In recent years, the rapid adoption of electric vehicles (EVs) has introduced significant challenges to power grid stability, particularly with high penetration of renewable energy sources. As a researcher focused on grid optimization, I have observed that traditional fixed time-of-use (TOU) pricing schemes fail to adapt to the dynamic nature of EV charging demand and renewable generation. This inadequacy often leads to increased peak load, inefficient utilization of renewables, and heightened carbon emissions. To address these issues, we propose a dynamic TOU pricing model that optimizes EV charging station operations by integrating user behavior responses, seasonal variations, and real-time grid conditions. Our approach aims to smooth net load curves, enhance renewable energy consumption, and balance the interests of users, grid operators, and the environment.
The core of our methodology revolves around modeling the net load, which combines conventional load, EV charging load, and renewable generation. Let $D_h$ represent the conventional load at hour $h$, $EV_h$ denote the EV charging load, and $RG_h$ signify renewable generation. The net load $NL_h$ is calculated as:
$$NL_h = D_h + EV_h – RG_h$$
However, to account for seasonal disparities in renewable output and EV charging patterns, we introduce a seasonal weighting factor $w_s$ for season $s$. This refines the net load model as:
$$NL_h^{EV} = D_h + EV_h – w_s RG_h$$
where $w_s$ (with $0 \leq w_s \leq 1$) quantifies the alignment between renewable generation and EV charging load in season $s$. A higher $w_s$ indicates better synchronization, allowing renewables to more effectively offset net load fluctuations. This adjustment is crucial for designing dynamic pricing strategies that respond to temporal and seasonal variations at EV charging stations.
To dynamically partition pricing periods (peak, flat, and valley), we employ a fuzzy membership model based on net load characteristics. For each hour $h$, the peak and valley membership degrees, $\mu_h^+$ and $\mu_h^-$, are computed as:
$$\mu_h^+ = \frac{NL_h – a}{|b – a|}, \quad \mu_h^- = \frac{b – NL_h}{|b – a|}$$
where $a$ and $b$ are the minimum and maximum net loads over the study period, respectively. These membership values form a matrix $X$ used in K-means clustering to group hours into peak, flat, and valley periods. The clustering objective minimizes intra-class variance:
$$J = \sum_{i=1}^{3} \sum_{t \in C_i} (L(t) – L_i)^2$$
where $C_i$ represents the set of hours for period $i$ (peak, flat, or valley), $L(t)$ is the load at time $t$, and $L_i$ is the average load for period $i$. This ensures that periods with similar load characteristics are grouped together, facilitating targeted pricing for EV charging stations.
User response to pricing signals is modeled through a load transfer mechanism. Let $\alpha$, $\beta$, and $\gamma$ represent the proportions of load transferred from peak to flat, peak to valley, and flat to valley periods, respectively. The adjusted net load $NL_h’$ after TOU pricing implementation is given by:
$$NL_h’ = NL_h – (\alpha + \beta) NL_p \quad \text{for } h \in T_p$$
$$NL_h’ = NL_h – \gamma NL_f + \alpha \frac{T_p}{T_f} NL_p \quad \text{for } h \in T_f$$
$$NL_h’ = NL_h + \beta \frac{T_p}{T_v} NL_p + \gamma \frac{T_f}{T_v} NL_f \quad \text{for } h \in T_v$$
where $T_p$, $T_f$, and $T_v$ are the durations of peak, flat, and valley periods, and $NL_p$ and $NL_f$ are the average net loads in peak and flat periods before pricing. This model captures how EV charging station users shift their charging behavior in response to price incentives, thereby flattening the net load curve.
Our dynamic TOU pricing optimization model aims to minimize net load fluctuations and peak-valley differences while considering user and grid operator interests. The decision variables are the peak, flat, and valley electricity prices, denoted as $P_p$, $P_f$, and $P_v$, respectively. These are expressed in terms of adjustment ratios $\mu$ and $\nu$ relative to the flat price: $P_p = P_f(1 + \mu)$ and $P_v = P_f(1 – \nu)$. The objective functions are the peak-valley difference $F_1$ and load variance $F_2$:
$$F_1 = \max_{t \in [1,24]} L(t) – \min_{t \in [1,24]} L(t)$$
$$F_2 = \frac{1}{24} \sum_{t=1}^{24} (L(t) – \bar{L})^2$$
where $\bar{L} = \frac{1}{24} \sum_{t=1}^{24} L(t)$ is the average load. A combined objective function $F$ is formulated using a weight $\lambda$:
$$F = \lambda \frac{F_1}{F_1^*} + (1 – \lambda) \frac{F_2}{F_2^*}$$
Here, $F_1^*$ and $F_2^*$ are the optimal values when optimizing $F_1$ and $F_2$ individually. Constraints include price order ($P_p > P_f > P_v$), user cost protection, and grid operator revenue limits. For instance, the user cost constraint ensures that the total electricity cost under TOU pricing does not exceed that under a flat rate $P_0$:
$$P_p Q_p + P_f Q_f + P_v Q_v \leq P_0 (Q_p + Q_f + Q_v)$$
Similarly, the grid operator revenue constraint limits the revenue loss 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 loads in each period. To handle uncertainties in user response, we integrate Monte Carlo simulation within a genetic algorithm, evaluating the expected fitness of each pricing scheme over multiple random samples of user behavior parameters.
For simulation, we design four scenarios to evaluate our dynamic pricing strategy for EV charging stations. The baseline scenario (BaU) uses fixed TOU prices, while scenarios 1–3 introduce progressively relaxed constraints on price differentials and load balancing. Key performance metrics include net load variance, peak-valley difference, renewable curtailment rate, and carbon emissions. The table below summarizes the pricing parameters and constraints for each scenario:
| Scenario | Peak Price Limit (¥/kWh) | Valley Price Limit (¥/kWh) | Load Balancing Constraint |
|---|---|---|---|
| BaU | 1.2357 | 0.3089 | None |
| 1 | 1.5000 | 0.2000 | Moderate |
| 2 | 1.8000 | 0.1000 | None |
| 3 | 1.8000 | 0.1000 | Strict (peak load ≤ 85% of original) |
Simulation results demonstrate that dynamic TOU pricing effectively shifts EV charging load from nighttime valleys to daytime photovoltaic (PV) peak periods. In scenario 3, for example, the charging load during PV peak hours (e.g., 10:00–14:00) increases by approximately 8% compared to BaU, reducing the net load peak-valley difference by up to 7%. The renewable curtailment rate drops from 15% in BaU to around 3% in optimized scenarios, indicating improved utilization of solar energy at EV charging stations. Carbon emissions also decline significantly, with annual reductions of 5.1%, 14.2%, and 10.0% in scenarios 1, 2, and 3, respectively, relative to BaU.
The economic impact on grid operators is carefully balanced. While scenario 2’s aggressive pricing leads to an 18% revenue loss, scenarios 1 and 3 maintain revenue losses within 5% through constraints on average price and load equilibrium. This highlights the importance of tailoring pricing strategies to local grid conditions and user acceptability. The following table compares key outcomes across scenarios for a typical seasonal day:
| Metric | BaU | Scenario 1 | Scenario 2 | Scenario 3 |
|---|---|---|---|---|
| Peak-Valley Difference (MW) | 848.6 | 764.2 | 295.0 | 434.3 |
| Load Variance (MW²) | 12,450 | 9,880 | 5,120 | 6,740 |
| Renewable Curtailment Rate (%) | 15.0 | 10.5 | 3.2 | 4.8 |
| Carbon Emissions (kt/year) | 886 | 841 | 761 | 797 |
Our discussion emphasizes that dynamic TOU pricing for EV charging stations must navigate trade-offs between price differentials, user response, and grid stability. Excessively large price gaps may induce load concentration in valley periods, creating new peaks, while insufficient differentials fail to motivate behavioral shifts. The seasonal weighting factor $w_s$ and fuzzy clustering enable adaptive period划分 that aligns with renewable generation patterns, enhancing the precision of pricing signals. For instance, in seasons with high PV output, $w_s$ approaches 1, allowing prices to incentivize charging during solar peaks. This adaptability is critical for regions with over 60% renewable penetration and growing EV adoption.
In conclusion, our dynamic TOU pricing model offers a robust framework for optimizing EV charging station operations in high-renewable power systems. By integrating net load modeling, user behavior response, and multi-objective optimization, we achieve significant improvements in load smoothing, renewable integration, and carbon reduction. The strategy’s flexibility ensures that it can be deployed across diverse climatic and grid conditions, providing a scalable solution for future energy systems. Future work will explore the integration of energy storage, multi-energy coupling, and digital twin technologies to further refine pricing mechanisms and enhance stakeholder coordination.
From a personal perspective, I believe that advancing dynamic pricing strategies for EV charging stations is essential for achieving carbon neutrality goals. The iterative nature of our model—continuously adapting to real-time data—holds promise for creating more resilient and efficient grids. As EV adoption accelerates, such approaches will play a pivotal role in harmonizing transportation electrification with renewable energy deployment, ultimately fostering a sustainable energy ecosystem.