I begin with a practical observation that motivates this entire study: electric vehicle charging is no longer a small, homogeneous auxiliary load. It is a growing, behavior-driven load whose temporal shape depends strongly on who uses a charging pile, when those users arrive, how long they stay, and how much energy they require. For grid operation, the consequence is not merely a need for a better point forecast. The consequence is a need for a forecast that separates heterogeneous electric vehicle charging behavior and quantifies uncertainty in a form that risk assessment and dispatch decisions can actually use. I therefore propose a forecasting framework that combines K-means clustering of charging piles with a long short-term memory network trained through a weighted quantile loss. The clustering step mitigates feature mixing among different electric vehicle charging patterns, and the quantile loss converts a conventional deterministic predictor into a probabilistic predictor that outputs a 10%–90% prediction interval.
My central argument is simple. If I pool every charging pile into one aggregate series, I force one model to learn private-car overnight charging, bus depot charging, official-vehicle daytime charging, taxi opportunity charging, and other usage patterns at the same time. Those patterns overlap in time but differ in level, ramp rate, duration, and tail behavior. The resulting feature mixing is not a minor nuisance. It directly increases the variance that the model must explain and weakens the value of electric vehicle charging forecasts for operational risk decisions. I show that after clustering charging piles into five service-oriented groups, the average mean squared error of load forecasting falls by approximately 16.6% relative to the unclustered total-load benchmark. I also show that the probabilistic model achieves empirical coverage close to the nominal 80% interval across the five clusters, which supports its use as an uncertainty-aware electric vehicle charging forecasting tool.
1. Problem Formulation and Research Objective
I formulate the forecasting problem as follows. For each charging pile or charging-pile cluster, I observe a normalized load series at 15-minute resolution. The model receives a fixed input window and predicts the next normalized load value. In the deterministic case, the model minimizes a mean squared error. In the probabilistic case, the model predicts multiple conditional quantiles and is trained with a weighted quantile loss. The difference matters because a grid operator does not only ask what the most likely electric vehicle charging load will be. The operator also asks how bad the upper tail could be, how low the lower tail could be, and whether the forecast interval is reliable enough to support reserve sizing, feeder loading checks, and demand-response activation.
I define the normalized load at time index \(t\) as \(x_t\), the input window length as \(L\), and the forecast horizon as \(H\). In this study, the data are sampled every 15 minutes, and the input length is 96 steps, corresponding to one full day. The output length is one step, so the model performs one-step-ahead forecasting in the reported experiments. The same framework can be extended to multi-step forecasting by changing the output layer and the training target.
$$x’_t=\frac{x_t-x_{\min}}{x_{\max}-x_{\min}}$$
I use normalization because charging-pile loads differ greatly in absolute magnitude. A private-car pile in a residential area and a bus-depot pile may both have morning and evening features, but their installed capacity and utilization levels can differ by orders of magnitude. Normalization allows the clustering and forecasting stages to focus on temporal shape and relative variation rather than on raw scale. After prediction, values can be transformed back to the original load scale if needed for engineering decisions.
2. Data, Splitting, and Experimental Setting
I use charging-pile load records and sampling timestamps provided by a provincial power grid company. The sampling interval is 15 minutes. I split the dataset into training, validation, and test subsets in a 7:1.5:1.5 ratio. I keep the chronological order of observations to avoid leakage from future electric vehicle charging behavior into the training set. The validation set is used for model selection and early stopping logic where applicable, and the test set is used only for final reporting.
| Item | Setting | Role in the study |
|---|---|---|
| Load signal | Charging-pile load | Target variable for electric vehicle charging forecasting |
| Sampling interval | 15 minutes | Captures intraday electric vehicle charging dynamics |
| Input length | 96 steps | One full day of historical electric vehicle charging load |
| Output length | 1 step | One-step-ahead load prediction |
| Training split | 70% | Parameter estimation |
| Validation split | 15% | Model selection and tuning checks |
| Test split | 15% | Final performance evaluation |
| Clustering range | \(K\in[2,8]\) | Silhouette-based selection of the number of charging-pile clusters |
| Selected clusters | \(K=5\) | Private, bus, official, taxi, and other usage groups |
| Quantile interval | 10%–90% | Probabilistic electric vehicle charging forecast output |
I emphasize that the data are not treated as a single undifferentiated stream in the main proposed method. Instead, I first learn a clustering structure from daily load shapes, then train separate probabilistic forecasters for the resulting clusters. This design choice is the core of my response to feature mixing in electric vehicle charging data.
3. Why Charging-Pile Heterogeneity Matters
Electric vehicle charging load is stochastic at the individual vehicle level, but it is not structureless at the pile level. A charging pile that primarily serves private cars tends to exhibit commuter-related evening or overnight concentration. A charging pile that primarily serves buses tends to exhibit depot-based scheduling, often with large blocks of energy transfer and clear operational windows. A charging pile that primarily serves official vehicles may show daytime availability patterns. A taxi-oriented pile may show more frequent, shorter, and less regular charging events across the day. Other usage types may mix commercial, public, or fleet behavior. When these are aggregated, the resulting series is not simply the sum of smooth components. It is a mixture of different arrival processes, different state-of-charge distributions, and different user constraints.
I therefore treat the charging pile as the unit of behavioral analysis. I cluster piles according to their normalized daily load patterns and then assign service-type labels based on the dominant vehicle type served by each cluster. The labeling rule I adopt is that a cluster is named after a vehicle-use type when that type accounts for more than 50% of the service objects in the cluster. This produces five interpretable groups: private-car usage, bus usage, official-vehicle usage, taxi usage, and other usage. The labels are not merely descriptive. They give me a way to check whether the clustering has separated distinct electric vehicle charging regimes rather than arbitrary statistical segments.
| Cluster | Dominant service type | Expected temporal behavior | Forecasting implication |
|---|---|---|---|
| Private-car usage | Private vehicles | Commuter-linked evening or overnight charging concentration | Model should capture stable daily cycles and lower tail uncertainty during work hours |
| Bus usage | Buses | Depot scheduling with block-like charging windows | Model should learn sharp ramps and scheduled high-load periods |
| Official-vehicle usage | Official vehicles | Daytime availability and administrative schedule effects | Model should separate weekday-like daytime peaks from private-car evening peaks |
| Taxi usage | Taxis | Frequent opportunity charging and irregular peaks | Model should tolerate higher variability and wider intervals |
| Other usage | Mixed or other vehicles | Composite behavior without one dominant private or fleet pattern | Model should act as a residual mixed-behavior group with moderate variance |
4. K-means Clustering of Electric Vehicle Charging Piles
I use K-means because it provides a transparent and computationally efficient way to group charging piles by load-shape similarity. For a set of normalized daily load vectors \(\{x_i\}_{i=1}^{N}\), K-means solves the following objective:
$$\min_{\{C_k\}_{k=1}^{K},\{\mu_k\}_{k=1}^{K}}\sum_{k=1}^{K}\sum_{x_i\in C_k}\left\|x_i-\mu_k\right\|_2^2$$
Here, \(C_k\) is the set of charging piles assigned to cluster \(k\), and \(\mu_k\) is the cluster centroid. The centroid represents the average normalized electric vehicle charging load shape of the cluster. I select the number of clusters by evaluating silhouette scores over \(K\in[2,8]\). The silhouette score for a sample \(i\) is defined as follows:
$$s(i)=\frac{b(i)-a(i)}{\max\{a(i),b(i)\}}$$
where \(a(i)\) is the average distance from sample \(i\) to other samples in its own cluster, and \(b(i)\) is the minimum average distance from sample \(i\) to samples in any other cluster. The mean silhouette score over all samples provides a compact measure of within-cluster cohesion and between-cluster separation. In my experiments, the best value is obtained at \(K=5\). This is consistent with the operational interpretation of the data: five clusters are sufficient to separate the dominant electric vehicle charging regimes without fragmenting the dataset into unstable micro-clusters.
| Step | Operation | Output |
|---|---|---|
| 1 | Normalize each charging-pile load series | Scale-independent daily load shapes |
| 2 | Run K-means for \(K=2,\ldots,8\) | Candidate partitions of charging piles |
| 3 | Compute mean silhouette score for each \(K\) | Cluster-quality comparison |
| 4 | Select the \(K\) with the best silhouette evidence | \(K=5\) |
| 5 | Inspect dominant vehicle-type labels in each cluster | Five interpretable service-oriented clusters |
| 6 | Train a separate probabilistic forecaster for each cluster | Cluster-specific electric vehicle charging forecasts |
The practical benefit of this step is not only statistical. It is operational. Once I know that a group of piles is dominated by private-car usage, I expect its electric vehicle charging load to have a different risk profile from a taxi-dominated group. The private-car group may have a more regular daily cycle, whereas the taxi group may exhibit sharper and less predictable deviations. A single aggregate model must average these behaviors, but a clustered model can allocate capacity and uncertainty more appropriately.
5. LSTM Backbone for Temporal Dependence
I use an LSTM as the forecasting backbone because electric vehicle charging load has strong temporal dependence. The load at a given time is related to recent charging activity, the time of day, and longer-range daily routines. An LSTM is suitable because its gating mechanism can retain useful history and suppress irrelevant history. I define the input at time \(t\) as \(x_t\) and the previous hidden state as \(h_{t-1}\). The forget gate is:
$$f_t=\sigma\left(W_f[h_{t-1},x_t]+b_f\right)$$
The input gate is:
$$i_t=\sigma\left(W_i[h_{t-1},x_t]+b_i\right)$$
The candidate cell state is:
$$\tilde{C}_t=\tanh\left(W_C[h_{t-1},x_t]+b_C\right)$$
The cell state update is:
$$C_t=f_t\odot C_{t-1}+i_t\odot\tilde{C}_t$$
The output gate is:
$$o_t=\sigma\left(W_o[h_{t-1},x_t]+b_o\right)$$
The hidden state output is:
$$h_t=o_t\odot\tanh(C_t)$$
In these equations, \(\sigma\) is the sigmoid activation, \(\tanh\) is the hyperbolic tangent activation, and \(\odot\) denotes elementwise multiplication. I use the hidden state \(h_t\) to produce the forecast. For deterministic forecasting, the output is a single value. For probabilistic forecasting, the output layer produces multiple quantile values, and the loss function is changed accordingly.
| Symbol | Meaning | Role in electric vehicle charging forecasting |
|---|---|---|
| \(x_t\) | Input load at time \(t\) | Current electric vehicle charging observation |
| \(h_{t-1}\) | Previous hidden state | Compressed recent charging dynamics |
| \(f_t\) | Forget gate | Controls retention of past charging patterns |
| \(i_t\) | Input gate | Controls injection of new charging information |
| \(\tilde{C}_t\) | Candidate cell state | Encodes new candidate memory |
| \(C_t\) | Cell state | Long-range memory of daily and multi-day behavior |
| \(o_t\) | Output gate | Controls the hidden representation used for prediction |
| \(h_t\) | Hidden state output | Feature vector passed to the forecasting layer |
I selected LSTM over simpler recurrent or convolutional alternatives after comparing it with GRU, RNN, and TCN under the same total-load forecasting setting. The comparison is reported later. The key reason for the LSTM advantage is that its gates provide a stable path for long-range dependence, which matters for daily electric vehicle charging cycles and for the distinction between working-hour and non-working-hour behavior.
6. Probabilistic Forecasting with Weighted Quantile Loss
I now turn to the main modification that makes the forecast useful for risk assessment. A conventional LSTM trained with mean squared error produces a conditional mean. That is useful for central expectation but insufficient for uncertainty-aware electric vehicle charging management. I therefore replace the mean squared error loss with a weighted quantile loss. For a target \(y_t\), a predicted quantile \(\hat{y}_t^{(q)}\), and a quantile level \(q\in(0,1)\), the pinball loss is:
$$\rho_q(y_t,\hat{y}_t^{(q)})=
\begin{cases}
q\left(y_t-\hat{y}_t^{(q)}\right), & y_t\ge \hat{y}_t^{(q)},\\
(1-q)\left(\hat{y}_t^{(q)}-y_t\right), & y_t<\hat{y}_t^{(q)}.
\end{cases}$$
Equivalently, I can write the same loss in compact form as:
$$\rho_q(y_t,\hat{y}_t^{(q)})=\max\left\{(q-1)\left(y_t-\hat{y}_t^{(q)}\right),\;q\left(y_t-\hat{y}_t^{(q)}\right)\right\}$$
I train the model on a set of quantile levels. The weighted quantile loss aggregates the pinball losses across quantiles:
$$\mathcal{L}_{W}=\frac{1}{K}\sum_{k=1}^{K}\lambda_k\rho_{q_k}\left(y_t,\hat{y}_t^{(q_k)}\right)$$
where \(K\) is the number of quantile levels, \(q_k\) is the \(k\)-th quantile level, and \(\lambda_k\) is its weight. I assign larger weight to the lower tail and median and smaller weight to the upper tail in the reported configuration, following the idea that underestimation risk and central behavior deserve explicit emphasis in electric vehicle charging forecasting. The weights used for the anchor quantiles are shown below. For intermediate quantiles, I use monotone interpolation between these anchors so that the weighted loss remains well defined across the whole 10%–90% interval.
| Quantile level \(q_k\) | Weight \(\lambda_k\) | Interpretation |
|---|---|---|
| 0.10 | 1.2 | Emphasizes the lower-tail electric vehicle charging load risk |
| 0.50 | 1.0 | Maintains a strong central forecast |
| 0.90 | 0.8 | Keeps the upper tail informative without dominating training |
The model parameters are updated by backpropagation through the weighted loss:
$$\frac{\partial \mathcal{L}_{W}}{\partial \Theta_{\mathrm{old}}}=
\frac{\partial \mathcal{L}_{W}}{\partial \hat{y}}
\frac{\partial \hat{y}}{\partial \mathrm{LSTM}}
\frac{\partial \mathrm{LSTM}}{\partial \Theta_{\mathrm{old}}}$$
$$\Theta_{\mathrm{new}}=\Theta_{\mathrm{old}}-\alpha
\frac{\partial \mathcal{L}_{W}}{\partial \Theta_{\mathrm{old}}}$$
Here, \(\Theta_{\mathrm{old}}\) is the parameter set before the update, \(\Theta_{\mathrm{new}}\) is the updated parameter set, and \(\alpha\) is the learning rate. After training, I load the best parameter set \(\Theta^*\) and produce the test forecast as:
$$\hat{Y}_{\mathrm{test}}=\mathrm{LSTM}\left(X_{\mathrm{test}};\Theta^*\right)$$
For each time step, the model outputs a set of quantile forecasts. The 10% and 90% quantiles form the prediction interval, and the median provides a central estimate. This is the output form I recommend for electric vehicle charging risk assessment because it gives both a central expectation and a quantified uncertainty band.
| Aspect | Deterministic LSTM | Probabilistic LSTM with weighted quantile loss |
|---|---|---|
| Output | Single point forecast | Multiple quantile forecasts |
| Loss | Mean squared error | Weighted pinball loss |
| Risk information | Limited to central expectation | Explicit lower-tail and upper-tail information |
| Operational use | Base scheduling | Reserve sizing, risk screening, and uncertainty-aware dispatch |
| Reported interval | None | 10%–90% prediction interval |
7. Evaluation Metrics
I evaluate point forecast accuracy with mean squared error, mean absolute error, mean absolute percentage error, and the coefficient of determination. These metrics are defined as follows:
$$\mathrm{MSE}=\frac{1}{n}\sum_{i=1}^{n}\left(y_i-\hat{y}_i\right)^2$$
$$\mathrm{MAE}=\frac{1}{n}\sum_{i=1}^{n}\left|y_i-\hat{y}_i\right|$$
$$\mathrm{MAPE}=\frac{1}{n}\sum_{i=1}^{n}\left|\frac{y_i-\hat{y}_i}{y_i}\right|\times 100\%$$
$$R^2=1-\frac{\sum_{i=1}^{n}\left(y_i-\hat{y}_i\right)^2}{\sum_{i=1}^{n}\left(y_i-\bar{y}\right)^2}$$
In these formulas, \(y_i\) is the observed value, \(\hat{y}_i\) is the predicted value, \(n\) is the number of test observations, and \(\bar{y}\) is the mean observed value. For probabilistic forecasting, I also report empirical coverage of the 10%–90% interval. The prediction interval coverage probability is:
$$\mathrm{PICP}=\frac{1}{N}\sum_{t=1}^{N}\mathbf{1}\left\{\hat{y}_t^{(0.1)}\le y_t\le \hat{y}_t^{(0.9)}\right\}$$
A well-calibrated nominal 80% interval should produce an empirical coverage close to 80%. I use this as a direct check on whether the probabilistic electric vehicle charging forecast is useful in practice. If coverage is far below the nominal level, the interval is too narrow and may understate risk. If coverage is far above the nominal level, the interval may be too wide and less useful for scheduling.
| Metric | Type | What it measures | Operational relevance |
|---|---|---|---|
| MSE | Point error | Squared deviation between forecast and observation | Penalizes large electric vehicle charging forecast errors |
| MAE | Point error | Absolute deviation | Interpretable average error magnitude |
| MAPE | Relative point error | Percentage deviation | Useful for comparing relative accuracy |
| \(R^2\) | Goodness of fit | Explained variation | Shows how well the forecast tracks observed load variation |
| PICP | Interval calibration | Empirical coverage of the prediction interval | Checks whether the 10%–90% interval is trustworthy |
8. Experimental Scenarios
I design two scenarios. Scenario 1 is the total-load benchmark. In this scenario, I do not cluster the charging piles. I train the forecasting model on the aggregate electric vehicle charging load and compare LSTM with GRU, RNN, and TCN. The purpose is to establish whether LSTM is a suitable backbone for this task. Scenario 2 is the clustered probabilistic forecasting scenario. In this scenario, I first partition charging piles into five clusters with K-means, then train the weighted-quantile LSTM separately for each cluster, and finally aggregate or compare the cluster-level results. The purpose is to test whether clustering reduces feature mixing and whether the probabilistic output is calibrated.
| Scenario | Clustering | Forecasting model | Purpose |
|---|---|---|---|
| Scenario 1 | No | GRU, RNN, TCN, LSTM | Establish the backbone comparison for total electric vehicle charging load |
| Scenario 2 | K-means with \(K=5\) | LSTM with weighted quantile loss | Test cluster-specific probabilistic electric vehicle charging forecasting |
9. Total-Load Backbone Comparison
I first report the total-load comparison without clustering. Table 9 shows the results. The LSTM achieves the lowest MSE and MAE and the highest \(R^2\). The improvement is large enough that I do not regard the choice of backbone as a secondary detail. The GRU and RNN have higher errors, and the TCN has the weakest \(R^2\) in this experiment. The very high MAPE for several baselines reflects the difficulty of percentage errors when normalized load values can be small; nevertheless, the relative ranking on MSE, MAE, and \(R^2\) is consistent and supports LSTM as the backbone.
| Algorithm | MSE | MAE | MAPE (%) | \(R^2\) |
|---|---|---|---|---|
| GRU | 0.051 | 0.184 | 85.935 | 0.362 |
| RNN | 0.034 | 0.133 | 50.081 | 0.497 |
| TCN | 0.084 | 0.180 | 76.076 | 0.031 |
| LSTM | 0.006 | 0.045 | 0.122 | 0.934 |
I interpret this result in terms of electric vehicle charging dynamics. The total load contains multiple usage regimes, and the LSTM’s gating mechanism is better able to retain daily-periodic information while suppressing short-lived noise. The GRU simplifies the gating structure and appears to lose some long-range discrimination in this dataset. The RNN suffers from the well-known difficulty of learning long dependencies. The TCN captures local patterns but does not model the global daily dependence as effectively in this setting. These observations justify using LSTM as the base model before adding clustering and quantile loss.
10. Clustered Probabilistic Forecasting Results
After clustering the charging piles into five groups, I train the weighted-quantile LSTM for each cluster. Table 10 reports the point-forecast metrics for each cluster. The private-car cluster has the lowest MSE and the highest \(R^2\), which is consistent with a relatively regular commuter-linked electric vehicle charging pattern. The taxi cluster has the highest MSE and MAE among the five groups, which is consistent with more irregular opportunity charging. The average MSE across clusters is 0.005, the average MAE is 0.043, the average MAPE is 0.120, and the average \(R^2\) is 0.942.
| Cluster | MSE | MAE | MAPE (%) | \(R^2\) |
|---|---|---|---|---|
| Private-car usage | 0.002 | 0.030 | 0.071 | 0.971 |
| Bus usage | 0.005 | 0.033 | 0.119 | 0.938 |
| Official-vehicle usage | 0.006 | 0.042 | 0.122 | 0.928 |
| Taxi usage | 0.007 | 0.062 | 0.156 | 0.916 |
| Other usage | 0.006 | 0.047 | 0.132 | 0.956 |
| Average | 0.005 | 0.043 | 0.120 | 0.942 |
I compare the cluster average with the total-load LSTM benchmark. The MSE falls from 0.006 to 0.005. Using the reported values, the relative reduction is:
$$\Delta_{\mathrm{MSE}}=
\frac{0.006-0.005}{0.006}\times 100\%
\approx 16.6\%$$
This is the central quantitative result of my study. The improvement is not caused by a more complex network. It is caused by changing the learning problem. By separating charging piles into behaviorally coherent clusters, I reduce the burden on the model to represent incompatible electric vehicle charging patterns with a single set of parameters. The model no longer has to average a private-car evening peak against a bus-depot schedule or a taxi opportunity-charging pattern. It can specialize.
| Setting | MSE | MAE | MAPE (%) | \(R^2\) |
|---|---|---|---|---|
| Total-load LSTM benchmark | 0.006 | 0.045 | 0.122 | 0.934 |
| Clustered weighted-quantile LSTM average | 0.005 | 0.043 | 0.120 | 0.942 |
| Relative MSE change | Approximately 16.6% reduction | |||
I also note that the cluster-level metrics are not uniform. The private-car cluster is easier to forecast than the taxi cluster. This is exactly what I expect from the behavioral interpretation. Private-car charging is more routine and more strongly tied to daily schedules. Taxi charging is more opportunistic and therefore has a higher conditional variance. A responsible forecasting report should not hide this difference by reporting only one aggregate error. The cluster-level table is more informative because it shows where the uncertainty is concentrated.
11. Prediction Interval Calibration
The probabilistic output is evaluated through the empirical coverage of the 10%–90% interval. Table 12 reports the coverage values. The private-car cluster has 81.82% coverage, the bus cluster 79.55%, the official-vehicle cluster 85.64%, the taxi cluster 75.00%, and the other cluster 78.09%. The average coverage is approximately 80.02%, which is very close to the nominal 80% level. I regard this as evidence that the weighted quantile loss produces usable uncertainty bands for electric vehicle charging forecasting.
| Cluster | Nominal coverage (%) | Empirical coverage (%) | Deviation from nominal (%) |
|---|---|---|---|
| Private-car usage | 80.00 | 81.82 | +1.82 |
| Bus usage | 80.00 | 79.55 | -0.45 |
| Official-vehicle usage | 80.00 | 85.64 | +5.64 |
| Taxi usage | 80.00 | 75.00 | -5.00 |
| Other usage | 80.00 | 78.09 | -1.91 |
| Average | 80.00 | 80.02 | +0.02 |
I do not interpret perfect coverage as the only goal. A wider interval can always increase coverage, but it may become less useful. The relevant point is that the reported interval is neither severely under-covering nor absurdly over-covering. The official-vehicle cluster has higher coverage than nominal, which suggests that its interval may be somewhat conservative in the test period. The taxi cluster has lower coverage than nominal, which suggests that taxi electric vehicle charging retains more tail risk than the model captures. This is a useful diagnostic. It tells me where future work should focus: taxi and other mixed-usage piles may require additional covariates such as trip intensity, queueing, or real-time availability.
12. Interpretation of the Clustering Gain
I attribute the clustering gain to three mechanisms. First, clustering removes between-cluster heterogeneity from the training target. A single total-load model must fit a mixture distribution. A cluster-specific model fits a narrower conditional distribution. Second, clustering improves the signal-to-noise ratio for each specialized model. The model does not waste capacity on representing charging patterns that are irrelevant to the cluster. Third, clustering makes the quantile calibration more interpretable because each cluster has its own uncertainty profile. The taxi cluster can have wider intervals, while the private-car cluster can have tighter intervals, without forcing a single global interval width.
| Mechanism | Statistical effect | Operational effect |
|---|---|---|
| Feature decoupling | Reduces mixing of heterogeneous electric vehicle charging patterns | Improves forecast accuracy for each service type |
| Model specialization | Lowers learning complexity within each cluster | Supports targeted reserve and feeder risk assessment |
| Uncertainty stratification | Allows cluster-specific interval behavior | Provides more honest risk information for different pile types |
I also emphasize that the clustering is not merely a preprocessing trick. It changes the object of prediction. In the unclustered case, the target is an aggregate electric vehicle charging load. In the clustered case, the target is a set of service-specific electric vehicle charging loads. For planning, the aggregate may still be useful. For operation and risk, the service-specific view is often more actionable because different charging-pile groups have different controllability and different consequences of forecast error.
13. Practical Implications for Grid Risk and Dispatch
The probabilistic output has direct implications for grid risk and dispatch. A central forecast tells an operator what to expect on average. A quantile forecast tells the operator how much reserve may be needed if electric vehicle charging demand lands in the upper tail. The 10% lower quantile is also useful because it indicates how low the load could fall, which matters for voltage control and reverse-flow conditions in some feeders. The 90% upper quantile is useful for transformer loading checks, feeder capacity assessment, and demand-response prequalification.
I see three operational uses. First, the clustered forecast can support feeder-level risk screening. If the taxi cluster is expected to enter a high upper-tail regime, the operator can prioritize that feeder for monitoring or flexible response. Second, the probabilistic forecast can support reserve sizing. Instead of adding a fixed safety margin to a point forecast, the operator can use the upper quantile directly. Third, the forecast can support demand-response targeting. If the upper tail of a particular cluster is high, the operator can target that cluster with incentives or charging-schedule adjustments.
| Operational task | Forecast element used | Why clustering helps |
|---|---|---|
| Feeder risk screening | Upper quantile by cluster | Identifies which service type drives tail risk |
| Reserve sizing | 90% quantile and interval width | Separates regular private-car uncertainty from irregular taxi uncertainty |
| Demand-response targeting | Cluster-level upper-tail load | Allows incentives to be aimed at the relevant charging behavior |
| Voltage and reverse-flow checks | Lower quantile by cluster | Reveals low-load regimes that may affect feeder operation |
| Planning studies | Cluster-level central forecast | Preserves service-type structure instead of hiding it in an aggregate |
14. Comparison with Alternative Modeling Choices
I did not adopt a more complex sequence model because the experiments show that the main gain comes from clustering and probabilistic loss design, not from adding architectural complexity. A deeper network trained on the aggregate load would still face the same feature-mixing problem. A more complex model trained on each cluster could be explored in future work, but the current LSTM with weighted quantile loss already provides a strong balance between accuracy, interpretability, and computational cost.
| Design choice | Observed consequence | My interpretation |
|---|---|---|
| No clustering | Higher MSE and lower \(R^2\) | Aggregate electric vehicle charging load mixes incompatible behaviors |
| K-means with \(K=5\) | Lower average MSE and higher average \(R^2\) | Behavioral separation improves learnability |
| MSE loss only | Point forecast only | Insufficient for risk-aware dispatch |
| Weighted quantile loss | 10%–90% interval with near-nominal average coverage | Provides usable uncertainty information |
| LSTM backbone | Best total-load comparison among tested models | Gating mechanism captures daily electric vehicle charging dependence |
15. Limitations and Threats to Validity
I acknowledge several limitations. The cluster labels depend on the available service-type information, and in a different dataset the dominant-type threshold may need recalibration. The K-means objective assumes that cluster shapes are reasonably compact in the normalized load-shape space; if future charging behavior becomes highly multimodal, a mixture model or density-based clustering method may be more appropriate. The current experiments use a one-step-ahead output. Multi-step and day-ahead probabilistic forecasting are important extensions because operational decisions often require longer lead times. The current probabilistic evaluation focuses on coverage; future studies should also report interval width, sharpness, and scoring rules such as the continuous ranked probability score.
Another limitation is that the data come from one provincial power grid company. The qualitative conclusion that clustering helps is likely to be robust, but the exact error values may differ in other regions. Future work should test the framework on multiple regions, seasons, and weather conditions. Electric vehicle charging is also sensitive to temperature, holidays, tariffs, and traffic conditions. I did not include those covariates in the current model. Adding them could improve both the central forecast and the tail calibration, especially for taxi and other mixed-usage clusters.
| Limitation | Possible extension | Expected benefit |
|---|---|---|
| Single-region data | Multi-region validation | Tests external validity of electric vehicle charging conclusions |
| One-step horizon | Multi-step and day-ahead forecasting | Supports scheduling and reserve procurement |
| No weather covariates | Temperature, precipitation, and seasonality inputs | Improves tail behavior during extreme conditions |
| No traffic or trip covariates | Taxi trip intensity and road-network features | Could reduce taxi-cluster under-coverage |
| Coverage-only probabilistic evaluation | Interval width and CRPS | Provides a sharper view of probabilistic forecast quality |
16. Reproducible Modeling Summary
I summarize the complete procedure in Table 17. The workflow is deliberately modular. The clustering stage can be replaced without changing the forecasting stage. The forecasting stage can be replaced without changing the cluster interpretation. This modularity is useful because electric vehicle charging data will evolve as fleet composition, charging infrastructure, and tariff design change.
| Stage | Operation | Output used downstream |
|---|---|---|
| Data preparation | Collect 15-minute charging-pile load and normalize | Scale-independent electric vehicle charging series |
| Cluster search | Run K-means for \(K=2,\ldots,8\) | Candidate cluster structures |
| Cluster selection | Evaluate silhouette scores | Five-cluster partition |
| Cluster labeling | Apply dominant service-type rule above 50% | Private, bus, official, taxi, and other groups |
| Model training | Train weighted-quantile LSTM per cluster | Cluster-specific probabilistic forecasts |
| Evaluation | Compute MSE, MAE, MAPE, \(R^2\), and PICP | Accuracy and calibration evidence |
| Operational translation | Map quantiles to risk and dispatch actions | Risk-aware electric vehicle charging management |
17. Discussion of the Probabilistic Forecast Value
I want to stress that the probabilistic part of the model is not an add-on for academic completeness. Electric vehicle charging is a load where the tail matters. If the upper tail is underestimated, a feeder or transformer may be loaded beyond its limit. If the lower tail is misrepresented, voltage control or reverse-flow assumptions may be wrong. A point forecast cannot express these risks. A quantile forecast can. The weighted quantile loss gives the model an explicit incentive to learn the lower tail, the median, and the upper tail rather than only the conditional mean.
I also observe that the cluster-specific coverage results are more informative than a single aggregate coverage number. The taxi cluster has 75.00% coverage against a nominal 80% level. This does not invalidate the overall method, but it identifies a direction for improvement. Taxi electric vehicle charging is likely influenced by passenger demand, shift changes, and opportunity availability, which are not in the current input. The official-vehicle cluster has 85.64% coverage, which suggests a conservative interval. This may be acceptable for risk-averse operation, but it also indicates that the model could be sharpened if more official-vehicle scheduling information were available.
18. Conclusion
I have presented a clustering-based probabilistic forecasting method for electric vehicle charging load. The method uses K-means to partition charging piles into five service-oriented clusters, then uses an LSTM trained with a weighted quantile loss to produce 10%–90% prediction intervals. The clustering step reduces feature mixing among different electric vehicle charging behaviors. The quantile loss step converts the LSTM from a deterministic point predictor into an uncertainty-aware probabilistic predictor. In my experiments, the clustered model achieves an average MSE of 0.005, compared with 0.006 for the total-load LSTM benchmark, corresponding to an approximately 16.6% reduction in average mean squared error. The average \(R^2\) rises to 0.942, and the empirical coverage of the nominal 80% interval averages approximately 80.02% across the five clusters.
The broader lesson I draw is that electric vehicle charging forecasting should not treat all charging piles as interchangeable. The behavior of private cars, buses, official vehicles, taxis, and other users is different enough that the modeling should respect that difference. Once the behavior is separated, a relatively standard LSTM becomes much more effective. Once the loss is changed to a weighted quantile loss, the forecast becomes useful for risk and dispatch rather than only for central expectation. I therefore see the combination of K-means clustering and weighted-quantile LSTM as a practical and extensible framework for electric vehicle charging load probability forecasting.
In future work, I plan to extend the framework to multi-step and day-ahead forecasting, add weather and traffic covariates, and evaluate additional probabilistic scoring rules. I also plan to test whether the cluster structure remains stable across seasons and regions. These extensions would strengthen the operational value of electric vehicle charging forecasting and support the transition from passive load accommodation to active, risk-aware charging management.