Flexibility Region Quantification and Optimal Scheduling of Fast Charging Stations Considering EV User Discharge Willingness

Case studies verify that the proposed model and methods enhance station revenue.

“Case studies verify that the proposed model and methods effectively improve the operational flexibility of FCS by coordinating flexible resources, enhancing station revenue, balancing flexibility supply and demand, and reducing users' expenses.”

As the discharge willingness threshold increases, the OC penalty fees of EV users continually rise.

“As the threshold increases, the OC penalty fees of EV users continually rise”

Case studies verify that the proposed model and methods reduce users' expenses.

“Case studies verify that the proposed model and methods effectively improve the operational flexibility of FCS by coordinating flexible resources, enhancing station revenue, balancing flexibility supply and demand, and reducing users' expenses.”

Case studies verify that the proposed model and methods balance flexibility supply and demand.

“Case studies verify that the proposed model and methods effectively improve the operational flexibility of FCS by coordinating flexible resources, enhancing station revenue, balancing flexibility supply and demand, and reducing users' expenses.”

Compared with the extended bandwidth KDE and the standard bandwidth KDE, the probability density curve obtained through the ABKDE method better reflects the trends of the sample data.

“Compared with the extended bandwidth KDE and the standard bandwidth KDE, the probability density curve obtained through the ABKDE method better reflects the trends of the sample data.”

During the 14:00 peak period, power is reduced for EVs and redistributed to neighboring time periods.

“during the 14:00 peak period, power is reduced for EVs and redistributed to neighboring time periods.”

The load at the FCS, when combined with the typical daily load, creates a new peak.

“the load at the FCS, when combined with the typical daily load, creates a new peak.”

Case studies verify that the proposed model and methods effectively improve the operational flexibility of FCS by coordinating flexible resources.

“Case studies verify that the proposed model and methods effectively improve the operational flexibility of FCS by coordinating flexible resources, enhancing station revenue, balancing flexibility supply and demand, and reducing users' expenses.”

Average discharge FR increases from 13.31 to 19.87 kW.

“The quantitative results show that the total discharge FR expands from 1277 to 1907 kW, while the average discharge FR increases from 13.31 to 19.87 kW.”

CASAP has substantially higher user penalty costs than the proposed method.

“Regarding economic indicators, the CASAP method achieves slightly higher FCS revenue than the proposed method but has substantially higher user penalty costs.”

UCD achieves the highest flexibility utilization.

“The UCD method achieves the highest flexibility utilization but at the expense of extremely high penalty costs, while the proposed method provides substantial flexibility with balanced economic performance.”

Discharge participation increases from 68% to 80%.

“Discharge participation increases from 68% to 80%”

Through the optimization strategy, overall OC penalty costs are maintained at a remarkably stable level across different penalty rate scenarios.

“Notably, through the optimization strategy, overall OC penalty costs are maintained at a remarkably stable level across different penalty rate scenarios, avoiding excessive penalty expenditures and ensuring the mechanism remains economically beneficial for EV users while providing effective behavioral incentives.”

Total discharge FR expands from 1277 to 1907 kW.

“The quantitative results show that the total discharge FR expands from 1277 to 1907 kW, while the average discharge FR increases from 13.31 to 19.87 kW.”

The total number of time slots where EVs exceed the 0.4 discharge willingness threshold increases.

“the total number of time slots where EVs exceed the 0.4 discharge willingness threshold increases”

Without V2G, FR relies on PV and ESS, resulting in upward flexibility shortages from 12:45 to 13:00 and 13:15 to 13:45.

“Without V2G, FR relies on PV and ESS, resulting in shortages from 12:45 to 13:00 and 13:15 to 13:45 due to limited upward flexibility.”

EV discharge flexibility reduces the penalty costs associated with OC.

“It not only compensates for the insufficiency of flexible resource supply caused by the large-scale integration of EVs but also reduces the penalty costs associated with OC.”

UCD has extremely high penalty costs.

“The UCD method achieves the highest flexibility utilization but at the expense of extremely high penalty costs, while the proposed method provides substantial flexibility with balanced economic performance.”

With 50 EVs, flexibility regulation capacity drops to 7.9%.

“However, with 50 EVs, flexibility regulation capacity drops to 7.9%.”

• AssumptionThe authors state this as an assumption: The FCS has unlimited EV connections.

Through the dynamic pricing approach, users are effectively incentivized to reduce charging during peak periods, ultimately resulting in an overall grid load reduction of 13.96%.

“Through this dynamic pricing approach, users are effectively incentivized to reduce charging during peak periods, ultimately resulting in an overall grid load reduction of 13.96%.”

At α = 0.70, the absolute MRS increases to 0.758.

“In contrast, at α = 0 . 55 and α = 0 . 65, the absolute MRS values are 0.730 and 0.664, respectively, while at α = 0 . 70, it increases to 0.758, all showing lower efficiency than at α = 0 . 60.”

The proposed method's penalty costs decrease by 38.4% compared with CASAP.

“The proposed method achieves significant penalty cost reduction through the incentive mechanism, with penalty costs decreasing by 38.4% compared with CASAP.”

In other off-peak charging periods, the FCS still faces a shortage of flexibility.

“In other off-peak charging periods, the FCS still faces a shortage of flexibility.”

Discharge activities are primarily concentrated during peak demand periods.

“The time-series plot demonstrates that as penalty costs increase, the EV discharge FR exhibits clear progressive growth, with discharge activities primarily concentrated during peak demand periods.”

Increased uncertainty factors have caused OC penalty costs to show a significant upward trend.

“Regarding assessment metrics, increased uncertainty factors have caused a decline in both AUFA and EDFCR, while OC penalty costs have shown a significant upward trend.”

The growth in discharge FR from increasing EV numbers is primarily concentrated during OCD.

“Although the increase in the number of EVs can enhance the discharge FR, this growth is primarily concentrated during OCD.”

Ignoring the adjustable potential of EVs leads to a significant flexibility shortfall during peak demand.

“ignoring the adjustable potential of EVs leads to a significant flexibility shortfall during peak demand.”

With α = 0.60, the FCS achieves revenue of 1320.33 CNY.

“With α = 0 . 60, the FCS achieves revenue of 1320.33 CNY, ensuring infrastructure sustainability; the overtime penalty cost remains at a reasonable 2780 CNY, user discharge preference maintains 306.23 CNY, only 12.2% lower than at α = 0 . 50, and total revenue reaches 916.17 CNY.”

The proposed dynamic pricing strategy achieves an EDFCR of 12.23% compared with 10.30% under TOU pricing.

“the proposed dynamic pricing strategy achieves an EDFCR of 12.23% compared with 10.30% under TOU pricing.”

At α = 0.60, the absolute MRS value reaches its minimum of 0.574.

“Results show that at α = 0 . 60, the absolute MRS value reaches its minimum of 0.574, indicating the most efficient resource allocation where increasing one unit of FCS revenue requires sacrificing only 0.574 units of user discharge preference.”

The willingness time ratio rises to 35.4%.

“The willingness time ratio rises to 35.4%”

Compared with traditional scheduling strategies that do not consider EV flexibility, EV discharge flexibility demonstrates a 12.23% improvement in flexibility contribution.

“Compared with traditional scheduling strategies that do not consider EV flexibility, the discharge flexibility of EVs demonstrates a 12.23% improvement in flexibility contribution, which significantly enhances the FR of FCS.”

As penalty costs increase, EV discharge FR exhibits clear progressive growth.

“The time-series plot demonstrates that as penalty costs increase, the EV discharge FR exhibits clear progressive growth, with discharge activities primarily concentrated during peak demand periods.”

UCD has the poorest OCIR performance.

“Although the UCD method has the lowest FCS revenue, its user penalty cost is the highest among all methods with the poorest OCIR performance.”

CASAP has an AUFA value of 0.

“For flexibility indicators, the CASAP method has an AUFA value of 0, indicating it cannot provide upward flexibility at all.”

Under OC, EV discharge flexibility contributes 12.2% to total FCS flexibility in Scenario 2.

“Under OC, EV discharge flexibility contributes 12.2% to total FCS flexibility in Scenario 2, significantly enhancing overall system flexibility.”

An increase in the number of EVs can enhance the discharge FR.

“Although the increase in the number of EVs can enhance the discharge FR, this growth is primarily concentrated during OCD.”

With α = 0.60, total revenue reaches 916.17 CNY.

“With α = 0 . 60, the FCS achieves revenue of 1320.33 CNY, ensuring infrastructure sustainability; the overtime penalty cost remains at a reasonable 2780 CNY, user discharge preference maintains 306.23 CNY, only 12.2% lower than at α = 0 . 50, and total revenue reaches 916.17 CNY.”

With α = 0.60, the overtime penalty cost remains at 2780 CNY.

“With α = 0 . 60, the FCS achieves revenue of 1320.33 CNY, ensuring infrastructure sustainability; the overtime penalty cost remains at a reasonable 2780 CNY, user discharge preference maintains 306.23 CNY, only 12.2% lower than at α = 0 . 50, and total revenue reaches 916.17 CNY.”

CASAP achieves slightly higher FCS revenue than the proposed method.

“Regarding economic indicators, the CASAP method achieves slightly higher FCS revenue than the proposed method but has substantially higher user penalty costs.”

Scenarios with V2G discharge flexibility outperformed those without.

“Scenarios with V2G discharge flexibility outperformed those without.”

UCD has the lowest FCS revenue.

“Although the UCD method has the lowest FCS revenue, its user penalty cost is the highest among all methods with the poorest OCIR performance.”

The average discharge willingness improves by 12.9%.

“the average discharge willingness improves by 12.9%.”

UCD has the highest user penalty cost among all methods.

“Although the UCD method has the lowest FCS revenue, its user penalty cost is the highest among all methods with the poorest OCIR performance.”

Raising the discharge willingness threshold increases charging costs for users.

“Raising the discharge willingness threshold increases the charging costs for users.”

A collaborative optimization scheduling model for FCS flexibility resources maximizes benefits for both operators and users.

“Finally, a collaborative optimization scheduling model for the flexibility resources of FCS is proposed to maximize benefits for both operators and users.”

The EUDW incentive model enhances the accuracy of EUDW decisions by accounting for the contextual variability of decision factors.

“Compared with existing incentive frameworks that typically employ single-factor approaches [23], [27], this approach enhances the accuracy of EUDW decisions by accounting for the contextual variability of decision factors.”

• cites [23] sourceNot checked — no full text of the source
• cites [27] Han, 2024, Incentive-willingness-decision framework: Unit discharge triangle-based maximum stable V2G capability evaluation, Appl. EnergyNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Over 90% of EV users opt for fast charging.

“Over 90% of users opt for fast charging [1], which presents unique operational challenges due to shorter dwell times and irregular usage patterns.”

• cites [1] 2024Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

When charging demand needs to be reduced during peak periods, the system preferentially shifts this demand to adjacent periods with relatively lower demand, thereby preserving charging continuity and minimizing disruption to users.

“When charging demand needs to be reduced during peak periods, the system preferentially shifts this demand to adjacent periods with relatively lower demand, thereby preserving charging continuity and minimizing disruption to users.”

The dual-layer interactive decision-making framework based on prospect theory and affine fuzzy logic control captures variations in EUDW under different pricing incentives.

“A dual-layer interactive decision-making framework based on prospect theory and affine fuzzy logic control is developed to capture variations in EUDW under different pricing incentives.”

The proposed model quantifies the adjustable flexibility of integrated resources, including PV, ESS, and EVs within FCS, providing a basis for real-time flexibility supply-demand balance evaluation.

“Unlike previous approaches that focus primarily on individual resource optimization [9], [17], the proposed model quantifies the adjustable flexibility of integrated resources, including PV, ESS, and EVs within FCS, providing a basis for real-time flexibility supply-demand balance evaluation.”

• cites [9] sourceNot checked — no full text of the source
• cites [17] sourceNot checked — no full text of the source

The EUDW incentive model considers temporal, economic, and technical feasibility factors, including OC duration, net discharge compensation cost, and discharge margin.

“To address the limitations of treating EUDW as static parameters, an EUDW incentive model is proposed that considers temporal, economic, and technical feasibility factors, including OC duration, net discharge compensation cost, and discharge margin.”

The FR analysis model comprising AFA, EFNS, and EDFA delineates the boundaries of power and energy flexibility in scenarios involving EV charging, discharging, and OC.

“A FR analysis model comprising three complementary metrics is developed for flexibility resources of FCSs integrated with PV and ESS: average flexibility adequacy (AFA), expected flexibility not satisfied (EFNS), and EV discharge flexibility adequacy (EDFA). This model delineates the boundaries of power and energy flexibility in scenarios involving EV charging, discharging, and OC.”

An incentive model considering OC duration, net discharge compensation, and discharge margin incentivizes users' participation.

“To address the randomness of EUDW, an incentive model is proposed, considering OC duration, net discharge compensation, and discharge margin to incentivize users' participation.”

A dual-layer decision framework incorporating behavioral economics and affine fuzzy logic control enhances decision-making under EUDW uncertainty.

“In addition, a dual-layer decision framework, incorporating behavioral economics and affine fuzzy logic control, is developed to enhance decision-making under EUDW uncertainty.”

When the willingness threshold reaches 0.5, the FCS faces a risk of reduced profits.

“In this scenario, the risk of reduced profits is faced by the FCS.”

• AssumptionRests on an assumption: OC at FCS diminishes the satisfaction of EV users' charging experiences.

EV discharge flexibility compensates for the insufficiency of flexible resource supply caused by the large-scale integration of EVs.

“It not only compensates for the insufficiency of flexible resource supply caused by the large-scale integration of EVs but also reduces the penalty costs associated with OC.”

Higher OC penalty costs enhance the discharge flexibility of EVs.

“Table I demonstrates that improvements in AUFA from 115.5626 to 126.4285 and EDFCR clearly indicate that higher OC penalty costs motivate EV users to participate in discharging more actively, thereby enhancing the discharge flexibility of EVs and increasing their willingness to participate in grid services.”

EV discharging effectively compensates for the upward flexibility gaps that occur without V2G.

“EV discharging effectively compensates for these gaps.”

CASAP cannot provide upward flexibility at all.

“For flexibility indicators, the CASAP method has an AUFA value of 0, indicating it cannot provide upward flexibility at all.”

The proposed method outperforms the comparison methods in overall performance.

“Comprehensive analysis shows that the proposed method outperforms the comparison methods in overall performance, especially in reducing user penalty costs.”

The gradual increase in EDFCR indicates an expansion of the EV discharge FR.

“In addition, the gradual increase in the EDFCR indicates an expansion of the EV discharge FR, as shown in Fig. 11.”

The proposed incentive mechanism converts higher penalty costs into enhanced system flexibility resources.

“These consistent improvements validate the effectiveness of the proposed incentive mechanism in converting higher penalty costs into enhanced system flexibility resources.”

EUDW values show progressive improvements, reflecting enhanced system operational efficiency.

“The EUDW values also show progressive improvements, reflecting enhanced system operational efficiency.”

Improvements in AUFA from 115.5626 to 126.4285 and EDFCR indicate that higher OC penalty costs motivate EV users to participate in discharging more actively.

“Table I demonstrates that improvements in AUFA from 115.5626 to 126.4285 and EDFCR clearly indicate that higher OC penalty costs motivate EV users to participate in discharging more actively, thereby enhancing the discharge flexibility of EVs and increasing their willingness to participate in grid services.”

The proposed method demonstrates superior ability to reduce users' economic burden.

“In addition, the proposed method achieves the highest OCIR performance, exceeding CASAP by 46.7% and UCD by 12.7 times, demonstrating superior ability to reduce users' economic burden.”

As the number of EVs continues to increase, the current PV and ES configuration struggles to meet rising flexibility demands.

“As the number of EVs continues to increase, the current PV and ES configuration struggles to meet rising flexibility demands, leading to a decrease in AUFA and DFICR metrics, while EUFNS and EDFNS metrics continue to rise.”

• AssumptionThe authors state this as an assumption: The FCS has unlimited EV connections.

This strategy coordinates EVs with PV and ESS resources to balance flexibility supply and demand more precisely, accommodating fluctuations.

“This strategy coordinates EVs with PV and ESS resources to balance flexibility supply and demand more precisely, accommodating fluctuations.”

According to equation (39), the discharge benefit for EV users is a concave function.

“According to (39), the discharge benefit for EV users is a concave function.”

Higher OC penalty costs increase EV users' willingness to participate in grid services.

“Table I demonstrates that improvements in AUFA from 115.5626 to 126.4285 and EDFCR clearly indicate that higher OC penalty costs motivate EV users to participate in discharging more actively, thereby enhancing the discharge flexibility of EVs and increasing their willingness to participate in grid services.”

The proposed method achieves significant penalty cost reduction through the incentive mechanism.

“The proposed method achieves significant penalty cost reduction through the incentive mechanism, with penalty costs decreasing by 38.4% compared with CASAP.”

The framework dynamically adjusts the discharge willingness of EV users.

“Moreover, this framework dynamically adjusts the discharge willingness of EV users, mitigating the issues of reduced flexibility and economic performance at FCS due to the uncertainty of discharge willingness.”

The proposed method is especially better in reducing user penalty costs.

“Comprehensive analysis shows that the proposed method outperforms the comparison methods in overall performance, especially in reducing user penalty costs.”

In CASAP, all available resources are prioritized for rapid charging completion with no capacity reserved for flexibility services.

“This reflects the strategy characteristics where all available resources are prioritized for rapid charging completion with no capacity reserved for flexibility services, and users focus solely on charging objectives without discharge participation.”

The proposed method is more suitable for actual FCS operation environments.

“This approach transforms unavoidable overstay situations into economic opportunities while providing system flexibility benefits, making it more suitable for actual FCS operation environments.”

The V2G scenario is clearly advantageous for FCS operation.

“This substantial improvement in upward flexibility provision far outweighs the minor reduction in downward flexibility capability, making the V2G scenario clearly advantageous for FCS operation.”

The proposed dual-layer interactive decision-making framework, based on prospect theory and affine fuzzy logic control, effectively motivates user participation.

“the proposed dual-layer interactive decision-making framework, based on prospect theory and affine fuzzy logic control, effectively motivates user participation.”

• AssumptionRests on an assumption: EV users, when evaluating value, tend to avoid losses and rely on subjective rather than objective probabilities, exhibiting a nonlinear probability weighting function.
• AssumptionRests on an assumption: The sigmoid function can be used to depict the response curve of consumers under various incentives.
• AssumptionRests on an assumption: EUDW can be interpreted as a subjective evaluation function of the potential profitability according to prospect theory.
• AssumptionRests on an assumption: A linear combination of fuzzy basis functions can approximate any real continuous function on a compact set with arbitrary precision.

Under OC, EV discharge flexibility significantly enhances overall system flexibility in Scenario 2.

“Under OC, EV discharge flexibility contributes 12.2% to total FCS flexibility in Scenario 2, significantly enhancing overall system flexibility.”

In CASAP, users focus solely on charging objectives without discharge participation.

“This reflects the strategy characteristics where all available resources are prioritized for rapid charging completion with no capacity reserved for flexibility services, and users focus solely on charging objectives without discharge participation.”

For the FCS, uncertainty in discharge willingness could result in actual discharge volumes falling short of expectations.

“For the FCS, uncertainty in discharge willingness could result in actual discharge volumes falling short of expectations.”

• AssumptionRests on an assumption: EV users' discharge willingness is generally low.

The framework mitigates the issues of reduced flexibility and economic performance at FCS due to the uncertainty of discharge willingness.

“Moreover, this framework dynamically adjusts the discharge willingness of EV users, mitigating the issues of reduced flexibility and economic performance at FCS due to the uncertainty of discharge willingness.”

The 12.23% improvement in flexibility contribution significantly enhances the FR of FCS.

“Compared with traditional scheduling strategies that do not consider EV flexibility, the discharge flexibility of EVs demonstrates a 12.23% improvement in flexibility contribution, which significantly enhances the FR of FCS.”

The substantial improvement in upward flexibility provision far outweighs the minor reduction in downward flexibility capability.

“This substantial improvement in upward flexibility provision far outweighs the minor reduction in downward flexibility capability, making the V2G scenario clearly advantageous for FCS operation.”

The increase in time slots where EVs exceed the 0.4 discharge willingness threshold indicates more sustained user engagement compared with rigid TOU schedules.

“indicating more sustained user engagement compared with rigid TOU schedules.”

The method is effective in mobilizing EV discharge flexibility.

“which demonstrates the method's effectiveness in mobilizing EV discharge flexibility.”

At α = 0.60, increasing one unit of FCS revenue requires sacrificing only 0.574 units of user discharge preference.

“Results show that at α = 0 . 60, the absolute MRS value reaches its minimum of 0.574, indicating the most efficient resource allocation where increasing one unit of FCS revenue requires sacrificing only 0.574 units of user discharge preference.”

The weight range α ∈ [0.55, 0.65] is a reasonable adjustment space for different operational stages.

“Analysis identifies the weight range α ∈ [ 0 . 55 , 0 . 65 ] as a reasonable adjustment space for different operational stages.”

For FCS, EV discharge flexibility contributes to lower investment and operational costs for ESS.

“For FCS, this contributes to lower investment and operational costs for ESS.”

The proposed optimization scheduling model can control penalty costs.

“The proposed optimization scheduling model can control penalty costs, protect users' economic interests, and improve the revenue and flexibility of FCS.”

A moderate threshold can incentivize EV users to participate in discharging, meeting the flexibility requirements of FCS.

“However, a moderate threshold can incentivize EV users to participate in discharging, meeting the flexibility requirements of FCS.”

The proposed optimization scheduling model protects users' economic interests.

“The proposed optimization scheduling model can control penalty costs, protect users' economic interests, and improve the revenue and flexibility of FCS.”