With the increasing proportion of renewable energy in power grids and the rising penetration of electric cars, the volatility of wind and solar power and the uncertainty of electric car charging loads pose significant challenges to the flexible operation of power systems. In China, the rapid adoption of China EV has accelerated these trends, necessitating innovative approaches to grid management. Considering that electric cars remain parked for most of the day while meeting user travel demands, and with advancements in vehicle-to-grid (V2G) technology, electric cars exhibit energy storage characteristics. This paper addresses the impact of charging and discharging strategies that account for the uncertainty of electric car user participation willingness on power system scheduling and analyzes its flexibility. First, to tackle the issue that existing electric car charging and discharging scheduling overlooks user participation willingness, we propose an optimistic and pessimistic participation willingness model based on the Logistic function for orderly electric car charging and discharging. This reflects the uncertainty in user willingness to participate in scheduled charging and discharging. Next, we compare and analyze the effects of different electric car charging and discharging modes on multi-time-scale power system scheduling, where intra-day scheduling builds upon day-ahead scheduling, with the objective of minimizing the comprehensive cost of power system scheduling. Finally, simulation results demonstrate that, by considering the energy storage characteristics of electric cars, the proposed charging and discharging strategy that incorporates user participation willingness not only effectively shaves peaks and fills valleys but also promotes flexible power system operation at lower costs.
The integration of electric cars into power systems has become a critical area of research, particularly in regions like China where China EV adoption is booming. Electric cars, when connected to the grid, can serve as distributed energy resources, providing flexibility through V2G operations. However, user participation in V2G is influenced by factors such as battery degradation concerns and financial incentives, leading to uncertainties in willingness. In this context, we develop a model to quantify this uncertainty and integrate it into power system scheduling. The flexibility of power systems is defined as their ability to respond to predictable and unpredictable fluctuations in supply and demand, and electric cars can significantly enhance this flexibility by adjusting their charging and discharging patterns based on grid conditions.
To model the uncertainty in electric car user participation willingness, we introduce an incentive pricing mechanism. The incentive price is adjusted according to the net load and daily average net load, as shown in the following equations:
$$ \lambda_{jl,t} = (1 + K_{p,t}) \lambda_{fs,t} $$
where $\lambda_{jl,t}$ is the incentive price at time $t$, $K_{p,t}$ is the compensation coefficient, and $\lambda_{fs,t}$ is the time-of-use electricity price. The incentive coefficient for user $i$ at time $t$ is given by:
$$ \varepsilon_{i,t} = \frac{\lambda_{jl,t}}{\lambda_{i,yq,t}} $$
Here, $\lambda_{i,yq,t}$ is the expected incentive price for user $i$ at time $t$. The compensation coefficient $K_{p,t}$ is calculated as:
$$ K_{p,t} = \rho \frac{P_{j,t} – P_{av}}{P_{av}} $$
where $\rho$ is the load fluctuation coefficient, $P_{j,t}$ is the net load at time $t$, and $P_{av}$ is the daily average net load. The net load $P_{j,t}$ is defined as:
$$ P_{j,t} = P_{base,t} – P_{wind,t} – P_{pv,t} $$
with $P_{base,t}$ as the base load, and $P_{wind,t}$ and $P_{pv,t}$ as wind and photovoltaic power outputs, respectively. The daily average net load is:
$$ P_{av} = \frac{1}{T} \sum_{t=1}^{T} P_{j,t} $$
Based on consumer psychology, user willingness to participate in V2G follows an S-shaped curve relative to the incentive coefficient. We use Logistic functions to model optimistic and pessimistic participation willingness:
$$ p_{op} = \frac{c_{op}}{1 + a_{op} e^{-b_{op} (\varepsilon – 1)}} $$
$$ p_{pess} = \frac{c_{pess}}{1 + a_{pess} e^{-b_{pess} (\varepsilon – 1)}} $$
where $p_{op}$ and $p_{pess}$ are the optimistic and pessimistic participation willingness curves, and $a_{op/pess}$, $b_{op/pess}$, $c_{op/pess}$ are parameters of the Logistic functions. The mean and standard deviation of user willingness at a given incentive coefficient $\varepsilon$ 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 of user $i$ at time $t$ follows a normal distribution:
$$ p = N(\mu(\varepsilon), \sigma(\varepsilon)) $$
This model captures the uncertainty in electric car user behavior, which is crucial for realistic scheduling in power systems, especially in the context of China EV integration.
For electric car charging and discharging models, we consider three modes: unordered charging, ordered charging, and V2G. In unordered charging, electric cars charge immediately upon connection until the desired state of charge (SOC) is reached, leading to peak load increases. The charging power for unordered charging is determined using Monte Carlo simulation. In ordered charging, electric cars are scheduled to charge during off-peak hours to minimize costs, based on time-of-use electricity prices. The objective function for ordered charging is to minimize the charging cost:
$$ \min F = \sum_{i=1}^{N} \sum_{t=1}^{T} \lambda_{fs,t} P_{i,t} $$
where $N$ is the number of electric cars, $T$ is the scheduling period, and $P_{i,t}$ is the charging power of electric car $i$ at time $t$. Constraints include charging power limits, SOC limits, and user travel demand constraints. For example, the SOC must satisfy:
$$ S_{min} \leq S_{i,t} \leq S_{max} $$
where $S_{i,t}$ is the SOC of electric car $i$ at time $t$, and $S_{min}$ and $S_{max}$ are the minimum and maximum SOC limits.
In V2G mode, electric cars can both charge and discharge, participating in grid services. The scheduling strategy accounts for user participation willingness and aims to minimize costs including battery degradation:
$$ \min (F_1 + F_2) = \sum_{i=1}^{N} \sum_{t=1}^{T} \left[ (u_{i,c} P_{i,c,t} + u_{i,d} P_{i,d,t}) \lambda_{jl,t} + C_0 P_{v2g,i,d,t} \right] $$
where $P_{i,c,t}$ and $P_{i,d,t}$ are the charging and discharging powers, $u_{i,c}$ and $u_{i,d}$ are binary variables indicating charging or discharging states, and $C_0$ is the unit battery degradation cost. Discharging constraints include power limits and SOC constraints to ensure user travel needs are met.
The power system scheduling model incorporates day-ahead and intra-day time scales. Flexibility demand is quantified as the net load fluctuation:
$$ F_{d1,t}^{up} = \max\{0, P_{j1,t+1} – P_{j1,t}\} $$
$$ F_{d1,t}^{down} = \max\{0, P_{j1,t} – P_{j1,t+1}\} $$
for day-ahead scheduling, and similarly for intra-day scheduling. Flexibility resources include conventional thermal units, pumped storage, energy storage, interruptible load, and renewable curtailment. The flexibility supply from thermal units is:
$$ F_{g,t}^{up} = \min\{ R_g^{up} \Delta t, P_{g,max} – P_{g,t} \} $$
$$ F_{g,t}^{down} = \min\{ R_g^{down} \Delta t, P_{g,t} – P_{g,min} \} $$
where $R_g^{up}$ and $R_g^{down}$ are the ramp rates, and $P_{g,max}$ and $P_{g,min}$ are the maximum and minimum outputs. For pumped storage, the flexibility is:
$$ F_{h,t}^{up} = \min \left\{ P_{h,max} – P_{h,t}, \frac{(W_{h,max} – W_{h,t}) \eta_h}{\Delta t} \right\} $$
$$ F_{h,t}^{down} = \min \left\{ P_{h,t} – P_{h,min}, \frac{W_{h,t} – W_{h,min}}{\eta_h \Delta t} \right\} $$
where $W_{h,t}$ is the storage capacity at time $t$, and $\eta_h$ is the efficiency. Energy storage flexibility is modeled similarly. The flexibility margin ensures supply meets demand:
$$ F_{t1}^{+} = F_{g,t}^{up} + F_{h,t}^{up} + F_{cut,t}^{up} + F_{wind,waste,t}^{up} + F_{pv,waste,t}^{up} – F_{d,t}^{up} $$
$$ F_{t1}^{-} = F_{g,t}^{down} + F_{h,t}^{down} + F_{cut,t}^{down} + F_{wind,waste,t}^{down} + F_{pv,waste,t}^{down} – F_{d,t}^{down} $$
for day-ahead, and with additional energy storage terms for intra-day.
The optimization model for day-ahead scheduling minimizes comprehensive costs:
$$ \min (F_g + F_h + F_{dg} + F_{cut} + F_{waste}) $$
where $F_g$ is the thermal generation cost, $F_h$ is the pumped storage cost, $F_{dg}$ is the renewable generation cost, $F_{cut}$ is the interruptible load cost, and $F_{waste}$ is the renewable curtailment cost. These are defined as:
$$ F_g = \sum_{t=1}^{T} (a P_{g,t}^2 + b P_{g,t} + c) $$
$$ F_h = \sum_{t=1}^{T} C_h (u_{h,d,t} P_{h,d,t} + u_{h,c,t} P_{h,c,t}) $$
$$ F_{dg} = \sum_{t=1}^{T} (C_{wind} P_{wind,t} + C_{pv} P_{pv,t}) $$
$$ F_{cut} = \sum_{t=1}^{T} C_{cut} u_{cut,t} P_{cut,t} $$
$$ F_{waste} = \sum_{t=1}^{T} (C_{wind,waste} u_{wind,waste,t} P_{wind,waste,t} + C_{pv,waste} u_{pv,waste,t} P_{pv,waste,t}) $$
Intra-day scheduling adds energy storage costs:
$$ F_{ess} = \sum_{t=1}^{T} C_{ess} (u_{ess,d,t} P_{ess,d,t} + u_{ess,c,t} P_{ess,c,t}) $$
Constraints include power balance, flexibility balance, and resource limits.
For case study, we simulate a typical day in a region with high electric car penetration, focusing on China EV scenarios. Parameters include time-of-use electricity prices as shown in Table 1.
| Time Period | Price (USD/kWh) |
|---|---|
| 22:00-3:00, 9:00-16:00 | 0.045 |
| 3:00-9:00, 21:00-22:00 | 0.090 |
| 16:00-21:00 | 0.150 |
Electric car parameters are set for 100 vehicles, with battery capacity of 60 kWh, maximum charging/discharging power of 7 kW, and charging efficiency of 0.95. The SOC limits are 0.2 to 1.0, and expected SOC is normally distributed with mean 0.85 and standard deviation 0.15. Travel times are based on normal distributions for commuting.
Simulation results show that unordered charging of electric cars increases peak loads, while ordered charging and V2G reduce fluctuations. The V2G strategy with user participation willingness minimizes costs and enhances flexibility. For example, the charging costs for different modes are summarized in Table 2.
| Charging Mode | Charging Cost (USD) |
|---|---|
| Unordered Charging | 180 |
| Ordered Charging | 85 |
| V2G | 45 |
In power system scheduling, without flexibility constraints, V2G reduces flexibility shortages compared to other modes. With flexibility constraints, the scheduling cost is minimized under V2G, as shown in Table 3.
| Charging Mode | Thermal Cost (USD) | Pumped Storage Cost (USD) | Energy Storage Cost (USD) | Wind Cost (USD) | Solar Cost (USD) | Penalty Cost (USD) | Total Cost (USD) |
|---|---|---|---|---|---|---|---|
| Unordered | 1630 | 79 | 199 | 124 | 118 | 825 | 2975 |
| Ordered | 1690 | 96 | 228 | 125 | 117 | 368 | 2624 |
| V2G | 1730 | 71 | 256 | 125 | 116 | 276 | 2574 |
The results demonstrate that electric cars, particularly through V2G, can significantly improve power system flexibility. The proposed model effectively captures user behavior uncertainties, enabling more efficient scheduling. This is especially relevant for China EV integration, where electric car adoption is rapidly growing. Future work could explore larger-scale simulations and real-time implementation.
In conclusion, the integration of electric car energy storage into power system scheduling, considering user participation willingness, offers a promising path toward enhanced flexibility and cost reduction. The use of Logistic functions to model uncertainty provides a realistic framework for scheduling, and the multi-time-scale approach ensures robust operation. As electric cars become more prevalent, strategies like V2G will be essential for managing grid stability and promoting renewable energy integration.