The integration of a massive number of electric vehicles into the power grid presents both unprecedented opportunities and significant challenges for the development of modern power systems. Effectively guiding the orderly charging and discharging behavior of these electric vehicle cars is paramount to enhancing demand-side flexibility, supporting the low-carbon transition of energy consumption, and ensuring grid stability. However, the mechanisms through which charging and discharging prices influence user behavior remain inadequately understood, primarily due to the inherent complexity of demand-side decision-making psychology and the dynamic nature of the supply-side transportation ecosystem.
This investigation first delves into the decision-making psychology of electric vehicle car users. Recognizing that charging and discharging decisions belong to distinct mental accounts, we analyze the influencing factors for each. Based on Reference-Dependent Theory, separate value measurement functions for charging (perceived as a cost) and discharging (perceived as a gain) are established to model user perception under deterministic price scenarios.
Subsequently, we model the supply-side context: a transportation system shared by conventional gasoline vehicles and electric vehicle cars. To accurately capture the root cause of travel—the need to participate in daily activities—we employ a Dynamic Activity-Travel Assignment (DATA) model. This framework reveals the spatiotemporal distribution mechanism of electric vehicles by simulating how users schedule their travel and activities within a multimodal supernetwork.
Finally, a numerical case study is conducted to explore the spatiotemporal patterns of charging and discharging demand for electric vehicle cars. The analysis examines the impact mechanisms of pricing strategies and heterogeneous user decision-making psychology on these behavioral patterns. The findings aim to provide valuable references for the strategic planning and deployment of V2G charging infrastructure, the refinement of pricing mechanisms, and the development of robust microgrids capable of harnessing the flexibility of electric vehicle car fleets.
The dynamic state of an electric vehicle car—its location and battery state of charge (SoC)—is fundamentally a consequence of its user’s daily activity-travel schedule. This complex process can be systematically described using a Multi-State Supernetwork (MSN) framework. Any complete path through this network consists of interconnected travel arcs (representing movement) and activity arcs (representing participation in an activity, potentially coupled with charging/discharging). The figure above illustrates a simplified MSN, where paths depict an electric vehicle car user driving from home (H) to a parking location (P) for an activity (A), and returning home. Crucially, the activity arc can branch into different states: performing no grid interaction (1,0,0), charging (1,1,0), or discharging (1,0,1). This representation allows us to track the electric vehicle car’s status comprehensively.
Modeling Charging and Discharging Value with Reference-Dependent Psychology
Decisions to charge or discharge an electric vehicle car hinge not only on the current SoC but also on the user’s subjective valuation of the economic transaction. Contrary to the assumption of perfect rationality, users are boundedly rational. For the deterministic price settings typical in many tariff schemes, Reference-Dependent Theory provides a suitable framework. It posits that individuals evaluate outcomes as gains or losses relative to a subjective reference point, exhibit loss aversion (losses loom larger than equivalent gains), and require more than one unit of gain to compensate for one unit of loss in a different attribute.
Charging Value Function (Perceived Cost): For a user of type \( m \), the perceived value (a negative cost) for charging at location \( l \) starting at time \( t \) for a duration \( d_l^{c,m} \) is the sum of the value perceived in each time interval \( \omega \). Let \( p_l^c(\omega) \) be the charging price at time \( \omega \) and \( p_m^{c,0} \) be the user’s reference price for charging.
$$R_l^{c,m}(t, d_l^{c,m}) = \sum_{\omega=t}^{t+d_l^{c,m}} R_l^{c,m}(\omega)$$
Where the value in each period is defined relative to the reference point:
$$
R_l^{c,m}(\omega) =
\begin{cases}
\beta_1^{c,m} (p_m^{c,0} – p_l^c(\omega)), & \text{if } p_l^c(\omega) \leq p_m^{c,0} \text{ (Gain)}\\
\beta_2^{c,m} (p_m^{c,0} – p_l^c(\omega)), & \text{if } p_l^c(\omega) > p_m^{c,0} \text{ (Loss)}
\end{cases}
$$
Here, \( \beta_1^{c,m} > 0 \) and \( \beta_2^{c,m} < 0 \) are perception coefficients for gain and loss, respectively, with \( |\beta_2^{c,m}| > |\beta_1^{c,m}| \) representing loss aversion.
Discharging Value Function (Perceived Gain): Similarly, for discharging, let \( p_l^d(\omega) \) be the discharging price and \( p_m^{d,0} \) be the reference point. The perceived value for discharging for duration \( d_l^{d,m} \) is:
$$R_l^{d,m}(t, d_l^{d,m}) = \sum_{\omega=t}^{t+d_l^{d,m}} R_l^{d,m}(\omega)$$
With the per-period value defined as:
$$
R_l^{d,m}(\omega) =
\begin{cases}
\beta_1^{d,m} (p_l^d(\omega) – p_m^{d,0}), & \text{if } p_l^d(\omega) \geq p_m^{d,0} \text{ (Gain)}\\
\beta_2^{d,m} (p_l^d(\omega) – p_m^{d,0}), & \text{if } p_l^d(\omega) < p_m^{d,0} \text{ (Loss)}
\end{cases}
$$
Again, \( \beta_1^{d,m} > 0 \), \( \beta_2^{d,m} < 0 \), and \( |\beta_2^{d,m}| > |\beta_1^{d,m}| \). The reference points \( p_m^{c,0} \) and \( p_m^{d,0} \) can differ among user types (e.g., optimistic, neutral, pessimistic) and can be based on factors like minimum, average, or maximum observed prices, or even the expected charging cost.
Dynamic Activity-Travel Assignment Model with Charging/Discharging Decisions
We integrate the above behavioral models into a Dynamic Activity-Travel Assignment (DATA) framework. The following core assumptions underpin the model:
- A1: Time is discretized. Prices vary in time and space. Users have full knowledge of system conditions.
- A2: Users are categorized by decision-making rule (optimistic, neutral, pessimistic), defining their reference points.
- A3: The transportation system includes both electric vehicle cars and gasoline vehicles (GVs). Grid interaction only occurs during parking for an activity.
- A4: Charging is triggered when SoC falls to a user-specific anxiety range lower bound. Discharging must stop before SoC reaches the anxiety range upper bound.
- A5: Energy consumption while driving is proportional to travel time.
- A6: Users choose complete activity-travel paths based on a generalized cost (disutility) following a boundedly rational “acceptable” rule.
Disutility Functions: The total disutility \( N_{hr}^m(k) \) for a user of type \( m \) choosing path \( r \) starting from home \( h \) at time \( k \) is the sum of disutilities on all travel arcs \( a_v \) and activity arcs \( a_a \) constituting that path.
$$N_{hr}^m(k) = \sum_{t} \sum_{a \in \{A_v \cup A_a\}} \delta_{at}^{hrk} N_a^{mll}(t)$$
Where \( \delta_{at}^{hrk} \) is an indicator variable, and \( N_a^{mll}(t) \) is the disutility on arc \( a \) from location \( l \) to \( \hat{l} \) at time \( t \).
1. Travel Arc Disutility: For a travel arc \( a \), the disutility combines travel time \( t_a^{mll}(t) \) and monetary cost \( \tau_a \):
$$N_a^{mll}(t) = \lambda_1^m \cdot t_a^{mll}(t) + \lambda_2^m \cdot \tau_a \cdot t_a^{mll}(t)$$
Travel time is modeled using a BPR-type function dependent on cumulative link flow \( x_{y(a)}(t) \). For an electric vehicle car arc, the SoC updates as:
$$S_a^{m\hat{l}}(t’) = S_a^{ml}(t) – \phi_e \cdot t_a^{mll}(t), \quad t’ = t + t_a^{mll}(t)$$
where \( \phi_e \) is the energy consumption rate.
2. Activity Arc Disutility: The disutility for an activity arc includes the basic activity participation utility \( N_a^{0,mll}(t) \) and, for electric vehicle car users, the utility/cost from grid interaction \( U_a^{cd,mll}(t) \).
$$N_a^{mll}(t) = N_a^{0,mll}(t) – U_a^{cd,mll}(t)$$
The grid interaction utility is determined by the charging/discharging decision:
$$
U_a^{cd,mll}(t) = \hat{\sigma}_a^{ml}(t) \cdot \alpha_l^{c,m} \cdot R_l^{c,m}(t, d_l^{c,m}) + (1 – \hat{\sigma}_a^{ml}(t)) \cdot \alpha_l^{d,m} \cdot R_l^{d,m}(t, d_l^{d,m}) \cdot \mathbb{1}(S_a^{ml}(t) \gg \underline{S}_m)
$$
Here, \( \hat{\sigma}_a^{ml}(t) \) is a binary indicator for the choice to charge (1) or not (0). The charging duration \( d_l^{c,m} \) and discharging duration \( d_l^{d,m} \) are limited by the activity duration, battery capacity \( S^{max} \), minimum SoC \( S^{min} \), and anxiety bounds \( \overline{S}_m, \underline{S}_m \).
Dynamic User Equilibrium Condition: The model solves for a boundedly rational dynamic user equilibrium where no user can reduce their path disutility below an acceptable margin \( \xi \). Let \( f_{hr}^m(k) \) be the flow on path \( r \) for user type \( m \), and \( N^{*,m}(k) = \min_{r} \{ N_{hr}^m(k) \} \) be the minimum perceived disutility at that time.
$$
\begin{cases}
N_{hr}^m(k) \leq (1+\xi) N^{*,m}(k), & \text{if } f_{hr}^m(k) > 0 \\
N_{hr}^m(k) \geq (1+\xi) N^{*,m}(k), & \text{if } f_{hr}^m(k) = 0
\end{cases}
$$
This is subject to flow conservation constraints across the network. The model is solved using a route-swapping algorithm until convergence.
Case Study and Analysis
A case study based on the Nguyen-Dupuis network is implemented to analyze the spatiotemporal characteristics of electric vehicle car charging and discharging behavior.
Parameter Settings: Key parameters for the simulation are summarized below.
| Category | Parameter | Value / Description |
|---|---|---|
| Demand | Total Users | 10,000 (60% own an electric vehicle car) |
| User Types (m) | Optimistic, Neutral, Pessimistic (equal proportion among EV owners) | |
| Temporal Scope | 06:00 – 22:00 (1-min intervals) | |
| Electric Vehicle Car | Battery Capacity (\(S^{max}\)) | 60 kWh |
| Consumption Rate (\(\phi_e\)) | 0.09 kWh/min | |
| Charging/Discharging Power (\(\phi_c, \phi_d\)) | 20 kW | |
| Initial SoC by Type | Optimistic: 50%, Neutral: 75%, Pessimistic: 100% | |
| Anxiety Range [\(\underline{S}_m, \overline{S}_m\)] | Optimistic: [9,15] kWh, Neutral: [15,30] kWh, Pessimistic: [30,45] kWh | |
| Behavioral Parameters | Value of Time (\(\lambda_1^m\)) | 0.2 /min |
| Value of Money (\(\lambda_2^m\)) | 0.1 /¥ | |
| Perception Coefficients (\(\beta_1\)) | 0.5 (for both gain in charging and discharging) | |
| Perception Coefficients (\(\beta_2\)) | -1.0 (for both loss in charging and discharging) | |
| Reference Points (\(p_m^{0}\)) | Charging Price (\(p_m^{c,0}\)) | Optimistic: Max price, Neutral: Avg price, Pessimistic: Min price |
| Discharging Price – Type 1 (\(p_m^{d,0}\)) | Optimistic: Min price, Neutral: Avg price, Pessimistic: Max price | |
| Discharging Price – Type 2 (\(p_m^{d,0}\)) | Based on charging price: Opt: Min, Neu: Avg, Pes: Max |
The time-of-use (TOU) pricing for charging is based on a practical tariff structure, with discharging prices initially set equal to the charging price (baseline scenario). Reference points are derived accordingly, as illustrated in the following summary for the neutral user:
| Price Type | Peak | Off-Peak | Valley | Avg. (\(p^0\) for Neutral User) |
|---|---|---|---|---|
| Charging Price (\(p^c(t)\)) | 1.20 ¥/kWh | 0.75 ¥/kWh | 0.35 ¥/kWh | 0.77 ¥/kWh |
| Discharging Price – Baseline (\(p^d(t)\)) | 1.20 ¥/kWh | 0.75 ¥/kWh | 0.35 ¥/kWh | 0.77 ¥/kWh |
Results and Discussion
1. Equilibrium Spatiotemporal Distribution: The model converges successfully, revealing distinct patterns. Activity participation peaks correspond to morning commutes (08:00-10:00) and evening returns (17:00-19:00). The spatiotemporal distribution of charging and discharging demands for the electric vehicle car fleet is highly correlated with TOU prices. Charging demand predominantly aggregates during off-peak and valley periods, especially at residential locations after daily trips conclude. Conversely, discharging demand is concentrated during peak price periods, often at workplace locations after the morning commute. This clearly demonstrates the spatial and temporal shifting potential of the electric vehicle car fleet in response to price signals.
2. Impact of Discharging Price: We analyze three scenarios by varying the discharging price multiplier relative to the fixed charging price: Scenario 1 (0.5x), Baseline (1.0x), and Scenario 2 (1.5x). The following table summarizes the aggregate demand changes for the six combined user types (3 psychological types × 2 discharge reference types).
| Scenario | Discharge Price Multiplier | Total Charging Demand | Total Discharging Demand | Key Behavioral Insight |
|---|---|---|---|---|
| 1 (Low) | 0.5x Charging Price | 3,508 | 7,073 | Lower price suppresses discharging willingness; charging demand also decreases slightly as the incentive to replenish sold energy is low. |
| Baseline | 1.0x Charging Price | 3,526 | 7,065 | Establishes the base interaction pattern between price and reference points. |
| 2 (High) | 1.5x Charging Price | 3,596 | 7,082 | Increase in demand is not proportional to price rise. Pessimistic users (Type 1 reference) perceive the high price as a potential “loss” if it falls below their even higher reference, thus their response is muted. |
The results indicate a non-linear and heterogeneous response. While lowering the price below the charging price dampens discharge activity, raising it does not yield a strong, uniform increase. The behavior of pessimistic users, whose reference point is the maximum price, is crucial. For them, even a high absolute price may be perceived as a “loss” if it is below their lofty reference, thereby inhibiting participation. This underscores the importance of modeling heterogeneous reference points.
3. The Necessity of Modeling Reference Dependence: To highlight the role of reference-dependent psychology, we compare our main model with a simplified version where users evaluate charging/discharging value based on absolute utility (reference point = 0). The simplified model shows higher and more temporally flat charging and discharging demand, lacking the nuanced sensitivity to peak/off-peak price differentials. It fails to capture the asymmetric responses observed when prices change and cannot explain the behavioral diversity across user types. This comparison validates that incorporating reference-dependent decision-making is essential for accurately modeling the complex and bounded rationality inherent in electric vehicle car user behavior.
Conclusion
Understanding the mechanisms through which prices influence the charging and discharging behavior of electric vehicle cars is a critical prerequisite for designing effective V2G management strategies. This study bridges the gap by integrating the bounded rationality of user decision-making, specifically Reference-Dependent Theory, with a high-fidelity model of activity-based travel demand. The proposed Dynamic Activity-Travel Assignment model successfully captures the spatiotemporal evolution of electric vehicle car states and their grid interaction decisions.
The key findings are: (1) The charging and discharging behavior of electric vehicle cars exhibits strong spatiotemporal dependence on electricity prices, with clear patterns of valley charging and peak discharging emerging. (2) The response to price changes is heterogeneous and non-linear, heavily modulated by user-specific psychological reference points. Merely increasing the discharge price does not guarantee a proportional increase in participation, especially among pessimistic users. (3) Models that ignore reference-dependent psychology overlook this critical heterogeneity and may overestimate the uniformity and flexibility of the electric vehicle car resource.
This work provides a foundational framework for policymakers and grid operators. It can inform the strategic placement of V2G charging infrastructure at locations with high discharging potential (e.g., workplaces), the design of personalized or segmented pricing tariffs that account for user psychology, and the development of accurate forecasting models for grid integration studies. Future research will incorporate constraints such as charger capacity at activity locations, model competitive pricing among multiple electric vehicle car aggregators, and investigate the feedback loop between electric vehicle car charging/discharging behavior and distribution grid power flow dynamics.