In recent years, the global challenges of climate change and environmental degradation have intensified, prompting a shift toward sustainable energy solutions. Electric vehicles (EVs) have emerged as a key technology due to their energy efficiency, low emissions, and high performance. In China, the rapid adoption of electric vehicles is supported by policies aimed at reducing carbon footprints and enhancing energy security. The integration of EVs into the power grid, particularly through vehicle-to-grid (V2G) technologies, offers significant potential for improving grid stability and flexibility. However, the uncertainty associated with renewable energy sources like wind and solar, combined with the stochastic nature of EV charging loads, poses challenges to power system operations. This paper addresses these issues by proposing a scheduling strategy that incorporates EV energy storage, accounting for user participation willingness, and analyzes its impact on power system flexibility.
The proliferation of electric vehicles in China is transforming the energy landscape. With the government promoting V2G pilot projects in regions like the Yangtze River Delta and Pearl River Delta, the potential for EVs to act as distributed energy resources is becoming increasingly viable. EVs spend most of their time parked, making them ideal for grid services if their charging and discharging can be optimized. However, user willingness to participate in V2G programs is uncertain, as factors such as battery degradation concerns and financial incentives influence behavior. This study introduces a model based on Logistic functions to capture this uncertainty and evaluates its effects on multi-timescale power system scheduling.
The core of this research lies in developing a comprehensive framework for EV charging and discharging strategies. First, an uncertainty model for user participation willingness is established, linking incentive electricity prices to user responses. Second, different charging modes—unordered charging, ordered charging, and V2G—are compared in terms of their impact on grid load and flexibility. Finally, a day-ahead and intra-day scheduling model is formulated, minimizing total costs while ensuring flexibility supply meets demand. Case studies demonstrate that the proposed V2G strategy, which considers user participation uncertainty, effectively reduces peak loads and enhances system flexibility at lower costs.
Uncertainty Model for Electric Vehicle User Participation Willingness
The success of V2G programs heavily depends on the willingness of electric vehicle users to participate. Users are often hesitant due to concerns about battery life and the limited financial benefits from peak-valley price arbitrage. To address this, an incentive electricity pricing mechanism is introduced, which adjusts based on net load fluctuations. The incentive price is derived from the time-of-use electricity price and a compensation coefficient that reflects net load deviations from the daily average. The incentive coefficient for each user is calculated as follows:
$$ \lambda_{jl,t} = (1 + K_{p,t}) \lambda_{fs,t} $$
$$ \varepsilon_{i,t} = \frac{\lambda_{jl,t}}{\lambda_{i,yq,t}} $$
$$ K_{p,t} = \rho \frac{P_{j,t} – P_{av}}{P_{av}} $$
$$ P_{j,t} = P_{base,t} – P_{wind,t} – P_{pv,t} $$
$$ P_{av} = \frac{1}{T} \sum_{t=1}^{T} P_{j,t} $$
Here, \( \lambda_{jl,t} \) is the incentive price at time \( t \), \( \varepsilon_{i,t} \) is the incentive coefficient for user \( i \), \( \lambda_{fs,t} \) is the time-of-use price, \( \lambda_{i,yq,t} \) is the user’s expected incentive price, \( K_{p,t} \) is the compensation coefficient, \( \rho \) is the load fluctuation coefficient, \( P_{j,t} \) is the net load, \( P_{base,t} \) is the base load, \( P_{wind,t} \) and \( P_{pv,t} \) are wind and PV power outputs, and \( P_{av} \) is the daily average net load.
User participation willingness is modeled using Logistic functions to capture the S-shaped relationship between the incentive coefficient and willingness. Optimistic and pessimistic curves are defined to represent the uncertainty range:
$$ p_{op} = \frac{c_{op}}{1 + a_{op} e^{-b_{op} (\varepsilon – 1)}} $$
$$ p_{pess} = \frac{c_{pess}}{1 + a_{pess} e^{-b_{pess} (\varepsilon – 1)}} $$
Parameters \( a_{op} \), \( b_{op} \), \( c_{op} \) and \( a_{pess} \), \( b_{pess} \), \( c_{pess} \) are estimated from user data. The mean and standard deviation of participation willingness at each incentive coefficient are:
$$ \mu(\varepsilon) = \frac{p_{op}(\varepsilon) + p_{pess}(\varepsilon)}{2} $$
$$ \sigma(\varepsilon) = \frac{p_{op}(\varepsilon) – p_{pess}(\varepsilon)}{6} $$
Thus, the participation willingness for each user follows a normal distribution \( p = N(\mu(\varepsilon), \sigma(\varepsilon)) \). This approach effectively models the uncertainty in user behavior, which is crucial for realistic scheduling.
Electric Vehicle Charging and Discharging Models
This study focuses on private electric vehicles, which are stationary for most of the day, making them suitable for grid services. Three charging modes are considered: unordered charging, ordered charging, and V2G. Each mode is evaluated based on its ability to meet user travel needs while supporting grid operations.
Unordered Charging
Unordered charging refers to unplanned EV charging, where users plug in their vehicles at will. The charging power is modeled using Monte Carlo simulation, assuming EVs charge at maximum power from the time of connection until the desired state of charge (SOC) is reached. The total unordered charging load is the sum of individual EV loads, which often exacerbates peak net loads and increases volatility.
Ordered Charging
Ordered charging optimizes charging schedules to minimize costs and reduce grid impact. The feasibility condition ensures that EVs can reach the desired SOC by the departure time. The minimum charging time \( t_c \) is calculated as:
$$ t_c = \frac{(S_e – S_0) E}{P_c \eta} $$
where \( S_e \) is the target SOC, \( S_0 \) is the initial SOC, \( E \) is the battery capacity, \( P_c \) is the charging power, and \( \eta \) is the charging efficiency. The optimization objective is to minimize charging costs:
$$ \min F = \sum_{i=1}^{N} \sum_{t=1}^{T} \lambda_{fs,t} P_{i,t} $$
subject to constraints on charging power, SOC, and travel requirements. Ordered charging helps shift loads to off-peak periods, reducing peak net loads.
V2G Strategy with User Participation Willingness
The V2G strategy allows EVs to discharge power back to the grid, providing additional flexibility. The minimum time for charge-discharge cycles \( t_{cd} \) is:
$$ t_{cd} = \frac{(S_e – S_{min}) E}{P_c \eta_c} + \frac{(S_0 – S_{min}) E}{P_d / \eta_d} $$
where \( P_d \) is the discharge power, and \( \eta_c \), \( \eta_d \) are charging and discharging efficiencies. The optimization objective includes minimizing costs and battery degradation:
$$ \min (F_1 + F_2) = \sum_{i=1}^{N} \sum_{t=1}^{T} \left[ (u_{i,c} P_{i,c,t} + u_{i,d} P_{i,d,t}) \lambda_{jl,t} + C_0 P_{v2g,i,d,t} \right] $$
Here, \( u_{i,c} \) and \( u_{i,d} \) are binary variables indicating charging and discharging states, and \( C_0 \) is the battery degradation cost per unit discharge. The V2G strategy is only applied if the user’s participation willingness, derived from the uncertainty model, is satisfied.
Power System Scheduling with Electric Vehicle Energy Storage
Power system flexibility is defined as the ability to balance supply and demand under uncertainties from renewables and loads. This study considers day-ahead and intra-day scheduling, with flexibility resources including conventional generators, pumped storage, energy storage systems, and interruptible loads.
Flexibility Demand
Flexibility demand is quantified as the net load ramp requirement. For day-ahead and intra-day schedules, upward and downward flexibility demands are:
$$ F_{d1,t}^{up} = \max\{0, P_{j1,t+1} – P_{j1,t}\} $$
$$ F_{d1,t}^{down} = \max\{0, P_{j1,t} – P_{j1,t+1}\} $$
$$ F_{d2,t}^{up} = \max\{0, P_{j2,t+1} – P_{j2,t}\} $$
$$ F_{d2,t}^{down} = \max\{0, P_{j2,t} – P_{j2,t+1}\} $$
where \( P_{j1} \) and \( P_{j2} \) are day-ahead and intra-day net loads, respectively:
$$ P_{j1,t} = P_{base,t} – P_{PV1,t} – P_{WIND1,t} $$
$$ P_{j2,t} = P_{base,t} + P_{EV,t} – P_{PV2,t} – P_{WIND2,t} $$
\( P_{EV,t} \) is the EV load, and \( P_{PV1,t} \), \( P_{WIND1,t} \), \( P_{PV2,t} \), \( P_{WIND2,t} \) are forecasted and actual renewable outputs.
Flexibility Resources
Flexibility resources are categorized based on their response times and costs. Thermal units and pumped storage are used in day-ahead scheduling, while energy storage systems provide intra-day flexibility. Additional resources include interruptible loads (upward flexibility) and renewable curtailment (downward flexibility). The flexibility from each resource is calculated as follows:
For thermal units:
$$ F_{g,t}^{up} = \min\{R_g^{up} \Delta t, P_{g,max} – P_{g,t}\} $$
$$ F_{g,t}^{down} = \min\{R_g^{down} \Delta t, P_{g,t} – P_{g,min}\} $$
For pumped storage:
$$ F_{h,t}^{up} = \min \left\{ P_{h,max} – P_{h,t}, \frac{(W_{h,max} – W_{h,t}) \eta_h}{\Delta t} \right\} $$
$$ F_{h,t}^{down} = \min \left\{ P_{h,t} – P_{h,min}, \frac{W_{h,t} – W_{h,min}}{\eta_h \Delta t} \right\} $$
For energy storage:
$$ F_{ess,t}^{up} = \min \left\{ P_{ess,max} – P_{ess,t}, \frac{(W_{ess,max} – W_{ess,t}) \eta_{ess}}{\Delta t} \right\} $$
$$ F_{ess,t}^{down} = \min \left\{ P_{ess,t} – P_{ess,min}, \frac{W_{ess,t} – W_{ess,min}}{\eta_{ess} \Delta t} \right\} $$
For interruptible loads and renewable curtailment:
$$ F_{cut,t}^{up} = P_{cut,t}, \quad F_{cut,t}^{down} = 0 $$
$$ F_{wind,waste,t}^{up} = 0, \quad F_{wind,waste,t}^{down} = P_{wind,waste,t} $$
$$ F_{pv,waste,t}^{up} = 0, \quad F_{pv,waste,t}^{down} = P_{pv,waste,t} $$
The power and energy levels of pumped storage and energy storage are updated as:
$$ P_{h,t} = u_{h,d,t} P_{h,d,t} – u_{h,c,t} P_{h,c,t} $$
$$ W_{h,t} = W_{h,0} – \sum_{\tau=1}^{t} \frac{P_{h,d,\tau} \Delta t}{\eta_h} + \sum_{\tau=1}^{t} P_{h,c,\tau} \Delta t \eta_h $$
$$ P_{ess,t} = P_{ess,d,t} – P_{ess,c,t} $$
$$ W_{ess,t} = W_{ess,0} – \sum_{\tau=1}^{t} \frac{P_{ess,d,\tau} \Delta t}{\eta_{ess}} + \sum_{\tau=1}^{t} P_{ess,c,\tau} \Delta t \eta_{ess} $$
Flexibility margins indicate the balance between supply and demand:
$$ F_{t1}^{+} = F_{g,t}^{up} + F_{h,t}^{up} + F_{cut,t}^{up} + F_{wind,waste,t}^{up} + F_{pv,waste,t}^{up} – F_{d,t}^{up} $$
$$ F_{t1}^{-} = F_{g,t}^{down} + F_{h,t}^{down} + F_{cut,t}^{down} + F_{wind,waste,t}^{down} + F_{pv,waste,t}^{down} – F_{d,t}^{down} $$
$$ F_{t2}^{+} = F_{g,t}^{up} + F_{h,t}^{up} + F_{cut,t}^{up} + F_{wind,waste,t}^{up} + F_{pv,waste,t}^{up} + F_{ess,t}^{up} – F_{d,t}^{up} $$
$$ F_{t2}^{-} = F_{g,t}^{down} + F_{h,t}^{down} + F_{cut,t}^{down} + F_{wind,waste,t}^{down} + F_{pv,waste,t}^{down} + F_{ess,t}^{down} – F_{d,t}^{down} $$
Optimization Scheduling Model with Flexibility
The day-ahead scheduling minimizes total costs, including thermal generation, pumped storage, renewables, interruptible loads, and curtailment:
$$ \min (F_g + F_h + F_{dg} + F_{cut} + F_{waste}) $$
where:
$$ F_g = \sum_{t=1}^{T} (a P_{g,t}^2 + b P_{g,t} + c) $$
$$ F_h = \sum_{t=1}^{T} C_h (u_{h,d,t} P_{h,d,t} + u_{h,c,t} P_{h,c,t}) $$
$$ F_{dg} = \sum_{t=1}^{T} (C_{wind} P_{wind,t} + C_{pv} P_{pv,t}) $$
$$ F_{cut} = \sum_{t=1}^{T} C_{cut} u_{cut,t} P_{cut,t} $$
$$ F_{waste} = \sum_{t=1}^{T} (C_{wind,waste} u_{wind,waste,t} P_{wind,waste,t} + C_{pv,waste} u_{pv,waste,t} P_{pv,waste,t}) $$
Intra-day scheduling incorporates energy storage costs:
$$ \min (F_g + F_h + F_{ess} + F_{dg} + F_{cut} + F_{waste}) $$
$$ F_{ess} = \sum_{t=1}^{T} C_{ess} (u_{ess,d,t} P_{ess,d,t} + u_{ess,c,t} P_{ess,c,t}) $$
Constraints include power balance, flexibility supply-demand balance, and operational limits for all resources.
Case Study and Analysis
A case study based on a typical daily load profile in China is used to validate the proposed models. The parameters for electric vehicles, time-of-use electricity prices, and renewable forecasts are summarized below.
| Time Period | Price (USD/kWh) |
|---|---|
| 22:00-3:00, 9:00-16:00 | 0.305 |
| 3:00-9:00, 21:00-22:00 | 0.615 |
| 16:00-21:00 | 1.025 |
| Time Period | Parameters |
|---|---|
| Morning Departure | \( N(7, 0.5^2) \) |
| Morning Arrival | \( N(8, 0.5^2) \) |
| Evening Departure | \( N(16.5, 0.5^2) \) |
| Evening Arrival | \( N(17.5, 0.5^2) \) |
For 100 electric vehicles, the battery capacity is 60 kWh, with maximum charge/discharge power of 7 kW. The target SOC is normally distributed with mean 0.85 and standard deviation 0.15. The无序 charging mode results in high costs and increased peak loads, while ordered charging reduces costs by shifting loads. The V2G strategy, with incentive pricing, further lowers costs and enhances flexibility.
| Charging Mode | Charging Cost (USD) |
|---|---|
| Unordered Charging | 1246 |
| Ordered Charging | 589 |
| V2G | 315 |
Two flexibility cases are analyzed: Case 1 without flexibility constraints and Case 2 with constraints. In Case 1, V2G reduces flexibility shortages compared to other modes. In Case 2, the scheduling ensures no flexibility shortages, with V2G achieving the lowest total cost.
| Charging Mode | Thermal (USD) | Pumped Storage (USD) | Energy Storage (USD) | Wind (USD) | PV (USD) | Penalty (USD) | Total (USD) |
|---|---|---|---|---|---|---|---|
| Unordered | 11308 | 549 | 1383 | 861 | 817 | 5725 | 20645 |
| Ordered | 11724 | 663 | 1585 | 866 | 811 | 2551 | 18204 |
| V2G | 12009 | 494 | 1778 | 866 | 807 | 1918 | 17876 |
The results demonstrate that the V2G strategy, accounting for user participation willingness, minimizes costs and penalties while maintaining flexibility. The integration of electric vehicles as energy storage resources significantly improves grid stability and supports the growth of renewables in China’s power system.
Conclusion
This study presents a comprehensive approach to power system scheduling that incorporates electric vehicle energy storage, with a focus on user participation uncertainty and flexibility analysis. The key findings are as follows:
First, the optimistic and pessimistic participation willingness model based on Logistic functions effectively captures the uncertainty in user responses to incentive prices. This model provides a realistic representation of how electric vehicle users in China might engage in V2G programs, considering factors like battery concerns and financial incentives.
Second, the proposed V2G strategy, which integrates user willingness, not only reduces charging costs for users but also achieves significant peak shaving and valley filling in net loads. By aligning charging and discharging with net load fluctuations, the strategy enhances grid stability and reduces the need for costly infrastructure upgrades.
Third, in scenarios without flexibility constraints, both ordered charging and V2G outperform unordered charging in terms of cost reduction and flexibility improvement. However, V2G yields the best results, with lower flexibility shortages and overall system costs. When flexibility constraints are enforced, the scheduling model ensures that flexibility supply meets demand, with V2G achieving the lowest total cost and penalty fees.
In conclusion, the integration of electric vehicles into power systems, particularly through V2G technologies, offers a promising path toward sustainable energy management. The methods developed in this study can guide policymakers and grid operators in designing effective incentive mechanisms and scheduling strategies. Future work could explore real-time implementation and the impact of evolving battery technologies on V2G economics. The rapid growth of China’s EV market underscores the importance of these efforts in achieving a flexible and resilient power system.