As the world grapples with the challenges of climate change, the transition to sustainable transportation has become a critical priority. In China, the rapid adoption of electric vehicles (EVs) is seen as a key strategy to reduce carbon emissions and achieve the “dual carbon” goals of peaking carbon emissions by 2030 and achieving carbon neutrality by 2060. The electric vehicle market in China has experienced exponential growth, with over 31.4 million EVs on the road by the end of 2024, driven by supportive policies such as tax incentives for new energy vehicles. However, the widespread use of electric vehicles introduces new complexities, particularly in terms of grid stability and indirect carbon emissions. Uncontrolled charging of electric vehicles can lead to significant peak load demands on the power grid, exacerbating the strain on existing infrastructure. Moreover, while electric vehicles produce zero tailpipe emissions, the indirect carbon emissions from electricity generation during charging can undermine their environmental benefits if not managed properly. This paper explores the development of a time-of-use (TOU) electricity pricing strategy that considers carbon emissions to optimize the charging behavior of electric vehicles in China, thereby reducing indirect carbon footprints and enhancing grid reliability.
The integration of electric vehicles into the power grid presents both opportunities and challenges. On one hand, electric vehicles can serve as distributed energy resources, potentially supporting grid balancing through vehicle-to-grid (V2G) technologies. On the other hand, uncontrolled charging patterns, often concentrated during peak hours, can lead to increased grid stress and higher carbon emissions due to reliance on fossil fuel-based power generation. In China, where the power sector is the largest single source of carbon emissions, addressing the indirect emissions from electric vehicle charging is crucial for achieving national climate targets. Traditional approaches to electricity pricing, such as flat rates, do not account for the temporal variations in carbon intensity of electricity generation. Therefore, a dynamic pricing model that incentivizes charging during periods of low carbon intensity and low grid demand is essential. This study proposes a TOU pricing model that incorporates carbon emission factors and grid load characteristics to guide electric vehicle charging behavior effectively.
To understand the baseline scenario, we first simulate the无序 charging behavior of electric vehicles using the Monte Carlo method. This approach models the stochastic nature of EV charging patterns based on factors such as charging start time, initial state of charge (SOC), and daily driving distance. The charging start time is assumed to follow a normal distribution, with a probability density function given by:
$$ f_s(t_s) = \begin{cases}
\frac{1}{\sigma_{t_s} \sqrt{2\pi}} \exp\left[-\frac{(t_s – \mu_{t_s})^2}{2\sigma_{t_s}^2}\right], & \mu_{t_s} – 12 < t_s \leq 24 \\
\frac{1}{\sigma_{t_s} \sqrt{2\pi}} \exp\left[-\frac{(t_s + 24 – \mu_{t_s})^2}{2\sigma_{t_s}^2}\right], & 0 < t_s \leq \mu_{t_s} – 12
\end{cases} $$
where \( t_s \) is the charging start time, \( \mu_{t_s} = 17.6 \), and \( \sigma_{t_s} = 3.4 \). The daily driving distance \( x \) follows a log-normal distribution with the probability density function:
$$ f_d(x) = \frac{1}{x \sigma_d \sqrt{2\pi}} \exp\left[-\frac{(\ln x – \mu_d)^2}{2\sigma_d^2}\right] $$
where \( \mu_d = 3.2 \) and \( \sigma_d = 0.88 \). The required charging time \( T_c \) for an electric vehicle is calculated as:
$$ T_c = \frac{W \cdot x}{P_c \cdot \eta_c} $$
Here, \( W = 0.15 \) kWh/km represents the energy consumption per kilometer, \( P_c = 7 \) kW is the charging power, and \( \eta_c = 0.9 \) is the charging efficiency. The total charging power at time \( t \) for \( N \) electric vehicles is given by:
$$ P_{\text{sum}}(t) = \sum_{i=1}^{N} P_{c_i} \cdot x_i^t $$
where \( x_i^t \) is a binary variable indicating whether vehicle \( i \) is charging at time \( t \). Using Monte Carlo simulation with \( N = 1000 \) electric vehicles, we generate a minute-by-minute load profile for无序 charging, which is then aggregated into hourly intervals for analysis. The resulting load curve shows significant peaks during evening hours, aligning with typical grid peak periods, thus highlighting the need for optimized charging strategies.
The core of our approach is the development of a TOU pricing model that minimizes both indirect carbon emissions and grid peak-valley differences. Indirect carbon emissions refer to the CO₂ emissions generated during electricity production to meet EV charging demand. Unlike direct emissions, these are not produced by the electric vehicles themselves but by power plants. To accurately quantify these emissions, we use dynamic carbon emission factors for electricity consumption, which vary by time of day based on the energy mix. For instance, in Jiangsu Province, the carbon emission factors range from approximately 568 gCO₂/kWh to 611 gCO₂/kWh throughout the day, as shown in Table 1. This temporal variation allows us to incentivize charging during low-carbon periods.
| Time Slot | Carbon Emission Factor | Time Slot | Carbon Emission Factor |
|---|---|---|---|
| 00:00-01:00 | 568.731 | 12:00-13:00 | 568.668 |
| 01:00-02:00 | 580.680 | 13:00-14:00 | 581.341 |
| 02:00-03:00 | 591.524 | 14:00-15:00 | 590.378 |
| 03:00-04:00 | 588.050 | 15:00-16:00 | 601.972 |
| 04:00-05:00 | 600.435 | 16:00-17:00 | 591.366 |
| 05:00-06:00 | 599.516 | 17:00-18:00 | 601.141 |
| 06:00-07:00 | 611.033 | 18:00-19:00 | 609.535 |
| 07:00-08:00 | 611.407 | 19:00-20:00 | 609.344 |
| 08:00-09:00 | 599.600 | 20:00-21:00 | 598.645 |
| 09:00-10:00 | 601.423 | 21:00-22:00 | 591.119 |
| 10:00-11:00 | 580.032 | 22:00-23:00 | 591.829 |
| 11:00-12:00 | 579.844 | 23:00-00:00 | 579.555 |
The TOU pricing model is formulated as a multi-objective optimization problem. The first objective function \( f_1 \) aims to minimize the total indirect carbon emissions from electric vehicle charging over a 24-hour period:
$$ f_1 = \min \sum_{t=1}^{T} \left( e_t \cdot P_{t,\text{EV}} \cdot \Delta t \right) $$
where \( e_t \) is the dynamic carbon emission factor at time \( t \), \( P_{t,\text{EV}} \) is the charging load of electric vehicles at time \( t \), and \( \Delta t \) is the time interval. The second objective function \( f_2 \) focuses on reducing the peak-valley difference in grid load, which is crucial for grid stability. It is defined as the minimization of the variance between the combined grid load (original load plus EV charging load) and the average load:
$$ f_2 = \min \frac{1}{T-1} \sum_{t=1}^{T} \left( P_{t,0} + P_{t,\text{EV}} – \bar{P}_s \right)^2 $$
Here, \( P_{t,0} \) is the original grid load at time \( t \), and \( \bar{P}_s \) is the arithmetic mean of the total grid load over \( T \) periods. To relate electricity price changes to demand shifts, we employ a price elasticity matrix \( E \), which captures the responsiveness of charging demand to price variations. The matrix includes self-elasticity coefficients \( \varepsilon_{kk} \), representing the effect of price changes in the same time slot, and cross-elasticity coefficients \( \varepsilon_{km} \), representing the effect of price changes in one time slot on demand in another. The elasticity coefficients are defined as:
$$ \varepsilon_{kk} = \frac{\Delta P_k / P_k}{\Delta C_k / C_k} $$
$$ \varepsilon_{km} = \frac{\Delta P_k / P_k}{\Delta C_m / C_m} $$
where \( \Delta P_k \) and \( P_k \) are the change in demand and initial demand in time slot \( k \), and \( \Delta C_k \) and \( C_k \) are the change in price and initial price in time slot \( k \). The demand after implementing TOU pricing can be expressed as:
$$ \begin{bmatrix} P’_1 \\ P’_2 \\ \vdots \\ P’_n \end{bmatrix} = \frac{1}{n} \begin{bmatrix} P_1 & 0 & \cdots & 0 \\ 0 & P_2 & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & P_n \end{bmatrix} \cdot E \cdot \begin{bmatrix} \Delta C_1 / C_1 \\ \Delta C_2 / C_2 \\ \vdots \\ \Delta C_n / C_n \end{bmatrix} + \begin{bmatrix} P_1 \\ P_2 \\ \vdots \\ P_n \end{bmatrix} $$
The optimization model is subject to several constraints to ensure practicality. The grid load constraint ensures that the total load at any time \( t \) does not exceed the grid’s maximum capacity \( P_{g,\max} \):
$$ 0 \leq P_{t,0} + P_{t,\text{EV}} \leq P_{g,\max} $$
The charging station capacity constraint limits the number of electric vehicles charging simultaneously to the available charging piles \( K_{t,\max} \):
$$ 0 \leq K_t \leq K_{t,\max} $$
The state of charge (SOC) constraint guarantees that each electric vehicle reaches a desired SOC level by the end of charging, ensuring sufficient range for subsequent trips:
$$ \text{SOC}_{i,\text{desire}} \leq \text{SOC}_{i,\text{end}} \leq \text{SOC}_{i,\max} $$
Finally, the price constraint keeps the TOU tariffs within feasible bounds, balancing user affordability and utility profitability:
$$ C_{\min} \leq C_t \leq C_{\max} $$
To solve this multi-objective optimization problem, we use the Non-dominated Sorting Genetic Algorithm II (NSGA-II), which efficiently handles multiple constraints and objectives without requiring subjective weight assignments. NSGA-II works by generating a population of potential solutions, evaluating them based on non-domination sorting, and using genetic operators like crossover and mutation to evolve better solutions over generations. The algorithm parameters include a population size of 200, a maximum of 100 generations, and a mutation rate of 0.33. The output is a set of Pareto-optimal solutions, from which we select the best compromise solution based on maximum comprehensive satisfaction. The satisfaction \( h_j \) for each objective function \( f_j \) is calculated as:
$$ h_j = \begin{cases}
1, & f_j \leq f_{j\min} \\
\frac{f_{j\max} – f_j}{f_{j\max} – f_{j\min}}, & f_{j\min} < f_j < f_{j\max} \\
0, & f_j \geq f_{j\max}
\end{cases} $$
The comprehensive satisfaction \( h \) is the sum of individual satisfactions \( h = \sum_{j=1}^{z} h_j \).
For the case study, we use grid load data from a distribution network in Jiangsu Province, China, considering 1,000 electric vehicles. The base electricity price is set at 1 CNY/kWh, with minimum and maximum price limits of 0.25 CNY/kWh and 2 CNY/kWh, respectively. Using K-means clustering, we divide the day into peak, flat, and valley periods: peak hours from 12:00-15:00 and 19:00-22:00, valley hours from 06:00-11:00, and flat hours for the remaining periods. The price elasticity matrix is defined as:
$$ E = \begin{bmatrix}
-0.6230 & 0.3241 & 0.2305 \\
0.3553 & -0.6166 & 0.2216 \\
0.3215 & 0.3038 & -0.6065
\end{bmatrix} $$
The initial grid load profile shows that无序 charging of electric vehicles exacerbates peak demands, with the highest load reaching 3,599.03 kW at 21:00, coinciding with high carbon emission factors. After applying the TOU pricing model, the optimized tariffs are 1.33 CNY/kWh for peak hours, 1.05 CNY/kWh for flat hours, and 0.71 CNY/kWh for valley hours. This represents a 33% increase for peak hours and a 29.2% decrease for valley hours compared to the base price. The resulting grid load and carbon emissions are significantly improved, as summarized in Table 2.
| Indicator | Before Optimization | After Optimization | Change | Change Rate (%) |
|---|---|---|---|---|
| Grid Peak (kW) | 3,599.03 | 3,525.92 | -73.11 | -2.03 |
| Grid Valley (kW) | 1,434.10 | 1,539.92 | +105.83 | +7.38 |
| Peak-Valley Difference Rate (%) | 60.15 | 56.33 | -3.83 | -6.37 |
| Maximum Indirect Carbon Emissions (kg) | 431.76 | 413.83 | -17.93 | -4.15 |
| Total 24-hour Indirect Carbon Emissions (kg) | 3,706.82 | 3,650.74 | -56.08 | -1.51 |
The optimized TOU pricing strategy effectively shifts charging demand from peak to off-peak hours, reducing the grid peak load by 2.03% and increasing the valley load by 7.38%. This leads to a 6.37% reduction in the peak-valley difference rate, enhancing grid stability. Additionally, the maximum indirect carbon emissions decrease by 4.15%, and the total daily emissions drop by 1.51%, equivalent to over 50 kg of CO₂ per day. These results demonstrate the dual benefits of the proposed model: mitigating grid stress and lowering the carbon footprint of electric vehicle charging in China.
In conclusion, this study presents a comprehensive framework for designing time-of-use electricity pricing for electric vehicles that incorporates carbon emission considerations. By using Monte Carlo simulation to model无序 charging and NSGA-II to optimize pricing, we demonstrate that dynamic tariffs can effectively guide charging behavior toward periods of low carbon intensity and low grid demand. The case study in Jiangsu Province confirms that the optimized TOU pricing reduces both indirect carbon emissions and grid peak-valley differences, contributing to the sustainability goals of China’s EV ecosystem. However, the study has limitations, such as its focus on a single region and a typical day without distinguishing between weekdays and weekends. Future research should expand to multiple regions and incorporate more granular data, including real-time carbon intensity and user behavior patterns, to further enhance the model’s applicability. As the adoption of electric vehicles continues to grow in China, such pricing strategies will play a vital role in ensuring that the transition to electric mobility supports both grid reliability and environmental objectives.
The rapid expansion of China’s electric vehicle market underscores the importance of integrated energy and transportation policies. With over 31 million electric vehicles on the road, the potential for grid impacts and carbon emissions is substantial. The TOU pricing model developed here offers a scalable solution that can be adapted to different regions and grid conditions. By aligning electricity prices with carbon emission factors and grid load profiles, utilities and policymakers can incentivize behaviors that benefit both the environment and the power system. Moreover, as renewable energy penetration increases, dynamic pricing can further enhance the synergy between electric vehicles and clean energy sources, such as solar and wind power. This approach not only supports China’s dual carbon goals but also sets a precedent for other countries seeking to decarbonize their transportation sectors. Ultimately, the success of electric vehicles in China will depend on innovative strategies that balance economic, environmental, and technical considerations, ensuring a sustainable future for all.