In the context of global energy transition, electric cars have emerged as a critical component for reducing fossil fuel dependence and carbon emissions. However, the large-scale integration of electric cars into power grids presents significant challenges, including temporal and spatial randomness in charging loads, which can lead to grid congestion, voltage violations, and system instability. Traditional fixed time-of-use (TOU) pricing schemes lack dynamic response mechanisms, making them inadequate for addressing the fluctuations introduced by high-penetration renewable energy sources. To tackle these issues, we propose a dynamic TOU pricing model that optimizes electric car charging behavior to smooth net load curves and enhance renewable energy consumption. This model incorporates user behavior response uncertainties, adaptive peak-valley period division using K-means clustering, and multi-objective optimization via genetic algorithms. Through simulations in high renewable energy penetration scenarios, we demonstrate the effectiveness of our strategy in reducing peak-valley differences, minimizing curtailment rates, and balancing stakeholder interests. This article provides a comprehensive framework for dynamic pricing optimization, contributing to the sustainable integration of electric cars into modern power systems.
The proliferation of electric cars is accelerating worldwide, driven by environmental policies and technological advancements. However, uncoordinated charging of electric cars can exacerbate grid stress, particularly when combined with intermittent renewable energy sources like solar and wind. Traditional pricing mechanisms, such as fixed TOU tariffs, fail to adapt to real-time grid conditions, leading to suboptimal load management and inefficient renewable energy utilization. Our research addresses this gap by developing a dynamic pricing approach that responds to net load variations and user behavior. By leveraging advanced computational techniques, we aim to create a pricing strategy that not only stabilizes grid operations but also incentivizes electric car owners to charge during periods of high renewable generation. This approach aligns with the broader goals of decarbonization and grid modernization, making it a pivotal tool for energy planners and policymakers.
Our methodology is grounded in several key models that capture the interactions between electric car charging, conventional loads, and renewable energy output. We begin by defining the net load, which represents the balance between total load and renewable generation. The net load at hour \( h \) is expressed as:
$$ NL_h = D_h + EV_h – RG_h $$
where \( D_h \) is the conventional load, \( EV_h \) is the electric car charging load, and \( RG_h \) is the renewable generation output. A negative \( NL_h \) indicates excess renewable energy that may be curtailed, while a positive value signifies a supply deficit requiring conventional generation. To account for seasonal variations in renewable energy availability, we introduce a seasonal weighting coefficient \( w_s \) that reflects the alignment between renewable output and electric car charging patterns. The adjusted net load model becomes:
$$ NL^{\text{EV}}_h = D_h + EV_h – w_s RG_h $$
Here, \( w_s \) (ranging from 0 to 1) quantifies the offset effect of renewable energy on electric car load during season \( s \). A higher \( w_s \) implies better temporal matching, enhancing the smoothing of net load fluctuations. This seasonal adjustment ensures that our pricing strategy adapts to changing environmental conditions, improving its robustness across different times of the year.
To dynamically划分 peak, flat, and valley periods for TOU pricing, we employ a fuzzy membership calculation model. This model translates net load values into membership degrees that indicate how much a given hour belongs to peak or valley states. The peak and valley fuzzy membership degrees for hour \( h \) are computed as:
$$ \mu^+_h = \frac{NL_h – a}{|b – a|} $$
$$ \mu^-_h = \frac{b – NL_h}{|b – a|} $$
where \( a \) and \( b \) are the minimum and maximum net load values over the study period, respectively. These membership degrees range from 0 to 1, with \( \mu^+_h = 1 \) indicating a pure peak hour and \( \mu^-_h = 1 \) indicating a pure valley hour. The resulting membership matrix \( X \) serves as input for clustering algorithms to group hours with similar load characteristics:
$$ X = \begin{bmatrix} \mu^+_1 & \mu^-_1 \\ \mu^+_2 & \mu^-_2 \\ \vdots & \vdots \\ \mu^+_H & \mu^-_H \end{bmatrix} $$
where \( H \) is the total number of hours in a typical day (e.g., 24). This approach allows for adaptive period division that reflects actual net load patterns, rather than relying on fixed time intervals.
Next, we develop a load transfer model to simulate how electric car charging behavior changes in response to TOU pricing. Users tend to shift charging from high-price periods to low-price periods to reduce costs. We define parameters \( \alpha \), \( \beta \), and \( \gamma \) to represent the proportions of load transferred from peak to flat, peak to valley, and flat to valley periods, respectively. The adjusted net load after pricing implementation is given by:
$$ NL’_h = NL_h – (\alpha + \beta) \overline{NL}_p \quad \text{for } h \in T_p $$
$$ NL’_h = NL_h – \gamma \overline{NL}_f + \alpha \frac{T_p}{T_f} \overline{NL}_p \quad \text{for } h \in T_f $$
$$ NL’_h = NL_h + \beta \frac{T_p}{T_v} \overline{NL}_p + \gamma \frac{T_f}{T_v} \overline{NL}_f \quad \text{for } h \in T_v $$
where \( \overline{NL}_p \) and \( \overline{NL}_f \) are the average net loads in peak and flat periods before pricing, and \( T_p \), \( T_f \), and \( T_v \) are the durations of peak, flat, and valley periods. This model ensures load conservation while capturing the redistribution of electric car charging demand. Constraints such as \( NL_{\text{min}} \leq NL’_h \leq NL_{\text{max}} \) are applied to maintain realistic load curves.
Building on these foundations, we formulate the dynamic TOU pricing model for electric cars. The model consists of three components: time period division, price difference optimization, and dynamic pricing adjustment. For time period division, we use K-means clustering to group hours into peak, flat, and valley categories based on typical daily load curves. The clustering objective is to minimize within-group variance:
$$ J = \sum_{i=1}^{3} \sum_{t \in C_i} (L(t) – \bar{L}_i)^2 $$
where \( C_i \) represents the set of hours in category \( i \) (peak, flat, or valley), \( L(t) \) is the load at hour \( t \), and \( \bar{L}_i \) is the average load for category \( i \). This data-driven approach ensures that periods are划分 in a way that reflects actual load patterns, enhancing the effectiveness of subsequent pricing signals.
For price difference optimization, we define peak, flat, and valley electricity prices as \( P_p \), \( P_f \), and \( P_v \), respectively. These are parameterized using adjustment ratios \( \mu \) and \( \nu \):
$$ P_p = P_f (1 + \mu), \quad P_v = P_f (1 – \nu) $$
The optimization aims to minimize both the peak-valley difference and the variance of the net load curve, which are key indicators of grid stability. The objective functions are:
$$ F_1 = \max_{t \in [1,24]} L(t) – \min_{t \in [1,24]} L(t) $$
$$ F_2 = \frac{1}{24} \sum_{t=1}^{24} (L(t) – \bar{L})^2 $$
where \( \bar{L} \) is the daily average load. We combine these into a single objective using a weighting coefficient \( \lambda \):
$$ F = \lambda \frac{F_1}{F_1^*} + (1 – \lambda) \frac{F_2}{F_2^*} $$
Here, \( F_1^* \) and \( F_2^* \) are the optimal values when optimizing each objective individually, providing normalization. The optimization is subject to several constraints to ensure practicality and fairness. First, price order must be maintained: \( P_p > P_f > P_v \). Second, user electricity bills should not increase: \( P_p Q_p + P_f Q_f + P_v Q_v \leq P_0 (Q_p + Q_f + Q_v) \), where \( Q_p \), \( Q_f \), and \( Q_v \) are the energy consumptions in each period after pricing, and \( P_0 \) is the original flat rate. Third, utility revenue loss is limited to a fraction \( \delta \): \( P_p Q_p + P_f Q_f + P_v Q_v \geq (1 – \delta) P_0 (Q_p^0 + Q_f^0 + Q_v^0) \), where \( Q_p^0 \), \( Q_f^0 \), and \( Q_v^0 \) are the original consumptions. Finally, load order must be preserved to avoid peak-valley inversion: \( \frac{Q_p}{T_p} \geq \frac{Q_f}{T_f} \geq \frac{Q_v}{T_v} \).
To solve this optimization problem under uncertainty, we employ a genetic algorithm integrated with Monte Carlo simulation. This approach accounts for randomness in user response parameters, such as load transfer rates and charging time choices. For each candidate price方案, Monte Carlo simulation generates multiple samples of user behavior, and the average objective value is used as the fitness in the genetic algorithm. This ensures that the optimized pricing strategy is robust against real-world variability.
The dynamic pricing adjustment model further refines the strategy by responding to real-time supply-demand imbalances. We define the imbalance power at hour \( h \) as \( \Delta P_h = P_{\text{load}} – P_{\text{renew}} – P_{\text{base}} \), where \( P_{\text{load}} \) is total load, \( P_{\text{renew}} \) is renewable output, and \( P_{\text{base}} \) is conventional generation baseline. Dynamic prices are adjusted within the bounds set by the optimized peak and valley prices:
$$ p_h = \begin{cases}
P_p + \phi \Delta P_h / \bar{P}_p, & h \in \text{peak period} \\
P_f, & h \in \text{flat period} \\
P_v + \psi \Delta P_h / \bar{P}_v, & h \in \text{valley period}
\end{cases} $$
where \( \phi \) and \( \psi \) are sensitivity coefficients, and \( \bar{P}_p \) and \( \bar{P}_v \) are average loads in peak and valley periods. This adjustment mechanism allows prices to fluctuate in response to grid conditions, providing finer control over electric car charging behavior. User response is modeled through a load transfer rate \( \gamma_h = \eta \cdot \frac{\Delta p_h}{p_{\text{ref}}} \), where \( \eta \) is price elasticity and \( p_{\text{ref}} \) is a reference price. The adjusted net load becomes:
$$ NL’_h = NL_h – \gamma_h (\overline{NL}_p I_p(h) + \overline{NL}_f I_f(h)) $$
where \( I_p(h) \) and \( I_f(h) \) are indicator functions for peak and flat periods. This closed-loop feedback ensures that pricing signals continuously adapt to achieve desired grid outcomes.
To validate our model, we conduct a case study in a coastal region with high renewable energy penetration, simulating conditions for the year 2030. We assume electric car ownership reaches 30% of vehicles, and wind and solar capacity exceed 65% of total generation. Four scenarios are designed: a baseline scenario (BaU) with fixed TOU pricing, and three optimization scenarios with varying constraints on price differentials and load balancing. The optimization objectives are to minimize net load variance and peak-valley difference while maximizing renewable energy utilization. Key parameters for the scenarios are summarized in the table below.
| Scenario | Peak Price Cap (¥/kWh) | Valley Price Floor (¥/kWh) | Average Price Constraint | Load Balancing Constraint |
|---|---|---|---|---|
| BaU (Baseline) | 1.2357 | 0.3089 | Fixed at 0.7723 | None |
| Scenario 1 | 1.5000 | 0.2000 | Equal to BaU average | None |
| Scenario 2 | 1.8000 | 0.1000 | Relaxed | None |
| Scenario 3 | 1.8000 | 0.1000 | Relaxed | Peak load ≤ 85% of original |
Simulation results show significant improvements in grid performance under the optimized pricing strategies. In the baseline scenario, net load curves exhibit sharp peaks and valleys, with substantial renewable curtailment during midday solar peaks and high conventional generation需求 at night. For instance, winter net load reaches negative values of -596.7 MW during noon hours, indicating wasted solar energy, while summer evenings see peaks above 549.8 MW. The peak-valley differences are 848.6 MW (winter), 863.1 MW (transition season), and 606.8 MW (summer). These fluctuations pose challenges for grid stability and efficiency.
Under Scenario 1, which imposes moderate price differentials, electric car charging load shifts partially from night to morning hours, reducing midday net load negatives. Winter negative peaks decrease to -516.3 MW, and summer peak-valley difference drops to 488.8 MW. However, the overall load curve remains U-shaped, indicating limited demand response. Scenario 2, with larger price differentials, drives more aggressive load shifting, aligning electric car charging closely with solar generation. Winter net load valleys improve to 102.7 MW, and summer afternoon loads stabilize around 500 MW. Peak-valley differences are reduced to 295.0 MW (winter), 508.3 MW (transition season), and 387.3 MW (summer). This demonstrates the effectiveness of price incentives in smoothing net load curves and enhancing renewable consumption.
Scenario 3 adds a load balancing constraint to prevent new peak formation due to excessive load concentration. This results in more uniform load distributions, with winter peak-valley difference further reduced to 434.3 MW and transition season valleys raised to -247.4 MW. Summer loads maintain stable levels above 500 MW during midday. The table below summarizes key performance metrics across scenarios for a typical winter day.
| Scenario | Peak-Valley Difference (MW) | Net Load Variance (MW²) | Renewable Curtailment Rate (%) | Carbon Emissions (10⁴ tons/year) | Utility Revenue Change (%) |
|---|---|---|---|---|---|
| BaU | 848.6 | 52,341 | 15.2 | 88.6 | 0.0 |
| Scenario 1 | 764.2 | 48,567 | 12.5 | 84.1 | -4.8 |
| Scenario 2 | 295.0 | 18,932 | 3.1 | 76.1 | -18.0 |
| Scenario 3 | 434.3 | 26,451 | 5.7 | 79.7 | -4.5 |
The data highlights trade-offs between grid smoothing and economic impacts. Scenario 2 achieves the best technical outcomes but incurs an 18% utility revenue loss due to extreme price differentials. In contrast, Scenarios 1 and 3 maintain revenue losses within 5% while still delivering substantial benefits. Carbon emissions are reduced by up to 14.2% in Scenario 2, contributing to climate goals. These results underscore the importance of balancing multiple objectives in pricing design.
Our discussion delves into the implications of these findings. The dynamic pricing model effectively addresses the limitations of fixed TOU schemes by adapting to seasonal and real-time conditions. The use of fuzzy membership and K-means clustering for period division improves alignment with actual load patterns, enhancing the precision of price signals. Moreover, incorporating user behavior uncertainty through Monte Carlo simulation ensures robustness, making the strategy applicable to diverse electric car populations. However, challenges remain, such as the need to account for heterogeneous user groups (e.g., private owners vs. fleet operators) and to integrate with multi-energy systems. Future work could explore digital twin platforms for testing and refine models to include detailed user profiling and cross-energy耦合. Despite these areas for improvement, our approach offers a scalable solution for regions with high electric car adoption and renewable penetration, supporting grid decarbonization and stability.
In conclusion, we have developed a comprehensive dynamic TOU pricing optimization framework for electric car charging that leverages user behavior response models. Our methodology combines net load smoothing, adaptive period division, and multi-objective optimization to create pricing strategies that reduce peak-valley differences, minimize renewable curtailment, and control economic impacts. Simulations demonstrate that dynamic pricing can shift electric car charging to align with renewable generation, lowering carbon emissions and enhancing grid efficiency. By incorporating seasonal adjustments and uncertainty handling, our model provides a robust tool for policymakers and utilities navigating the transition to sustainable energy systems. The integration of electric cars into power grids is inevitable, and our research offers a pathway to harness their potential for a cleaner, more resilient electricity future.
The widespread adoption of electric cars presents both opportunities and challenges for modern power systems. Our dynamic pricing approach not only mitigates grid instability but also promotes renewable energy integration, aligning with global sustainability targets. As electric car technologies evolve and renewable capacity expands, adaptive pricing mechanisms will become increasingly vital. We encourage further research into user-centric models and real-world implementations to refine these strategies. Ultimately, the synergy between electric cars and smart grids can drive progress toward a low-carbon economy, and our work contributes a foundational element for achieving this vision.