The Research on V2G Grid Optimization and Incentive Pricing Considering Battery Health

Abstract

This study proposes a dynamic incentive-based vehicle-to-grid (V2G) strategy grounded in the battery state of health (SOH) to enhance the incentive for electric vehicles (EVs) to participate in grid peak shaving and to mitigate the load fluctuations and grid stability issues caused by large-scale EV grid integration. This strategy constructs a mobility-chain-based charging demand model and establishes a quantitative relationship between the depth of discharge (DOD) and battery lifespan degradation. It incorporates a segmented dynamic incentive mechanism that integrates load fluctuation compensation with SOH degradation compensation. This study employed multi-objective optimization to minimize both grid load fluctuations and user charging costs. Results demonstrate that this strategy effectively achieves optimized regulation of the grid load curve while maximizing economic benefits for EV users.

1. Introduction

In the face of the global energy crisis and climate change, China’s sustainability efforts indicate that accelerating energy transition is the only viable path for our nation to achieve sustainable development. The core approach lies in progressively replacing traditional fossil fuels and driving the energy structure towards a clean, low-carbon transformation. New energy vehicles can substitute electricity for conventional fuels, thereby reducing carbon emissions and contributing to green development [1].

Against this backdrop, China has launched V2G (vehicle-to-grid) demonstration projects in multiple locations, including Shanghai [2,3,4]. This initiative stems from the fact that electric vehicles (EVs) can dynamically adjust power output to counteract grid-frequency deviations, thereby enhancing power system stability [5,6,7]. Concurrently, V2G technology plays a pivotal role in voltage regulation within distribution networks, enabling reactive power compensation and grid voltage stabilization while reducing reliance on conventional voltage regulation equipment [8]. Furthermore, Ref. [9] indicates that V2G technology can optimize charging strategies to mitigate battery degradation, thereby extending battery lifespan and reducing replacement costs. At the same time, intelligent scheduling can lower the charging expenses for vehicle owners.

Time-of-use (TOU) tariffs are widely used to encourage EV owners to charge during off-peak hours, thereby balancing grid loads and reducing peak demand [10,11]. However, the report Commercial Prospects for Electric Vehicle-Grid Interaction: A Case Study of Shanghai’s Demand Response Pilot also notes that current electricity market mechanisms, characterized by narrow peak–off-peak price differentials in most cities, limit users’ ability to profit from arbitrage opportunities. This constraint hinders the large-scale deployment of V2G responses. To address this situation, the Notice on Promoting Pilot Programmes for Scaled Application of Vehicle-Grid Interaction issued by the General Office of the National Development and Reform Commission, as well as other bodies, advocates exploring pricing mechanisms for the grid discharge caused by new energy vehicles and charging/swapping stations with the aim of increasing user participation frequency and response scale. References [12,13] demonstrate how flexible pricing mechanisms—such as adjustments based on electricity demand or grid load—can incentivize EV owners to participate in load regulation and peak shaving, thereby optimizing grid operations and enhancing economic benefits for EV owners. Furthermore, integrating dynamic pricing models with real-time price signals can improve both the flexibility and the cost-effectiveness of dispatch operations.

When different types of electric vehicles are considered, the effectiveness of V2G technology varies between electric buses and private EVs, primarily due to the differences in their usage scenarios, charging requirements, and participation frequency. Electric buses typically possess larger battery capacities, endowing them with significant potential for large-scale grid regulation and energy feedback [14]. For example, Ref. [15] employed a two-level optimization model to balance bus company costs against grid peak–valley differentials, incorporating multi-stakeholder interests through hierarchical decision making. However, this model does not fully validate the actual grid regulation capabilities of small-scale electric bus fleets, thereby limiting its practical applicability. In contrast, private EVs, owing to their widespread accessibility and flexibility, can charge and discharge across diverse scenarios. They participate extensively in grid frequency regulation and load balancing, thereby effectively supporting power system stability [16].

Accurate forecasting of EV charging loads and optimized grid scheduling are crucial for enhancing power system stability. Travel chain models, which can effectively simulate EV users’ travel patterns—particularly the spatiotemporal distribution of charging demand—have been widely employed in related research [17,18,19,20]. Such models enable more precise forecasting of charging behavior and peak demand, thereby supporting the deployment of charging infrastructure and the design of grid scheduling strategies. Existing research indicates that travel chain models not only perform well in forecasting charging loads, but they also provide a useful basis for evaluating the charging and discharging capabilities of V2G-enabled EV fleets, thus helping to improve the overall efficiency and stability of the power system.

Moreover, the health status of EV batteries directly impacts user willingness to participate in V2G and the long-term sustainability of the system. Most EV users perceive that frequent charging and discharging cycles (particularly deep discharges) and improper charging/discharging practices (such as excessive discharging or overly rapid charging) accelerate battery degradation, significantly increasing operational costs (e.g., battery replacement expenses). In this context, Refs. [21,22] quantified the impact of V2G scheduling on battery lifespans through mathematical modeling, revealing that mild V2G services exert only limited influence on batteries. Regarding deep discharges, Ref. [23] proposed a dynamic battery lifespan degradation model that accounts for discharge depth and degradation effects; by means of this model, EV charging and discharging schedules are optimized to minimize battery degradation. In further optimizing EV charging and discharging behavior, Ref. [24] enhanced charging/discharging decisions by integrating battery degradation models with dynamic electricity pricing. The research also reduced degradation through real-time assessments based on dynamic battery models while incentivizing off-peak charging and peak-time discharging via adjusted tariffs, thereby helping to stabilize grid loads.

In response to the above issues, this study developed a V2G scheduling framework that combines dynamic pricing incentives, EV travel chain modeling, and battery degradation considerations. The main features of the proposed approach can be summarized as follows:

(1)

Travel chain-based V2G flexibility modeling. Instead of assuming exogenous plug-in profiles, the available charging/discharging capacity of the EV fleet is derived from the statistical distributions of the departure times, return times, and trip distances. This links the time-varying and location-dependent V2G potential more explicitly to the user travel behavior.

(2)

SOH- and cycle-aware incentive pricing. A degradation-aware incentive tariff was designed, in which both the battery state of health (SOH) and accumulated equivalent cycle count are incorporated through an explicit compensation term. In this way, grid-side peak-shaving requirements are considered together with user-side degradation costs and participation thresholds within the same pricing mechanism.

(3)

Two-stage coordination of grid and user objectives. A two-stage optimization framework was adopted, where a meta-heuristic method in the upper stage determines the charging/discharging time slots and a quadratic programming model in the lower stage optimizes power allocation. This structure seeks a practical trade-off between load smoothing and user economic benefits, and its performance is illustrated through numerical case studies and SOC/SOH sensitivity analysis.

Overall, the framework is intended to provide a structured way to coordinate grid peak-shaving requirements, user economic benefits, and battery ageing considerations when EVs participate in V2G operations.

2. Modeling V2G Mobility Behavior

This section focuses on the modeling of V2G travel behavior. V2G not only facilitates bidirectional interactions between electric vehicles and the grid, but it also involves the precise modeling of vehicle travel patterns. Factors such as user departure times, return times, and travel distances must be taken into account.

2.1. Travel Chain Model

To characterize the travel behavior of EV users, a travel chain structure is adopted to represent the sequence of destinations visited within a single day. The main travel purposes include returning home (H), leisure activities (O)—including shopping, public recreation, pick-ups/drop-offs, and dining—and work (W) [18]. Only V2G charging and discharging at residential locations are considered.

Given that the average travel chain length is approximately 2.5 [19] and that Ref. [18] reported that daily trips are dominated by commuting-type chains of the form “home–work/other–home”, this study focused on the most representative commuting-oriented patterns and only explicitly modeled four travel chains: H–W–H, H–O–H, H–W–O–H, and H–O–W–H. Existing travel surveys and related studies generally indicate that weekday trips starting from and returning to residential and workplace zones account for a large share of total travel demand, and the associated charging demand constitutes an important part of the daily EV load [18]. In contrast, multi-stop and irregular chains (e.g., H–O–O–H) occur less frequently and have a limited impact on the aggregated EV load curve. To control model complexity, the aggregate effect of these low-frequency trips is indirectly represented in the simulation through randomness in departure times, dwell times, and travel distances rather than by explicitly constructing every possible chain structure.

Regarding parameter selection, the distributions of the departure time, return time, and travel distance used in Equations (1) and (2) were mainly based on the fitted results from existing travel surveys and related studies [18,19], with certain parameters shifted or scaled to match the city size and commuting rhythm considered in this work. The simple statistics of the simulated samples show that the generated departure and return times exhibit clear morning and evening peaks (approximately 7:00–9:00 and 17:00–19:00) and that the daily travel distances mostly fall in the range of 20–60 km. The resulting temporal patterns and mileage magnitudes are consistent with typical urban travel statistics, providing a representative usage background for the subsequent V2G scheduling analysis.

2.2. Modeling Spatiotemporal Parameters of Journeys

To reveal the statistical characteristics of users’ temporal behavioral patterns and spatial mobility, it is necessary to construct a joint stochastic model that incorporates departure times, return times and travel distances. This model provides a theoretical foundation for the spatiotemporal forecasting of V2G charging loads.

2.2.1. Departure Return Time Coupling Model

The travel times $T_s$ of electric vehicle (EV) users during weekdays were modeled using a third-order Gaussian mixture model (GMM) [18], which is a weighted combination of multiple Gaussian distributions that aids in understanding the typical travel patterns of EV users. The probability density function for travel times is expressed as shown in Equation (1).

$$f(T_s)={\displaystyle \sum _{i=1}^3{a}_i}{\displaystyle \frac{1}{{\sigma }_i\sqrt{2\pi }}}{e}^{-{\displaystyle \frac{{(T_s-u_i)}^2}{2{\sigma }_i^2}}}\hspace{1em}0<T_s<24.$$

(1)

In Equation (1), $a_1,a_2,a_3$ take values of 0.21, 0.53, and 0.26, respectively; $u_1,u_2,u_3$ are 7.14, 8.04, and 12.73, respectively; and ${\sigma }_1,{\sigma }_2,{\sigma }_3$ are 0.68, 1.74, and 3.11, respectively [18].

For the travel chains H-W-H and H-E-H, the return times $T_{\mathrm{e}1},T_{e2}$. can be modeled by a normal distribution and a three-parameter $\mathrm{Weibull}$ distribution, respectively [19], as given in Equation (2):

$$f\left(T_e\right)=\left\{\begin{array}{c}{\displaystyle \frac{1}{{\sigma }_1\sqrt{2\pi }}}exp\left(-{\displaystyle \frac{{\left(T_{e1}-{\mu }_1\right)}^2}{2{\sigma }_1^2}}\right)\\ \left({\displaystyle \frac{k_2}{c_2}}\right){\left({\displaystyle \frac{T_{e2}-{\gamma }_2}{c_2}}\right)}^{k_2-1}exp\left(-{\left({\displaystyle \frac{T_{e2}-{\gamma }_2}{c_2}}\right)}^{k_2}\right)\end{array}\right.,$$

(2)

$$T_{O\text{-}H}=T_{W\text{-}H}+b.$$

(3)

In Equation (2), ${\mu }_1$ may be approximated using a $\mathrm{Weibull}$ distribution with ${\mu }_1=c_1\cdot \mathsf{\Gamma }\left(1+1/k_1\right)$. The values for $c_1,k_1$ are 1061.4 and 8063, respectively; ${\sigma }_1$ is fitted to a normal distribution with a value of 91.17; and there is the three-parameter $\mathrm{Weibull}$ distribution (with $c_2,k_2,r_2$ taking values of 341, 1.85, and 706, respectively).

To account for the return-time constraints inherent in complex travel chains, the return time for the W-H segment within the H-O-W-H chain inherits the $\mathrm{Weibull}$ distribution of the simpler H-W-H chain (parameters were set as shown in Equation (2)). To ensure statistical consistency in commuting behavior, within the H-W-O-H chain, the departure time for the W-O segment followed the same distribution as the W-H segment. The start time for the O-H segment was dynamically constrained via Equation (3), where the uniform distribution perturbation term $b~U(0,80)$ quantifies the 80 min adjustable time window for non-commuting journeys.

2.2.2. Path Selection and Distance Configuration

As illustrated in Figure 1, this study employed a path distance generation model constructed on a typical urban road network topology with 16 nodes and 33 edges. Nodes 1–7 were designated as residential areas, Nodes 8–11 were set as commercial and industrial zones, Nodes 12–14 were denoted as leisure and entertainment districts, and Nodes 15–16 were taken as charging stations. For different travel chain types, the origin node $vo$ and destination node $vd$ were randomly selected from the corresponding sets of regional nodes. Considering factors such as the journey time and distance, the $\mathrm{Dijkstra}$ algorithm is employed to determine the shortest path distance $d$ [25].

It should be noted that the urban road network shown in Figure 1 is an abstract topological network based on a monocentric urban structure (16 nodes and 33 edges) rather than an exact replica of any specific city. The numbers and relative locations of residential, commercial/industrial, leisure, and charging station nodes were chosen with reference to typical land use structures and network scales reported for medium-sized Chinese cities, and they were appropriately simplified and aggregated according to the needs of the V2G analysis. The road length parameters are listed in

Table 1. Road length data.

Road Section	Road Length/km	Road Section	Road Length/km	Road Section	Road Length/km
1, 2	7.60	4, 11	6.54	7, 13	3.62
1, 8	7.85	4, 14	8.76	7, 14	7.10
1, 9	4.08	4, 15	3.83	7, 16	3.17
1, 15	3.88	4, 16	6.72	8, 9	5.87
2, 3	3.30	5, 6	9.26	9, 10	7.48
2, 10	8.82	5, 8	9.54	9, 12	8.15
2, 15	3.27	5, 12	4.21	10, 11	8.07
3, 4	8.41	5, 16	3.12	10, 13	4.79
3, 11	7.81	6, 7	8.80	11, 14	9.23
3, 15	3.30	6, 12	8.80	12, 13	7.52
4, 7	4.59	6, 16	2.20	13, 14	9.73

; their values were selected such that the typical travel distances between different functional zones (e.g., home–work and home–leisure) fell within a reasonable range of 5–15 km, capturing the general spatial layout and travel scale of an urban area rather than reproducing the detailed road network of a specific city.

3. Modeling Electric Vehicle Battery Degradation and V2G Electricity Consumption

3.1. Battery Degradation Model

High-frequency charging and discharging accelerates irreversible physicochemical changes in EV batteries, leading to capacity degradation and reduced economic viability. These degradation phenomena are closely related to the choice of electrode and cathode materials, which strongly influence the capacity, lifespan, and safety in lithium ion batteries [26]. To quantify the battery life loss in V2G scenarios, a life cycle loss model (Equation (4)) was employed, which dynamically characterizes the rate of the capacity fade as a function of the depth of discharge (DOD) and state-of-charge deviation (ΔSOC).

$$N_{life}=N_0{\left({\displaystyle \frac{DOD}{DO{D}_{ref}}}\right)}^{-{\lambda }_1}{e^{-{\lambda }_2}}^{(SO{C}_{di{s}_{\_}init}-SO{C}_{dis\_ref})}.$$

(4)

The depth of discharge (DOD) is defined as the difference in capacity before and after a single discharge cycle of the battery. $DO{D}_{\mathrm{ref}}$ denotes the reference discharge depth, $N_0$ represents the standard life cycle of the battery, while ${\lambda }_1$ and ${\lambda }_2$ are experimental calibration parameters. In this study, ${\lambda }_1$ and ${\lambda }_2$ were set to 1.98 and 2.79, respectively, and $DO{D}_{\mathrm{ref}}$ was taken as 0.8 [23].

$SO{C}_{dis\_init},SO{C}_{dis\_ref}$ denote the initial state of charge at discharge commencement and its standard value, respectively. Based on this model, the battery loss cost $C_{cap\_loss}$ for a single discharge cycle may be expressed as shown in Equation (5):

$$C_{cap\_loss}={\displaystyle \frac{n_{V2G}}{N_0}}{C}_{cap}={\displaystyle \frac{C_{cap}}{N_0}}{\left({\displaystyle \frac{DOD}{DO{D}_{ref}}}\right)}^{{\lambda }_1}{e^{{\lambda }_2}}^{\left(SO{C}_{di{s}_{\_}init}-SO{C}_{dis\_ref}\right)}.$$

(5)

In Formula (5), $C_{cap}$ denotes the battery cost, and $n_{V2G}$ denotes the equivalent number of cycle discharges under typical conditions for the battery in V2G discharge applications.

3.2. Cycle Count-Driven Dynamic Capacity Degradation

Addressing the limitations of lithium ion battery capacity degradation models under variable operating conditions, the classical Formula (6) based on the Arrhenius law was extended through differential expansion. This yielded the dynamic capacity degradation model (7):

$$\xi (n)=A{e}^{-E_a/RT}{n}^Z,$$

(6)

$$\left\{\begin{array}{c}\xi (n+1)-\zeta (n)=k_1{e}^{{\displaystyle \frac{k_2}{T}}}{\xi }^{k_3}(n)\\ k_1=z{A}^{1/z}\\ k_2=-{\displaystyle \frac{E_a}{zR}}\\ k_3={\displaystyle \frac{z-1}{z}}\end{array}\right.,$$

(7)

where $\xi \left(n\right)$ denotes the relative capacity decay after $n$ cycles, $A$ is a constant, $Ea$ represents the activation energy, $R$ is the gas constant, $T$ denotes temperature, $n$ indicates the number of cycles, and $z$ is the exponent. In this study, $A,E_a/R,z$ were calibrated so that the model reproduced typical LFP capacity-fade behavior over cycling, and a representative parameter set was $A=0.15$, $E_a/R=1400K,\mathrm{and}z=0.5$.

The two aforementioned models, respectively, quantify the increased battery costs resulting from V2G charging and discharging (based on depth of discharge) and the rate of capacity degradation (based on temperature and cycle count). These quantitative findings underpin subsequent cost calculations for users employing batteries in V2G applications. Taking lithium iron phosphate (LFP) batteries as an example—and setting two typical ambient temperature conditions, winter (5 °C) and summer (45 °C)—we quantified the dynamic degradation relationship between the number of charge–discharge cycles and the remaining capacities of LFP batteries.

Figure 2 shows the evolution of the battery capacity over the number of charge–discharge cycles. As the cycle count increased, the remaining capacity gradually decreased and displayed a clear downwards trend. The curve was smooth and continuous, indicating that the degradation process was gradual and sustained. Overall, the rate of capacity loss exhibited a nonlinear relationship with the number of cycles, with relatively slow degradation in the early stage followed by an accelerated decline in the later stage.

3.3. Electric Vehicle Power Consumption Model

For computational convenience, it was assumed that, during EV operation, the state of charge of the battery decreases linearly with the increasing distance traveled. The model for a single EV arriving at the next location during operation, under charge–discharge mode, is shown in Equation (9).

$$w=0.208-0.002v+1.553/v,$$

(8)

$$S_k^i=\left(S_{k-1}^i-{\displaystyle \frac{l_{k-1}^i\cdot w}{C_{batt}}}\right),$$

(9)

$$\left\{\begin{array}{c}{S}_t^i=S_{t-1}^i+{\displaystyle \frac{\eta P_{t\_ch}^i\mathsf{\Delta }t}{C_{\mathrm{batt}}}}{d}_t^i-{\displaystyle \frac{P_{t\_disch}^i\mathsf{\Delta }t}{\eta C_{\mathrm{batt}}}}{b}_t^i\\ d_t^i+b_t^i\le 1,\hspace{1em}{d}_t^i,\hspace{1em}{b}_t^i\in \left\{\begin{array}{l}0,1\hfill \end{array}\right\}\end{array}\right.,$$

(10)

$$C_{init\_batt}^i=SO{C}_{init}^i·SO{H}^i·C_{batt}.$$

(11)

In the formula, $SO{C}_{init}^i,C_{init\_batt}^i$ denote the initial state of the charge value and battery capacity of $E{V}^i$ at the start of each day; $S_{k-1}^i,S_k^i$ represent the SOC at the commencement and conclusion of the kth journey for the ith vehicle, respectively; $l_{k-1}^i$ indicates the distance traveled by the ith vehicle during the kth journey; and parameter $w$ denotes the energy consumption per unit distance traveled. The formula’s calculation method is based on a driving condition–energy consumption correlation model, incorporating requirements from China’s Urban Road Traffic Organization Design Specifications, where the vehicle speed is set to 30 km/h; $C_{batt}$ denotes the $EV$ battery capacity; $S_t^i,S_{t-1}^i$ represent the state of charge of the $E{V}^i$ during time periods $t,t-1$, respectively; $\eta$ denotes the charging/discharging efficiency, with a value of 0.92; and $P_{t\_ch}^i,P_{t\_disch}^i$ denote the charging/discharging power. When dividing 1 day into 24 time periods, we have $\mathsf{\Delta }t=1 \mathrm{h}$, where $d_t^i,b_t^i$ are the 0–1 variables representing the $E{V}^i$ charging/discharging state during period $t$: when charging, we have $d_t^i=1,b_t^i=0$, and when discharging, we have $d_t^i=0,b_t^i=1$.

3.4. Battery Health-Coupled Dynamic Pricing Model

Although Shandong Province’s Notice on Launching Pilot Reforms for Vehicle–Grid Interaction Pricing Mechanisms permits charging facility operators to set their own prices, employing a single peak–off-peak price differential makes it difficult to accurately quantify the marginal cost of the time-of-use load pressure. Moreover, a reasonable discharge fee must incentivize greater EV user participation [11]. Existing mechanisms also fail to account for the impact of battery life cycle degradation costs on users’ long-term economic viability, thereby reducing their willingness to participate. To address these issues, a battery health-coupled dynamic pricing model is proposed. By embedding both grid load volatility and battery cycling-induced degradation as endogenous factors within the pricing function (Equation (12)), the model aims to achieve a dynamic equilibrium between peak-shaving benefits and user economics.

$$C_{j1}=\left\{\begin{array}{ll}{K}_{xb}\cdot C_{dj}\cdot K_{db}^i,\hfill & P_t>P_b^t\hfill \\ C_{dj},\hfill & P_t\le P_b^t\hfill \end{array}\right.,$$

(12)

$$K_{xb}=1+{\displaystyle \frac{P_t-P_b}{P_b}}·k_1,$$

(13)

$$P_b=Average(P_t^{(k)}),k=1,\dots ,N_b,$$

(14)

$$K_{db}^i=1+\alpha \left(1-SO{H}^i\right)+\beta {\left({\displaystyle \frac{cycle{s}^i}{cycle{s}_{max}}}\right)}^{\gamma }.$$

(15)

Considering the volatility of the grid load, the peak-shaving control value $P_b$ is defined in Equation (14) as the average load in the same time interval over the preceding $N_b$ days. In this study, the baseline load was computed using historical data with $N_b\in \left[\mathrm{7,15}\right]$. Such a window length can both smooth out random fluctuations on individual days and still track slow changes in the overall load level. Numerical comparisons show that, when $N_b$ is set to 7, 10, or 15 days, the improvements in the daily peak–valley difference and load variance only vary slightly, and the relative comparison among different SOH/SOC scenarios remains unchanged. Therefore, the model is not sensitive to the choice of baseline window length, and a representative value within $N_b\in \left[\mathrm{7,15}\right]$ was adopted in the subsequent analysis.

When the real-time grid load $P_t$ exceeds $P_b$, the corresponding interval is identified as a peak-shaving period. In this case, the incentive tariff $C_{jl}$ is determined by the three components in Equation (12): the load-pressure compensation coefficient $K_{xb}$, the base tariff $C_{dj}$, and the battery compensation coefficient $K_{db}^i$. In non-peak-shaving periods ($P_t\le P_b$), $C_{jl}$ reduces to the regular electricity tariff. The coefficient $K_{xb}$ is calculated from the deviation between the real-time load and the baseline load, as given in Equation (13), where $k_1$ is the peak-shaving demand price compensation factor. In this paper, $k_1$ was set to 1.1 [13] to amplify the impact of load deviation on the price signal and thereby strengthen the economic incentive for users to participate in peak shaving.

The battery compensation coefficient $K_{db}^i$ jointly accounts for the effects of the battery state of health ${SOH}^i$ and the cycle count ${cycles}^i$ on lifetime degradation, as defined in Equation (15). To prevent excessive depletion of battery life, an upper bound $\alpha <0.3$ was imposed on the health-related compensation term, and $\alpha =0.15$ was used in the case studies. When the peak period load deviation lies in the typical range of 10–20%, this choice of $\alpha$ leads to an increase in the tariff due to SOH compensation of, roughly, a few tens of percent relative to the base time-of-use tariff, which is sufficient to enhance the peak period discharge revenues without causing excessive price distortion. The parameter $\beta$ controls the weight of the cycle-based compensation, where $\beta =0.25$, so that under high SOH and large cycle counts, the battery compensation accounts for approximately 20–30% of the total incentive price. The exponent $\gamma =0.8(<1)$ shapes the saturation behavior of the cycle compensation term: the compensation grows relatively fast in the early participation stage to attract new users, then it gradually slows down in the mid-stage to maintain stability, and it finally approaches saturation in the later stage, avoiding an excessive bias towards a small number of high-frequency participants.

For clarity, the main symbols used in the incentive tariff model are summarized in

Table 2. The selected symbols in the incentive tariff model and their meanings.

Symbol	Meaning	Unit/Dimension
$C_{jl}$	Incentive tariff for EV	CNY/kWh
$C_{dj}$	Base electricity tariff (time-of-use price) for EV	CNY/kWh
$K_{xb}$	Load–pressure compensation coefficient	–
$K_{db}^i$	Battery compensation coefficient for EV i	–
$P_t$	Real-time grid load in interval t	kW
$P_b$	Baseline/control load for peak shaving	kW
$k_1$	Peak-shaving demand price compensation factor	–
${SOH}^i$	State of health of EV i	–
${cycles}^i$	Accumulated equivalent cycle count of EV i	–
$\alpha$	Weighting factor for health-related compensation	–
$\beta$	Weighting factor for cycle-related compensation	–
$\gamma$	Saturation exponent of the cycle compensation term	–

.

4. Two-Stage Optimization Model for Electric Vehicles Based on Supply and Demand Requirements

4.1. Framework for Electric Vehicle Charging and Discharging Scenarios

To coordinate the large-scale charging and discharging behavior of electric vehicles, this study introduced an EV aggregator and established a tripartite collaborative framework comprising the power grid, the aggregator, and charging stations/users. As an intermediary entity, the aggregator receives the peak-shaving requirements and time-of-use price signals from the grid side, aggregates vehicle status information uploaded by multiple charging stations, and interacts with EV owners via mobile terminals, thereby enabling unified coordination and optimal scheduling of large numbers of EVs.

The roles of the three parties were divided as follows.

Charging station/charger side: Charging stations (or chargers) collect real-time information on the connected EVs, including the vehicle ID, plug-in/unplug time, rated battery capacity, and current SOC, as well as other operating states, and these data are then uploaded to the aggregator via a vehicle–charger–cloud communication network. For charging equipment that supports V2G, battery health-related indicators (such as the SOH level or equivalent cycle count range) can also be obtained during the interaction between the BMS and the charging controller.

Aggregator side: Based on intra-day load forecasts and peak-shaving instructions issued by the grid, which are combined with the current status of the connected EV fleet, the aggregator estimates the flexible capacity available for charging and discharging. On this basis, a two-stage optimization model is constructed to generate fleet-level charging/discharging power schedules and price incentive schemes, which are then sent to each charging station for execution.

User side: EV owners use a mobile app or in-vehicle terminal to view the expected revenues and participation conditions of V2G, and they then autonomously decide whether to “join the network” and authorize the aggregator to control charging and discharging within a specified time window. Users can also set personalized parameters, such as the minimum SOC and maximum allowable depth of discharge, so as to ensure that their travel demand is not adversely affected.

As shown in Figure 3, the V2G charging/discharging scenario is modeled on the basis of EV travel characteristics. First, travel chain information is used to obtain, for each vehicle, its daily round trip mileage and travel start/finish times, from which the initial SOC when the vehicle returns to the residential area after completing its daily trips is predicted. For vehicles choosing to join the network, the charging station measures their remaining energy in real time upon connection and, considering the remaining intra-day or next-day travel demand, determines whether the minimum SOC constraint can still be satisfied after executing V2G operations. If so, the vehicle is allowed to participate in charging/discharging optimization; otherwise, only conventional charging is performed and discharging is not scheduled. It is assumed that, after completing its daily travel and arriving at the residential area, the plug-in time of each vehicle is randomly distributed within 0–30 min. During a single connection period, the vehicle may switch multiple times between charging and discharging modes according to the optimization results, but it must not violate the SOC, SOH, and travel demand constraints. Through this process, the set of “dispatchable capacities” available for grid peak shaving in each time interval is obtained and used as a core input to the subsequent two-stage optimization model.

It should be emphasized that this work adopted a modeling and simulation framework. All the state variables, such as SOC, SOH, and cycle count, used in this paper were generated by battery degradation models and travel models, and the optimization assumes that the aggregator can access equivalent health status information. In practical engineering applications, however, OEMs often restrict the direct disclosure of internal battery parameters, and aggregators are more likely to indirectly obtain battery health-related data through the following means:

Using standardized communication interfaces between the charger and the on-board BMS, with equipment operators or OEMs providing processed SOH indicators or health levels.

Accessing aggregated or anonymized health information via the OEM’s telematics platform, subject to user consent and data-sharing agreements.

Transmitting only coarse-grained indicators, such as the SOH category by interval and equivalent cycle count range, rather than complete time-series data.

To reduce privacy and data security risks, the aggregator only needs limited, anonymized health status information to perform incentive calculations, without accessing detailed internal battery data. How to implement the above data acquisition methods under existing communication standards and privacy protection requirements, and how different data granularities affect optimization performance, lies beyond the scope of this simulation study and will be investigated in future work.

4.2. Multi-Objective Function Formulation

4.2.1. Grid Side: Minimization of Daily Load Variance

To quantify the peak-shaving and valley-filling effects of V2G, minimization of the daily load standard deviation was selected as the objective function for the grid side.

$$min{F}_1={\displaystyle \frac{1}{24}}{\displaystyle \sum _{t=1}^{24}{\left(P_l^t+{\displaystyle \sum _{i=1}^N\left(P_{t\_ch}^i-P_{t\_disch}^i\right)}-P_b\right)}^2}.$$

(16)

In Equation (16), $F_1$ represents the daily load standard deviation of the system. Minimizing this quantity ensures a flatter system load curve, thereby enhancing grid operational stability, extending equipment lifespan, and improving energy utilization efficiency. $P_l^t$ denotes the distribution network load power during time interval $t$, excluding EV load.

4.2.2. User Side: Minimizing User-Side Costs

V2G technology can also reduce users’ electricity costs through dynamic charging and discharging strategies. Specifically, users utilize batteries as energy storage media, charging during off-peak periods when electricity prices are low and discharging during peak periods when prices are high. This arbitrage of price differentials reduces net electricity expenditure. This process requires the construction of a cost minimization model on the user side:

$$min{F}_2={\displaystyle \sum _{t=1}^{24}{\displaystyle \sum _{i=1}^N\left(C_{t\_ch}^i-C_{t\_disch}^i+C_{t\_loss}^i\right)}},$$

(17)

$$\left\{\begin{array}{l}{C}_{t\_ch}^i={\displaystyle \frac{P_{t\_ch}^i·\Delta t·C_{dj}·d_t^i}{\eta }}\hfill \\ C_{t\_disch}^i=P_{t\_disch}^i.\Delta t·C_{jl}·\eta ·b_t^i\hfill \end{array}\right..$$

(18)

In the equation, $F_2$ represents the user cost, which is optimized through the arbitrage of electricity price differentials and battery degradation control to minimize net expenditure; $C_{t\_ch}^i$ and $C_{t\_disch}^i$ denote the charging cost and discharging revenue, respectively, for $E{V}_i$ during time period $t$; $C_{t\_loss}^i$ denotes the battery degradation cost incurred by $E{V}_i$ during the discharging in period $t$; and $DO{D}_t^i$ and $SO{C}_{t\_disinit}^i$ represent the depth of discharge and initial state of charge for $E{V}_i$ in period $t$, respectively.

4.2.3. Constraints

(1) Mutual exclusion of charging and discharging: a single vehicle cannot simultaneously charge and discharge during the same time period.

$$d_t^i+b_t^i\le 1,d_t^i,b_t^i\in (0,1),$$

(19)

where $d_t^i,{\mathrm{b}}_t^i$ denote the charging and discharging indicators, respectively.

(2) Limiting the number of discharges:

$${\displaystyle \sum _{t=2}^T\left|b_t^i-b_{t-1}^i\right|}\le 2N_{disch}^{max},$$

(20)

where $N_{disch}^{\max }$ denotes the maximum discharge cycle count.

(3) Charging target constraints:

$$SO{C}_0^i+{\displaystyle \sum _{t=1}^{t_{depart}^i}\left(\frac{\eta P_{t\_ch}^i\mathsf{\Delta }t}{C_{\mathrm{batt}}}{d}_t^i-\frac{P_{t\_disch}^i\mathsf{\Delta }t}{\eta C_{\mathrm{batt}}}{b}_t^i\right)}\ge {\displaystyle \frac{l_{\mathrm{next}}^{i}w}{C_{\mathrm{batt}}}},$$

(21)

where ${SOC}_0^i$ denotes the initial state of charge (SOC) of ${EV}_i$ at the beginning of the day, and $l_{next}^i$ is the target travel distance of ${EV}_i$ for the next trip after leaving the grid. The left-hand side of the constraint describes the SOC evolution of vehicle i from grid connection to the planned disconnection time: it includes the initial SOC, plus the energy gained through charging in each time interval, minus the energy consumed by discharging and by driving. The term ${\displaystyle \frac{l_{next}^{i}w}{C_{batt}}}$ on the right-hand side converts the next trip distance into an equivalent SOC requirement based on the unit energy consumption w, and it thus represents the minimum SOC needed for the next trip, i.e., the lower bound of the remaining energy after the vehicle leaves the grid. This constraint ensures that, while executing the V2G charging/discharging schedule, the vehicle always retains sufficient energy to complete the planned next journey so that participation in V2G does not compromise the user’s travel reliability.

(4) SOC range limitation: prevents overcharging and over-discharging.

$$SO{C}_{\min }\le SO{C}_t^i\le SO{C}_{\max }.$$

(22)

4.3. Solution Algorithm for Multi-Objective Coordinated Scheduling Models

To address the conflict between grid peak-shaving requirements and user economic benefits, the grid-side load fluctuation objective and the user-side electricity cost objective are first normalized so that indicators with different physical dimensions are converted into dimensionless form. On this basis, weighting coefficients are introduced to assign a certain priority to the grid-side objective, ensuring that user benefits are taken into account while satisfying the peak-shaving requirements of the grid. When denoting the grid-side objective function by $F_1$ (e.g., the daily load variance or standard deviation) and the user-side cost objective function by $F_2$, their normalized forms are given by the following:

$$\overline{F_1}={\displaystyle \frac{F_1-F_{1,min}}{F_{1,max}-F_{1,min}}} \overline{F_2}={\displaystyle \frac{F_2-F_{2,min}}{F_{2,max}-F_{2,min}}}.$$

(23)

Its comprehensive objective function is as follows:

$$minF=J=\lambda \overline{F_1}+(1-\lambda )\overline{F_2},\hspace{1em}(0<\lambda <1).$$

(24)

In the formula, $F_{1,min},F_{1,max}$ denote the historical minimum and maximum values of the grid load’s root mean square deviation, and $F_{2,min},F_{2,max}$ represent the theoretical lower bound (under optimal scheduling across all time periods) and upper bound (under disordered charging scenarios) of user costs. A weighting factor $\lambda \in \left[\mathrm{0,1}\right]$ is introduced to adjust the priority of the grid-side objective, where a larger $\lambda$ places more emphasis on peak shaving. In this study, a compromise between the grid and users is pursued by fixing $\lambda =0.5$, yielding a relatively balanced trade-off between load smoothing and user economics.

For medium- and large-scale EV scheduling, a two-stage hierarchical framework is adopted, consisting of a time-slot decision layer and a power optimization layer.

Time-slot decision layer: An improved particle swarm optimization (PSO) algorithm with binary encoding is used, where 0–1 variables indicate the charging/discharging status of each EV in each time interval. The algorithm performs global exploration in the early stage and local refinement in the later stage, and it then outputs discrete charging/discharging indicators ($d_t^i,b_t^i$), i.e., “when to charge and when to discharge”.

Power optimization layer: Given the time-slot indicators, a quadratic programming (QP) model is formulated to determine the optimal charging and discharging powers ($P_{ch}^i$,$P_{disch}^i$). Relaxation variables are introduced to linearize SOC-related constraints, and a standard QP solver is used to obtain the optimal power schedule, jointly optimizing the grid peak shaving and user cost.

To assess the effectiveness of the hierarchical strategy, a single-layer PSO baseline is constructed. In the baseline method, both time-slot decisions and power levels are encoded into one high-dimensional mixed continuous–discrete decision vector, and a conventional PSO directly searches in the full decision space, without the “time-slot–power” decomposition. Both methods use the same composite objective function $J$, the same constraints, and identical PSO parameters to ensure a fair comparison.

PSO parameters follow typical settings in the literature and are fixed after limited trial runs: population size $N_{pop}=50$ N, maximum iterations ${iter}_{max}=400$, the inertia weight $w$ linearly decreases from 0.9 to 0.4, and the learning factors $c_1=c_2=2.0$. A detailed sensitivity analysis of PSO parameters is beyond the scope of this paper.

Table 3. Comparison between PSO-QP and single-layer PSO.

Algorithm	T/s	Maximum Number of Iterations	Final Objective J
PSO-QP (proposed)	1.88	115	0.517
Single-layer PSO (baseline)	3.06	260	0.530

compares the two methods. The proposed PSO–QP framework achieves shorter computation time (1.88 s vs. 3.06 s), fewer iterations to convergence (115 vs. 260), and a better final composite objective value (J = 0.517 vs. J = 0.530) than the single-layer PSO baseline. These results indicate that the hierarchical PSO–QP approach improves both solution quality and convergence efficiency for large-scale EV V2G scheduling problems.

5. Case Study Analysis

5.1. Parameter Settings

(1)

Vehicle parameters: Fifty BYD e6 models were selected, with lithium iron phosphate batteries specified and a battery capacity of 60 kWh.

(2)

Battery cost parameters: The cost of automotive lithium ion batteries ranges from 0.5–0.8 CNY/Wh [27].

(3)

SOH degradation stratification: Classified into four tiers based on the battery state of health (SOH ≥ 0.95, 0.90 ≤ SOH < 0.95, 0.85 ≤ SOH < 0.90, and 0.80 ≤ SOH < 0.85), with stratification proportions of 30%, 30%, 20%, and 20%, respectively.

(4)

Initial SOC distribution: Assume that, at the initial time point each day, ${SOC}_{init}^i$ follows a uniform distribution over [0.6, 1]. Similarly, the initial time point ${SOC}_{init}^i$ for the EV battery the following day follows a uniform distribution over [0.6, 1].

(5)

Travel chain proportion: Four travel chain patterns are defined (H-W-H, H-O-H, H-W-O-H, and H-O-W-H), with respective proportions of 30%, 10%, 30%, and 30%.

(6)

Only scenarios where EV users charge at home are considered. EV users whose battery charge during travel falls short of meeting daily travel requirements will be excluded.

(7)

Multi-objective weighting: Set parameters to balance grid peak-shaving and user economic objectives, preventing dominance by any single objective.

(8)

Time-of-use electricity pricing: Referencing industrial electricity tariffs in a Chinese city. Specific values are shown in

Table 4. Industrial electricity tariffs in a Chinese city.

Time Slot		Electricity Price (CNY/kWh)
Off-Peak Hours	0:00–6:00, 12:00–14:00	0.4
Shoulder Hours	6:00–12:00, 14:00–16:00	0.65
On-Peak Hours	16:00–18:00, 20:00–24:00	0.88
Super-Peak Hours	18:00–20:00	1.02

.

5.2. Analysis of Simulation Results

As shown in Figure 4, during the peak-shaving period ($P_t>P_b$, Periods 10–23), the dynamic gain term $(P_t-P_b)/P_b$ in the load pressure compensation coefficient $K_{xb}$ (Equation (13)) causes $K_{xb}>1$. This results in incentive prices exceeding the time-of-use rates $(C_{jl}>C_{dj})$. For instance, during Periods 14 and 20, the incentive prices for SOH = 0.85 are 1.32 and 1.49 times the time-of-use rates, respectively. This yields higher discharge revenue for users compared to traditional peak valley arbitrage models, thereby incentivizing user participation in V2G and EV battery discharge. During non-peak-shaving periods ($P_t<P_b$), specifically Periods 1–10 and 23, the discharge price is set equal to the charging price. This prevents users from artificially amplifying load fluctuations through “buy low, sell high” arbitrage, thereby safeguarding grid dispatch stability.

As shown in Figure 5, when the SOH declines from 0.95 to 0.80, the discharge electricity prices exhibit significant differences during the peak-shaving periods, with a maximum variance reaching 0.24 CNY/kWh. This validates the dominant role of the sensitivity term $\alpha (1-SOH)$ in the compensation formula, where variations in the compensation coefficient $K_{db}^i$ lead to an 18.3% increase in peak-period electricity prices. During non-peak-shaving periods, both electricity prices are identical, demonstrating the dynamic selectivity of the compensation mechanism. This concentrates compensation resources during periods of greatest grid pressure, avoiding market distortions caused by unnecessary economic incentives, thereby enhancing the efficiency of grid dispatch resource allocation.

Figure 6 illustrates how the battery’s charging and discharging power varies across different time periods under the influence of the system load and the V2G strategy. During Periods 1 to 6, when the system load is relatively low, the charging power reaches up to 900 kW while the battery does not discharge because the discharge prices are low and the premature discharge in low-load periods is avoided to protect the battery life. During Periods 17 to 20, when the system load increases to about 5500–5700 kW, the maximum battery discharge power reaches 582.77 kW, demonstrating the critical role of EVs in supporting the grid during high-load periods.

Figure 7 shows that introducing V2G significantly reshapes the daily system load profile by reducing the peaks and filling valleys. In a high-load period (e.g., Time Slot 20), the base load decreases from 5736.71 kW to 5153.94 kW, which is a reduction of 582.77 kW (about 10.2%). In a low-load period (e.g., Time Slot 5), the base load increases from 3464.62 kW to 4116.00 kW, which is an increase of 651.38 kW (about 18.8%). Over the whole day, the peak–valley difference is reduced from 2302.75 kW to 1782.82 kW, and the daily load variance decreases from $5.81\times {10}^5 {\mathrm{kW}}^2$ to $3.11\times {10}^5 {\mathrm{kW}}^2$ (standard deviation from 762.38 kW to 557.71 kW), confirming that the proposed V2G scheduling scheme smooths the load curve and enhances the stability of grid operation.

As shown in Figure 8, during the peak load periods (such as Periods 19 to 21), the discharge revenue is relatively high, amounting to CNY 530.36, CNY 682.52, and CNY 614.92, respectively. Particularly during Period 20, when the grid load reached 5736.71 kW, the discharge power peaked and discharge tariffs were elevated, leading to increased revenue. During low-load periods (e.g., Periods 1 to 6), the battery remains in a state of no discharge, yielding zero revenue. By storing energy through charging, the battery performs peak shaving and valley filling, supplying electricity during high-load periods to alleviate grid pressure.

As shown in Figure 9, the battery SOH has a clear impact on the cumulative V2G discharge revenue. The SOH = 0.95 group achieved the highest revenue (about CNY 1003) due to its larger usable capacity and higher efficiency, while the SOH = 0.80 group was restricted by capacity and lifetime constraints and obtained the lowest revenue (about CNY 628). It is noteworthy that the SOH = 0.85 group (about CNY 831) slightly outperformed the SOH = 0.90 group (about CNY 797). This non-strictly monotonic behavior was caused by the SOH-dependent incentive and the coordinated dispatch: the tariff includes a small correction factor that moderately increases compensation for moderately degraded batteries, and the scheduling model tends to allocate more high-price discharge opportunities to vehicles with higher marginal net benefits. Overall, the global trend remains intuitive: higher-SOH batteries have greater revenue potential over the long term, whereas low-SOH batteries are evidently limited by capacity and safety constraints.

Figure 10a presents the optimized daily load profiles under different initial SOC distributions. Compared with the original base load without V2G, all three scenarios (baseline SOC: 0.6–1.0, high SOC: 0.8–1.0, and low SOC: 0.3–0.7) achieved a clear peak-shaving and valley-filling effect, but the strength of this effect varied with the SOC distribution. In a typical valley period (Time Slot 5), the system load increases from the base value of 3464.62 kW to 4018.29 kW in the high-SOC scenario and to 4311.41 kW in the low-SOC scenario, indicating that, when the initial SOC is lower, EVs have stronger charging demand in valley periods, and the valley-filling effect becomes more pronounced. In a typical peak period (Time Slot 20), the load decreases from 5736.71 kW to 4891.69 kW in the high-SOC scenario, whereas it only decreases to 5416.19 kW in the low-SOC scenario, showing that the high-SOC scenario provides significantly stronger peak shaving. Over the whole day, the reduction in peak–valley difference is about 23.7% in the high-SOC scenario and about 14.8% in the low-SOC scenario, which indicates that shifting the initial SOC distribution upwards increases the available flexible capacity and leads to a smoother load profile.

Figure 10b shows the impact of different SOH compositions on the optimized daily load profile. The fleet SOH is divided into four bands, [0.95, 1.00), [0.90, 0.95), [0.85, 0.90), and [0.80, 0.85). The three scenarios adopt band weightings of 3:3:2:2 for the baseline SOH case, 4:3:2:1 for the high-SOH case, and 1:2:3:4 for the low-SOH case, meaning that the high-SOH scenario allocates more weight to healthier batteries, whereas the low-SOH scenario is dominated by more degraded batteries. The three curves are close to each other and all of them are much smoother than the original base load, indicating that the proposed V2G scheduling scheme is fairly robust to moderate changes in the SOH distribution. Nevertheless, some differences can be observed: in a typical peak period (Time Slot 20), the high-SOH scenario reduces the load to 5008.25 kW, while the low-SOH scenario only reduces it to 5387.05 kW. The corresponding reduction in peak–valley difference is roughly in the range of 21.9–22.8%, with the high-SOH scenario performing slightly better and the low-SOH scenario slightly worse. Overall, a higher share of high-SOH batteries marginally enhances the available discharge capacity and peak-shaving capability, whereas a low-SOH-dominated fleet still achieves noticeable load smoothing but with somewhat reduced effectiveness.

To provide a quantitative evaluation of the proposed V2G scheme,

Table 5. Summary of the key quantitative indicators before and after V2G optimization.

Indicator	Base Load	With V2G Optimization
Peak–valley difference ΔP (kW)	2302.75	1782.82 (−22.6%)
Daily load variance (kW2)	$5.81\times {10}^5$	$3.11\times {10}^5$ (−46.5%)
24 h charging cost (CNY)	-	2368.86
24 h discharging revenue (CNY)	-	3259.58
Net user benefit (CNY)	-	890.72

summarizes the key system-level and user-side indicators before and after V2G optimization.

6. Conclusions

Based on existing battery lifetime and degradation model parameters, this study developed an analysis framework for EV-based V2G load regulation that simultaneously considers the battery SOH, V2G incentive pricing, and grid load requirements. From the case study, the main conclusions are as follows.

(1)

Under the given scenarios, introducing V2G and optimizing charging/discharging periods and power levels smooths the daily load profile to a noticeable extent. The daily peak–valley difference of the base load is reduced from 2302.75 kW to 1782.82 kW (a reduction of about 22.6%), and the daily load variance decreases by approximately 46.5%, while the total daily energy remains essentially unchanged. This corresponds to the expected peak-shaving and valley-filling effect.

(2)

The initial SOC distribution and the fleet SOH composition influence the available flexibility and the achievable peak-shaving performance. In the numerical example, the reduction in the peak–valley difference was about 23.7% in the high-SOC scenario and about 14.8% in the low-SOC scenario. Across different SOH scenarios, a higher proportion of high-SOH batteries leads to slightly lower peak loads and better peak shaving, whereas fleets dominated by lower-SOH batteries show weaker peak reduction but still maintain a clear load-smoothing effect.

(3)

Incorporating the SOH and equivalent cycle count into the incentive tariff allows battery degradation cost to be directly reflected in the user-side compensation, linking economic returns more closely to battery usage intensity. For the 50-EV fleet in the 24 h case study, the total charging cost was about CNY 2368.86 and the total discharging revenue was about CNY 3259.58, resulting in a positive net benefit, while the SOC constraints prevented deep discharges and ensured that subsequent travel demands were met. The results indicate that high-SOH vehicles achieve higher individual revenues, whereas low-SOH vehicles are more strongly constrained by capacity and lifetime limits. But, at the fleet level, it is still possible to obtain both economic benefits and a useful contribution to load regulation.