Abstract With the global pursuit of “dual carbon” goals, electric vehicles (EVs) have emerged as a pivotal solution for reducing carbon emissions in transportation. This study aims to develop a time-of-use (TOU) electricity pricing strategy for EVs that minimizes indirect carbon emissions and stabilizes grid load. We employed the Monte Carlo method to simulate disordered charging patterns, established a multi-objective optimization model with NSGA-II algorithm, and validated the strategy using real-world data. The results demonstrate that the proposed TOU pricing effectively reduces indirect carbon emissions by 1.51% and mitigates grid peak-valley load difference by 6.37%, enhancing grid stability and sustainability.
1. Introduction
The widespread adoption of electric vehicles has brought both opportunities and challenges. While EVs offer zero tailpipe emissions, their uncoordinated charging behavior can exacerbate grid peak loads and indirectly increase carbon emissions from power generation. As of 2024, China’s EV fleet reached 31.4 million, highlighting the urgency to manage charging demand efficiently .
1.1 Research Background
Traditional TOU pricing strategies often overlook indirect carbon emissions from EV charging. The power sector, being the largest carbon emitter in China, necessitates a coordinated approach to align EV charging with low-carbon power generation periods. Previous studies have focused on grid load balancing but lacked integration of dynamic carbon emission factors .
1.2 Research Objectives
- Develop a TOU pricing model for EVs considering dynamic carbon emission factors.
- Minimize indirect carbon emissions and grid peak-valley load difference through multi-objective optimization.
- Validate the model’s effectiveness using case studies in Jiangsu Province.
2. EV Charging Demand Simulation
2.1 Simulation Framework
We considered a urban distribution grid scenario, excluding commercial EVs like buses and taxis. EV charging demand is influenced by three key factors: initial state of charge (SOC), charging start time, and charging duration, which are modeled using probability distributions –.
2.2 Probability Models
- Charging Start Time: Follows a normal distribution:\(f_s(t_s) = \begin{cases} \frac{1}{\sigma_{ts}\sqrt{2\pi}} \exp\left[-\frac{(t_s – \mu_{ts})^2}{2\sigma_{ts}^2}\right], & \mu_{ts}-12 < t_s \leq 24 \\ \frac{1}{\sigma_{ts}\sqrt{2\pi}} \exp\left[-\frac{(t_s + 24 – \mu_{ts})^2}{2\sigma_{ts}^2}\right], & 0 < t_s \leq \mu_{ts}-12 \end{cases}\) where \(\mu_{ts} = 17.6\), \(\sigma_{ts} = 3.4\) –.
- Daily Driving Range: Follows a log-normal distribution:\(f_d(x) = \frac{1}{x\sigma_d\sqrt{2\pi}} \exp\left[-\frac{(\ln x – \mu_d)^2}{2\sigma_d^2}\right]\) where \(\mu_d = 3.2\), \(\sigma_d = 0.88\) –.
2.3 Charging Duration Calculation
The charging duration \(T_c\) is given by:\(T_c = \frac{Wx}{P_c\eta_c}\) where \(W = 0.15\ \text{kW·h/km}\) (energy consumption per km), \(P_c = 7\ \text{kW}\) (charging power), and \(\eta_c = 0.9\) (charging efficiency) –.
2.4 Total Charging Load
For \(N = 1000\) EVs, the total charging power at time t is:\(P_{\text{sum}}(t) = \sum_{i=1}^{N} P_{ci}x_t^i\) where \(x_t^i = 1\) if EV i is charging at t, otherwise 0 –.
3. TOU Pricing Model with Carbon Emission Consideration
3.1 Dynamic Carbon Emission Factor
Unlike average carbon factors, dynamic factors reflect temporal and spatial variations in power generation carbon intensity. Table 1 shows Jiangsu Province’s dynamic carbon emission factors for a typical day –.
| Time Period | Carbon Emission Factor (g/kW·h) |
|---|---|
| 0:00–6:00 | 420.5 |
| 6:00–11:00 | 512.3 |
| 11:00–15:00 | 579.5 |
| 15:00–19:00 | 543.2 |
| 19:00–22:00 | 598.7 |
| 22:00–24:00 | 456.1 |
Table 1: Jiangsu Province dynamic carbon emission factors
3.2 Price Elasticity Matrix
The electricity demand-price elasticity matrix E quantifies how charging demand responds to price changes:\(E = \begin{bmatrix} \varepsilon_{11} & \varepsilon_{12} & \cdots & \varepsilon_{1n} \\ \varepsilon_{21} & \varepsilon_{22} & \cdots & \varepsilon_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ \varepsilon_{n1} & \varepsilon_{n2} & \cdots & \varepsilon_{nn} \end{bmatrix}\) where \(\varepsilon = \frac{\Delta P/P}{\Delta C/C}\). The matrix includes self-elasticity (\(\varepsilon_{kk}\)) and cross-elasticity (\(\varepsilon_{km}\)) coefficients –.
For Jiangsu’s grid, the elasticity matrix is:\(E = \begin{bmatrix} -0.623 & 0.3241 & 0.2305 \\ 0.3553 & -0.6166 & 0.2216 \\ 0.3215 & 0.3038 & -0.6065 \end{bmatrix}\) corresponding to peak, normal, and valley periods .
3.3 Objective Functions
- Minimize Indirect Carbon Emissions:\(f_1 = \min \sum_{t=1}^{T} (e_t \cdot P_{t,\text{EV}} \cdot \Delta t)\) where \(e_t\) is the dynamic carbon factor, \(P_{t,\text{EV}}\) is EV charging load, and \(\Delta t = 1\ \text{h}\) –.
- Minimize Grid Peak-Valley Load Difference:\(f_2 = \min \frac{1}{T-1} \sum_{t=1}^{T} \left(P_{t,0} + P_{t,\text{EV}} – \overline{P}_s\right)^2\) where \(P_{t,0}\) is the base grid load, and \(\overline{P}_s\) is the average total load –.
3.4 Constraints
- Grid Load Constraint:\(0 \leq P_{t,0} + P_{t,\text{EV}} \leq P_{g,\text{max}}\)
- Simultaneous Charging Limit:\(0 \leq K_t \leq K_{t,\text{max}}\)
- SOC Constraint:\(\text{SOC}_{i,\text{desire}} \leq \text{SOC}_{i,\text{end}} \leq \text{SOC}_{i,\text{max}}\)
- Price Constraint:\(C_{\text{min}} \leq C_t \leq C_{\text{max}}\) where \(C_{\text{min}} = 0.25\ \$/kW·h\), \(C_{\text{max}} = 2\ \$/kW·h\) –.
4. NSGA-II Algorithm for Model Solution
4.1 Algorithm Framework
NSGA-II is used to solve the multi-objective problem, featuring fast non-dominated sorting and crowding distance calculation. The steps include:
- Initialize population and set generation \(t = 0\).
- Perform non-dominated sorting and calculate crowding distances.
- Select, crossover, and mutate to generate offspring.
- Combine parent and offspring populations, sort, and select the next generation.
- Repeat until maximum iterations (100) are reached –.
4.2 Satisfaction Function
The comprehensive satisfaction h for each Pareto solution is:\(h_j = \begin{cases} 1, & f_j \leq f_{j,\text{min}} \\ \frac{f_{j,\text{max}} – f_j}{f_{j,\text{max}} – f_{j,\text{min}}}, & f_{j,\text{min}} < f_j < f_{j,\text{max}} \\ 0, & f_j \geq f_{j,\text{max}} \end{cases}\) where \(h = \sum_{j=1}^{2} h_j\) –.
5. Case Study and Results
5.1 Data Setup
- Study Area: Jiangsu Province, China.
- EV Population: 1000 vehicles.
- Base Price: 1 $/kW·h.
- Peak Periods: 12:00–15:00, 19:00–22:00; Valley Period: 6:00–11:00; Normal Periods: rest –.
5.2 Optimal TOU Prices
The NSGA-II algorithm yields the optimal TOU prices:
- Peak period: 1.33 $/kW·h (33% increase from base).
- Normal period: 1.05 $/kW·h (5% increase).
- Valley period: 0.71 $/kW·h (29.2% decrease) –.
5.3 Performance Metrics
| Indicator | Pre-optimization | Post-optimization | Change | Change Rate (%) |
|---|---|---|---|---|
| Grid Peak Load (kW) | 3599.03 | 3525.92 | -73.11 | -2.03 |
| Grid Valley Load (kW) | 1434.10 | 1539.92 | +105.83 | +7.38 |
| Peak-Valley Difference (%) | 60.15 | 56.33 | -3.83 | -6.37 |
| Max Indirect Emission (kg) | 431.76 | 413.83 | -17.93 | -4.15 |
| 24h Total Emission (kg) | 3706.82 | 3650.74 | -56.08 | -1.51 |
Table 2: Performance comparison before and after TOU optimization
5.4 Impact Analysis
- Grid Load: The optimized TOU pricing reduces the peak load by 2.03% and increases the valley load by 7.38%, effectively “shaving the peak and filling the valley” .
- Carbon Emissions: The 24-hour total indirect emissions decrease by 1.51%, with the maximum emission reduced by 4.15% .
6. Conclusions
This study presents a novel TOU pricing strategy for electric vehicles that integrates dynamic carbon emission factors. Key findings include:
- The proposed model, solved by NSGA-II, effectively balances carbon emission reduction and grid load stability.
- TOU pricing guides EV users to shift charging to low-carbon periods, reducing daily emissions by over 50 kg and peak-valley difference by 6.37%.
- The strategy shows promising potential for large-scale EV deployments, though regional and temporal variations require further study.
Future work will expand the dataset to include weekends and diverse regions, enhancing the model’s generalizability for sustainable grid-EV integration.