In recent years, the global shift toward sustainable transportation has accelerated, with electric car adoption rising exponentially. As a key enabler for this transition, charging and swapping infrastructure must keep pace to support the growing fleet of electric car vehicles. However, planning such infrastructure is fraught with challenges, including data scarcity, dynamic policy changes, and technological disruptions. In this article, I explore the application of grey system theory, specifically the GM(1,1) model, to predict the quantity of electric car charging and swapping facilities. By leveraging historical data and incorporating buffer operators to handle uncertainties, I aim to provide a robust forecasting framework that can guide investment and policy decisions for electric car ecosystems.
The proliferation of electric car models worldwide has underscored the critical need for reliable and accessible charging and swapping stations. Without adequate infrastructure, range anxiety can stifle electric car adoption, hindering environmental goals. Traditional forecasting methods often rely on large datasets or explicit causal factors, which may be lacking in emerging sectors like electric car infrastructure. Grey models, however, excel in “small sample, poor information” scenarios, making them ideal for this context. I will detail how the GM(1,1) model, enhanced with weakening buffer operators, can capture the underlying growth trends of electric car facilities, offering insights into future demands.
To begin, I delve into the theoretical foundations of grey prediction models. The GM(1,1) model is a first-order, single-variable grey differential equation that transforms discrete time-series data into a continuous pattern. Let me define the original sequence as \( X^{(0)} = (x^{(0)}(1), x^{(0)}(2), \dots, x^{(0)}(n)) \), where \( n \) is the number of observations, often representing annual counts of electric car charging piles or swapping stations. Given the exponential-like growth in electric car infrastructure data, I apply a first-order average weakening buffer operator to smooth fluctuations caused by external shocks like policy shifts. The buffered sequence \( Y^{(0)} \) is calculated as:
$$ y^{(0)}(k) = \frac{1}{n-k+1} \sum_{i=k}^{n} x^{(0)}(i), \quad k=1,2,\dots,n $$
This operator reduces randomness and highlights the inherent trend, crucial for accurate electric car facility predictions. Next, I generate the first-order accumulated generating operation (1-AGO) sequence \( Y^{(1)} \) to convert the data into a monotonic series:
$$ y^{(1)}(k) = \sum_{i=1}^{k} y^{(0)}(i), \quad k=1,2,\dots,n $$
The 1-AGO sequence forms the basis for the grey differential equation:
$$ \frac{dy^{(1)}}{dt} + a y^{(1)} = b $$
Here, \( a \) is the development coefficient, indicating the growth rate of electric car infrastructure, and \( b \) is the grey input, reflecting external influences. The solution to this equation yields the time-response function for the accumulated sequence:
$$ \hat{y}^{(1)}(k+1) = \left( y^{(0)}(1) – \frac{b}{a} \right) e^{-ak} + \frac{b}{a} $$
To estimate parameters \( a \) and \( b \), I use the least squares method. Let me define the background value \( z^{(1)}(k) = 0.5 \left( y^{(1)}(k) + y^{(1)}(k-1) \right) \) for \( k=2,3,\dots,n \). The parameter vector \( [a, b]^T \) is computed as:
$$ [a, b]^T = (B^T B)^{-1} B^T Y $$
where
$$ B = \begin{bmatrix} -z^{(1)}(2) & 1 \\ -z^{(1)}(3) & 1 \\ \vdots & \vdots \\ -z^{(1)}(n) & 1 \end{bmatrix}, \quad Y = \begin{bmatrix} y^{(0)}(2) \\ y^{(0)}(3) \\ \vdots \\ y^{(0)}(n) \end{bmatrix} $$
Finally, I revert the predicted accumulated values to the original scale via inverse accumulation:
$$ \hat{y}^{(0)}(k+1) = \hat{y}^{(1)}(k+1) – \hat{y}^{(1)}(k) $$
Model accuracy is assessed using posterior variance ratio \( C \) and small error probability \( P \). The residual sequence \( \epsilon(k) = y^{(0)}(k) – \hat{y}^{(0)}(k) \) has variance \( S_1^2 \), while the original sequence variance is \( S_2^2 \). Then:
$$ C = \frac{S_1}{S_2}, \quad P = P(|\epsilon(k) – \bar{\epsilon}| < 0.6745 S_2) $$
Based on established criteria, a model is rated excellent if \( C \leq 0.35 \) and \( P \geq 0.95 \). This rigorous validation ensures reliable forecasts for electric car infrastructure planning.
Now, I apply this grey model to historical data on electric car charging and swapping facilities. The data spans from 2017 to 2024, sourced from industry reports and governmental statistics, focusing on cumulative counts. For electric car charging piles, the raw data shows rapid growth, while swapping stations exhibit a steeper rise in recent years. I preprocess the data using the buffer operator to mitigate outliers, as shown in the tables below.
| Year | Public Charging Piles (10k units) | Buffered Sequence (10k units) |
|---|---|---|
| 2017 | 24.0 | 139.99 |
| 2018 | 38.7 | 156.56 |
| 2019 | 51.6 | 176.20 |
| 2020 | 80.7 | 201.12 |
| 2021 | 114.7 | 231.23 |
| 2022 | 179.7 | 270.07 |
| 2023 | 272.6 | 315.25 |
| 2024 | 357.9 | 357.90 |
| Year | Swapping Stations (units) | Buffered Sequence (units) |
|---|---|---|
| 2019 | 306 | 1961 |
| 2020 | 535 | 2292 |
| 2021 | 1192 | 2731.25 |
| 2022 | 1973 | 3244.33 |
| 2023 | 3567 | 3880 |
| 2024 | 4193 | 4193 |
Using the buffered sequences, I construct GM(1,1) models for both electric car infrastructure types. For public charging piles, the parameters are estimated as \( a = -0.14 \) and \( b = 122.28 \), indicating a steady growth rate influenced by market expansion. The model’s time-response function is:
$$ \hat{y}^{(1)}(k+1) = (139.99 – \frac{122.28}{-0.14}) e^{0.14k} + \frac{122.28}{-0.14} $$
Simplifying, I derive predictions for the original scale. The fitting errors are minimal, as summarized below:
| Year | Buffered Data | Predicted Value | Residual | Relative Error (%) |
|---|---|---|---|---|
| 2017 | 139.99 | 139.99 | 0.00 | 0.00 |
| 2018 | 156.56 | 152.72 | 3.84 | 2.46 |
| 2019 | 176.20 | 175.99 | 0.21 | 0.12 |
| 2020 | 201.12 | 202.82 | -1.70 | 0.85 |
| 2021 | 231.23 | 233.74 | -2.51 | 1.08 |
| 2022 | 270.07 | 269.37 | 0.70 | 0.26 |
| 2023 | 315.25 | 310.43 | 4.82 | 1.53 |
| 2024 | 357.90 | 357.75 | 0.15 | 0.04 |
The average relative error is 0.91%, with \( C = 0.035 \) and \( P = 1 \), denoting excellent precision. This model effectively captures the growth pattern of electric car charging infrastructure, accounting for technological advancements like ultra-fast charging that may alter demand dynamics.
For swapping stations, the GM(1,1) model yields \( a = -0.15 \) and \( b = 1900.82 \), reflecting a higher growth impetus due to increasing adoption of battery-swapping modes for electric car fleets. The time-response function is:
$$ \hat{y}^{(1)}(k+1) = (1961 – \frac{1900.82}{-0.15}) e^{0.15k} + \frac{1900.82}{-0.15} $$
The fitting performance is shown in the following table:
| Year | Buffered Data | Predicted Value | Residual | Relative Error (%) |
|---|---|---|---|---|
| 2019 | 1961 | 1961 | 0.00 | 0.00 |
| 2020 | 2292 | 2366.73 | -74.73 | 3.26 |
| 2021 | 2731.25 | 2748.58 | -17.33 | 0.63 |
| 2022 | 3244.33 | 3192.04 | 52.29 | 1.61 |
| 2023 | 3880 | 3707.06 | 172.94 | 4.46 |
| 2024 | 4193 | 4305.16 | -112.16 | 2.67 |
The average relative error is 2.53%, with \( C = 0.142 \) and \( P = 1 \), also indicating a high-quality model. These results validate the grey model’s capability to forecast electric car swapping facilities, even with limited data points.
Based on the models, I predict the quantity of electric car charging and swapping infrastructure from 2025 to 2028. The forecasts are derived by extending the time-response functions and applying inverse accumulation. The results are summarized in the table below:
| Year | Public Charging Piles (10k units) | Swapping Stations (units) |
|---|---|---|
| 2025 | 412.28 | 4999 |
| 2026 | 475.13 | 5806 |
| 2027 | 547.55 | 6743 |
| 2028 | 631.02 | 7831 |
These projections suggest a sustained expansion in electric car infrastructure, with public charging piles expected to reach approximately 6.31 million units by 2028, and swapping stations nearing 7,831 units. This growth aligns with the accelerating adoption of electric car vehicles worldwide, emphasizing the need for coordinated planning. The grey model inherently smooths out short-term volatilities, such as policy incentives or technological breakthroughs, providing a stable outlook for electric car ecosystem stakeholders.
To contextualize the predictions, I analyze the implications for electric car infrastructure development. The rising numbers indicate that charging piles will remain dominant due to their versatility and lower upfront costs, but swapping stations are gaining traction for commercial electric car fleets requiring rapid turnaround. Key factors influencing these trends include:
- Technological Innovation: Advancements in ultra-fast charging (e.g., 800V systems) could reduce per-station demand but may be offset by increased electric car sales. The grey model’s buffer operator implicitly accounts for such shifts by dampening extreme fluctuations.
- Policy Support: Government subsidies and mandates for electric car charging networks can accelerate deployment, reflected in the model’s grey input parameter \( b \).
- Market Dynamics: The ratio of electric car vehicles to charging points is a critical metric; predictions help maintain an optimal balance to prevent congestion or underutilization.
I further explore the mathematical robustness of the grey model through sensitivity analysis. By varying the buffer operator or initial data points, I assess the impact on electric car infrastructure forecasts. For instance, if I adjust the buffering strength using a weighted average, the development coefficient \( a \) may change slightly, but the overall growth trajectory for electric car facilities remains consistent. This resilience underscores the model’s utility in uncertain environments.
Building on the forecasts, I propose strategic recommendations to enhance electric car infrastructure planning. First, policymakers should prioritize the integration of ultra-fast charging technologies with grid storage systems to manage peak loads from electric car charging. This can be guided by the predicted increase in charging piles, ensuring sufficient capacity. Second, standardizing battery-swapping protocols across electric car manufacturers is crucial to scale up swapping stations efficiently, leveraging the projected growth. Third, promoting “vehicle-battery separation” business models can reduce costs for electric car users, aligning with the infrastructure expansion. Lastly, regional planning should use these forecasts to allocate resources, targeting underserved areas to support equitable electric car adoption.
In conclusion, the grey GM(1,1) model, augmented with weakening buffer operators, offers a powerful tool for forecasting electric car charging and swapping infrastructure. My analysis demonstrates high accuracy in predicting future quantities, with models achieving excellent validation metrics. The forecasts indicate robust growth through 2028, highlighting the ongoing evolution of electric car ecosystems. By applying this approach, stakeholders can make data-driven decisions to foster sustainable transportation. Future work could incorporate more variables, such as economic indicators or electric car battery technology trends, but the grey model provides a solid foundation for near-term planning. As electric car adoption continues to surge, such predictive insights will be invaluable for building resilient and accessible infrastructure networks.
To reiterate, the success of electric car mobility hinges on reliable charging and swapping options. Through grey modeling, I have shown how to anticipate needs and optimize investments, ensuring that infrastructure keeps pace with the electric car revolution. This methodology is adaptable to other sectors with limited data, but its application here underscores the transformative potential for electric car industries globally.