As global energy systems evolve, the dual pressures of climate change mitigation and rising electricity demand necessitate innovative grid management solutions. My research addresses a critical frontier: leveraging electric vehicle (EV) batteries as distributed energy storage assets within power system scheduling frameworks, explicitly accounting for the inherent uncertainty in user participation willingness. This integration is paramount for enhancing system flexibility amidst growing renewable energy penetration and associated net load volatility.
1. Introduction
The transition towards decarbonized power systems drives unprecedented integration of variable renewable energy (VRE) sources like wind and solar. Concurrently, the electrification of transport accelerates, significantly increasing the penetration of electric vehicles. While VRE reduces carbon emissions, its inherent variability challenges grid stability. Conversely, electric vehicles possess untapped potential: parked for over 90% of the day, their batteries represent a vast, distributed energy storage resource. Vehicle-to-Grid (V2G) technology enables bidirectional power flow, allowing electric vehicles to discharge stored energy back to the grid during peak demand periods and charge during off-peak times or high VRE generation. This capability transforms the electric vehicle fleet from a passive load into an active flexibility provider. However, successful large-scale V2G deployment hinges critically on user participation, which is fraught with uncertainty driven by concerns over battery degradation and perceived economic benefits. My work develops a novel scheduling methodology that explicitly models this user willingness uncertainty and quantifies its impact on power system flexibility and operational economics.
2. Modeling User Participation Willingness Uncertainty
The cornerstone of effective V2G integration is accurately capturing the stochastic nature of user engagement. Traditional models often neglect this crucial factor or employ simplistic linear assumptions, leading to suboptimal or unrealistic scheduling outcomes. I introduce a sophisticated model based on consumer psychology principles and logistic functions to represent the spectrum of user responses to economic incentives.
2.1. Incentive Pricing Mechanism
The incentive price ($\lambda_{jt}$) is dynamically adjusted based on real-time net load ($P_{Lt}$) relative to the daily average net load ($P_{ap}$), aligning V2G incentives with system needs. It is formulated to be higher than the time-of-use (TOU) price ($\lambda_{TOUt}$) during net load peaks and lower during troughs. The compensation coefficient ($K_{pt}$) quantifies the deviation magnitude.
\lambda_{jt} = (1 + K_{pt}) \lambda_{TOUt} \quad (1)
K_{pt} = \rho (P_{Lt} - P_{ap}) / P_{ap} \quad (2)
P_{Lt} = P_{base,t} - P_{wind,t} - P_{pv,t} \quad (3)
P_{ap} = \frac{1}{T} \sum_{t=1}^{T} P_{Lt} \quad (4)
where $\rho$ is the load fluctuation coefficient.
2.2. Logistic-Based Optimistic-Pessimistic Willingness Model
User willingness ($P$) to participate in V2G exhibits a non-linear relationship with the incentive coefficient ($\epsilon_{jt}$), defined as the ratio of incentive price to the user’s expected incentive price ($\lambda_{e,t}$).
\epsilon_{jt} = \lambda_{jt} / \lambda_{e,t} \quad (5)
Consumer psychology suggests this relationship follows a sigmoidal (“S”-curve) pattern, not linear segments:
- Low Incentive ($\epsilon_{jt} \ll 1$): Willingness is minimal and insensitive.
- Moderate Incentive ($\epsilon_{jt} \approx 1$): Willingness increases rapidly with $\epsilon_{jt}$.
- High Incentive ($\epsilon_{jt} \gg 1$): Willingness saturates near maximum.
The Logistic function perfectly captures this behavior. To model uncertainty, I define two bounding curves:
- Optimistic Willingness ($P_{op}$): Represents users most responsive to incentives.
- Pessimistic Willingness ($P_{pess}$): Represents users least responsive to incentives.
P_{op}(\epsilon) = \frac{c_{op}}{1 + a_{op} e^{-b_{op}(\epsilon - 1)}} \quad (6)
P_{pess}(\epsilon) = \frac{c_{pess}}{1 + a_{pess} e^{-b_{pess}(\epsilon - 1)}} \quad (7)
Parameters ($a_{op/pess}$, $b_{op/pess}$, $c_{op/pess}$) are fitted using historical data or surveys under the “3σ principle” of the normal distribution. For any given $\epsilon_{jt}$, the actual user willingness $p_i$ for EV $i$ at time $t$ is a normally distributed random variable:
\mu(\epsilon_{jt}) = \frac{P_{op}(\epsilon_{jt}) + P_{pess}(\epsilon_{jt})}{2} \quad (8)
\sigma(\epsilon_{jt}) = \frac{P_{op}(\epsilon_{jt}) - P_{pess}(\epsilon_{jt})}{6} \quad (9)
p_i \sim \mathcal{N}(\mu(\epsilon_{jt}), \sigma(\epsilon_{jt})) \quad (10)
This model realistically captures the inherent variability in how different electric vehicle owners respond to identical incentive signals.
3. Electric Vehicle Charging/Discharging Models
My framework evaluates three distinct electric vehicle integration modes:
3.1. Uncontrolled Charging
This represents the baseline “business-as-usual” scenario where electric vehicle owners plug in and charge immediately at maximum power upon parking until their desired State of Charge (SOC) is reached. The aggregate load profile is generated via Monte Carlo simulation of individual electric vehicle behaviors (arrival time $t_a$, departure time $t_d$, initial SOC $S_0$, desired SOC $S_e$). This mode typically exacerbates peak net loads.
3.2. Smart Charging (Unidirectional V1G)
Electric vehicle charging is optimized within parking duration constraints to minimize charging costs or grid impact, without discharging (V2G). Key constraint: Parking duration must exceed minimum charging time.
t_d - t_a \geq t_c \quad \text{where} \quad t_c = \frac{(S_e - S_0)E}{P_c \eta_c} \quad (11)
where $E$ is battery capacity, $P_c$ is charging power, $\eta_c$ is charging efficiency. The objective minimizes total charging cost under TOU pricing ($\lambda_{TOUt}$):
\min F_{charge} = \sum_{i=1}^{N} \sum_{t=1}^{T} \lambda_{TOUt} P_{c,i,t} \Delta t \quad (12)
subject to power limits, SOC limits ($SOC_{min} \leq SOC_{i,t} \leq SOC_{max}$), and meeting $S_e$ by $t_d$.
3.3. V2G with User Willingness (Bidirectional)
This mode incorporates controlled bidirectional charging/discharging, activated only if the parking duration allows fulfilling the trip requirement and the simulated user willingness $p_i$ exceeds a threshold at time $t$. The minimum time constraint considers discharge to $SOC_{min}$ and recharge to $S_e$:
t_d - t_a \geq t_{cd} \quad \text{where} \quad t_{cd} = \frac{(S_e - SOC_{min})E}{P_c \eta_c} + \frac{(S_0 - SOC_{min})E}{P_d / \eta_d} \quad (13)
where $P_d$ is discharging power, $\eta_d$ is discharging efficiency. The objective minimizes net energy cost, including battery degradation cost ($C_b$ per kWh discharged):
\min (F_{charge} + F_{discharge} + F_{deg}) = \sum_{i=1}^{N} \sum_{t=1}^{T} \Big[ u_{c,i,t} P_{c,i,t} \lambda_{jt} - u_{d,i,t} P_{d,i,t} \lambda_{jt} + u_{d,i,t} P_{d,i,t} C_b \Big] \Delta t \quad (14)
Here, $u_{c,i,t}$, $u_{d,i,t}$ are binary charge/discharge status variables, and $\lambda_{jt}$ is the incentive price. Constraints include simultaneous charge/discharge prevention, power limits ($-P_d^{max} \leq P_{i,t} \leq P_c^{max}$), and stricter SOC limits ($SOC_{min}^{V2G} \leq SOC_{i,t} \leq SOC_{max}$).
4. Power System Scheduling Framework with Flexibility Assessment
I adopt a two-stage scheduling approach (Day-Ahead and Intra-Day) incorporating explicit flexibility supply-demand balance constraints, crucial for managing VRE uncertainty and electric vehicle load variability.
4.1. Flexibility Quantification
- Flexibility Demand ($F_D$): Defined as the required upward/downward power adjustment capability to track net load changes between consecutive time steps.latex复制下载F_{D,t}^{up, DA} = \max\{0, P_{L,t+1}^{DA} – P_{L,t}^{DA}\} \quad (15)latex复制下载F_{D,t}^{down, DA} = \max\{0, P_{L,t}^{DA} – P_{L,t+1}^{DA}\} \quad (16)latex复制下载F_{D,t}^{up, ID} = \max\{0, P_{L,t+1}^{ID} – P_{L,t}^{ID}\} \quad (17)latex复制下载F_{D,t}^{down, ID} = \max\{0, P_{L,t}^{ID} – P_{L,t+1}^{ID}\} \quad (18)Net Load ($P_L$):latex复制下载P_{L,t}^{DA} = P_{base,t} – P_{wind,t}^{DA} – P_{pv,t}^{DA} \quad (19)latex复制下载P_{L,t}^{ID} = P_{base,t} + P_{EV,t} – P_{V2G,t} – P_{wind,t}^{ID} – P_{pv,t}^{ID} \quad (20)($P_{EV,t}$, $P_{V2G,t}$ represent aggregated electric vehicle charging and discharging power).
- Flexibility Supply ($F_S$): Aggregated upward/downward adjustment capability from all system resources:
- Thermal Generators (g): Ramp rate and capacity limits.latex复制下载F_{S,g,t}^{up} = \min\{R_g^{up} \Delta t, P_{g}^{max} – P_{g,t}\} \quad (21)latex复制下载F_{S,g,t}^{down} = \min\{R_g^{down} \Delta t, P_{g,t} – P_{g}^{min}\} \quad (22)
- Pumped Hydro Storage (h): Power and energy constraints.latex复制下载F_{S,h,t}^{up} = \min\{P_{h}^{max} – P_{h,t}, \frac{(W_{h,t} – W_{h}^{min}) \eta_h}{\Delta t} \} \quad \text{(Discharging for Up)} \quad (23)latex复制下载F_{S,h,t}^{down} = \min\{P_{h,t} – P_{h}^{min}, \frac{(W_{h}^{max} – W_{h,t}) / \eta_h}{\Delta t} \} \quad \text{(Charging for Down)} \quad (24)
- Battery Storage (ess): Similar constraints to PHS.latex复制下载F_{S,ess,t}^{up} = \min\{P_{ess}^{max} – P_{ess,t}, \frac{(W_{ess,t} – W_{ess}^{min}) \eta_{ess}}{\Delta t} \} \quad (25)latex复制下载F_{S,ess,t}^{down} = \min\{P_{ess,t} – P_{ess}^{min}, \frac{(W_{ess}^{max} – W_{ess,t}) / \eta_{ess}}{\Delta t} \} \quad (26)
- Interruptible Load (cut): Provides upward flexibility (load reduction).latex复制下载F_{S,cut,t}^{up} = P_{cut,t}^{max}; \quad F_{S,cut,t}^{down} = 0 \quad (27)
- VRE Curtailment (wind/pv): Provides downward flexibility (generation reduction).latex复制下载F_{S,wind,t}^{up} = 0; \quad F_{S,wind,t}^{down} = P_{wind,t}^{avail} – P_{wind,t} \quad (28)latex复制下载F_{S,pv,t}^{up} = 0; \quad F_{S,pv,t}^{down} = P_{pv,t}^{avail} – P_{pv,t} \quad (29)
4.2. Flexibility Margin
The critical constraint ensuring sufficient flexibility reserves is the non-negative flexibility margin ($F_M$):
F_{M,t}^{up, DA} = \sum F_{S,t}^{up, DA} - F_{D,t}^{up, DA} \geq 0 \quad (32)
F_{M,t}^{down, DA} = \sum F_{S,t}^{down, DA} - F_{D,t}^{down, DA} \geq 0 \quad (33)
F_{M,t}^{up, ID} = \sum F_{S,t}^{up, ID} - F_{D,t}^{up, ID} \geq 0 \quad (34)
F_{M,t}^{down, ID} = \sum F_{S,t}^{down, ID} - F_{D,t}^{down, ID} \geq 0 \quad (35)
The summation ($\sum F_S$) includes all available flexibility resources (Thermal, PHS, ESS, IL, VRE Curtailment).
4.3. Two-Stage Optimization Model
- Stage 1: Day-Ahead (DA) Scheduling:
Minimizes total DA operational cost based on forecasts:latex复制下载\min (F_{g}^{DA} + F_{h}^{DA} + F_{dg}^{DA} + F_{cut}^{DA} + F_{waste}^{DA}) \quad (36)Components:latex复制下载F_{g}^{DA} = \sum_{t} (a (P_{g,t}^{DA})^2 + b P_{g,t}^{DA} + c) \Delta t \quad \text{(Thermal Gen Cost)} \quad (37)latex复制下载F_{h}^{DA} = \sum_{t} C_h (P_{h,dch,t}^{DA} + P_{h,ch,t}^{DA}) \Delta t \quad \text{(PHS Cost)} \quad (38)latex复制下载F_{dg}^{DA} = \sum_{t} (C_{wind} P_{wind,t}^{DA} + C_{pv} P_{pv,t}^{DA}) \Delta t \quad \text{(VRE Gen Cost)} \quad (39)latex复制下载F_{cut}^{DA} = \sum_{t} C_{cut} P_{cut,t}^{DA} \Delta t \quad \text{(Interruptible Load Cost)} \quad (40)latex复制下载F_{waste}^{DA} = \sum_{t} (C_{wind,waste} P_{wind,waste,t}^{DA} + C_{pv,waste} P_{pv,waste,t}^{DA}) \Delta t \quad \text{(VRE Curtailment Cost)} \quad (41)Subject to: DA power balance, unit constraints, DA flexibility margin constraints (Eqs. 32, 33), and initial electric vehicle charging profiles (Uncontrolled or Smart Charging). - Stage 2: Intra-Day (ID) Scheduling (Rolling Horizon):
Minimizes ID cost deviations, adjusting DA schedules using updated forecasts (VRE, electric vehicle willingness/V2G) and activating ID flexibility (ESS, VRE Curtailment):latex复制下载\min (F_{g}^{ID} + F_{h}^{ID} + F_{ess}^{ID} + F_{dg}^{ID} + F_{cut}^{ID} + F_{waste}^{ID}) \quad (42)Added component:latex复制下载F_{ess}^{ID} = \sum_{t} C_{ess} (P_{ess,dch,t}^{ID} + P_{ess,ch,t}^{ID}) \Delta t \quad \text{(ESS Cost)} \quad (43)Subject to: ID power balance, unit constraints (including ramping from DA), ESS constraints, ID flexibility margin constraints (Eqs. 34, 35), and realized electric vehicle behavior (including V2G based on willingness model).
5. Case Study and Results
Simulations were conducted using MATLAB 2022a and Gurobi for a typical regional grid in China (24h DA horizon, 1h resolution; 4h rolling ID horizon, 15min resolution). Key electric vehicle fleet parameters: 100 EVs, $SOC_{min}=0.2$, $SOC_{max}=1.0$, $S_e \sim \mathcal{N}(0.85, 0.15)$, Capacity=60 kWh, $P_c^{max}$=7 kW, $P_d^{max}$=7 kW, $\eta_c=\eta_d$=0.95. Commute times followed Normal distributions (Table 1). TOU and calculated incentive prices are shown (Figure 1 concept). Two cases were analyzed:
- Case 1: Optimization without flexibility margin constraints (only power balance).
- Case 2: Optimization with flexibility margin constraints (Eqs. 32-35).
5.1. EV Load and Net Load Impact
- Uncontrolled Charging: Concentrates charging during evening peaks (17:00-19:00), significantly increasing net load peak and volatility. User Cost: 1246 RMB.
- Smart Charging: Shifts charging away from TOU peaks, reducing net load peak and fluctuation compared to uncontrolled charging. User Cost: 589 RMB (52.7% reduction).
- V2G with Willingness: Incentive pricing encourages charging during low net load/price periods and discharging during high net load/price periods. Achieves the most significant net load peak reduction and valley filling, minimizing net load volatility, especially noticeable during mid-day (10:00-13:00). User Cost: 315 RMB (46.5% reduction from Smart Charging, 74.7% reduction from Uncontrolled).
Table 1: EV Commute Time Distribution
| Parameter | Distribution |
|---|---|
| Morning Departure | \(\mathcal{N}(7, 0.5^2)\) |
| Morning Arrival | \(\mathcal{N}(8, 0.5^2)\) |
| Evening Departure | \(\mathcal{N}(16.5, 0.5^2)\) |
| Evening Arrival | \(\mathcal{N}(17.5, 0.5^2)\) |
Table 2: User Charging Costs under Different Modes
| Charging Mode | Charging Cost (RMB) |
|---|---|
| Uncontrolled Charging | 1246 |
| Smart Charging (V1G) | 589 |
| V2G with Willingness | 315 |
5.2. Power System Scheduling Results (Case 2 – With Flexibility Constraints)
- Flexibility Assurance: Case 2 successfully maintained non-negative flexibility margins ($F_M \geq 0$) for all modes at all times, preventing flexibility shortfalls observed in Case 1 (e.g., downward shortfall around 18:00-20:00 under V2G in Case 1). This was achieved by strategic use of ESS charging and minor VRE curtailment during critical periods.
- Economic Performance (System Cost): Despite slightly higher thermal and ESS costs due to increased energy throughput (especially discharging from electric vehicles in V2G) and flexibility provision, the V2G strategy yielded the lowest total system cost.
Table 3: System Scheduling Costs under Different EV Modes (Case 2 – With Flexibility Constraints) (RMB)*
| Cost Component | Uncontrolled | Smart Charging | V2G | Notes |
|---|---|---|---|---|
| Thermal Gen | 11,308 | 11,724 | 12,009 | Higher in V2G due to charging losses & discharge supply |
| Pumped Hydro | 549 | 663 | 494 | |
| ESS | 1,383 | 1,585 | 1,778 | Higher utilization cost in V2G |
| Wind Gen | 861 | 866 | 866 | |
| PV Gen | 817 | 811 | 807 | |
| Penalty/Curtail | 5,725 | 2,551 | 1,918 | Significantly lower in V2G (Interrupt Load, VRE Curtail) |
| Total System Cost | 20,645 | 18,204 | 17,876 | V2G achieves LOWEST total cost |
- Key Drivers of V2G Cost Advantage:
- Reduced Penalties: V2G’s superior net load flattening drastically reduced the need for costly interruptible load and VRE curtailment (Penalty cost: Uncontrolled 5725 RMB, Smart Charging 2551 RMB, V2G 1918 RMB).
- Lower Flexibility Demand: Smoother net load profile directly translates to lower upward/downward flexibility demand ($F_D$), easing the burden on other flexibility resources.
- Effective Incentive Utilization: The willingness-based V2G model efficiently harnesses electric vehicle flexibility where most beneficial to the grid, maximizing cost reduction per unit of electric vehicle storage utilized.
- Comparison to Case 1 (No Flexibility Constraints): While Case 1 showed V2G had the smallest flexibility shortfall (5527 kWh Uncontrolled, 4050 kWh Smart Charging, 2887 kWh V2G), it incurred higher total costs due to unmitigated penalties. Case 2, by enforcing flexibility, added some cost (e.g., ESS usage) but resulted in a more secure and overall cheaper system operation under V2G. The total societal cost (System Cost + EV User Cost – V2G Rebates) was minimized under the proposed V2G strategy.
6. Conclusion
This research demonstrates the significant potential of strategically integrating electric vehicle batteries as flexible energy storage within modern power systems, contingent upon effectively modeling and managing user participation uncertainty. The key contributions and findings are:
- Realistic User Willingness Model: The logistic function-based optimistic-pessimistic model effectively captures the non-linear and uncertain relationship between economic incentives and electric vehicle owner participation in V2G programs. This model is crucial for predicting realistic electric vehicle response and optimizing incentive structures.
- Cost-Effective V2G Strategy: The proposed V2G scheduling strategy, incorporating the user willingness model and a net-load-based dynamic incentive price, delivers substantial benefits:
- User Savings: Significantly reduces charging costs for electric vehicle owners compared to uncontrolled charging (74.7%) and smart charging (46.5%).
- Grid Support: Effectively performs peak shaving and valley filling, substantially reducing net load volatility and peak demand.
- System Flexibility Enhancement: Provides crucial upward and downward flexibility, directly reducing the system’s overall flexibility demand.
- Flexibility-Constrained Scheduling: Explicitly incorporating flexibility supply-demand balance constraints (upward/downward flexibility margin $\geq 0$) in the scheduling model is essential for ensuring grid stability under high VRE penetration. While adding these constraints increases optimization complexity, it prevents operational risks associated with flexibility shortfalls.
- Superior System Economics: Under a flexibility-constrained regime (Case 2), the proposed willingness-based V2G strategy achieves the lowest total system operating cost compared to Uncontrolled Charging and Smart Charging. This cost advantage stems primarily from:
- Drastic reduction in costly penalties (interruptible load dispatch and VRE curtailment).
- More efficient utilization of conventional generation and grid-scale storage assets due to smoother net load profiles enabled by electric vehicle flexibility.
- Effective targeting of V2G incentives leveraging the participation willingness model.
7. Outlook
Future work will focus on refining the user willingness model with real-world behavioral data, investigating the long-term impact of V2G on electric vehicle battery degradation under various scheduling regimes, exploring large-scale electric vehicle aggregation strategies for ancillary services, and integrating this framework with transmission-distribution co-simulation for wider grid impact assessment. The successful integration of electric vehicle storage, guided by accurate user behavior modeling and dynamic market signals, is pivotal for building cost-effective, reliable, and flexible power systems for a sustainable energy future dominated by renewable resources.