residential District Area | 3, 5, 6, 11 | Night-time high demands (22:00–6:00) |
| Industrial Park District | 7, 8, 9, 10 | Low yet stable consumption patterns |
| Highway Adjacent Installation | 12 | Long-distance travel-specific load surges |
From the prediction outputs on a typical day, I observed that stations located in commercial areas exhibit remarkably similar load curves with peak times during the 9:00 to 12:00 early peak and the 18:00 to 21:00 late peak, recording 37% and 46% of total daily consumption, respectively. Conversely, residential zone stations primarily see load aggregations concentrated in the late evening. This similarity in load curves between close spatial nodes shows that my model successfully mimics the spatio-temporal behavioral patterns inherent in the transportation network data.
3.7 Baseline Model Comparisons and Accuracy Assessment
To objectively assess the performance of my proposed GCN-Transformer model, I benchmarked its results against BP neural networks, standard LSTM recurrent networks, and standalone GCNs. Experiments were conducted on load predictions for Sample Station No.1 and Station No.5. While all classical deep learning architectures could approximate the general load trend, I observed distinct accuracy differences. For typical commercial or residential-commercial zones, LSTM captured sequential correlation rather well, and GCN focused on spatial structures. Yet, these models often stalled in minimizing errors when faced with noise and unpredictable outlier load peaks. The GCN-Transformer, however, was significantly more aligned when it came to anticipating steep load rises and falls, given that it benefits from the parallel multi-head attention to map long-range dependencies.
| Model | RMSE (kW) | MAPE | MAE (kW) | R² |
|---|---|---|---|---|
| BP | 94.292 | 16.598% | 80.378 | 0.881 |
| LSTM | 55.328 | 8.325% | 45.363 | 0.855 |
| GCN | 64.371 | 13.753% | 55.235 | 0.823 |
| GCN-Transformer (Proposed) | 40.657 | 2.413% | 28.473 | 0.926 |
From the performance evaluation, my model achieved a striking 56.9% improvement in Root Mean Square Error when compared to the BP network. Moreover, comparing against the LSTM baseline, the Mean Absolute Percentage Error dropped by 71%. This lower error demonstrates the influence of spatial information and structural dependencies, which are difficult to interpret by purely recurrent networks. The R² value of 0.926, surpassing that of all baselines, further validates the capacity of my model to grasp highly complex patterns. I also evaluated model residuals. Where BP showed signs of overestimation at higher-value ranges, and LSTM presented a flattened curve at middle-range points, my GCN-Transformer had residuals that were tightly clustered around zero, even at extreme demand intervals, proving the model’s stability in handling sudden fluctuations.
4. Electric Vehicle Scheduling Strategy Considering Spatio-Temporal Distribution Features
4.1 Modeling of User Behavior Temporal and Spatial Characteristics
The daily travel distance distribution of electric vehicle users is consistent with a Gaussian distribution that exhibits specific statistical features:
$$f(x) = \frac{1}{\sqrt{2\pi\sigma^2}}\exp\left(-\frac{(x – \mu)^2}{2\sigma^2}\right)$$
where $\mu$ is the mean daily driving distance and $\sigma$ its standard deviation. Data from my simulation show that roughly 68.3% of users drive within the band of $[\mu – \sigma, \mu + \sigma]$.
Electric vehicles generally remain idle for an estimated 95% of the day, highlighting their potential as schedulable distributed resources. When plugged in, electric vehicles capable of Vehicle-to-Grid (V2G) operation can act as dispatchable sources. Designating the charge/discharge state as $U_n$ for vehicle $n$, the following constraints must be respected:
$$E_{n}^{init} + \sum_{t=t_{in}}^{t_{off}} U_n P(n,t)\Delta t \geq E_n^{off}$$
where $E_n^{init}$ is the initial energy upon arrival, $P(n,t)$ is the active or reactive power supplied during time interval $t$, and $E_n^{off}$ is the desired energy at the departure time set by the user. Each vehicle is modeled with potential limitations of its battery pack, constraining the state of charge ($SOC$):
$$SOC_{\min} \leq SOC(n,t) \leq SOC_{\max}$$
4.2 Transportation Network Energy Consumption Modeling
To account for spatial characteristics comprehensively, my traffic network is modeled as a topology $G(V,E,W)$. The nodes represent road intersections, while the edges are directed transportation lines. Weight functions with time as an independent variable represent dynamic traffic flow:
$$w_{ij}(t) = \frac{d_{ij}}{v_{road}(t)}$$
where $d_{ij}$ is the road segment length, and $v_{road}(t)$ is the velocity dependent on peak-hour or off-peak traffic congestion. The model assigns these speed profiles according to my simulation periods:
| Period Segment | Rapid Transit Road Speed (km/h) | Main Road Speed (km/h) |
|---|---|---|
| Morning Peak (07:00–09:00) | 40 | 30 |
| Evening Peak (17:00–19:00) | 45 | 35 |
| Flat Hours (09:00–17:00) | 60 | 50 |
| Valley Hours (20:00–06:00) | 70 | 60 |
To allocate electric vehicles to appropriate charging stations, I applied the Dijkstra algorithm to discover the shortest-time paths based on dynamic edge weights. The energy consumption $E$ per unit distance ($kWh/km$) for different road levels is computed using distinct empirical formulas to reflect the driving conditions:
$$
E_{v,bes} =
\begin{cases}
1.520 – 0.004vv + 0.247\frac{bes}{vv} \\
5.492 – 0.004vv + 0.179\frac{bes}{vv} \\
1.531 – 0.001vv + 0.2\frac{bes}{vv} \\
1.553 – 0.02vv + 0.208\frac{bes}{vv}
\end{cases}
$$
I further ensured that the remaining battery capacity is sufficient for the route length ($d_{ab}$) to the assigned charging station:
$$\sum E_{unit} d_{ab} \leq \frac{E_{SOC} – E_{\min}}{\eta}$$
where $E_{SOC}$ corresponds to current battery energy, $E_{\min}$ is the lower consumption boundary, and $\eta$ is the motor efficiency.
Given the economic aspects of route planning, I considered that the grid pays electric vehicle owners a subsidy for transportation energy consumption when they respond to charging scheduling orders and drive to distant stations:
$$C_{net}^{ev,dis} = \sum_{t=1}^{24} \sum_{i=1}^{N_{ev}(t)} p_{dis}^{ev} d_{i}^{‘ev}$$
Here, $p_{dis}^{ev}$ calculates a per-kilometer subsidy equal to 0.8 of the real-time price, while $d^{‘ev}$ is the distance driven after the dispatch and $N_{ev}(t)$ is the number of vehicles in service at interval $t$. This provides proper incentives and accurately factors realistic travel costs into the overall scheduling framework.
4.3 Distribution Network Modeling and Optimal Scheduling Objectives
The power flow mechanism inside the distribution network forms the grid-side baselines for operation. I established nodal power balance equations including electric vehicle load terms $P_i^{M}$. With $P_i^G$ being the generator injection power and $P_i^L$ the fixed load, the active power at node $i$ is:
$$P_i^{G} = P_i^{L} + \sum_{j \in \Omega_i} P_{ij} + P_i^{M}$$
If the electric vehicle is charging, $P_i^{M} > 0$; conversely, for V2G discharge, $P_i^{M} < 0$. The power flowing through branch $ij$ is formalized by the given AC power-flow equation:
$$P_{ij} = V_i V_j(G_{ij}\cos\theta_{ij} + B_{ij}\sin\theta_{ij}) – G_{ij}V_i^2$$
where $V_i$, $V_j$ represent the voltage amplitudes, and $G_{ij}$ and $B_{ij}$ are the conductance and susceptance values of the line. The loss associated with the branch is:
$$P_{loss,ij} = I_{ij}^2 R_{ij} = \frac{P_{ij}^2 + Q_{ij}^2}{V_i^2}R_{ij}$$
For time-dependent behavior when calculating safety margins, a Continuation Power Flow model considering electric vehicles may be introduced:
$$\begin{cases} P_{L,h} = K_{P,h}P_{L0,h}\lambda_h \\ Q_{L,h} = K_{Q,h}Q_{L0,h}\lambda_h \end{cases}$$
In this framework, $\lambda_h$ is the time-varying load parameter at node $h$, which depends on the number of plugged-in electric vehicles.
My objective function integrates grid operation economics and spatiotemporal load management to solve the following dynamic multi-objective optimization model:
$$f_{total} = k_1 f_{fgc} + k_2 f_{netloss} + k_3 f_{traffic}$$
In the above model: The peak-valley penalty load difference $f_{fgc}$ is calculated globally from the load curve, ensuring load balance over time. The quantity is defined as the economic loss caused by insufficient smoothing of the load:
$$f_{fgc} = p_{fgc}^{penalty}(\Delta P_{peak-valley}^{before} – \Delta P_{peak-valley}^{after}) $$
$$P_{peak-valley} = \max_{t}(P_{total}(t)) – \min_{t}(P_{total}(t))$$
The distribution network loss minimization function is evaluated by aggregating network power losses across 24 periods:
$$f_{netloss} = \sum_{t=1}^{24} p_{netloss} \cdot E_{loss,t}$$
The coupling-based traffic energy expenses describe the economic price of travel distance required to move electric vehicles to their selected station:
$$f_{traffic} = \sum_{t=1}^{24}\sum_{n=1}^{N_{ev}(t)} P_{dis}^{ev}(d(n,t))$$
To handle heterogeneous units among these targets, I used the Entropy Weight Method. In my approach, a decision matrix was initially established based on these three metrics. Each criterion is normalized to eliminate dimensional impact:
$$N_b = \frac{K_b – K_{b,\min}}{K_{b,\max} – K_{b,\min}}$$
where $K_b$ is criterion $b$, and $K_{b,\max}$, $K_{b,\min}$ denote its historical range. The degree of dispersion for each indicator is calculated using an entropy formulation:
$$d_b = 1 + \frac{1}{\ln(n)} \sum_{i=1}^{n}N_i \ln(N_i)$$
Since my optimization needs dynamic weights, I introduced spatio-temporal correction factors $\lambda_b$ in each node and time period. Therefore, dynamic load weights are allocated by:
$$w_b = \frac{d_b \cdot \lambda_b(t,i)}{\sum_{b=1}^{3}d_b \cdot \lambda_b(t,i)}$$
Finally, the scheduling objective can be stated as:
$$f_{total}^{norm} = \sum_{b=1}^{3} w_b N_b$$
4.4 Improved Spatio-Temporal Adaptive Particle Swarm Optimization
The large-scale nature of electric vehicle charging makes applying exact mathematical optimization difficult. Instead, heuristic methods more readily handle such discontinuity and multi-dimensional constraints. I made improvements to the standard Particle Swarm Optimization (PSO), which often struggles with premature convergence, by enabling adaptive adjustments at both temporal and spatial levels.
Standard PSO velocity and position updates are represented as:
$$v_i^{k+1} = w \cdot v_i^{k} + c_1r_1(pbest_i^k – x_i^k) + c_2r_2(gbest^k – x_i^k)$$
$$x_i^{k+1} = x_i^{k} + v_i^{k+1}$$
where $v_i^k$ and $x_i^k$ delineate the velocity and position of particle $i$ at iteration $k$. $w$ tracks the trade-off between local and global searches, while $c1$ and $c2$ define the cognitive and social coefficients. In order to move towards an adaptive mechanism along the timeline, I designed a weight-scheduling policy based on intervals; e.g., in peak demand windows, the global search ability of particles is raised accordingly:
$$w(t) = w_{\max} – \frac{w_{\max} – w_{\min}}{T_{max}}t + \Delta w(t)$$
where $\Delta w(t)$ is adjusted based on whether the current interval matches peak or shoulder-hour patterns.
Spatial adaptivity becomes possible if the learning coefficients shift with the loading level of the bus nodes they occupy. $c_1$ is enlarged when the node is heavily loaded, improving exploration in problem areas:
$$c_{1}(i) = c_{1,base}+\alpha\frac{P_{load}(i)}{P_{\max}}$$
$$c_{2}(i) = c_{2,base}-\alpha\frac{P_{load}(i)}{P_{\max}}$$
To produce a solid initial swarm that does not get trapped in suboptimal local basins, I generated the initial population using a Tent chaotic mapping:
$$x_{i+1} =
\begin{cases}
2x_i, & \text{if } x_i < 0.5 \\
2(1 – x_i), & \text{otherwise}
\end{cases}$$
Furthermore, to prevent premature maturity of a swarm and boosting exploration in the latter portions of an iteration, I added a Cauchy mutation strategy. It encourages longer jumps out of local minima thanks to the fat-tail characteristics of Cauchy random numbers:
$$X_i^{k*} = X_i^{k} + \beta e^{-k/T_{\max}} \cdot C(0,1)$$
where $C(0,1)$ draws from a standard Cauchy distribution, and $\beta$ is the mutation intensity. This step is instrumental when solving the integrated spatio-temporal scheduling model, because it assists the optimizer in avoiding premature convergence and allows it to react flexibly to large electric vehicle load fluctuations.
5. Simulation and Case Study Results
5.1 Test System Configuration
To verify the feasibility of my scheduling policy, I conducted tests on the commonly used IEEE 33-bus distribution network coupled with a city transportation topology. Transportation network nodes represent a mix of zones, including residential, commercial, and industrial sectors. Charging infrastructure was placed at certain key nodes, with differing charging capacities:
| Transportation Node Index | Area Topology Type | Charger Category | Number of Chargers | Power Rating (kW) |
|---|---|---|---|---|
| 3 | Residential use | Slow Charging spot | 15 | 7 |
| 9 | Residential use | Slow Charging spot | 15 | 7 |
| 6 | Industrial zone | Fast Charging spot | 10 | 120 |
| 11 | Transportation hub | Super charging spot | 5 | 250 |
| 14 | Transportation hub | Super charging spot | 5 | 250 |
| 15 | Commercial cluster | Fast Charging spot | 10 | 120 |
For validating the algorithm performance, I established three different scenarios:
| Scenario Identifier | Electric Vehicle Fleet Size | Traffic Cost Factors Considered? | Optimization Solver Type |
|---|---|---|---|
| Scenario 1 | 200 | No | Standard Particle Swarm Optimization |
| Scenario 2 | 200 | Yes | Standard Particle Swarm Optimization |
| Scenario 3 | 200 | Yes | Improved Spatio-Temporal Particle Swarm Optimization |
5.2 Analysis of Node Voltage Deviations and Loss reduction
Through coordinated scheduling, my approach effectively curbed the risk of voltage limit violations. In the test, node 26 illustrated severe dip before any optimization, with voltage deviations approaching the lower limit (-5.0% to -2.0%). Once my spatio-temporal scheduling algorithm optimized the charge and discharge cycles of electric vehicles, the node’s voltage deviation was significantly adjusted to fall within the allowable safe interval (-3.0% to -1.5%). This effect stems from decentralized storage injection at peak times and absorption of surplus at valley periods, both flattening the overall network power flow profiles and ultimately raising voltage stability margins.
I also evaluated the distribution grid loss changes at Bus node 10, where Dijkstra path planning prevented vehicles from driving through longer and more-high-impedance segments. The original peak value registered 12.5 kW, but the optimized system reduced the maximum network loss to 8.7 kW. That is a sizable 30.4% reduction, an excellent indicator of the spatial contribution of the scheduling plan.
5.3 Spatio-Temporal Charging and Discharging Distribution
The resulting charging and discharging power distribution across time and nodes shows strong alignment with zone-level temporal characteristics. Positive values indicate the charging activity, while negative values indicate V2G discharging. During high-price morning and night periods, the optimizer mainly schedules discharge at commercial zones, whereas residential region slow charging emerges in the late night to benefit from lower tariff rates. This means the proposed model successfully shifts large blocks of demand in both space and time.
Figure 5-1. The distribution of charge and discharge load across time and location, where positive values represent charging and negative values represent discharging.
| EV Fleet Proportion | User Engagement Rate $\gamma$ | Peak-Valley Reduction Rate | Total Operational Cost (RMB) |
|---|---|---|---|
| 15% | 55% | 48% | 65,820 |
| 25% | 65% | 59% | 60,632 |
| 35% | 70% | 52% | 64,210 |
Interestingly, I identified that merely growing the EV share does not guarantee a lower peak-valley differential, as very high percentages (35%) led to load congestion and higher valley-filling deficiency, reducing the rate to 52%.
5.4 System-Level Multi-Scenario Comparisons
In my comparison experiments, Scenario 1 (optimization without considering traffic costs) achieved only a 22% peak-valley reduction. Adding routing constraints in Scenario 2 pushed this value to 41.8%. However, because static PSO runs the risk of premature saturation, convergence quality suffered. In Scenario 3, after incorporating dynamic weight adjustment and mutation operations, the peak-valley difference was reduced by 59%. Distribution losses dropped to 21.76 kW, and the overall grid operating cost was trimmed to 60,632.47 RMB, saving roughly 11% over the baseline scenario. These substantial improvements prove the effectiveness and synergies of adjusting both search inertia and learning coefficients as a function of the charging and location patterns.
| Scenario | Pre-optimization Peak-Valley Load gap (kW) | Post optimization Peak-Valley gap (kW) | Network losses (kW) | Grid Economic cost (RMB) | Transportation-related cost (RMB) | Total Cost (RMB) |
|---|---|---|---|---|---|---|
| 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 |
6. Conclusion
In this thesis, I proposed a GCN-Transformer architecture for prediction and a spatio-temporal optimal scheduling model for large-scale electric vehicle integration. The pertinent conclusions are summarized below.
First, regarding the electric vehicle charging load prediction: I built a prediction model that embeds a transportation network topology directly into the training structure. By treating charging stations as graph nodes, the GCN can extract adjacency-based spatial correlations between different districts. The Transformer simultaneously captures complex nonlinear temporal information, producing an effective spatio-temporal feature representation. This method outperformed competing algorithms in all key error metrics: RMSE was 56.9% lower than the classic BP; MAPE fell by 71% relative to LSTM; MAE dropped 48.5% compared with the sole GCN, and R² rose to 0.926. It is thus highly beneficial for exactly forecasting load fluctuations induced by social behaviors and weather.
Second, regarding the electric vehicle charging/discharging scheduling strategy: I integrated the user’s travel preferences, dynamic dynamic route selection, and distribution grid flow constraints into a multi-objective optimization model aiming at an economic peak-valley load shaving and loss reduction strategy. To address the complexity and dynamics of solution spaces, I developed an improved Spatio-Temporal Particle Swarm Optimizer. Dynamically changed inertial weight (based on peak/valley period), node-based adaptive learning adjustment, Tent chaotic initialization, and late-stage Cauchy mutation offered a better global and local search capability trade-off. Simulation on the IEEE33 system validated the proposed scheduling policy with reduced peak-valley gap by 59%, lower network loss, and 11% lower total daily cost. This confirms the feasibility and versatility of the spatio-temporal scheduling plan.
Nevertheless, there are several future directions to explore for capacity expansion. For example, the current framework deals exclusively with electric vehicles. With the development of multi-energy loads and storage systems, integration with hydrogen energy vehicles and mobile energy storage likely holds greater potential for system-level optimization. For more accurate predictions, communication between the power grid and transportation networks should grow to include real-time high-resolution traffic flows. The impact of battery life cycles and battery degradation when using V2G services should also be modeled in the user-centric cost structure so that all stakeholders—owners, operators, and utilities—can align in achieving more economical and stable grid operations.