With the rapid development of smart grids, smart communities have emerged as a key component for integrating distributed energy resources and managing electricity demand. In these communities, electric vehicles (EVs) are becoming increasingly prevalent, posing challenges to grid stability due to their uncontrolled charging patterns. Traditional static pricing mechanisms often fail to account for real-time load responses, leading to new peak loads and increased volatility in the equivalent load profile. To address this, I propose a dynamic pricing strategy that not only varies with time but also correlates with the net load within the community. This approach leverages a Stackelberg game framework, where the community operator acts as the leader to minimize load fluctuations, while EV owners, as followers, optimize their charging schedules to reduce costs. The dynamic pricing induces an aggregative game among EVs, solved via Nash equilibrium, and a genetic algorithm is employed to determine optimal pricing parameters. Simulation results demonstrate that this strategy effectively flattens the load curve, avoids new peaks, and benefits both operators and EV users.
The integration of electric vehicles into smart communities is a critical step toward sustainable urban development. However, uncontrolled charging of EVs can exacerbate peak demand, especially when combined with intermittent renewable generation like photovoltaic (PV) systems. In China, the adoption of EVs is accelerating, driven by government policies and technological advancements. The “Implementation Opinions on Further Enhancing the Service Guarantee Capacity of Electric Vehicle Charging Infrastructure” emphasizes the need for charging facilities in residential areas, highlighting the importance of managed charging strategies. Static time-of-use tariffs, while common, often lead to concentrated charging during low-price periods, creating secondary peaks. Dynamic pricing, in contrast, adapts to real-time load conditions, incentivizing distributed charging behavior. This paper explores a dynamic pricing model that incorporates PV generation and energy storage systems (ESS) to optimize community-level load management.
Electric vehicle charging behavior is influenced by daily travel patterns, including distance traveled, return times, and departure times. Based on survey data, these parameters can be modeled using probability distributions: daily mileage follows a log-normal distribution, while return and departure times follow normal distributions. For instance, the probability density function for daily mileage \( s \) is given by \( \ln(s) \sim \mathcal{N}(\mu_s, \sigma_s^2) \). Similarly, return time \( t_s \) and departure time \( t_e \) are distributed as \( t_s \sim \mathcal{N}(\mu_{t_s}, \sigma_{t_s}^2) \) and \( t_e \sim \mathcal{N}(\mu_{t_e}, \sigma_{t_e}^2) \), respectively. Uncoordinated charging occurs when EVs start charging immediately upon return, often coinciding with evening peak hours. This results in a “peak-on-peak” phenomenon, straining the grid. Coordinated charging, guided by dynamic pricing, can shift loads to off-peak periods, reducing stress on infrastructure.
The smart community operator aims to minimize the variance of the equivalent load, which includes base load, EV charging load, PV output, and ESS power. The equivalent load \( P_t^{\text{Eload}} \) at time \( t \) is defined as:
$$ P_t^{\text{Eload}} = P_t^{\text{base}} + P_t^{\text{EV}} + P_t^{\text{store}} – P_t^{\text{PV}} $$
where \( P_t^{\text{base}} \) is the base load, \( P_t^{\text{EV}} \) is the aggregate EV charging load, \( P_t^{\text{store}} \) is the ESS power (positive for charging, negative for discharging), and \( P_t^{\text{PV}} \) is the PV output. The net load \( P_t^{\text{Nload}} \) is \( P_t^{\text{base}} + P_t^{\text{EV}} – P_t^{\text{PV}} \). The operator’s objective is to minimize the variance:
$$ \min \frac{1}{T} \sum_{t=1}^{T} \left( P_t^{\text{Eload}} – P_{\text{avg}} \right)^2 $$
with \( P_{\text{avg}} = \frac{1}{T} \sum_{t=1}^{T} P_t^{\text{Eload}} \). The dynamic pricing function is linear in the net load:
$$ \lambda_t(P_t^{\text{Nload}}) = a_t P_t^{\text{Nload}} + b_t $$
where \( a_t \geq 0 \) is the sensitivity coefficient, \( b_t \geq 0 \) is the base coefficient, and \( \lambda_t \) is bounded by \( \lambda_t^{\min} \) and \( \lambda_t^{\max} \). The ESS constraints include charging and discharging limits, state of charge (SOC) dynamics, and periodicity:
$$ 0 \leq P_t^+ \leq z_t R^+, \quad 0 \leq P_t^- \leq (1 – z_t) R^- $$
$$ S_t = S_{t-1} + \frac{\eta^+ P_t^+ – P_t^- / \eta^-}{C^{\text{cap}}} $$
$$ S^{\min} \leq S_t \leq S^{\max}, \quad S_1 = S_T = S_0 $$
$$ P_t^- \leq P_t^{\text{Nload}}, \quad P_t^{\text{store}} = P_t^+ – P_t^- $$
Here, \( z_t \) is a binary variable for ESS mode, \( R^+ \) and \( R^- \) are power limits, \( \eta^+ \) and \( \eta^- \) are efficiencies, and \( C^{\text{cap}} \) is capacity.
For EV owners, the goal is to minimize charging cost over the scheduling horizon \( T \):
$$ \min \sum_{t=1}^{T} \lambda_t p_{a,t} $$
subject to:
$$ p_{a,t}^{\text{EVmin}} \leq p_{a,t} \leq p_{a,t}^{\text{EVmax}} \quad \forall t \in T_a $$
$$ p_{a,t} = 0 \quad \forall t \notin T_a $$
$$ \sum_{t \in T_a} p_{a,t} \geq E_a $$
where \( p_{a,t} \) is the charging power of EV \( a \), \( T_a \) is the available charging time window, and \( E_a \) is the required energy. The dynamic pricing creates an aggregative game among EVs, as each owner’s cost depends on the aggregate load through \( \lambda_t \). The Nash equilibrium condition is:
$$ c_a(p_a^*, P^{\text{Nload}}) \leq c_a(p_a, P^{\text{Nload}}) \quad \forall p_a \in \theta_a, a \in A $$
This equilibrium is unique when \( a_t > 0 \), and it can be computed using variational inequality methods or best-response iterations.
To solve for the optimal dynamic pricing parameters, a genetic algorithm (GA) is employed. The GA initializes a population of \( m \) pricing parameter sets \( (a_t, b_t) \). For each set, the lower-level EV game is solved to obtain charging loads, and the operator computes the equivalent load variance. The GA then evolves the population through selection, crossover, and mutation until convergence. The process is summarized as follows:
- Initialize community and EV parameters, set GA parameters (population size, mutation rate, etc.).
- Generate \( m \) sets of dynamic pricing parameters.
- For each set, compute EV charging powers via Nash equilibrium.
- Calculate equivalent load variance and ESS schedule.
- Update pricing parameters using GA operations until stopping criteria are met.
A case study of a smart community with 500 households and 40% EV penetration is conducted. The scheduling period is 24 hours with 1-hour intervals. PV capacity is 500 kW, and ESS capacity is 1400 kWh with 400 kW power limits. Base load and PV data are adapted from standard datasets. EVs have a capacity of 70 kWh and charging power of 7.3 kW. Three scenarios are compared: uncoordinated charging, static pricing, and dynamic pricing.
In uncoordinated charging, EVs start charging upon return, leading to a peak load of 1592.1 kW during evening hours. The equivalent load curve shows a high peak-to-valley difference of 1210.7 kW. With static pricing, charging shifts to low-price periods, but a new peak of 1249.0 kW forms overnight, increasing volatility. Dynamic pricing avoids this by correlating prices with real-time load, reducing the peak to 898.4 kW and the standard deviation to 98.5 kW. Key metrics are summarized in Table 1.
| Scenario | Evening Peak (kW) | Overnight Peak (kW) | Valley (kW) | Peak-Valley Difference (kW) | Standard Deviation (kW) |
|---|---|---|---|---|---|
| Uncoordinated | 1592.0 | 909.5 | 381.2 | 1210.7 | 305.3 |
| Static Pricing | 944.2 | 1249.0 | 653.7 | 595.4 | 144.8 |
| Dynamic Pricing | 939.5 | 898.4 | 675.2 | 264.4 | 98.5 |
The charging costs for EVs are also reduced under dynamic pricing. For a sample of 10 EVs, costs decrease by up to 24.6% compared to uncoordinated charging and 20.9% compared to static pricing. The total electricity cost, including base load, is slightly lower in dynamic pricing (11470.6 yuan) versus uncoordinated (11592.8 yuan) and static (11525.3 yuan). The flexibility of EVs, such as longer charging windows and lower energy demands, enhances cost savings, as shown in Table 2.
| Flexibility Factor | Savings vs. Uncoordinated (%) | Savings vs. Static Pricing (%) |
|---|---|---|
| Short Charging Window (5 hours) | 9.9 | 0.5 |
| Medium Charging Window (9 hours) | 17.5 | 12.3 |
| Long Charging Window (12 hours) | 24.6 | 20.9 |
| Low Energy Demand (10 kWh) | 22.1 | 18.4 |
| High Energy Demand (50 kWh) | 15.8 | 11.2 |
The synergy between dynamic pricing and ESS is further analyzed in four scenarios: static pricing without ESS, static pricing with ESS, dynamic pricing without ESS, and dynamic pricing with ESS. With ESS, the equivalent load peak is reduced to 939.5 kW, and the standard deviation drops to 98.5 kW. The ESS charges during low-load periods and discharges during peaks, complementing the price signals. This combination achieves the lowest load volatility, demonstrating the importance of integrated management for China EV adoption in smart communities.
In conclusion, the proposed dynamic pricing strategy effectively addresses the challenges of EV charging in smart communities. By correlating prices with real-time net load, it avoids the pitfalls of static pricing, such as new peaks, and reduces load fluctuations. The Stackelberg game framework ensures that both operator and EV owner interests are balanced, while the genetic algorithm efficiently computes optimal pricing. Future work could focus on real-time updates of EV parameters and online pricing mechanisms to enhance adaptability. This approach supports the growth of electric vehicles in China, promoting grid stability and sustainable energy use.