In the pursuit of achieving carbon neutrality goals, the energy sector is undergoing a rapid low-carbon transformation, with distributed renewable energy sources such as photovoltaic and wind power experiencing significant growth. However, the increasing integration of these intermittent sources poses challenges to power system stability, particularly in terms of peak shaving and renewable energy consumption. To address these issues, leveraging flexibility resources on the user side has become a critical strategy. Among these resources, hybrid cars, especially fuel-cell hybrid electric vehicles (FCHEVs), which can utilize both electricity and hydrogen, emerge as promising assets for enhancing system flexibility due to their dual-energy capability. This paper proposes a method for assessing the flexibility potential of hybrid car clusters, explicitly considering the differences in owners’ charging willingness, to facilitate their effective participation in power system optimization and renewable energy integration.
The integration of hybrid cars into the energy-transportation nexus offers a novel pathway for decarbonization. Unlike conventional electric vehicles, hybrid cars equipped with fuel cells and batteries can switch between electric charging and hydrogen refueling, providing enhanced operational flexibility. However, existing research on hybrid cars has predominantly focused on energy management and control strategies, with limited attention paid to evaluating their flexibility potential. This gap is critical because the effectiveness of hybrid car clusters in supporting grid services depends on accurately quantifying their adjustable capacity, which is influenced by heterogeneous owner behaviors. Owners’ decisions regarding charging and refueling are shaped by multiple factors, including cost, time, environmental awareness, and safety concerns, leading to variability in their willingness to participate in demand response programs. Ignoring these differences may result in overestimation or underestimation of the cluster’s flexibility, undermining grid reliability and economic efficiency.
To tackle this challenge, I develop a comprehensive framework for hybrid car cluster flexibility potential assessment. The approach begins by modeling the urban transportation network to simulate hybrid car travel patterns, which directly impact charging and refueling behaviors. Each hybrid car is then represented as a virtual energy storage unit with dual-energy states, allowing for unified modeling of electric and hydrogen energy levels using an equivalent mileage model. This model converts battery energy and hydrogen mass into a common metric—drivable range—simplifying the analysis of energy interactions. The core innovation lies in establishing a综合评价 system for owners’ charging willingness, which accounts for subjective and objective factors through an improved Analytic Hierarchy Process (AHP) combined with entropy weighting. This system evaluates indicators such as charging cost, refueling duration, carbon reduction awareness, and safety perceptions, generating a composite score that reflects individual owner preferences. Furthermore, I incorporate behavioral economics principles by considering endowment effects and environmental consciousness to model owners’ response willingness degrees, introducing a positive response bias factor to capture variability in participation incentives. Finally, the flexibility potential assessment model computes the adjustable range of charging power for the hybrid car cluster, providing actionable insights for grid operators. Simulation results demonstrate that this method effectively characterizes owner heterogeneity, enhances the accuracy of flexibility estimates, and improves system flexibility when hybrid car clusters are integrated into optimization scheduling.
The urban transportation network is modeled using graph theory to capture hybrid car mobility, which influences charging demand spatiotemporal distribution. The network is defined as a directed graph \( G = (V, E, U, W) \), where \( V \) represents nodes (e.g., intersections), \( E \) denotes edges (road segments), \( U \) is the set of time intervals, and \( W \) indicates edge weights reflecting traffic conditions like congestion. The weight \( w_{ij}^t \) for edge \( v_{ij} \) at time \( t \) is calculated based on node impedance \( N_i^t \) and link impedance \( L_{ij}^t \), incorporating saturation levels to model traffic flow dynamics:
$$ w_{ij}^t = N_i^t + L_{ij}^t $$
Node impedance accounts for signal delays at intersections, while link impedance uses a time-flow model. For example, under uncongested conditions (\(0 < u \leq 0.6\)), the node impedance is:
$$ N_i^{1,t} = \frac{9}{10} \left[ \frac{h(1-\delta)^2}{2(1-\delta u)} + \frac{u^2}{2r(1-u)} \right] $$
And link impedance is:
$$ L_{ij}^{1,t} = t_0 \left(1 + \alpha u^\beta\right) $$
Here, \( u \) is saturation, \( h \) is signal cycle length, \( \delta \) is green ratio, \( r \) is arrival rate, \( t_0 \) is free-flow travel time, and \( \alpha, \beta \) are calibration parameters. These impedance values are used in Dijkstra’s algorithm to determine shortest paths based on real-time traffic, influencing hybrid car routing and energy consumption. Origin-destination (OD) matrices are employed to estimate trip distributions, with travel probability \( \xi_{ij}^t \) derived from traffic counts \( c_{ij}^t \):
$$ \xi_{ij}^t = \frac{c_{ij}^t}{\sum_{j=1}^M c_{ij}^t} $$
This transportation model ensures realistic simulation of hybrid car movements, which is essential for predicting charging events.
For individual hybrid car energy modeling, I adopt an equivalent mileage approach to unify battery state of charge (SOC) and hydrogen state of charge (SOH). The drivable range \( R_{i,t} \) for hybrid car \( i \) at time \( t \) is expressed as:
$$ R_{i,t} = \text{SOE}_{i,t} E_i^{\max} \xi_{E-R} + \text{SOH}_{i,t} M_i^{\max} \xi_{M-R} $$
where \( \text{SOE}_{i,t} \) and \( \text{SOH}_{i,t} \) are the electric and hydrogen energy states, \( E_i^{\max} \) and \( M_i^{\max} \) are battery and hydrogen tank capacities, and \( \xi_{E-R} \) and \( \xi_{M-R} \) are conversion coefficients from energy to range (e.g., km/kWh for electricity and km/kg for hydrogen). This formulation allows seamless integration of dual-energy dynamics. The hybrid car is treated as a virtual storage unit with charging and refueling constraints. The energy states evolve as:
$$ \text{SOE}_{i,t} = \text{SOE}_{i,t-1} + \eta_{\text{ch}} P_{i,t-1}^{\text{cha}} / E_i^{\max}, \quad t \in [t_{\text{arr}}, t_{\text{dep}}] $$
$$ \text{SOH}_{i,t} = \text{SOH}_{i,t-1} + m_{i,t-1}^{H} / M_i^{\max}, \quad t \in [t_{\text{arr}}, t_{\text{dep}}] $$
with power and hydrogen flow limits:
$$ 0 \leq P_{i,t}^{\text{cha}} \leq P_i^{\text{cha},\max} $$
$$ 0 \leq m_{i,t}^{H} \leq m_i^{H,\max} $$
where \( \eta_{\text{ch}} \) is charging efficiency, \( P_{i,t}^{\text{cha}} \) is charging power, and \( m_{i,t}^{H} \) is hydrogen refueling mass. The hybrid car must achieve a desired range \( R_i^{\text{der}} \) by departure time:
$$ R_{i,t_{\text{dep}}} \geq R_i^{\text{der}} $$
The total range increase \( \Delta R_i \) is split between electric and hydrogen contributions:
$$ \Delta R_i = \Delta R_{E,i} + \Delta R_{H,i} $$
$$ \Delta R_{E,i} = \zeta_{E,i} \Delta R_i, \quad \Delta R_{H,i} = \zeta_{H,i} \Delta R_i $$
Here, \( \zeta_{E,i} \) and \( \zeta_{H,i} \) represent the proportions of range increase from charging and refueling, respectively, which are derived from the owner’s charging willingness assessment.
The owner charging willingness综合评价 system is pivotal for capturing behavioral diversity among hybrid car owners. I identify four key indicators: charging cost, refueling duration, carbon reduction awareness, and charging safety. Each indicator is quantified based on owner-specific parameters. For example, the charging cost indicator \( x_1 \) for owner \( i \) is defined as:
$$ x_1 = \begin{cases} e^{-c_s}, & 0 < c_s < c_s^{\text{Tr}} \\ e^{-c_s^{\text{Tr}}}, & c_s \geq c_s^{\text{Tr}} \end{cases} $$
where \( c_s \) is the expected cost to achieve the desired range, \( c_s^{\text{Tr}} \) is a cost threshold, and \( e \) represents owner education level (higher values indicate greater cost sensitivity). Similarly, the refueling duration indicator \( x_2 \) is:
$$ x_2 = \begin{cases} e^{-t_d}, & 0 < t_d < t_d^{\text{Tr}} \\ e^{-t_d^{\text{Tr}}}, & t_d \geq t_d^{\text{Tr}} \end{cases} $$
with \( t_d \) as expected refueling time and \( t_d^{\text{Tr}} \) as a duration threshold. Carbon reduction awareness \( x_3 \) incorporates education, age, and policy incentives:
$$ x_3 = \lambda_e \lambda_a \lambda_i / \max(\lambda_e, \lambda_a, \lambda_i) $$
where \( \lambda_e \) is education coefficient (e.g., 0.3 for primary school, 0.8 for university), \( \lambda_a = q_4 e^{-\frac{(a-\phi)^2}{2}} \) with age \( a \) and threshold \( \phi = 18 \), and \( \lambda_i = 1 – e^{-i} \) for policy incentive intensity \( i \). Charging safety \( x_4 \) is modeled as:
$$ x_4 = \begin{cases} q_5, & 0 < s_a < s_a^{\text{Tr}} \\ \frac{1}{1 + e^{-s_a}}, & s_a \geq s_a^{\text{Tr}} \end{cases} $$
where \( s_a \) is safety perception (decreasing with higher hydrogen storage) and \( s_a^{\text{Tr}} \) is a safety threshold. These indicators are normalized to a common scale for aggregation.
To determine indicator weights, I combine improved AHP and entropy weighting. Improved AHP constructs a judgment matrix using a scale (e.g., 1.0 for equal importance, 1.8 for extreme importance) to derive subjective weights \( w_j^1 \). For \( n \) indicators, the matrix \( A = [a_{ij}]_{n \times n} \) has elements:
$$ a_{ij} = \prod_{k=i}^{j-1} g_k \quad \text{for } i < j, \quad a_{ji} = 1/a_{ij} $$
where \( g_k \) are adjacent importance ratios. The subjective weight is computed as:
$$ w_j^1 = \frac{\left( \prod_{j=1}^n a_{ij} \right)^{1/n}}{\sum_{i=1}^n \left( \prod_{j=1}^n a_{ij} \right)^{1/n}} $$
Entropy weighting assesses objective variability based on data dispersion. For \( m \) owners and \( n \) indicators, the normalized matrix \( X^s = [x_{i,j}^s]_{m \times n} \) is used to calculate entropy \( r_j \):
$$ r_j = -D \sum_{i=1}^m k_{ij} \ln k_{ij}, \quad k_{ij} = \frac{x_{i,j}^s}{\sum_{i=1}^m x_{i,j}^s}, \quad D = 1/\ln m $$
The objective weight is:
$$ w_j^2 = \frac{1 – r_j}{\sum_{j=1}^n (1 – r_j)} $$
The combined weight \( w_j \) is:
$$ w_j = \frac{w_j^1 w_j^2}{\sum_{j=1}^n w_j^1 w_j^2} $$
Table 1 summarizes the indicator descriptions and example weights derived from a case study with 2,000 hybrid cars.
| Indicator | Description | Normalization | Subjective Weight | Objective Weight | Combined Weight |
|---|---|---|---|---|---|
| Charging Cost (\(x_1\)) | Sensitivity to electricity and hydrogen prices | Higher values favor charging | 0.35 | 0.30 | 0.32 |
| Refueling Duration (\(x_2\)) | Time sensitivity for refueling vs. charging | Lower values favor refueling | 0.25 | 0.25 | 0.25 |
| Carbon Reduction Awareness (\(x_3\)) | Environmental concern influenced by age, education, policy | Higher values favor refueling | 0.20 | 0.25 | 0.23 |
| Charging Safety (\(x_4\)) | Perceived risk of hydrogen storage | Lower values favor charging | 0.20 | 0.20 | 0.20 |
The composite charging willingness score \( s_i \) for owner \( i \) is:
$$ s_i = \sum_{j=1}^n w_j x_{i,j}, \quad s_i \in [s_{\min}, s_{\max}] $$
This score determines the energy mix preference: the proportion of range increase from charging \( \zeta_{E,i} \) is:
$$ \zeta_{E,i} = \frac{s_{\max} – s_i}{s_{\max} – s_{\min}}, \quad \zeta_{H,i} = 1 – \zeta_{E,i} $$
Thus, owners with higher scores lean toward hydrogen refueling, while lower scores indicate a preference for electric charging.
Owner response willingness is modeled to account for participation variability in demand response programs. The response willingness degree \( f_{i,c}^r \) under incentive price \( c \) is:
$$ f_{i,c}^r = f_{i,c}^p + \tau_i (f_{i,c}^o – f_{i,c}^p) $$
where \( f_{i,c}^o \) and \( f_{i,c}^p \) are positive and negative response willingness degrees, respectively, defined as functions of incentive price (e.g., sigmoidal curves). The positive response bias factor \( \tau_i \) incorporates endowment effect \( E_i^e \) and environmental awareness \( E_i^a \):
$$ \tau_i = \frac{1}{2} (1 – E_i^e + E_i^a), \quad E_i^e, E_i^a \in [0,1] $$
Here, \( E_i^e \) close to 1 indicates strong endowment effect (resistance to change), reducing \( \tau_i \), while high \( E_i^a \) boosts \( \tau_i \), promoting积极响应. This factor captures behavioral nuances, ensuring realistic participation estimates.
The flexibility potential assessment model computes the adjustable range of charging power for the hybrid car cluster. First, a baseline optimization minimizes total refueling cost under wholesale electricity prices:
$$ \min F_0 = \min \sum_{t=1}^T \sum_{i=1}^N \left( C_t P_{i,t}^{\text{cha}} + C_H m_{i,t}^H \right) $$
subject to the hybrid car energy constraints. Solving this yields baseline charging power \( P_{i,t}^{\text{cha},0} \) and hydrogen refueling \( m_{i,t}^{H,0} \). The cluster charging power \( P_t^{\text{CL}} \) has adjustable margins:
$$ P_t^{\text{CL},\min} \leq P_t^{\text{CL}} \leq P_t^{\text{CL},\max} $$
The downward adjustment margin \( P_t^{\text{CL},\min} \) includes both load reduction and substitution from refueling:
$$ P_t^{\text{CL},\min} = \sum_{i=1}^N \theta_{i,t} \left[ P_{i,t}^{\text{cha},0} – P_{i,t}^H – f_{i,c}^r \left( P_{i,t}^{\text{cha},0} – P_i^{\text{cha},\min} \right) \right] $$
where \( \theta_{i,t} \) is connection status (1 if connected), \( P_{i,t}^H \) is the charging power offset from refueling:
$$ P_{i,t}^H = f_{i,c}^r \left( m_{i,t}^{H,0} \xi_{M-R} / (\xi_{E-R} \Delta h) \right) $$
with \( \Delta h \) as time interval. The upward adjustment margin \( P_t^{\text{CL},\max} \) is:
$$ P_t^{\text{CL},\max} = \sum_{i=1}^N \theta_{i,t} \left[ P_{i,t}^{\text{cha},0} – f_{i,c}^r \left( P_{i,t}^{\text{cha},0} – P_i^{\text{cha},\max} \right) \right] $$
These margins define the flexibility potential, representing the maximum charging power variation the hybrid car cluster can provide for grid services.
I conduct simulations using a 24-node urban traffic network with 2,000 hybrid cars. Parameters are listed in Table 2.
| Parameter | Value | Description |
|---|---|---|
| Number of hybrid cars | 2,000 | Fleet size |
| Battery capacity \(E_i^{\max}\) | 50 kWh | Per hybrid car |
| Hydrogen tank capacity \(M_i^{\max}\) | 3 kg | Per hybrid car |
| Charging power limit \(P_i^{\text{cha},\max}\) | 17.5 kW | Per hybrid car |
| Electricity-to-range coefficient \(\xi_{E-R}\) | 9 km/kWh | Conversion factor |
| Hydrogen-to-range coefficient \(\xi_{M-R}\) | 200 km/kg | Conversion factor |
| Charging efficiency \(\eta_{\text{ch}}\) | 0.9 | Coulombic efficiency |
| Hydrogen price \(C_H\) | 45 ¥/kg | Assumed constant |
| Wholesale electricity price \(C_t\) | Time-varying | From market data |
The baseline charging load under wholesale prices shows multi-peak patterns due to price-sensitive charging during low-cost periods. For instance, peaks occur at hours 2-5 and 10-13 when prices are low, while off-peak hours see reduced charging. This aligns with hybrid car owners’ cost-minimization behavior. The flexibility potential assessment results are depicted in Figure 1, illustrating the adjustable range over a 24-hour period. The downward margin is significantly enhanced when refueling substitution is considered, highlighting the dual-energy advantage of hybrid cars. For example, during hour 14, the downward margin increases from 500 kW to 800 kW, a 60% improvement, enabling greater grid support during peak demand.
To analyze the impact of owner charging willingness indicators, I examine two cases focusing on carbon reduction awareness and charging cost sensitivity. In Case A, owners have high carbon awareness (education level 0.8, age under 30, policy incentive 0.9), leading to composite scores favoring refueling. The resulting flexibility potential shows reduced downward margins (e.g., 600 kW at hour 18) due to lower baseline charging. In Case B, owners have low carbon awareness (education 0.3, age over 40, policy incentive 0.2), favoring charging, which increases downward margins to 900 kW at hour 18. Similarly, for charging cost sensitivity, higher sensitivity (indicator value 0.8) boosts charging preference, raising flexibility potential, while lower sensitivity (0.3) reduces it. Table 3 summarizes these effects.
| Case | Indicator Focus | Composite Score Trend | Preferred Energy Mode | Downward Margin at Hour 18 (kW) | Flexibility Potential Change |
|---|---|---|---|---|---|
| Case A | High carbon awareness | Higher scores | Refueling | 600 | Decreased |
| Case B | Low carbon awareness | Lower scores | Charging | 900 | Increased |
| Case C | High cost sensitivity | Lower scores | Charging | 950 | Increased |
| Case D | Low cost sensitivity | Higher scores | Refueling | 550 | Decreased |
The positive response bias factor \( \tau_i \) also influences flexibility. I test values from 0.1 to 0.9, representing从消极到积极响应. As \( \tau_i \) increases, both upward and downward margins expand linearly. For instance, at \( \tau_i = 0.1 \), the maximum downward margin across hours is 700 kW; at \( \tau_i = 0.9 \), it reaches 1,300 kW. This underscores the importance of incentivizing owner participation through tailored policies or pricing signals to unlock flexibility.
The hybrid car cluster flexibility potential is further quantified using metrics like total adjustable energy \( E_{\text{adj}} \) over a day:
$$ E_{\text{adj}} = \sum_{t=1}^T \left( P_t^{\text{CL},\max} – P_t^{\text{CL},\min} \right) \Delta h $$
For the base case, \( E_{\text{adj}} \) is 12 MWh, which can be increased to 18 MWh with high owner responsiveness. This capacity can significantly aid in renewable energy integration, e.g., absorbing excess solar generation during midday by shifting charging loads. Additionally, the model’s robustness is validated through sensitivity analyses on traffic conditions and energy prices. Variations in traffic congestion alter travel times and charging schedules, but the flexibility margins remain stable within ±10%, demonstrating methodological resilience.
In conclusion, this paper presents a novel framework for assessing the flexibility potential of hybrid car clusters, incorporating owner charging willingness differences. The key contributions include: (1) a dual-energy hybrid car model based on equivalent mileage, enabling unified treatment of electric and hydrogen energy; (2) a综合评价 system for charging willingness using improved AHP and entropy weighting, capturing behavioral heterogeneity; and (3) a response willingness model integrating endowment effects and environmental awareness to refine participation estimates. Simulation results confirm that the method effectively characterizes owner diversity, with flexibility potential varying based on indicator profiles and response biases. For instance, hybrid car clusters with cost-sensitive owners can provide up to 30% more downward adjustment capacity, while high carbon awareness reduces flexibility by 20%. These insights guide grid operators in designing incentive programs to maximize hybrid car utilization for peak shaving and renewable integration.
Future work will extend this assessment to aggregate hybrid car participation in integrated electricity-hydrogen market optimization, considering dynamic pricing and grid constraints. Additionally, real-world data from hybrid car fleets can be incorporated to validate and refine the models. The proliferation of hybrid cars offers immense opportunities for energy-transportation synergy, and this assessment framework provides a critical tool for unlocking their flexibility potential in the transition to sustainable energy systems. By repeatedly emphasizing the role of hybrid cars, this study underscores their versatility as both transportation assets and grid resources, paving the way for smarter, more resilient power systems.